Journal of Petroleum Exploration and Production Technologies - Vol. 1, Numbers 1-4, 2011

ORIGINAL PAPER - EXPLORATION GEOLOGY

Bimodal pore size behavior of the Shajara Formation Reservoirsof the Permo-Carboniferous Unayzah Group, Saudi Arabia

K. E. Al-Khidir • A. A. Al-Quraishi •

A. A. Al-Laboun • M. S. Benzagouta

Received: 29 September 2010 / Accepted: 21 March 2011 / Published online: 5 April 2011

� The Author(s) 2011. This article is published with open access at Springerlink.com

Abstract The sandstones of the Permo-Carboniferous

Shajara Formation form the main part of the Unayzah

Reservoir in the Greater Arabian Basin. It is divided into

three reservoirs, namely from base to top Lower, Middle,

and Upper Shajara reservoirs. Mercury intrusion technique

was carried out on representative sandstone samples col-

lected from the type section and the three reservoirs are

generally characterized as heterogeneous megaporous res-

ervoirs. The best reservoir quality is assigned to the lower

sand unit of the Lower Shajara followed by the Middle

Shajara Reservoir. One sample collected from the upper

part of the Lower Shajara was described as low quality due

to its fine grain characteristic and its proximity to the

unconformity surface. Reservoir quality is controlled to a

large extent by the depositional facies and specifically by

rock texture illustrated by petrophysical description. The

quality of the three reservoirs of the Shajara Formation,

increases with the increase of grain size and grain sorting.

Keywords Shajara Reservoirs � Shajara Formation �Unayzah Group � Pore size distribution

Introduction

The Permo-Carboniferous Unayzah Reservoirs are oil and

gas bearing in more than 30 oil and gas fields in Saudi

Arabia. These reservoirs are partially represented in out-

crops by the Shajara, Safra, and Shiqqah sandstones of the

Unayzah Group. These formations are exposed as a thin

belt below the Khuff carbonates in central Arabia.

Fossil plants of the late Carboniferous–early Permian

age were first reported at the town of Unayzah by El-

Khayal et al. (1980). Later, the term Unazyah Formation

was informally introduced by Al-Laboun (1982) as sili-

ciclastics and minor carbonate section at the base of the

Khuff Formation. This definition was adopted by Aramco

Stratigraphic Committee (1983) and formally defined by

Al-Laboun (1987)in the American Association of Petro-

leum Geologist (AAPG). The Unayzah Formation was then

correlated with its equivalent units in different parts of the

Greater Arabian basin (Al-Laboun 1988) and its type

locality was established within Unayzah town with a ref-

erence section assigned at Wadi Ash-Shajara at the

Qusayba depression, Al-Qasim region (Fig. 1).

The subsurface informal reference section (Hawtah-1) of

the Unayzah Formation was studied by Ferguson and

Chambers (1991). The section consists of two sandstone

intervals separated by a coarsening upward siltstone unit.

Similarly, McGillivray and Husseini (1992) divided the

Unayzah Formation in the Hawtah–Hazmiyah fields into

two informal sequences identified as Unayzah A and

Unayzah B members. The two members are separated by a

red-brown siltstone or fine-grained silty sandstone. Senalp

and Al-Dauji (1995) studied the stratigraphy and sedimen-

tation of the Unayzah Reservoir in central Arabia. They

redefined the Unayzah Formation at its type locality by

introducing the term ‘‘basal Khuff clastics’’ (Ash-Shiqqah

K. E. Al-Khidir (&) � M. S. Benzagouta

Department of Petroleum and Natural Gas Engineering,

King Saud University, Riyadh, Saudi Arabia

e-mail: [email protected]

A. A. Al-Quraishi

Oil and Gas Research Institute, King Abdulaziz City for Science

and Technology, Riyadh, Saudi Arabia

A. A. Al-Laboun

Department of Geology, King Saud University,

Riyadh, Saudi Arabia

123

J Petrol Explor Prod Technol (2011) 1:1–9

DOI 10.1007/s13202-011-0007-5

member) of the Khuff Formation to be the upper contact of

the Unayzah Formation.

Evans et al. (1997) studied the stratigraphic trap in the

Permian Unayzah Formation, in Usaylah-1, central Arabia,

and they reported that the trap is an up dip pinch out. An oil

column 31 ft thick is encountered in the eolian sandstone

facies of the upper part of the Unayzah Formation. Later,

Wender et al. (1998) divided the Early Permian Unayzah

Formation into three units, the Unayzah-A Reservoir,

Unayzah Siltstone Member, and Unayzah-B Reservoir.

Melvin and Spraque (2006) studied origin and stratigraphic

architecture of glaciogenic sediments in Permian–Carbon-

iferous lower Unayzah sandstones in eastern central Saudi

Arabia. They subdivided the lower Unayzah sandstones

into three members, from base to top are: Unayzah C

Member, Unayzah B Member, and an un-named middle

Unayzah member.

Reservoir characteristics of the Permo-Carboniferous

Unayzah Formation, at Wadi Shajara was thoroughly

investigated through field and petrophysical examinations.

An exposed clastic sequence consisting of three sandstone

intervals separated by two mudstone units were observed

(Fig. 2). The clastic sequence is bounded from top and

bottom, by two regional unconformities, namely sub-Khuff

and sub-Unayzah unconformity, respectively. Based on

Saudi Stratigraphic Code (1983), a group is defined as a

lithostratigraphic unit bounded by two regional unconfo-

rmities. Therefore, we propose raising the Permo-Carbon-

iferous Unayzah Formation to a group status and identify a

new formation named Shajara Formation (Al-Khidir 2007).

The term Unayzah Formation was restricted to the upper

unit of the group which is best represented in its original

type locality in Unayzah town, while the term Shajara

Formation was assigned to the Lower unit which is best

represented at Wadi Ash-Shajara (Laboun 2010). Depend-

ing on sub-Unayzah unconformity, sub-middle Shajara

local unconformity, the lower mudstone interval, and sub-

Khuff unconformity (Fig. 2), the Shajara Formation was

divided into three members, from base to top: the Lower

Shajara, the Middle Shajara, and the Upper Shajara

(Al-Khidir 2007).

The Shajara Reservoirs of the Shajara Formation is oil

and gas bearing in many fields in Saudi Arabia. In addition,

it is the principal Paleozoic clastic reservoir. To our

knowledge no petrophysical examination was conducted on

the surface samples of the Shajara Formation. The aim of

this work is to categorize the Shajara reservoirs by char-

acterizing the pore geometry and the pore aperture sizes of

the sandstones. This is done by integrating capillary pres-

sure obtained by the mercury injection porosimetry tech-

nique, petrofacies determination and lithofacies description

of outcrop samples collected.

Experimental work

The most obvious and straightforward measurements of

pore size are with geometric analysis of images of indi-

vidual pores. This can be done using various types of

microscopy on thin sections or other flat soil surfaces, or

tomography. Image-based techniques can be prohibitively

tedious because enough pores must be analyzed to give an

adequate statistical representation. Therefore, the determi-

nation of pore geometry and pore aperture size using

mercury injection technique is believed to be more helpful

in categorizing rocks by pore types (i.e. nanno, micro,

meso, macro or mega). Autopore III 9420 mercury intru-

sion unit was used to determine the capillary pressure,

porosity, pore throat accessibility, and pore level hetero-

geneity of the three reservoirs comprising the Shajara

Formation. This was conducted on nine outcrop sandstone

samples selected among 13 samples from the type section.

All samples except for one (SJ3) are friable sand and their

locations are presented in stratigraphic column illustrated

in Fig. 2.

Samples’ permeability (k) was calculated utilizing Pur-

cell’s equation (1948) stated as:

K ¼ 14; 260� k� /�Zs¼1

s¼0

dSHg

Pc

ð1Þ

where, k is a lithology factor (equal to 0.216), dSHg is

incremental mercury saturation and Pc is the capillary

pressure measured in psi.

The pore aperture size is calculated utilizing Washburn

equation expressed as:

Fig. 1 Location map of the studied area

2 J Petrol Explor Prod Technol (2011) 1:1–9

123

r ¼ 2� r� cos hPc

ð2Þ

where, r is the pore radius in micron, r is the surface tension

of mercury in Dynes/cm, h is the contact angle of mercury

in air and Pc is the capillary pressure in Dynes/cm2.

To reveal the heterogeneity of the investigated reser-

voirs, the pore aperture distribution (PSD) was plotted as a

function of pore radius. The PSD function is defined as the

rate of change of mercury intrusion volume with respect to

the difference of pore radius logarithm relative to the

maximum value of that term. To confirm the findings of the

PSD plots, the cumulative percent of mercury saturation

was plotted with respect to log pore radius.

On average, the pore throats entered by a non-wetting

fluid (mercury) at 35% saturation (R35) or less during a

capillary analysis, represent the pores that dominate fluid

flow in a reservoir samples (Kolodzie 1980). The pore

throat corresponding to a mercury saturation of 35% was

evaluated using Winland equation expressed as:

LogR35 ¼ 0:732þ 0:588� log k � 0:864� log / ð3Þ

Pittman (2001) reported that, pore throat radius

corresponding to the apex has the potential for delineating

Fig. 2 Stratigraphic column of

the type section of the Permo-

carboniferous Shajara

Formation of the Unayzah

Group, Wadi Shajara, Qusayba

area, al Qassim district, Saudi

Arabia, N 26�52 17.4, E 43�36

18

J Petrol Explor Prod Technol (2011) 1:1–9 3

123

stratigraphic traps in the same manner as the pore aperture

corresponding to 35th percentile of a cumulative mercury

saturation curve, which was developed by Winland.

Therefore, the pore aperture size corresponding to the

apex (Rapex) was determined from Pittman equation stated

as follows:

LogRapex ¼ �0:117þ 0:475� Logk � 0:099� Log/

ð4Þ

Results and discussion

In order to determine the behavior of the pore geometry of

Shajara Reservoirs, samples capillary pressures were

measured and the measurements were used to determine

the pore size distribution. Figure 3 is the pore size distri-

bution of sample SJ1 representing the Lower Shajara

Reservoir. This sample is characterized as red in color,

medium grain size and moderately well sorted. The figure

indicates a bimodal pore size distribution of two distinct

pore sizes, minor macro pores of sizes less than 10 lm and

major mega pores with size greater than 10 lm according

to Libny et al. classification (2001). Within the mega pores

there exist a variation in pore size. The sample is charac-

terized with maximum pore radius of 173.9 lm, and a

minimum radius of 0.01 lm, and an average pore size of

41.6 lm. Variation in pore size distribution demonstrates

the possibility of anisotropy. This anisotropy is well

defined in Fig. 4 where three distinct tracks have been

obtained. The pore radii of the first track ranges from 60.2

to 173.9 lm. The second represents pore radii varying from

0.1 to 60.2 lm, whereas the third track is characterized by

very low pore radii ranging in size from 0.1 to 0.01 lm.

Sample SJ2 is the second sample representing the Lower

Shajara Reservoir. It is described as medium-grained, well

sorted sandstone. Figure 5 is the pore size distribution of

the sample indicating a bimodal pore size distribution with

Fig. 3 Incremental and cumulative PSD versus pore radius of sample

SJ1 from the Lower Shajara Reservoir

Fig. 4 Cumulative % SHg versus pore radius of sample SJ1 from the

Lower Shajara Reservoir






123

a maximum pore radius of 173.9 lm, and an average pore

size of 25.4 lm. Again two distinct pore sizes exist with

majority of the sizes classified as megapores. Figure 6

confirms the heterogeneity of the sample as presented by

multiple tracks with distinctive pore radius ranges.

Sample SJ3 of the Lower Shajara Reservoir is charac-

terized with finer grain size when compared to samples SJ1

and SJ2. Such grain size variability as well as compaction

noticed through grains visual inspection is believed to be

due to the sample proximity to the unconformity surface.

This is reflected in a drastic drop in permeability of sample

SJ3 as stated in Table 1. The sample is also identified with

bimodal pore size distribution with skewness towards finer

pore size as indicated in Fig. 7. The sample is characterized

with narrower range of pore radii variation and smaller

pore sizes compared to that of samples SJ1 and SJ2. Again,

Fig. 8 exhibits two tracks of pore radii ranging in size from

10 to 45 lm, and from 1 to 10 lm.

Grain size assessment, pore size distributions and calcu-

lated petrophysical properties of porosity and permeability

of samples SJ1, SJ2 and SJ3 can help assessing the Lower

Shajara Reservoir. This can be confirmed by the Winland

R35 and Pittman Rapex (Table 1). Based on the grain size

description and the obtained porosity and particularly per-

meability, it can likely be stated that the average pore size

decreases as the grain size gets finer and as a consequence

flow capacity declines. This is observed as we proceed

upward in the reservoir. Based on that and the reservoir

classification utilizing the Winland R35, the lower part of the

reservoir can be classified as megaporous (pore radius

greater than 10 lm), whereas the upper portion of the res-

ervoir represented by sample SJ3 is classified as macropo-

rous (pore radius between 2 and 10 lm) with lower flow

capacity as stated by the low permeability value (Table 2).

Middle Shajara Reservoir were characterized using

samples SJ7, SJ8 and SJ9. Sample SJ7 is described as

coarse-grained, moderately well sorted sandstone. This

sample is characterized by bimodal pore size distribution as

shown in Fig. 9 with pore radii ranging from 1.2 to

180.8 lm with an average value of 46.15 lm. The sample

heterogeneity is revealed in Fig. 10, where two tracks of

pore radii exists. The first represents a pore radii ranging

from 10 to 180.8 lm, whereas the second represents pore

radii that vary from 1.2 to 10 lm.

Table 1 Petrophysical properties of samples tested

Petrophysical facies U (%) K (mD) R35 (lm) Rapex (lm) h (feet) U avg. (%) K avg. (mD) Reservoir

Sj-1 29.2 1,680 23 18.6 11.8 31.1 1,592 Lowe Shajara Reservoir

Sj-2 35.5 1,955 21.3 19.6 3.9

Sj-3 34.2 56 2.7 3.6 1.6

Sj-7 35.1 1,472 18.2 17.2 13.4 33.4 1,407 Middle Shajara Reservoir

Sj-8 31.9 1,344 18.7 16.8

Sj-9 31.5 1,395 19.3 16.9 0.9

Sj-11 36.2 1,197 15.7 15.5 13.1 29.9 1,204 Upper Shajara Reservoir

Sj-12 28.2 1,440 21.7 17.4

Sj-13 25.4 973 18.8 14.6 6.5






123

Sample SJ8 is also identified as medium-grained, mod-

erately well sorted sandstone. This sample is characterized

with bimodal pore size distribution as shown in Fig. 11

with an average pore radius of 28.65 lm indicating smaller

average pore size than that of sample SJ7. The heteroge-

neity of this sample is affirmed in Fig. 12 which displays

Table 2 Lithofacies description of samples tested

Facies no. Color Grain size Sorting Hardness

SJ-1 Red Medium-grained Moderately well sorted Friable

SJ-2 Yellow Medium-grained Well sorted Friable

SJ-3 White–pink Fine-grained Poorly sorted Hard

SJ-7 Red Coarse-grained Moderately well sorted Friable

SJ-8 Red Medium-grained Moderately well sorted Friable

SJ-9 Yellow Medium-grained Moderately well sorted Friable

Sj-11 Yellow Medium-grained Poorly sorted Friable

SJ-12 Yellow Very coarse-grained Moderately sorted Friable

SJ-13 Light brown Coarse-grained Moderately sorted Friable





Fig. 11 Incremental and cumulative PSD versus pore radius of

sample SJ8 from the Lower Shajara Reservoir




123

two tracks of pore radii. The first is for a pore radii that

range in size from 37 to 180.8 lm, whereas the second is

characterized by pore radii varying in size from 1 to

10 lm.

Similar to the above two samples of the Middle Shajara

Reservoir, sample SJ9 is described as medium-grained,

moderately well sorted sandstone. This sample is charac-

terized with bimodal pore size distribution as indicated in

Fig. 13 with an average pore radius of 73.9 lm indicating

the largest mean pore size for this section of the reservoir.

Further verification of heterogeneity of this sample is

indicated in Fig. 14 which indicates two tracks of pore

radii, ranging in size from 10 to 164.4 lm and 1 to 10 lm.

Based on the outcomes obtained and the Winland R35 and

Pittman Rapex (Table 1), the whole Middle Shajara Reser-

voir is classified as megaporous reservoir with good flow

capacity.

The Upper Shajara Reservoir is also represented by

three samples, namely from base to top SJ11, SJ12, and

SJ13. Sample SJ11 is identified as medium-grained, poorly

sorted sandstone. This sample is characterized with bimo-

dal pore size distribution as illustrated in Fig. 15. This

variation in pore size distribution is proved in Fig. 16

where three tracks of pore distribution are observed. The

first track is for pore radii varying in size from 30 to

173.9 lm. The second track represents distribution of pore

radii ranging in size from 0.1 to 30 lm. The third track

represents a very small pore radii range of 0.01–0.1 lm.

This sample has a mean pore radius of 42.9 lm.

Sample SJ12 is identified as very coarse-grained, mod-

erately sorted sandstone. This sample is also characterized

with bimodal pore size distribution as illustrated in Fig. 17.

This sample possesses an average pore radius of 67.7 lm.

The pore heterogeneity is verified in Fig. 18 where two







Fig. 16 Cumulative % SHg versus pore radius of sample SJ11 from

the Lower Shajara Reservoir


123

tracks of pore size distribution exist. The first having pore

radii ranging in size from 36 to 173.9 lm, whereas the

second ranges from 3.6 to 36 lm.

Sample SJ13 represents the upper section of the reser-

voir. It is described as coarse-grained, moderately sorted

sandstone. Again it is characterized with bimodal pore size

distribution as illustrated in Fig. 19 with an average pore

radius of 25.2 lm. This sample is also considered hetero-

geneous as indicated in Fig. 20 where three distinct tracks

of pore radii are observed. Reservoir classification of the

Upper Shajara can be considered as megaporous.

In an overall view, and based on the relationship of R35

and Rapex presented in Fig. 21, the reservoir quality of the

Shajara Formation increases with the increase in mean pore

radius corresponding to the apex and to that corresponding

to 35% mercury saturation. Good correlation was obtained



Fig. 18 Incremental and cumulative % SHg versus pore radius of




Fig. 20 Cumulative % SHg versus pore radius of sample SJ13 from

the Lower Shajara Reservoir

Fig. 21 Winland R35 versus Pittman Rapex


123

for the R35 versus Rapex and all samples mean pore sizes are

grouped at megaporous category except for sample SJ3

which falls on macroporous category confirming the pre-

viously discussed pore size identification. In conclusion,

grain and pore size variability are the controlling factor on

the Shajara reservoir quality assessment.

Conclusions

• The three reservoirs of the Shajara Formation are

characterized as heterogeneous reservoirs.

• In general, the three Shajara Reservoirs are classified as

megaporous, with average pore size of 22, 49 and

45 lm for the Lower, Middle, and Upper Shajara

Reservoirs, respectively. However, the best reservoir

quality is assigned to the lower sand unit of the Lower

Shajara followed by the Middle Shajara Reservoir.

• Pore radius corresponding to the apex and that corre-

sponding to the 35% mercury saturation confirms the

reservoir classification indicating megaporous reser-

voirs except for SJ3 of the Lower Shajara which has

low quality due to its fine grain characteristic and its

proximity to the unconformity surface.

• An excellent correlation factor of 0.93 was obtained

when Winland R35 was plotted versus Pittman Rapex.

• Reservoir quality is controlled to a large extent by the

depositional facies and specifically by rock texture

illustrated by petrophysical description. The quality of

the Shajara Formation reservoirs increases with the

increase in grain size and grain sorting.

Open Access This article is distributed under the terms of the

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References

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123

ORIGINAL PAPER - EXPLORATION GEOPHYSICS

Theory of 3-D angle gathers in wave-equation seismic imaging

Sergey Fomel

Received: 26 September 2010 / Accepted: 24 January 2011 / Published online: 22 February 2011


Abstract I present two methods for constructing angle

gathers in 3-D seismic imaging by downward extrapola-

tion. Angles in angle gathers refer to the scattering angle at

the reflector and provide a natural access to analyzing

migration velocity and amplitudes. In the first method,

angle gathers are extracted at each downward-continuation

step by mapping transformations in constant-depth fre-

quency slices. In the second method, one extracts angle

gathers after applying the imaging condition by trans-

forming local offset gathers in the depth domain. The

second approach generalizes previously published algo-

rithms for angle-gather construction in 2-D and common-

azimuth imaging.

Keywords Geophysics � Seismic imaging �Velocity analysis � Amplitude analysis

Introduction

Wave extrapolation provides an accurate method for seis-

mic imaging in structurally complex areas (Biondi 2006;

Etgen et al. 2009). Wave extrapolation methods have

several known advantages in comparison with direct

methods such as Kirchhoff migration thanks to their ability

to handle multi-pathing, strong velocity heterogeneities,

and finite-bandwidth wave-propagation effects (Gray et al.

2001). However, velocity and amplitude analysis in the

prestack domain are not immediately available for wave

extrapolation methods. To overcome this limitation, sev-

eral authors (de Bruin et al. 1990; Prucha et al. 1999;

Mosher and Foster 2000; Rickett and Sava 2002; Xie and

Wu 2002; Soubaras 2003; Sava and Fomel 2003, 2005,

2006) suggested methods for constructing angle gathers

from downward-continued wavefields. Angles in angle

gathers are generally understood as the reflection (scatter-

ing) angles at reflecting interfaces (Xu et al. 2001;

Brandsberg-Dahl et al. 2003). Angle gathers facilitate

velocity analysis (Liu et al. 2001; Stork et al. 2002) and

can be used in principle for extracting angle-dependent

reflectivity information directly at the target reflectors

(Sava et al. 2001). Stolk and de Hoop (2002) assert that

angle gathers generated with wavefield extrapolation are

genuinely free of artifacts documented for Kirchhoff-gen-

erated angle gathers (Stolk and Symes 2002, 2004).

There are two possible approaches to angle-gather

construction with wavefield continuation. In the first

approach, one generates gathers at each depth level con-

verting offset-space-frequency planes into angle-space

planes simultaneously with applying the imaging condi-

tion. The offset in this case refers to the local offset

between source and receiver parts of the downward con-

tinued prestack data. Such a construction was suggested,

for example, by Prucha et al. (1999). This approach is

attractive because of its localization in depth. However,

the method of Prucha et al. (1999) produces gathers in the

offset ray parameter as opposed to angle. As a result, the

angle-domain information becomes structure-dependent:

the output depends not only on the scattering angle but also

on the structural dip.

In the second approach, one converts migrated images in

offset-depth domain to angle-depth gathers after imaging

of all depth levels is completed. Sava and Fomel (2003)

suggested a simple Radon-transform procedure for

S. Fomel (&)

Bureau of Economic Geology, John A. and Katherine G. Jackson

School of Geosciences, The University of Texas at Austin,

University Station, Box X, Austin, TX 78713-8924, USA


123


DOI 10.1007/s13202-011-0004-8

extracting angle gathers from migrated images. The

transformation is independent of velocity and structure.

Rickett and Sava (2002) adopted it for constructing angle

gathers in the shot-gather migration. Biondi and Symes

(2004) demonstrate that the method of Sava and Fomel

(2003) is strictly valid in the 3-D case only in the absence

of cross-line structural dips. They present an extension

of this method for the common-azimuth approximation

(Biondi and Palacharla 1996).

In this paper, I present a more complete analysis of the

angle-gather construction in 3-D imaging by wavefield

continuation. First, I show how to remove the structural

dependence in the depth-slice approach. The improved

mapping retains the velocity dependence but removes the

effect of the structure. Additionally, I extend the second,

post-migration approach to a complete 3-D wide-azimuth

situation. Under the common-azimuth approximation, this

formulation reduces to the result of Biondi et al. (2003)

and, in the absence of cross-line structure, it is equivalent

to the Radon construction of Sava and Fomel (2003).

Traveltime derivatives and dispersion relationships

for a 3-D dipping reflector

Theoretical analysis of angle gathers in downward con-

tinuation methods can be reduced to analyzing the geom-

etry of reflection in the simple case of a dipping reflector in

a locally homogeneous medium. Considering the reflection

geometry in the case of a plane reflector is sufficient for

deriving relationships for local reflection travel time

derivatives in the vicinity of a reflection point (Goldin

2002). Let the local reflection plane be described in

{x, y, z} coordinates by the general equation

x cos aþ y cos bþ z cos c ¼ d; ð1Þ

where the normal angles a, b, and c satisfy

cos2 aþ cos2 bþ cos2 c ¼ 1; ð2Þ

The geometry of the reflection ray paths is depicted in

Fig. 1. The reflection travel time measured on a horizontal

surface above the reflector is given by the known

expression (Slotnick 1959; Levin 1971)

tðhx; hyÞ ¼2

v

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 þ h2

x þ h2y � hx cos aþ hy cos b

� �2q

;

ð3Þwhere D is the length of the normal to the reflector from

the midpoint (distance MM0 in Fig. 2)

D ¼ d � mx cos a� my cos b; ð4Þmx and my are the midpoint coordinates, hx and hy are the

half-offset coordinates, and v is the local propagation

velocity.

According to elementary geometrical considerations

(Figs. 1, 2), the reflection angle h is related to the previ-

ously introduced quantities by the equation

cos h ¼ DffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiD2 þ h2

x þ h2y � hx cos aþ hy cos b

� �2q : ð5Þ

Explicitly differentiating Eq. 3 with respect to the

midpoint and offset coordinates and utilizing Eq. 5 leads to

the equations

tmx� ot

omx¼ � 2

vcos h cos a; ð6Þ

tmy� ot

omy¼ � 2

vcos h cos b; ð7Þ

reflector

surface

SR

θ

θ

O

S"

S’

Fig. 1 Reflection geometry in 3-D (a scheme). S and R and the

source and the receiver positions at the surface. O is the reflection

point. S0 is the normal projection of the source to the reflector. S00 is

the ‘‘mirror’’ source. The cumulative length of the incident and

reflected rays is equal to the distance from S00 to R

S R

OM’

S"

θ

S’reflector

θ

M

Fig. 2 Reflection geometry in the reflection plane (a scheme). M is

the midpoint. As follows from the similarity of triangles S00SR and

S0SM; the distance from M to S0 is twice smaller than the distance

from S00 to R


123

thx� ot

ohx¼ 4

v2 thx sin2 a� hy cos a cos b� �

; ð8Þ

thy� ot

ohy¼ 4

v2 thy sin2 b� hx cos a cos b� �

: ð9Þ

Additionally, the traveltime derivative with respect to

the depth of the observation surface is given by

tz �ot

oz¼ � 2

vcos h cos c ð10Þ

and is related to the previously defined derivatives by

the double-square-root equation

�v tz ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmx� thx

ð Þ2� v2

4tmy� thy

� �2

r

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmxþ thx

ð Þ2� v2

4tmyþ thy

� �2

r:

ð11Þ

In the frequency-wavenumber domain, Eq. 11 serves as

the basis for 3-D shot-geophone downward-continuation

imaging. In the Fourier domain, each tx derivative

translates into -kx/x ratio, where kx is the wavenumber

corresponding to x and x is the temporal frequency.

Equations (6), (7), and (10) immediately produce the

first important 3-D relationship for angle gathers

cos h ¼ v

2x

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffik2

mxþ k2

myþ k2

z

q: ð12Þ

Expressing the depth derivative with the help of the

double-square-root Eq. 11 and applying a number of

algebraic transformations, one can turn Eq. 12 into the

dispersion relationship

ðk2mxþ k2

myÞ sin2 h

v2þ ðk2

hxþ k2

hyÞ cos2 h

v2

¼ 1

4x2kmx

khy� kmy

khx

� �2þ4x2 cos2 hv2

sin2 hv2

:

ð13Þ

For each reflection angle h and each frequency x, Eq. 13

specifies the locations on the four-dimensional

(kmx; kmy

; khx; khy

) wavenumber hyperplane that contribute

to the common-angle gather. In the 2-D case, Eq. 13

simplifies by setting khyand ky to zero. Using the notation

kmx¼ km and khx

¼ kh; the 2-D equation takes the form

k2m sin2 hþ k2

h cos2 h ¼ 4x2

v2cos2 h sin2 h ð14Þ

and can be explicitly solved for kh resulting in the

convenient 2-D dispersion relationship

kh ¼2x sin h

v

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 4k2

mv2

x2 cos2 h

r: ð15Þ

In the next section, I show that a similar simplification is

also valid under the common-azimuth approximation.

Equations (13) and (15) describe an effective migration of

the downward-continued data to the appropriate positions

on midpoint-offset planes to remove the structural

dependence from the local image gathers.

Another important relationship follows from eliminating

the local velocity v from Eqs. 11 and 12. Expressing v2

from Eq. 12 and substituting the result in Eq. 12, we arrive

(after a number of algebraical transformations) to the fre-

quency-independent equation

tan2 h ¼k2

z ðk2hxþ k2

hyÞ þ ðkhx

kmxþ khy

kmyÞ2

k2z ðk2

mxþ k2

myþ k2

z Þ: ð16Þ

Equation (16) can be expressed in terms of ratios kmx=kz

and kmy=kz; which correspond at the zero local offset to

local structural dips (zmxand zmy

partial derivatives), and

ratios khx=kz and khy

=kz; which correspond to local offset

slopes. As shown by Sava and Fomel (2005), it can be also

expressed as

tan2 h ¼k2

hxþ k2

hyþ k2

hz

k2mxþ k2

myþ k2

z

; ð17Þ

where khzrefers to the vertical offset between source and

receiver wavefields (Biondi and Shan 2002).

In the 2-D case, Eq. 16 simplifies to the form, inde-

pendent of the structural dip:

tan h ¼ kh

kz; ð18Þ

which is the equation suggested by Sava and Fomel

(2003). Equation (18) appeared previously in the theory of

migration-inversion (Stolt and Weglein 1985).

Common-azimuth approximation

Common-azimuth migration (Biondi and Palacharla 1996)

is a downward continuation imaging method tailored for

narrow-azimuth streamer surveys that can be transformed

to a single common azimuth with the help of azimuth

moveout (Biondi et al. 1998). Employing the common-

azimuth approximation, one assumes the reflection plane

stays confined in the acquisition azimuth. Although this

assumption is strictly valid only in the case of constant

velocity (Vaillant and Biondi 2000), the modest azimuth

variation in realistic situations justifies the use of the

method (Biondi 2003).

To restrict equations of the previous section to the

common-azimuth approximation, it is sufficient to set the

cross-line offset hy to zero assuming the x coordinate is

oriented along the acquisition azimuth. In particular, from

Eqs. 8, 9, we obtain

hx sin a ¼ vt

2sin h ð19Þ


123

thx¼ 4hx

v2tsin2 a ¼ 2

vsin h sin a; ð20Þ

thy¼ � 4hx

v2tcos a cos b ¼ � 2

vsin h cot a cos b : ð21Þ

With the help of Eqs. 6, 7, and 10), Eq. 21 transforms to

the form

thy¼ tmy

tan htan a

¼ tmy

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmxþ thx

ð Þ2q

�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmx� thx

ð Þ2q

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmxþ thx

ð Þ2q

þffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2

4tmx� thx

ð Þ2q ;

ð22Þ

suggested by Biondi and Palacharla (1996). Combining

Eqs. 6, 7, 10, and 20 and transforming to the frequency–

wavenumber domain, we obtain the common-azimuth

dispersion relationship

ðk2hxþ k2

myþ k2

z Þ ðk2mxþ k2

myþ k2

z Þ ¼4x2

v2ðk2

myþ k2

z Þ; ð23Þ

which shows that, under the common-azimuth

approximation and in a laterally homogeneous medium,

3-D seismic migration amounts to a cascade of a 2-D

prestack migrations in the in-line direction and a 2-D zero-

offset migration in the cross-line direction (Canning and

Gardner 1996).

Under the common-azimuth approximation, the angle-

dependent relationship (13) takes the form

k2mx

sin2 hþ k2hx

cos2 h ¼ 4x2

v2cos2 h sin2 h; ð24Þ

which is identical to the 2-D Eq. 14. This proves that

under this approximation, one can perform the structural

correction independently for each cross-line wavenumber.

The post-imaging Eq. 16 transforms to the equation

tan2 h ¼k2

hx

k2myþ k2

z

; ð25Þ

obtained previously by Biondi et al. (2003). In the

absence of cross-line structural dips ðkmy¼ 0Þ; it is

equivalent to the 2-D Eq. 18.

Algorithm I: Angle gathers during downward

continuation

This algorithm follows from Eq. 13. It consists of the

following steps, applied at each propagation depth z:

1. Generate local offset gathers and transform them to

the wavenumber domain. In the double-square-root

migration, the local offset wavenumbers are immedi-

ately available. In the shot gather migration, local

offsets are generated by cross-correlation of the source

and receiver wavefields (Rickett and Sava 2002).

2. For each frequency x, transform the local offset wave-

numbers khx; khy

into the angle coordinates sin h=v

according to Eq. 13. The angle coordinates depend on

velocity but do not depend on the local structural dip. In

the 2-D case, each frequency slice is simply the km; kh

plane, and each angle coordinate corresponds to a circle

in that plane centered at the origin and described by

Eq. 14. Figure 3 shows an example of a 2-D frequency

slice transformed to angles.

3. Accumulate contributions from all frequencies to

apply the imaging condition in time.

This algorithm is applicable for targets localized in

depth. The local offset gathers need to be computed for all

lateral locations, but there is no need to store them in

memory, because conversion to angles happens on the fly.

The algorithm outputs not angles directly, but velocity-

dependent parameters sin h=v: Alkhalifah and Fomel

(2009, 2011) have recently extended this algorithm to

transversally isotropic media.

Algorithm II: Post-migration angle gathers

The second algorithm follows from Eq. 16. It applies after

the imaging has completed and consists of the following

steps applied at each common-image location:

1. Generate and store local offset gathers. In the double-

square-root migration, the local offsets are immedi-

ately available. In the shot gather migration, local

Fig. 3 Constant-depth constant-frequency slice mapped to reflection

angles according to the 2-D version of Algorithm I. Zero offset

wavenumber maps to zero (normal incidence) angle. The top rightcorner is the evanescent region


123

offsets are generated by cross-correlation of the source

and receiver wavefields.

2. Estimate the dominant local structural dips at the

common image point by using one of the available dip

estimation methods: local slant stack, plane-wave

destruction, etc.

3. After the imaging has completed, transform local-

offset gathers into the slant-stack domain either by

slant-stacking in the fz; hx; hyg physical domain or by

radial-trace construction in the fkz; khx; khyg Fourier

domain (Sava and Fomel 2003).

4. Using estimated dips, convert slant stacks into angles

by applying Eq. 16. The mapping from offset-depth

slopes to angles is illustrated in Fig. 4.

The last two steps can be combined into one. It is

sufficient to compute the effective offset h ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffih2

x þ h2y þ ðhxzy � hyzxÞ2

qand apply the basic 2-D angle

extraction algorithm to the effective offset gather.

The second method is applicable to selected common-

image gathers, which can be spread on a sparse grid. The

local offset gathers need to be computed and stored at all

depths. The method works independent of the velocity. The

main disadvantage is the need to estimate local structural

dips. In the common-azimuth approximation, only the

cross-line dip is required (Biondi et al. 2003). In the 2-D

case (zero cross-line dip), the method is dip-independent

(Sava and Fomel 2003).

Discussion

Since the first presentation of the 3-D angle-gather theory

(Fomel 2004), many new research results have appeared in

the literature. By the end of 2000s, prestack 3-D reverse-

time migration has become a standard tool for depth

imaging in structurally-complex areas, and it is becoming

feasible to generate 3-D angle gathers as part of routine

processing (Luo et al. 2010; Vyas et al. 2010; Xu et al.

2010). The most important new theoretical developments

are the ability to extract angle information from time-shift

angle gathers (Sava and Fomel 2006; Vyas et al. 2010), the

ability to extract not only reflection-angle but also azimuth

information (Xu et al. 2010), and the extension of the

angle-gather theory to anisotropy (Biondi 2007; Alkhalifah

and Fomel 2009, 2011).

Conclusions

Angle gathers present a natural tool for analyzing velocities

and amplitudes in wave-equation imaging. I have discussed

two approaches for angle-gather construction. In the first

approach, angle gathers are constructed on the fly at dif-

ferent depth steps of the wave extrapolation process. In the

second approach, angle gathers are extracted from the

local-offset gathers after imaging has completed. The

second method was previously presented for the 2-D case

and for the case of a common-azimuth approximation. Both

approaches have advantages and disadvantages. The pref-

erence depends on the application and the input data

configuration.

Acknowledgments I am grateful to Nanxun Dai, John Etgen,

Sergey Goldin, and Paul Sava for enlightening discussions.

This publication is authorized by the Director, Bureau of Economic

Geology, The University of Texas at Austin.





Fig. 4 Mapping from the offset

slope plane to angles according

to Algorithm II. Zero slopes

map to zero (normal-incidence)

angle


123

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http://dx.doi.org/10.1111/j.1365-2478.2010.00930.x

ORIGINAL PAPER - EXPLORATION GEOPHYSICS

The basic components of residual migration in VTI media usinganisotropy continuation

Tariq Alkhalifah • Sergey Fomel

Received: 3 May 2010 / Accepted: 3 March 2011 / Published online: 24 March 2011


Abstract We introduce anisotropy continuation as a

process which relates changes in seismic images to per-

turbations in the anisotropic medium parameters. This

process is constrained by two kinematic equations, one for

perturbations in the normal-moveout (NMO) velocity and

the other for perturbations in the dimensionless anisotropy

parameter g. We consider separately the case of post-stack

migration and show that the kinematic equations in this

case can be solved explicitly by converting them to

ordinary differential equations using the method of char-

acteristics. When comparing the results of kinematic ana-

lytical computations with synthetic numerical experiments

confirms the theoretical accuracy of the method.

Keywords Velocity continuation � Residual migration �Anisotropy

Introduction

A well-known paradox in seismic imaging is that the

detailed information about the subsurface velocity is

required before a reliable image can be obtained. In prac-

tice, this paradox leads to an iterative approach to building

the image. It looks attractive to relate small changes in

velocity parameters to inexpensive operators perturbing the

image. This approach has been long known as residual

migration. A classic result is the theory of residual post-

stack migration (Rothman et. al. 1985), extended to the

prestack case by Etgen (1990). In a relatively recent paper,

Fomel (1996) introduced the concept of velocity continu-

ation as the continuous model of the residual migration

process. All these results were based on the assumption of

the isotropic velocity model.

Recently, emphasis has been put on the importance of

considering anisotropy and its influence on data. Alkhalifah

and Tsvankin (1995) demonstrated that, for TI media with

vertical symmetry axis (VTI media) and mild lateral

inhomogeneity, just two parameters are sufficient for per-

forming all time-related processing, such as normal

moveout (NMO) correction (including non-hyperbolic

moveout correction, if necessary), dip-moveout (DMO)

correction, and prestack and poststack time migration in a

homogeneous medium. One of these two parameters, the

short-spread NMO velocity for a horizontal reflector, is

given by

vnmoð0Þ ¼ vv

ffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ 2dp

; ð1Þ

where vv is the vertical P-wave velocity, and d is one of

Thomsen’s anisotropy parameters (Thomsen 1986). Taking

vh to be the P-wave velocity in the horizontal direction, the

other anisotropy parameter, g, is given by

g � 0:5v2

h

v2nmoð0Þ

� 1

� �¼ �� d

1þ 2d; ð2Þ

where � is another of Thomsen’s parameters. In addition,

Alkhalifah (1998) has showed that the dependency on just

two parameters becomes exact when the vertical shear wave

velocity (VS0) is set to zero. Setting VS0 = 0 leads to

T. Alkhalifah (&)

Physical Sciences and Engineering Division, King Abdullah

University for Science and Technology (KAUST),

Thuwal, Saudi Arabia


S. Fomel

Bureau of Economic Geology,

The University of Texas at Austin, Austin, TX, USA


123


DOI 10.1007/s13202-011-0006-6

remarkably accurate kinematic representations. It also

results in much simpler equations that describe P-wave

propagation in VTI media. Throughout this paper, we use

these simplified, yet accurate with respect to conventional

data processing objectives, equations, based on setting

VS0 = 0, to derive the continuation equations. Because we

are only considering time sections, and for the sake of sim-

plicity, we denote vnmo by v. Thus, time processing in VTI

media, depends on two parameters (v and g), whereas in

isotropic media only v counts. To emphasize the importance

of anisotropy to the dip moveout process, Alkhalifah (2005)

introduced residual dip moveout for VTI media.

In this paper, we generalize the velocity continuation

concept to handle VTI media. We define anisotropy con-

tinuation as the process of seismic image perturbation

when either v or g change as migration parameters. This

approach is especially attractive, when the initial image is

obtained with isotropic migration (that is with g = 0). In

this case, anisotropy continuation is equivalent to intro-

ducing anisotropy in the model without the need for

repeating the migration step.

For the sake of simplicity, we start from the post-

stack case and purely kinematic description. We define,

however, the guidelines for moving to the more com-

plicated and interesting cases of prestack migration and

dynamic equations. The results open promising oppor-

tunities for seismic data processing in the presence of

anisotropy.

The general theory

In the case of zero-offset reflection in homogeneous media,

the ray travel distance, l, from the source to the reflection

point is related to the two-way zero-offset time, t, by the

simple equation

l ¼ 1

2vgt; ð3Þ

where vg is the group velocity, best expressed in terms of

its components, as follows:

vg ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiv2

gx þ v2vv2

gs

q:

Here vgx denotes the horizontal component of group

velocity, vv is the vertical P-wave velocity, and vgs is the

vv-normalized vertical component of the group velocity.

Under the assumption of zero shear-wave velocity in VTI

media, these components have the following analytic

expressions:

vgx ¼v2 px 1þ 2 g� 2 g ps

2ð Þ2� v2 1þ 2 gð Þ px

2 � ps2; ð4Þ

and

vgs ¼1� 2 v2 g px

2ð Þ ps

2� v2 1þ 2 gð Þ px2 � ps

2; ð5Þ

where px is the horizontal component of slowness, and ps is

the normalized (again by the vertical P-wave velocity vv)

vertical component of slowness. The two components of

the slowness vector are related by the following eikonal-

type equation (Alkhalifah 1998):

ps ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� v2 px

2

1� 2 v2 g px2

s: ð6Þ

Equation (6) corresponds to a normalized version of the

dispersion relation in VTI media.

If we consider v and g as imaging parameters (migration

velocity and migration anisotropy coefficient), the ray

lengthl can be fixed through the imaging process. This

implies that the partial derivatives of with respect to the

imaging parameters are zero. Therefore,

ol

ov¼ ovg

ovt þ vg

ot

ov¼ 0; ð7Þ

and

ol

og¼ ovg

ogt þ vg

ot

og¼ 0: ð8Þ

Applying the simple chain rule to Eqs. (7) and (8), we

obtain

ot

ov¼ ot

ososov;

ot

og¼ ot

ososog; ð9Þ

where otos ¼ �ps, and the two-way vertical travel time is

given by

s ¼ vgst:

Combining Eqs. (7–9) eliminates the two-way zero-offset

time t, which leads to the equations

osov¼ ovg

ov

sps vgsvg

; ð10Þ

and

osog¼ ovg

ogs

ps vgsvg: ð11Þ

After some tedious algebraic manipulation, we can

transform Eqs. (10) and (11) to the general form

osov¼ sFv px; v; gð Þ; ð12Þ

and

osog¼ sFg px; v; gð Þ: ð13Þ


123

Since the residual migration is applied to migrated data,

with the time axis given by s and the reflection slope given byosox ; instead of t and px, respectively, we need to eliminate px

from Eqs. (12) and (13). This task can be achieved with the

help of the following explicit relation, derived in Appendix 1,

p2x ¼

2 sx2

1þ v2 1þ 2 gð Þ sx2 þ S

; ð14Þ

where sx = osox, and

S ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi� 8 v2 g sx

2 þ 1þ v2 1þ 2 gð Þ sx2ð Þ2

q:

Inserting Eq. (14) into Eqs. (12) and (13) yields exact,

yet complicated equations, describing the continuation

process for v and g. In summary, these equations have the

form

osov¼ sfv

osox; v; g

� �ð15Þ

and

osog¼ sfg

osox; v; g

� �: ð16Þ

Equations of the form (15) and (16) contain all the

necessary information about the kinematic laws of anisotropy

continuation in the domain of zero-offset migration.

Linearization

A useful approximation of Eqs. (15) and (16) can be

obtained by simply setting g equal to zero in the right hand

side of the equations. Under this approximation, Eq. (15)

leads to the kinematic velocity-continuation equation for

elliptically anisotropic media, which has the following

relatively simple form:

osov¼ v s 2 v2 � vv

2ð Þ sx2 1þ v2 sx

2ð Þvv

2 þ v4 sx2

: ð17Þ

It is interesting to note that setting v = vv, yields

Fomel’s expression for isotropic media (Fomel 1996) given

by

osov¼ v s sx

2: ð18Þ

Alkhalifah (1998) have shown that time–domain

processing algorithms for elliptically anisotropic media

should be the same as those for isotropic media. However,

in anisotropic continuation, elliptical anisotropy and

isotropy differ by a vertical scaling factor that is related

to the difference between the vertical and NMO velocities.

In isotropic media, when velocity is continued, both the

vertical and NMO velocities (which are the same) are

continued together, whereas in anisotropic media

(including elliptically anisotropic) the NMO-velocity

continuation is separated from the vertical velocity one,

and Eq. (17) corresponds to continuation only in the NMO

velocity. This also implies that Eq. (17) is more flexible

than Eq. (18), in that we can isolate the vertical velocity

continuation (a parameter that is usually ambiguous in

surface processing) from the rest of the continuation

process. Using s ¼ zvv; where z is depth, we immediately

obtain the equation

osovv¼ � s

vv;

which represents the vertical velocity continuation.

Setting g = 0 and v = vv in Eq. (16) leads to the fol-

lowing kinematic equation for g-continuation:

osog¼ sv4 sx

4

1þ v2 sx2: ð19Þ

We include more discussion about different aspects of

linearization in Appendix 2. The next section presents the

analytic solution of Eq. (17). Later in this paper, we

compare the analytic solution with a numerical synthetic

example.

Ordinary differential equation representation:

anisotropic rays

According to the classic rules of mathematical physics, the

solution of the kinematic equations (15) and (16) can be

obtained by solving the following system of ordinary dif-

ferential equations:

dx

dm¼ �s

ofmosx

;dsdm¼ �ssx

ofm

osxþ sm;

dsm

dm¼ s

ofm

omþ smfm;

dsx

dm¼ sxfm:

ð20Þ

Here m stands for either v or g, sx = osox, fm ¼ os

om. To trace

the v and g rays, we must first identify the initial values

x0,s0,sx0, and sm0 from the boundary conditions. The vari-

ables x0 ands0 describe the initial position of a reflector in a

time-migrated section, sx0 describes its migrated slope,

andsm0 is simply obtained from Eqs. (15) or (16).

Using the exact kinematic expressions for f, the results

in rather complicated representations of the ordinary dif-

ferential equations. The linearized expressions, on the other

hand, are simple and allow for a straightforward analytical

formulation of the ray tracing system.

From kinematics to dynamics

The kinematic g-continuation equation (17) corresponds to

the following linear fourth-order dynamic equation


123

o4P

ot3 ogþ v2 o4P

ox2 ot ogþ tv4 o4P

ox4¼ 0; ð21Þ

where the t coordinate refers to the vertical traveltime s,

and P (t, x, g) is the migrated image, parameterized in the

anisotropy parameter g. To find the correspondence

between Eqs. (17) and (21), it is sufficient to apply a ray-

theoretical model of the image

Pðt; x; gÞ ¼ Aðx; gÞf ðt � sðx; gÞÞ ð22Þ

as a trial solution to (21). Here the surface t = s (x, g) is

the anisotropy continuation ‘‘wavefront’’—the image of a

reflector for the corresponding value of g, and the function

A is the amplitude. Substituting the trial solution into the

partial differential equation (21) and considering only the

terms with the highest asymptotic order (those containing

the fourth-order derivative of the wavelet f), we arrive at

the kinematic equation (17). The next asymptotic order (the

third-order derivatives of f) gives us the linear partial

differential equation of the amplitude transport, as follows:

1þ v2s2x

� � oA

ogþ 2v2sx sg � 2v2ss2

x

� � oA

oxþ v2A

� 2sxsxg þ sgsxx � 6v2ss2xsxx

� �¼ 0: ð23Þ

We can see that when the reflector is flat (sx = 0 and

sxx = 0), equation (23) reduces to the equality

oA

og¼ 0;

and the amplitude remains unchanged for different g. This

is of course a reasonable behavior in the case of a flat

reflector. It does not guarantee although that the ampli-

tudes, defined by Eq. (23), behave equally well for dipping

and curved reflectors. The amplitude behavior may be

altered by adding low order terms to Eq. (21). According to

the ray theory, such terms can influence the amplitude

behavior, but do not change the kinematics of the wave

propagation.

An appropriate initial value condition for Eq. (21) is the

result of isotropic migration that corresponds to the g = 0

section in the (t, x, g) domain. In practice, the initial value

problem can be solved by a finite-difference technique.

Synthetic test

Residual post-stack migration operators can be obtained by

generating synthetic data for a model consisting of dif-

fractors for given medium parameters and then migrating

the same data with different medium parameters. For

example, we can generate diffractions for isotropic media

and migrate those diffractions using an anisotropic migra-

tion. The resultant operator describes the correction needed

to transform an isotropically migrated section to an

anisotropic one, that is the anisotropic residual migration

operator.

Figure 1 shows such synthetic operators overlaid by

kinematically calculated operators that were computed

with the help of Eq. (17) (the continuation equations for

the case of smallg). Despite the inherent accuracy of the

synthetic operators, they suffer from the lack of aperture

in modeling the diffractions, and therefore, beyond a

certain angle the operators vanish and start to deviate.

The agreement between the synthetic and calculated

operators for small angles, especially for the g = 0.1

case, promises reasonable results in future dynamic

implementations.

0

0.5

1.0

1.5

Tim

e (s

)

-0.6 -0.4 -0.2 0 0.2 0.4

Distance (km)

0.60

0.5

1.0

1.5

Tim

e (s

)

-0.6 -0.4 -0.2 0 0.2 0.4

Distance (km)

0.6

Fig. 1 Residual post-stack

migration operators calculated

by solving Eq. (17), overlaid

above synthetic operators. The

synthetic operators are obtained

by applying TI post-stack

migration with g = 0.1 (left)and g = 0.2 (right) to three

diffractions generated

considering isotropic media.

The NMO velocity for the

modeling and migration is

2.0 km/s


123

Conclusions

We have extended the concept of velocity continuation in

isotropic media to continuations in both the NMO velocity

and the anisotropy parameter g for VTI media. Despite

the fact that we have considered the simple case of post-

stack migration separately, the exact kinematic equations

describing the continuation process are anything, but simple.

However, useful insights into this problem are deduced from

linearized approximations of the continuation equations.

These insights include the following observations:

• The leading order behavior of the velocity continuation

is proportional to sx2, which corresponds to small or

moderate dips.

• The leading order behavior of the g continuation is

proportional to sx4, which corresponds to moderate or

steep dips.

• Both leading terms are independent of the strength of

anisotropy (g).

In practical applications, the initial migrated section is

obtained by isotropic migration, and, therefore, the residual

process is used to correct for anisotropy. Setting g = 0 in

the continuation equations for this type of an application is

a reasonable approximation, given that g = 0 is the starting

point and we consider only weak to moderate degrees of

anisotropy (g & 0.1). Numerical experiments with syn-

thetically generated operators confirm this conclusion.

Acknowledgments Tariq Alkhalifah would like to thank KAUST

and KACST for their financial support, and Sergey Fomel likes to

thank the University of Texas, Austin for its support.





Appendix 1

Relating the zero-offset and migration slopes

The chain rule of differentiation leads to the equality

px ¼ot

ox¼ � ps

osox; ð24Þ

where ps ¼ � otos : It is convenient to transform equality (24)

to the form

osox¼ � px

ps: ð25Þ

Using the expression for ps from the main text, we can

write Eq. (25) as a quadratic polynomial in px2 as follows

ap4x þ bp2

x þ c ¼ 0; ð26Þ

where

a ¼ �2v2g;

b ¼ osox

� �2

v2ð1þ 2gÞ þ 1;

and

c ¼ � osox

� �2

:

Because g can be small (as small as zero for isotropic

media), we use the following form of solution to the

quadratic equation

p2x ¼

2c

�b�ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffib2 � 4acp

(Press et al. 1992). This form does not go to infinity asgapproaches 0. We choose the solution with the negative

sign in front of the square root, because this solu-

tion complies with the isotropic result wheng is equal to

zero.

Appendix 2

Linearized approximations

Although the exact expressions might be sufficiently con-

structive for actual residual migration applications, linear-

ized forms are still useful, because they give us valuable

insights into the problem. The degree of parameter

dependency for different reflector dips is one of the most

obvious insights in the anisotropy continuation problem.

Perturbation of a small parameter provides a general

mechanism to simplify functions by recasting them into

power series expansion over a parameter that has small

values. Two variables can satisfy the small perturbation

criterion in this problem: The anisotropy parame-

terg (g � 1) and the reflection dip sx (sx v� 1 or px

v � 1).

Setting g = 0 yields Eq. (17) for the velocity continu-

ation in elliptical anisotropic media and

osog¼ v4 s sx

4 �3 vv2 þ 2 v4 sx

2 þ v2 4� vv2 sx

2ð Þð Þ1þ v2 sx

2ð Þ vv2 þ v4 sx

2ð Þ : ð27Þ

which represents the case when we initially introduce

anisotropy into our model.

Because px (the zero-offset slope) is typically lower than

sx (the migrated slope), we perform initial expansions in

terms of y = px v. Applying the Taylor series expansion of


123

Eqs. (12) and (13) in terms of y and dropping all terms

beyond the fourth power in y, we obtain

osov¼ v s px

2 2 v2 � vv2ð Þ

vv2

� v3 s px4 2 v2 � vv

2ð Þ v2 � 2 1þ 6 gð Þ vv2ð Þ

vv4

; ð28Þ

and

osog¼ v4 s px

4 4 v2 � 3 vv2ð Þ

vv2

: ð29Þ

Although both equations are equal to zero for px=0, the

leading term in the velocity continuation is proportional to

px2, whereas the the leading term in the g continuation is

proportional to px4. As a result the velocity continuation has

greater influence at lower angles than the g continuation. It

is also interesting to note that both leading terms are

independent of the size of anisotropy (g).

Despite the typically lower values of px, expansions in

terms of sx are more important, but less accurate. For small

sx, px & sx, and, therefore, the leading-term behavior of sx

expansions is the same as that of px. As a result, we arrive

at the equation

osov¼ v s 2 v2 � vv

2ð Þ sx2

vv2

þ v4

�� v s 2 v2 � vv

2ð Þvv

4þ s 2 v2 � vv

2ð Þv vv

2

þ 12 g s 2 v2 � vv2ð Þ

v vv2

�sx

4; ð30Þ

and

osog¼ v4 s 4 v2 � 3 vv

2ð Þ sx4

vv2

: ð31Þ

Most of the terms in Eqs. (30) and (31) are functions of

the difference between the vertical and NMO velocities.

Therefore, for simplicity and without a loss of generality,

we set vv = v and keep only the terms up to the eighth

power in sx. The resultant expressions take the form

osov¼ v s sx

2 þ 12 v3 g s sx4 � 4 v5 g 4� 25 gð Þ s sx

6

þ 4 v7 g 5� 83 gþ 144 g2� �

s sx8 ð32Þ

and

osog¼ v4 s sx

4 � v6 1� 20 gð Þ s sx6

þ v8 1� 54 gþ 156 g2� �

s sx8: ð33Þ

Curiously enough, the second term of the g continuation

heavily depends on the size of anisotropy (*20g). The first

term of Eq. (32) (* sx2) is the isotropic term; all other terms

in Eqs. (32) and (33) are induced by the anisotropy.

References

Alkhalifah T (1998) Acoustic approximations for processing in

transversely isotropic media. Geophysics 63:623–631

Alkhalifah T (2005) Residual dip moveout in VTI media. Geophys

Prosp 53:1–12

Alkhalifah T, Tsvankin I (1995) Velocity analysis for transversely

isotropic media. Geophysics 60:1550–1566

Etgen J (1990) Residual prestack migration and interval velocity

estimation. PhD thesis, Stanford University

Fomel S (1996) Migration and velocity analysis by velocity

continuation

Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992)

Numerical recipes, the art of scientific computing. Cambridge

University Press, Cambridge

Rothman DH, Levin SA, Rocca F (1985) Residual migration—

applications and limitations. Geophysics 50:110–126

Thomsen L (1986) Weak elastic anisotropy. Geophysics 51:1954–

1966 (discussion in GEO-53-04-0558-0560 with reply by author)


123

ORIGINAL PAPER—PRODUCTION ENGINEERING

Investigation of polymer and surfactant-polymer injectionsin South Slattery Minnelusa Reservoir, Wyoming

Panqing Gao • Brian Towler

Received: 29 April 2010 / Accepted: 20 December 2010 / Published online: 29 January 2011


Abstract This paper presents an investigation of the

enhanced oil recovery (EOR) potential in the South Slat-

tery Minnelusa formation. The South Slattery Field, which

is characterized by low permeability and high saline brine,

is stepping into the economic limits of secondary water-

flood. A chemical flooding simulation model which was

based on experimental parameters was set up for the

potential investigation of EOR. Both polymer and surfac-

tant-polymer floods were investigated. The recoveries of

these EOR methods are presented, and the development

efficiencies are analyzed.

Keywords Polymer flood � Surfactant-polymer flood �Low permeability � High salinity

List of symbols

Hwj Average thickness of injection well

Hwj Thickness of injection well

a Heterogeneous factor

Hoi Thickness of response producer

i Response producer

j Injection well

Qwj Injection rate of polymer solution

Qw Total injection rate of region

V Injection volume in 1 year

HPAM Partially hydrolyzed polyacrylamide

PV Pore volume

IPV Inaccessible pore volume

IFT Interfacial tension

Introduction

The South Slattery Field is on the southwest toe of a large

anticlinal structure, which is on the eastern flank of the

Powder River basin. Its priority pay zone is the Minnelusa

A, which is a sequence of carbonates and sandstones

formed in the Permian age. These rocks were deposited in a

shallow evaporitic basin, and responses to sea-level chan-

ges were recorded. The stacking pattern, or parasequences

consist of (1) a marine flood of a dune field and carbonate

deposition, (2) shallowing marine deposition due to eu-

static lowering of the sea level, and (3) renewed progra-

dation of eolian dune fields (Sheppy 1986). Just as the

unconformity at the top of the Minnelusa has long been

recognized as an important trapping mechanism, these

parasequence boundaries can also provide significant traps

because the geomorphic relief on the dune fields was lar-

gely preserved during each transgression. The dominant

trapping mechanism is stratigraphic. According to Sheppy,

there are minor Cretaceous muddy sandstones and pro-

ductive sandstones in the upper part of the sequence. But

the Permo-Pennsylvanian Minnelusa ‘‘A’’ Formation is the

principal reservoir (Towler 1991). Figure 1 shows the

structure on the top of the Minnelusa formation. Table 1

presents the reservoir properties of the Minnelusa.

From 1964 to 1995, the field was in the depletion stage;

the primary drive mode had been shown to be a solution

gas drive, in conjunction with fluid expansion, aquifer

influx, and gravity drainage (Towler 1991). At the end of

P. Gao (&) � B. Towler

Department of Chemical and Petroleum Engineering,

University of Wyoming, Laramie, WY, USA


P. Gao � B. Towler

Enhanced Oil Recovery Institute,

University of Wyoming, Laramie, WY, USA

123


DOI 10.1007/s13202-010-0002-2

this stage, the average individual water cut in the north-

eastern zone was relatively low, while the southwest part

showed a high water cut. At the end of 1995, a holistic

water flood began, and oil recovery rate was significantly

increased. The interest in this simulation was initially

spurred by the fact that the water cut kept increasing and

the oil production rate kept decreasing in the past several

years. Figure 2 shows that the oil production rate in this

field began to decline since 2003. The water cut rose sig-

nificantly due to the water injection. To slow down the oil

production decline, an investigation of enhanced oil

recovery (EOR) becomes necessary. In this EOR simula-

tion model, two methods, polymer and surfactant-polymer

(SP) floods, were investigated.

Eclipse has been employed to conduct the simulation

investigation. E100 has been used to finish the history

matching of the depletion and water flooding. Polymer and

surfactant models were used to model the chemical injec-

tions. The parameters of chemical simulation were all from

relative laboratory investigation.

Screening criteria and feasibility investigation

Polymer flood

Use of the polymeric waterflood is a technique to enhance

oil recovery from a reservoir by improving the reservoir

sweep and reducing the amount of injection fluid needed to

produce the same amount of oil (Sorbie and Phil 1991).

Polymer floods work by adding a certain amount of water-

soluble polymers to the injection fluid to increase the vis-

cosity of the injectant (Chang et al. 2006). In this way, the

mobility ratio between the displaced phase and displacing

phase can be reduced significantly, and the sweep volume

is increased accordingly.

Two ways were investigated to optimize the mobility

control: increasing the concentration and increasing the

molecular weight. The former method is a question of

economics; the later one, however, is a question of tech-

nical feasibility (Wang and Li 2006; Carcoana 1991). The

change of molecular weights would result in the basic

changes in the polymer solution properties and the solu-

tion-rock properties, such as residual reduction factor,

adsorption, shear thinning, and inaccessible pore volume

(Pu and Yin 2008; Kaminsky and Szafranski 2007). These

parameters will impact the formation injectivity and

determine the feasibility of the process. Therefore, the first

task of the polymer flood for a given reservoir is to fix an

injection system both technically and economically; espe-

cially for reservoirs with strong heterogeneity (Gharbi

2001; David and Gary 2003), the optimization of the

polymer injection system is extremely important. In this

research, three kinds of polymer of different molecular

weights were used to estimate the effects of polymer flood

in this field.

According to industry experience, the criteria for devel-

oping a successful polymer flood include the following:

1. The oil gravity is greater than 25�API with an oil

viscosity less than 30 cp at reservoir conditions.

2. Oil saturation greater than 30% and light intermediates

desirable.

3. The oil reservoir depth must be less than 8,000 ft with

a reservoir temperature less than 175�F.

4. Formation permeability should be greater than 20 mD

with a net thickness (sandstones preferred) of greater

than 10 ft is favorable.

-5280 -2640 0 2640 5280 7920-5280

-2640

0

2640

5280

Fig. 1 The structure map of Minnelusa formation

Table 1 Property of the South Slattery Field

Property Value

Porosity (%) 15.20

Permeability (mD) 23.34

Depth (ft) 3,785

Density (�API) 32

Initial GOR (SCF/STB) 80

Initial reservoir pressure (Psi) 3,244

Bubble point pressure (Psi) 491

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

5000

10000

15000

20000

25000

30000

35000

J-64 S-77 M-91 J-05

Oil

Pro

duct

ion

bbl/d

Date

wat

er c

ut %

Fig. 2 Regional oil production and water cut history


123

5. Salinity environment which depends on the selected

polymer.

Surfactant-polymer flood

The success of an SP flood depends upon the ability to

propagate the surfactant and polymer, overcome chemical

adsorption, and improve the sweep efficiency and dis-

placement efficiency (Osterrloh and Jante 1992; Gabitto

2006). The mechanism mainly combines the function of the

surfactant in decreasing interfacial tension and the function

of the polymer in mobility control. The former function is

used to improve the displacement efficiency; the later

function is used to increase the sweep efficiency.

There are several factors that influence the actual SP

process, which includes the mobility control design, sur-

factant concentration, residual permeability reduction,

surfactant retention, dispersion of the surfactant slug, and

the rheological behavior of surfactant solution in a porous

medium (Gabitto 2006). With regard to the design of the

flood process, all factors should be taken into account,

and correlations should also be considered. For a field-

scale SP flood, the screening criteria are similar to that of

a polymer flood. What must be mentioned is that net pay

is not a critical consideration for an SP flood and the

favorable viscosity can increase to 35 cp at reservoir

conditions.

Fundamental modeling

The research mainly covered the history match, analysis of

the current injection and production system, and the esti-

mation of different EOR methods. The simulation model

was based on the properties of the South Slattery Field. A

110 9 114 grid model consisting of three layers was

defined to describe the reservoir. Totally, 25 wells were

involved in the simulation. The active cell number was

13,266.

History match

The important history matching indices included water cut,

production, reservoir pressure, bottomhole pressure, and

production GOR. The accuracy of history matching is

important to the following simulation work. In the history

match, the RMS errors are less than 6.5% averagely.

Instead of explaining the history matching in detail here,

the author made analysis of history matching to have more

space to illustrate the EOR simulation.

The depletion stage was from 1964 to 1985. Seven

production wells were drilled during this stage. The main

mechanism has been shown to be solution gas drive, in

conjunction with fluid expansion and gravity drainage. By

analyzing the geological data and the development history,

the bottom water breakthrough also played an important

role, especially in slowing the pressure drop. The invading

aquifer, which intruded into the southwest nose of the

reservoir, resulted in an imbalance of the reservoir pres-

sure, thus an imbalance of the production and water cut. At

the end of this stage, the average individual water cut in the

northeastern zone was less than 5%, while the southwestern

part was roughly 65%.

The water flood began in 1995. Three injectors started

injecting in this year. The oil production rate was

increased by 60%. During the water flood, the imbalance

of pressure and a low sweep volume factor also existed.

The recovery factor was 36.13% at the end of the history

match of the primary and secondary phases. According to

the outcomes of simulations, only some of the producers

responded to the injected water. Others were still domi-

nated by the solution gas drive. Some un-swept areas were

left, especially the north part of the reservoir, which has

not been swept well by the water flood. There were two

factors which formed the rich zone of the remaining oil in

the central reservoir: (1) the unevenness of production and

injection and (2) the heterogeneous nature of the reservoir.

There is also a blind side on the boundary of the reservoir

where it is difficult to form a circulation of the reservoir

fluids in a closed region.

Development adjustment

A robust network pattern is fundamental to a successful

water flood. As analyzed above, the existing well pattern

was imperfect. To improve the sweep efficiency and to

raise the recovery, a pattern adjustment was necessary.

Based on the outcomes of the history match, three new

injectors were assigned to the rich remaining oil zone

(designated New-1, 2, and 3). Meanwhile, to minimize the

imbalance of the reservoir pressure, three producers were

converted to injectors. The new pattern has five injectors

and nine producers (some producers were shut in during

the water flood), as seen in Fig. 3b.

Result The adjustment has improved the flood efficiency

significantly by comparing the oil saturation maps with

different well patterns. Through the saturation change, we

can see that the un-swept areas were mobilized gradually

after the network adjustment. The number of responding

producers increased. As shown in Fig. 4, the incremental

recovery of the new well pattern is much higher than that

of the old one. When the water cut reaches 97% in 2038,

the adjusted pattern has an incremental recovery of

3.85%.


123

EOR investigation

The significant improvement in oil recovery makes EOR

technologies more and more widely accepted in the

petroleum industry. In this research, the simulation method

was used to estimate the feasibility of some EOR methods

at the South Slattery Field. As we know, the adoption of an

EOR method mainly depends on the characteristics of the

reservoir and the efficiency of the current development.

Theoretically, the Slattery Field has the conditions for the

success of the EOR methods mentioned above. The

research evaluated the development efficiencies of the

EOR methods. Several plans were designed to optimize the

key indices for different EOR methods. According to the

economic injection volume of chemical in Daqing, China,

the simulated chemical injection in this research was fixed

at 0.7 PV. In order to compare the efficiency of different

injections, all processes take the same injection volume.

Polymer flood

To find a reliable polymer-flood injection system, several

factors have been investigated to optimize the injection

parameters, such as the molecular weight, injection rates,

and solution concentration. Here, the optimization of

molecular weight for the polymer flood is presented.

Laboratory data

All of the polymer properties are a function of the

molecular weight in polymer flooding. At the same con-

centration, the key viscosity parameter will increase with

the molecular weight. This research investigated three

molecular weights and demonstrated how the behavior

changed when the polymer solutions were injected into the

formation. The molecular weights adopted were 4, 6, and 9

millions (HPAM). The viscosity curves are shown in

Fig. 5. The adsorption curves are shown in Fig. 6.

Viscosity and injection parameters

Based on the mobility control function, the viscosity loss is

the first concern for the application. In the model, several

factors which related to viscosity loss have been consid-

ered. The loss from the pipeline flow (surface and well-

bore) and the perforations was also estimated. A shearing

model based on lab experiments has been used. The tested

loss from brine was based on NaCl; the viscosity change at

STA-1

KRA-F22

BUR-1430 BUR-18

HAM-1

KRA-C2

KRA-4

KRA-5

KRA-6

MID-361

STA-362

STA-652

KRA-4430

-1600 -800 0a

b

800 1600 2400 3200 4000

-1600 -800 0 800 1600 2400 3200 4000

-320

0-2

400

-160

0-8

000

800

1600

2400

-3200-2400

-1600-800

0800

16002400

STA-1

KRA-F22

BUR-1430 BUR-18

HAM-1

KRA-C2

KRA-4

KRA-5

KRA-6

MID-361

STA-362

STA-652

KRA-4430

New-1

New-1

-1600 -800 0 800 1600 2400 3200 4000

-1600 -800 0 800 1600 2400 3200 4000

-320

0-2

400

-160

0-8

000

800

1600

2400

-3200-2400

-1600-800

0800

16002400

Fig. 3 a Existing network, b network after adjustment

0.0

4.0

8.0

12.0

16.0

0 5 10 15 20 25 30 35

New Pattern

Old Pattern

Time (Years)

Incr

emen

tal r

ecov

ery

(%)

Fig. 4 Incremental recoveries for different networks


123

different salinities was illustrated in the simulation. Taking

the viscosity loss into account, the injection concentration

is fixed at 1,200 ppm to maintain the effective viscosity

(adsorption). Injectivity reflects both the characteristics of

the formation and the properties of the injected solution.

For polymer floods, the injectivity is not only the parameter

of interest, also demonstrated is the change of reservoir

properties when the polymer solution is injected. The rel-

evant formulas for initial individual rate used in this

research are the following:

Hwj ¼1

a � nXn

i¼1

Hwj þ Hoi

2; ð1Þ

Qwj ¼HwjPmj¼1 Hwj

� V � PV : ð2Þ

Results

When the polymer solution was injected into the formation,

the sweep efficiency was significantly increased, as seen in

Fig. 7 (6-million molecular weight). The channels formed

by the water flood were improved, and the polymer caused

the flood to move into the un-swept zones.

According to the predictions for different polymers, at

0.7 PV injection volume, the 6-million MW had the best

incremental recovery factor of 24.74%; the recovery factor

of the 9-million MW was 22.01%; the factor of the 4-mil-

lion MW was 23.59%, as seen in Fig. 8. The difference

happened after 0.5 PV injection, mainly because the rela-

tively high molecular weight polymer had a lower recovery

in flank zones. With increasing injection time, the 6-million

MW polymer had an improved recovery efficiency, and the

efficiency difference between the 6 million and the 9 mil-

lion was enlarged. The cause of this phenomenon was that

the injectivity of the 9-million polymer solution decreased

due to the unsuitability between the formation and the

polymer solution. By increasing the molecular weight to 9

million, there was a sharp downtrend in injectivity due to

the effect of adsorption, and the decrease in permeability,

especially near KRA-4430 and BUR-4330, was significant

at the late injection phase. As a result, the recovery rate

significantly decreased, as seen in Fig. 9.

Application concerns

Compared with successful floods, the polymer flood in the

South Slattery field will have a longer development period,

0

10

20

30

40

50

60

70

0 200 400 600 800 1000 1200 1400

Vis

cosi

ty (

mP

a.s)

Polymer Concentration (mg/L)

6 Million

4 Million

9 Million

Fig. 5 Viscosities of different polymers at different concentration

0

20

40

60

80

100

120

0 500 1000 1500 2000 2500

4-million

6-million

9-million

Concentration of polymersolution (PPM)

Ads

orpt

ion

dens

ity (

µg/g

)

Fig. 6 Adsorptions of polymers at different concentration

Fig. 7 Oil saturation after polymer flood (6 million)

0.0

6.0

12.0

18.0

24.0

30.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

MW_1

MW_2

MW_3

Injection Volume (PV)

Incr

emen

tal R

ecov

ery

(%)

Fig. 8 Incremental recoveries from polymer at different injection

volumes


123

mainly because the injectivity of the whole field is favor-

able for a short-term injection. The average model per-

meability is only 23.3 mD. Developmentally, the well

density is another unfavorable factor. The field injection

rate is much lower than the capacity of the pore volume.

Furthermore, the well spacing may fail to form effective

driving pressure during a polymer application.

One more concern is the effects of high salinity in the

reservoir fluid. The salinity of the Minnelusa formation

water is relatively high. The initial salinity was close to

seawater. The sodium salt accounts for around 92.5%; the

calcium salt accounts for 5.5%; the magnesium salt

accounts for the rest. The compositional analysis of the

produced water can be seen in Table 2. Two main effects

of the high salinity should be considered. One effect is

the viscosity loss of polymer solution. In a high-salinity

environment, the tendency of scrolling makes the motions

of molecular chains weak, which gives rise to a serious

viscosity loss. The other effect is polymer adsorption. The

high salinity will speed up and increase the adsorption.

The effect of divalent ions especially should not be

ignored.

Surfactant-polymer flood

Compared with a polymer flood, the use of surfactant

makes SP flooding more complicated. The slug design

plays an important role in a flood. To develop a successful

flood, adequate design of the injection process is required.

Based on the literature and the experience of successful

floods, two injection processes were simulated. The dif-

ference between these two processes is the use of pre-

polymer. In the first process, a pre-polymer slug was used.

The initial thinking was that a small slug of pre-polymer

solution can partially solve the channeling which was

formed by the water flood.

Laboratory data

Surfactant Parameters of an anionic surfactant were used.

Viscosity versus concentration is shown in Fig. 10. For the

measurement of adsorption, Berea sandstone was used (the

brine used to prepare the surfactant solution was 3.2%wt

NaCl). The plot of the adsorption densities at different

solution concentrations is shown in Fig. 11. Figure 12

shows the interfacial tension (IFT) change at different

surfactant concentrations (measuring environment:

1,200 ppm polymer solution system, measured with crude

oil from another Minnelusa field with similar oil proper-

ties). The 6-million MW polymer was used (the optimum

polymer in the polymer flooding section, properties seen

above).

Injection case

Process 1:

1. Pre-flush 6 months (0.3 PV) water flood, which was

the volume of brine to lower resident salinity.

2. Pre-polymer 0.15 PV, 1,000 ppm polymer solution,

which was to minimize by-passing and channeling, and

0.0

6.0

12.0

18.0

24.0

30.0

0 5 10 15 20 25 30 35

6_Miliion

9_Miliion

4_Miliion

Time (Year)

Incr

emen

tal R

ecov

ery

(%)

Fig. 9 Incremental oil recovery from polymer at different times

Table 2 Field water sample analysis

Components Produced water Injection water

Calcium (mg/L) 911 2.53

Iron (mg/L) 1.24 \0.01

Magnesium (mg/L) 156 0.11

Sodium (mg/L) 21,400 332

Potassium (mg/L) 342 0.28

Barium (mg/L) \0.01 \0.01

Bicarbonate (as CaCO3) (mg/L) 499 381

Carbonate (as CaCO3) (mg/L) 0 30

pH, std. Units 7.31 8.79

Chloride (mg/L) 29,101 35

Sulfate (mg/L) 4,507 310

40

44

48

52

56

0 500 1000 1500 2000 2500

Concentration of Surfactant (mg/L)

Vis

cosi

ty o

f S-P

sys

tem

(m

p.s)

Fig. 10 Solution viscosity at different surfactant concentrations

(1,200 mg/L polymer solution system)


123

to make sure that the surfactant-polymer slug, can

reach a considerable volumetric coverage.

3. S-P slug 0.45 PV, the main slug of surfactant and

polymer, the concentration of surfactant was

1,200 ppm, concentration of polymer was 1,200 ppm.

4. Mobility buffer 0.10 PV, 600 ppm polymer solution,

which was a dilute solution. The purpose was to drive

the S-P slug and banked-up fluids toward the produc-

tion wells.

5. Chase water This fluid was injected to reduce the cost

of continuous injection of polymer.

Process 2:

Based on the above procedure, process 2 removed the

pre-polymer slug, and the slug size of S-P was increased

to 0.6 PV.

Flood efficiency and recovery

The predictions of the two processes that showed the dis-

placement efficiency in the central reservoir were signifi-

cantly improved due to the desaturation function of

surfactant; the remaining oil zone was minimized since the

sweep efficiency has been improved significantly. How-

ever, the southeastern corner still had a remaining oil rich

zone, principally due to the low injectivity of well KRA-

4430. The injection volume from KRA-4430 was not

enough to mobilize the oil bank further. Figure 13 shows

the oil saturation distribution after process 1.

The oil saturation distribution showed that process 1 had

the better sweep efficiency. The pre-polymer slug played

its role. But the displacement efficiency of process 1,

especially in the relatively high-perm zone, was a little

lower than that of process 2. Compared with the polymer

flood at 0.70 PV of injection, process 1 had another 2.49%

incremental recovery in addition to what the polymer flood

did. The recovery factor of process 1 showed 0.43% higher

than that of process 2.

The difference between the results of processes 1 and 2

can be accredited to the pre-polymer slug. In the process 1,

the 0.1 PV of low concentration polymer solution had a

profile control function which slightly improved flow

environment of the following injections. The injected sur-

factant had a wider sweep area compared with the injection

in process 2.

The incremental recovery and water cut of process 1 are

shown in Fig. 14. According to the water cut curve, from

0.26 PV injection volume, the water cut began decreasing,

not as significantly as the polymer flood did; however, it

0

1

2

3

4

5

6

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

Ads

orpt

ion

Den

sirt

(m

g/g)

Surfactant concentration (wt%)

Fig. 11 adsorption densities of surfactant at different concentrations

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0 0.05 0.1 0.15 0.2 0.25

Inte

rfac

ial T

ensi

on (

mN

/m)

Surfactant Concentration wt%

Fig. 12 Interfacial tension at different surfactant concentrations

Fig. 13 Remaining oil distribution after the buffer slug

0

5

10

15

20

25

30

60.0

65.0

70.0

75.0

80.0

85.0

90.0

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

Incr

emen

tal r

ecov

ery

(%)

Injection Volume (PV)

Water Cut

Incremental Recovery

Wat

er C

ut %

Fig. 14 Water cut and incremental recovery against injection volume

in S-P (process 1)


123

kept the water cut from increasing for a longer time; thus,

the peak oil period was extended.

Application concerns

Besides the above concerns about the polymer flood, the SP

injection has a few more issues to be considered: the

estimation of the critical micelle concentration at the res-

ervoir conditions which depends on the salinity and pH.

The salinity distribution after 14 years of water injection is

a critical factor to the evaluation of chemical injections.

The employed simulator is not able to simulate ion

exchange and the existence of emulsions. But the desatu-

ration function is perfect to reflect the residual oil satura-

tion change based on IFT alteration. A further research

would be needed to investigate the estimation of mecha-

nisms of the surfactant-related injection which could be

used to offer verified parameters for a detailed simulation

research.

Discussion

The recovery factory for each case can be seen in Table 3.

The incremental value displays the incremental recovery

based on the adjusted water flood. The optimum polymer

flood has a recovery contribution of 8.80%. The optimum

surfactant-polymer process has another 2.49% incremental

recovery based on polymer flood. Economics analysis is

necessary for the comparison and estimation of these EOR

methods in the further research.

Due to the high salinity of Minnelusa water at the

Slattery, the effects of salinity which relates to the viscosity

loss of polymer floods and the interfacial tension change

during a surfactant injection were considered cautiously.

Making a further estimation of salts distribution in the

formation is necessary. Specifically, the viscosity losses of

polymer floods also include the effects of shear. The vis-

cosity loss from reservoir flow was considered accurately

in the model. The losses from other factors should also be

modeled accurately for a further polymer simulation.

Combining the lab analysis, the damages due to chemical

floods, like chemical adsorptions, wettability alteration,

and permeability reduction have to be considered to esti-

mate the injection efficiency.

Conclusion

1. Based on the water-flooding history match, the

recovery was 36.13% of the water flood. To get a

better effect in EOR simulation, a network adjustment

was made to improve the injection and production

pattern. The ultimate recovery of the new well pattern

is 3.85% higher than that of the old pattern.

2. The polymer flood significantly improved the sweep

efficiency. For the three kinds of polymers of different

molecular weights, the 6-million MW polymer was

more suitable for the South Slattery Field. The

estimated incremental recovery was 8.80% compared

with that of water flood.

3. The optimum S-P process increased the recovery by

2.49% compared to the polymer flood at 0.70 PV of

injection. The use of pre-polymer slug improved

development efficiency after a sort. The analysis of

the predictions showed the remaining oil saturation

that mainly depended on the sweep efficiency of SP

slug.

Acknowledgments Support for this work by the Enhanced Oil

Recovery Institute of the University of Wyoming, under the direction

of David Mohrbacher, is gratefully acknowledged.





References

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polymer processes as developed and applied in the People’s

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113845

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tem for improved oil mobility and conformance control.

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exhibition, San Antonio, TX, Paper SPE 102328

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Method Polymer Surfactant-polymer

Simulation case 4 million 6 million 9 million Process 1 Process 2

Ultimate recovery (%) 58.21 60.78 59.13 63.27 62.84

Incremental value of OOIP (%) 6.23 8.80 7.15 11.29 10.86


123

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SPE 100855


123

ORIGINAL PAPER - PRODUCTION GEOLOGY

Mapping the productive sands of Lower Goru Formation by usingseismic stratigraphy and rock physical studies in Sawan area,southern Pakistan: a case study

Khyzer Munir • M. Asim Iqbal • Asam Farid •

Syed Mohammad Shabih

Received: 11 May 2010 / Accepted: 6 January 2011 / Published online: 24 February 2011


Abstract This study has been conducted in the Sawan

gas field located in southern Pakistan. The aim of the study

is to map the productive sands of the Lower Goru For-

mation of the study area. Rock physics parameters (bulk

modulus, Poisson’s ratio) are analysed after a detailed

sequence stratigraphic study. Sequence stratigraphy helps

to comprehend the depositional model of sand and shale.

Conformity has been established between seismic stratig-

raphy and the pattern achieved from rock physics investi-

gations, which further helped in the identification of gas

saturation zones for the reservoir. Rheological studies have

been done to map the shear strain occurring in the area.

This involves the contouring of shear strain values

throughout the area under consideration. Contour maps

give a picture of shear strain over the Lower Goru For-

mation. The identified and the productive zones are

described by sands, high reflection strengths, rock physical

anomalous areas and low shear strain.

Keywords Stratigraphy � Rock physics � Rheology �Sawan

Introduction

Sawan field lies in southern Indus Basin that is extending

between 24� and 28�N latitude and from 66�E longitude to

the eastern boundary of Pakistan (Zaigham and Mallick

2000). To go with the prominent convergence and the late

Paleocene collision between the Indian and the Eurasian

plates in the north Pakistan, the area was also affected by

the translation between Indian plate and Afghan Craton in

the northwest (Banks and Warburton 1986) and by territory

convergence between Arabian Plate and Afghan Craton

(Zaigham and Mallick 2000). The effect of the western rift

margin of the Indian plate dominance can be observed in

the form of many normal fault and horst and associated

grabens on the seismic sections and also in the form of

Sibbi-Jacobabbad, Khairpur, Mari-Kandkot highs as its

surface expressions (Michalchuk 2006). The study area to

go with other parts of southern Indus Basin has thick

Mesozoic–Tertiary sedimentary sequences overlain by

Quaternary sediments (Kadri 1995). The area was tecton-

ically stable until the Jurassic and probably Early Creta-

ceous but rifting started to occur during Late Cretaceous

and Early Paleocene, the effects of which can be seen on

seismic sections, where the post-Eocene strata are either

not affected or very less deformed. Information about the

description and deposition of various rock units is available

in literature (e.g. Kadri 1995; Shah 1977). The present

study is confined to the discussion on Cretaceous rock with

K. Munir

King Abdulaziz City for Science and Technology (KACST),

P.O. Box 6086, Riyadh, Saudi Arabia


M. A. Iqbal (&)

Physical Science and Engineering Division, King Abdullah

University of Science and Technology, P.O. Box 2104, Building

1 Room 3209, Thuwal, 23955-66900 Jeddah, Saudi Arabia


A. Farid

Department Of Petroleum Geosciences, The Petroleum Institute,

P.O. Box 2533, Ruwais Building, Abu Dhabi,

United Arab Emirates


S. M. Shabih

Norwegian Energy Company ASA (NORECO),

Nykirkebakken 2, 4025 Stavanger, Norway


123


DOI 10.1007/s13202-011-0003-9

special reference to the Goru Formation. Cretaceous rocks

are widely distributed in different parts of Lower Indus

Basin. There is wide range of lithological heterogeneity in

these rocks, mainly attributed to change in sediment supply

and environmental conditions. The thick (?760 m) Neo-

comian Sembar Formation consists of black shale, which is

silty and has interbeds of black siltstone and nodular

argillaceous limestone. There are some sandstone beds as

well. The siliciclastics were probably derived from the

Indian Shield and have sand in more abundance in the

eastern parts of the basin, while the western part is more

silty and shaley (Kadri 1995). The Aptian-Albian Goru

Formation is mainly composed of black to gray and locally

maroon shale/mudstone in the lower part. The upper part of

Lower Goru is composed of sandstone that is of significant

importance in terms of its reservoir character in different

parts of the southern Indus Basin, to go with Sawan area.

Sandstone is rare in the upper part of the Formation that has

shale as dominant lithology. The name Lower Goru is used

for the lower sandy part of the Formation, whereas the

upper shale unit is termed as Upper Goru (Kadri 1995). The

generalized depositional environments of the Formation

appear to be relatively deep marine, with minor shallow

phases of benthic rich fauna being indicated. The Lower Goru

may, however, represent barrier to deltaic environments.

The overlying Cretaceous rocks include light gray,

white colour thin-bedded argillaceous Parh Limestone that

is overlain by mixed siliciclastics and carbonates of

Mughal Kot Formation while Fort Munro Formation with

its sandy, argillaceous limestone and the overlying Pab

Sandstone being the other younger Cretaceous rock units in

the Southern Indus Basin

Sawan gas field Fig. 1 is one of the major gas producing

areas with early–late Cretaceous Lower Goru Formation

acting as the potential reservoir here. During the past two

decades these sands have emerged to be a significant

hydrocarbon producer from the Middle and Lower Indus

Basin in Southern Pakistan. The Sawan gas field comprises

total proven reserves of 2–2.5 TCF gas. Total of five wells

have been used in the study. The Lower Goru Formation is

Fig. 1 Location map of the studied area


123

found to be productive in only three wells out of six (i.e.

Sawan-01, Sawan-02 and Sawan-03). The other three wells

(Gajwaro-01, Judge-10 and Nara-01) are unproductive

within the Lower Goru Formation C Sand horizon. Seismic

stratigraphy approach has been used to understand the

stratigraphic system of the area. The analysis of seismic

stratigraphy, seismic attributes, rock physics parameters

helps us to delineate the sands which can act as reservoirs

in the area.

Seismic sequence stratigraphy

Seismic sections provide the best means of recognizing

onlap and toplap patterns within the depositional sequences

and well control can provide data for the distinction

between coastal and marine facies within the sequences

(Vail et al. 1977). The seismic stratigraphic interpretation

method depends upon the observation of all the seismic

parameters (continuity, amplitude, apparent frequency,

configuration, reflection terminations, search for unconfo-

rmities, and their classification within uniform units to

define seismic ‘‘facies’’ and then on the 3D analysis of their

lateral and vertical variations) (Ravenne 2002).

The horizons are identified by using the synthetic seis-

mograms prepared for Sawan-01 and Gajwaro-01 wells.

The lateral changes in facies are mapped using the

sequence stratigraphic analysis after Ahmed et al. 2004.

The seismic stratigraphic interpretation is based on

regional E–W seismic lines. Figure 3 shows the interpre-

tation over line PSM96-114. The late Jurassic Chiltan

Limestone can be recognized easily as a strong reflector on

these lines at around 2.5sec TWT. Three sequence

boundaries have been identified in Fig. 2 (i.e. SB1, SB2

and SB3). SB-1 is recognized as the first sequence

boundary that exists within Sembar Formation and gets

downlap at the top of the Chiltan.

The sequence up to SB1 comprises the downlapping pro-

grades of the Sembar above Chiltan. SB2 is identified as the

second sequence boundary. The sequence between SB1 and

SB2 is a lowstand system tract (LST) dominated by the

slopping fans. SB3 is the third sequence boundary that exists

within the Lower Goru Formation. SB2 is followed by a

gradual rise in sea level until it approaches a maximum

flooding surface (MFS) between SB2 and SB3. The onlapping

pattern demonstrates a transgressive nature for the sequence.

There are prograding sands trapped in the A, B and C

horizons of the Lower Goru Formation. These can be easily

identified on the seismic sections as bright spots as shown

in Fig. 3.

Sand shale sequences of Lower Goru Formation

The Early Cretaceous silciclastics of Sembar and Goru

Formations were deposited on the top of an extensive

carbonate platform (Chiltan Limestone). Sembar–Goru

Play is an important petroleum system of the studied area.

Various stratigraphic traps are found, most of which are gas

Fig. 2 Sequence stratigraphic interpretation on an EW regional seismic line. The section is flattened on the Chiltan Limestone. Three sequence

boundaries, MFS and reflection termination patterns like onlaps, downlaps and topsets are clearly visible (after Ahmed et al. 2004)


123

producing. Lower Goru is divided into three members or

intervals ‘‘A’’, ‘‘B’’ and ‘‘C’’ (Fig. 3). Above Sembar and

Goru Formations, lay the Tertiary Ranikot Formation and

Sui Main Limestone. Goru Formation consists of inter-

bedded sandstone, shale and siltstone with very thin-bedded

limestone (Kazmi and Jan 1997).

The bottom layers of the Lower Goru Formation con-

sists of sands interlayered with shales which are further

divided into as Sand A, Sand B, Sand C and Sand D in the

studied area as shown in Fig. 4. The upper portion of

Lower Goru comprises thick shales which are acting as

regional seal. Sembar Formation acts as a source rock for

this petroleum system. Sands B and C are serving as a

potential gas reservoirs in this area.

Figure 5 is developed from Fig. 2 and shows the depo-

sitional pattern of Sembar–Goru petroleum system. The

system has been deposited on the Chiltan Limestone which

acted as the platform for deposition. The Sembar deposi-

tion is marked by various drops and rise in sea level.

Between SB1 and SB2 is the SEQ A which demonstrated

the lowstand time. It constitutes the lowstand slope fan and

the prograding delta. The delta downlaps over the slope

fan. Between SB2 and MFS is the SEQ B and is the

highstand time. Between MFS and SB3 is the SEQ C and is

the lowstand time. It is characterised by lowstand fan and

prograding delta. After SB3 lithologies have been termed

as SEQ D and constitute Lower Goru deposition. Lower

Goru horizons A Sand, B Sand and C Sand are dominated

by progrades. Various sand bodies have been identified by

these reflection patterns.

Fig. 4 The stratigraphic column showing the subdivisions of Lower

Goru Formation into Sand intervals A, B, C and D after Ahmed et al.

2004

Fig. 3 Bright spots seen in the A, B and C Sand horizons of Lower Goru Formation. Bright spots are named accordingly to the horizons in which

they occur


123

Rock physics

Well log data and petrophysical analysis provide the basic

input for the rock physics analysis and the generation of

different lithology classes (Bachrach et al. 2004). Rock

physics modelling has been performed by Gommesen et al.

2004 to study porosity and fluid effects on the elastic

properties. According to models the elastic properties of

the studied formation are primarily controlled by porosity

and to secondary degree by the changes in fluids.

The seismic interval velocities from different CDP

locations, corresponding to the Lower Goru interval are

employed for a series of mathematical calculations for

calculating different rock physics parameters, such as bulk

modulus, and Poisson’s ratio. Two-way seismic times and

their corresponding interval velocities (P) are noted at all

the CDP locations. They are then converted to the S-wave

velocities and densities using the Castagna’s and Gar-

dener’s equations, respectively. This data is finally used for

calculating each of the rock physics parameter.

Royle and Bezdan 2001 have demonstrated the com-

parison of shear wave velocity estimation techniques.

The equation Vp = 1.16Vs ? 1.36 (km/s) by Castagna

et al. 1985 has been used to convert P wave velocities to

S-wave velocities. The relationships between compres-

sional wave and shear wave velocities were discussed by

Castagna et al. 1985 for clastic silicate rocks. There has

been increased use of Vp, Vs and Vp/Vs in seismic explo-

ration for estimation of porosity, lithology and saturating

fluids in particular seismic intervals (Castagna et al. 1985).

Figure 6a shows the crossplots for the Sawan-01 well

and Fig. 6b shows the crossplots for Gajwaro-01 well.

Each of the mentioned rock physics parameter is dis-

cussed separately in the following.

Bulk modulus

Primary and shear wave velocities are used in the following

equation to calculate the bulk modulus which is the mea-

sure of compressibility

K ¼ q ðV2p � 4 =3 V2

s Þ

where q is the density obtained from the equation den-

sity = 0.31 9 (Vp)1/4 as demonstrated by Gardner et al.

1974. Vp is the primary wave velocity and Vs is the shear

wave velocity obtained from Vp.

Using this equation we calculated the bulk modulus for

our potential reservoir, Sand C, for all the seismic lines

Fig. 5 Depositional pattern of Lower Goru Formation (after Ahmed et al. 2004)


123

Fig. 6 a Low GR, low impedance, good effective porosity, Poisson’s

ratio (0.25–0.35) and low water saturation suggest that the reservoir is

productive in Sawan-01 well. b The reservoir is marked by low

effective porosity, relatively higher impedance and lower Poisson’s

ratio (0.2–0.3) for Gajwaro-01 well


123

present in the study area. These values are then contoured

in Fig. 7, to highlight the anomalous zones with low bulk

modulus values when compared with the surroundings. The

producing C Sand exhibit the high values of bulk modulus

apart from places where hydrocarbons occur. Figure 7

represents the variation of bulk modulus in the study area.

Poisson’s ratio

This is basically the ratio of compressibility and rigidity, or

the readiness of a compressed material to bulge. It has been

calculated at the same location and time interval as the bulk

modulus, using the following equation

m ¼ 0:5 V2p � 2V2

s

� �.V2

p � V2s

� �

Therefore, Poisson’s ratio for Sand C is calculated on all the

seismic lines and is then contoured Fig. 8. This map dif-

ferentiates the dry sands and gas sands on the basis of low

and high value contours. The values of the gas saturated

areas are in between 0.28 and 0.31 which are confirmed by

well Sawan-01 which is 0.28 for the same interval.

Rheological studies

Rheological studies are carried out to understand the

occurrence of stress and strains on Lower Goru sands in the

study area. These include the measurement of longitudinal

strain, shear strain and total stresses which are discussed

individually in the following.

Shear strain

In order to calculate the shear strain, the angle which all the

faults form with the vertical is required. Shear strain will in

fact be the tangent of that particular angle, and it is cal-

culated at all the points where the major faults are evident.

Shear strain values are also contoured to show the degree

of shear (angular) deformation in the area as described on

Fig. 9. It also shows that the productive wells lies in the

low shear strain area and the nonproductive wells in the

high shear strain area.

Uncertainty analysis

Figure 10 shows the correlation between the velocities

derived from sonic log (Sawan-01) and interval velocities

for the line PSM96-115. The figure shows a fair correlation

between the velocities. Also, Fig. 11 shows a correlation

between the velocities derived from sonic log (Gajwaro-01)

and interval velocities for the line PSM96-115. Figure shows

a reasonable correlation between the velocities. The corre-

lation for both the wells suggests that the calculations done

for the rock physical studies are reasonable.

Fig. 7 Contour map prepared for bulk modulus values estimated for the whole area. It is clear from the map that all the six wells fall in the

anomalous zone with comparatively low values


123

Since the aim of the study was to map the productive

sands of the Lower Goru Formation, Figs. 7 and 8 shed

some light on the occurrence of productive sands. The

high values of Poisson’s ratio and low values of bulk

modulus suggest the gas saturation for the sands as

calibrated with the wells. The reservoir is bounded by

the contour values (0.28–0.31) of Poisson’s ratio. The

map also highlights favourable areas for hydrocarbon

saturation in the study area. The areas with Poisson’s

ratio values greater than 0.28 other than the wells should

be evaluated in detail for possible hydrocarbon

accumulations.

Fig. 8 Contour map prepared for the Poisson’s ratio values through out the study area. It is evident that all the six wells lie in a zone where the

Poisson ratio values are on the higher side. This shows that the sands encountered at these well locations are filled with gas

Fig. 9 The contour map prepared for the shear strain values in the studied area. It is clear from the map that the strain produced at dry well

(Gajwaro-01, Judge-01 and Nara-01) locations is relatively more than the producing gas wells


123

Conclusions

The following conclusion can, therefore, be drawn:

1. The bulk modulus map (Fig. 7), confirms that the

locations where the above-mentioned wells were

drilled falls within low value contours, thus, favouring

the hydrocarbon presence over there.

2. The Lower Goru Sands are confirmed to be gas

saturated through a Poisson’s ratio contour map

(Fig. 8), that suggest high values for these well

locations as compared with Sawan-01 well data.

3. A correlation has been established between the

sequence stratigraphic studies with the bulk modulus

and the Poisson’s ratio maps, for marking the gas

saturation zones. Therefore, the relatively higher

Poisson’s ratio closures favours the occurrence of

hydrocarbons.

4. The Poisson’s ratio map can be compared to Fig. 5

which suggests a match between the bright spots and

high Poisson’s ratio closures.

5. The shear strain contour map implies that the produc-

ing gas wells (Sawan-01, Sawan-02, Sawan-03) lies in

Fig. 10 The crossplot shows

the correlation between the

velocities derived from sonic

log (Sawan-01) and interval

velocities for the line PSM96-

115. Figure shows a fair

correlation between the

velocities

Fig. 11 The crossplot shows

the correlation between the

velocities derived from sonic

log (Gajwaro-01) and interval

velocities for the line PSM96-

115. Figure shows a fair

correlation between the

velocities


123

the low shear strain area whereas the dry wells

(Gajwaro-01, Nara-01) falls relatively in the relatively

high shear strain area.

6. The reservoir is productive in low strain area, as this is

necessary for the trap generation.

7. The well Gajwaro-01 lies considerable distance away

from the centre of bright spot A (Fig. 3) which is

attributed to its nonproduction, although gas shows

have been reported for the well.

8. Study suggests that a bright spot B could be saturated

with gas and may yield production if evaluated

properly.

Acknowledgments The work presented here is based on the prin-

cipal authors’ masters study (2005–2007) at Quaid-i-Azam Univer-

sity. We acknowledge subsequent suggestions from Dr. Nadeem

Ahmed for this study. The Directorate General of Petroleum Con-

cessions is acknowledged for the release of seismic and well data

used.





References

Ahmed N, Fink P, Sturrock S, Mahmood T, Ibrahim M (2004)

Sequence stratigraphy as predictive tool in Lower Goru Fairway,

Lower and Middle Indus Platform, Pakistan. PAPG, ATC

Bachrach R, Beller M, Liu Ching C, Shelander D, Dutta N (2004)

Combining rock physics analysis, full waveform prestack

inversion and high-resolution seismic interpretation to map

lithology units in deep water: a Gulf of Mexico case study. The

Leading Edge, pp 378–383

Banks BP, Warburton J (1986) Passive-roof, duplex geometry in the

frontal structures of the Kirthar and Suleiman belts, Pakistan.

J Struct Geol 8:229–237

Castagna PJ, Batzle LM, Eastwood LR (1985) Relationships between

compressional-wave and shear-wave velocities in clastic silicate

rocks. Geophysics 50(4):571–581

Gardner GHF, Gardner LW, Gregory AR (1974) Formation velocity

and density—the diagnostic basics for stratigraphic traps.

Geophysics 39:770–780

Gommesen L, Hansen PH, Pedersen MJ, Marsden G, Schiott RC

(2004) Rock physics templates and seismic modeling of chalk

reservoirs in the South Arne Field of the Danish North Sea. In:

EAGE 66th conference and exhibition, Paris

Kadri IB (1995) Petroleum geology of Pakistan. Graphic Publishers,

Karachi, Pakistan, pp 93–108

Kazmi AH, Jan MQ (1997) Geology and tectonics of Pakistan.

Graphic Publishers, Karachi, Pakistan

Michalchuk RB (2006) Synthetic seismograms and physical proper-

ties generated from sediments in Maxwell Bay, Antarctica—a

study of climate history. Middlebury, Vermont

Ravenne Ch (2002) Stratigraphy and oil: a review. Part 1: exploration

and seismic stratigraphy: observation and description. Oil and

Gas Science and Technology, Rev. Editions Technip, IFP,

57(3)211–250

Royle A, Bezdan S (2001) Shear-wave velocity estimation tech-

niques: a comparison: CSEG convention, Geo-X Systems Ltd, 1

Shah SMI (1977) Stratigraphy of Pakistan. Geol Surv Pakistan,

Quetta, Pakistan, vol 12, pp 43–51

Vail PR, Mitchum RM, Thompson S (1977) Seismic stratigraphy and

global changes of sea level. Part 3: relative changes of sea level

from coastal onlap, applications to hydrocarbon exploration.

AAPG Memoir

Zaigham NA, Mallick KA (2000) Prospect of hydrocarbon associated

with fossil-rift structures of the southern Indus basin, Pakistan.

Am Assoc Pet Geol Bull 84(11):1833–1848


123

ORIGINAL PAPER - PRODUCTION GEOPHYSICS

Micro-earthquake monitoring with sparsely sampled data

Paul Sava

Received: 1 October 2010 / Accepted: 10 February 2011 / Published online: 3 March 2011


Abstract Micro-seismicity can be used to monitor the

migration of fluids during reservoir production and hydro-

fracturing operations in brittle formations or for studies of

naturally occurring earthquakes in fault zones. Micro-

earthquake locations can be inferred using wave-equation

imaging under the exploding reflector model, assuming

densely sampled data and known velocity. Seismicity is

usually monitored with sparse networks of seismic sensors,

for example located in boreholes. The sparsity of the sensor

network itself degrades the accuracy of the estimated loca-

tions, even when the velocity model is accurately known.

This constraint limits the resolution at which fluid pathways

can be inferred. Wavefields reconstructed in known velocity

using data recorded with sparse arrays can be described as

having a random character due to the incomplete interference

of wave components. Similarly, wavefields reconstructed in

unknown velocity using data recorded with dense arrays can

be described as having a random character due to the

inconsistent interference of wave components. In both cases,

the random fluctuations obstruct focusing that occurs at

source locations. This situation can be improved using

interferometry in the imaging process. Reverse-time imag-

ing with an interferometric imaging condition attenuates

random fluctuations, thus producing crisper images which

support the process of robust automatic micro-earthquake

location. The similarity of random wavefield fluctuations

due to model fluctuations and sparse acquisition is illustrated

in this paper with a realistic synthetic example.

Keywords Microearthquakes � Imaging � Interferometry

Introduction

Seismic imaging based on the single scattering assumption,

also known as Born approximation, consists of two main

steps: wavefield reconstruction which serves the purpose of

propagating recorded data from the acquisition surface

back into the subsurface, followed by an imaging condition

which serves the purpose of highlighting locations where

scattering occurs.

This framework holds both when the source of seismic

waves is located in the subsurface and the imaging target

consists of locating this source, as well as when the source

of seismic waves is located on the acquisition surface and

the imaging target consists of locating the places in the

subsurface where scattering or reflection occurs. In this

paper, I concentrate on the case of imaging seismic sources

located in the subsurface, although the methodology dis-

cussed here applies equally well for the more conventional

imaging with artificial sources.

An example of seismic source located in the subsurface

is represented by micro-earthquakes triggered by natural

causes or by fluid injection during reservoir production or

fracturing. One application of micro-earthquake location is

monitoring of fluid injection in brittle reservoirs when

micro-earthquake evolution in time correlates with fluid

movement in reservoir formations. Micro-earthquakes can

be located using several methods including double-differ-

ence algorithms (Waldhauser and Ellsworth 2000),

Gaussian-beam migration (Rentsch et al. 2004, 2007),

diffraction stacking (Gajewski et al. 2007) or time-reverse

imaging (Gajewski and Tessmer 2005; Artman et al. 2010).

Micro-earthquake location using time-reverse imaging,

which is also the technique advocated in this paper, follows

the same general pattern mentioned in the preceding

paragraph: wavefield-reconstruction backward in time

P. Sava (&)

Center for Wave Phenomena, Colorado School of Mines,

1500 Illinois Str., Golden, CO 80401, USA


123


DOI 10.1007/s13202-011-0005-7

followed by an imaging condition extracting the image, i.e.

the location of the source. The main difficulty with this

procedure is that the onset of the micro-earthquake is

unknown, i.e. time t = 0 is unknown, so the imaging

condition cannot be simply applied as it is usually done in

zero-offset migration. Instead, an automatic search needs to

be performed in the back-propagated wavefield to identify

the locations where wavefield energy focuses. This process

is difficult and often ambiguous since false focusing loca-

tions might overlap with locations of wavefield focusing.

This is particularly true when imaging using an approxi-

mate model which does not explain all random fluctuations

observed in the recorded data. This problem is further

complicated if the acquisition array is sparse, e.g. when

receivers are located in a borehole. In this case, the sparsity

of the array itself leads to artifacts in the reconstructed

wavefield which makes the automatic picking of focused

events even harder.

The process by which sampling artifacts are generated is

explained in Fig. 1a–d. Each segment in Fig. 1a corre-

sponds to a wavefront reconstructed from a receiver. For

dense, uniform and wide-aperture receiver coverage and

for reconstruction using accurate velocity, the wavefronts

overlap at the source position (Fig. 1b). This idealized

situation resembles the coverage typical for medical

imaging, although the physical processes used are differ-

ent. However, if the velocity used for wavefield recon-

struction is inaccurate, then the wavefronts do not all

overlap at the source position (Fig. 1c), thus leading to

imaging artifacts. Likewise, if receiver sampling is sparse,

reconstruction at the source position is incomplete

(Fig. 1d), even if the velocity used for reconstruction is

accurate. The cartoons depicted in Fig. 1a–d represent an

ideal situation with receivers surrounding the seismic

source, which is not typical for seismic experiments. In

those cases, source illumination is limited to a range which

correlates with the receiver coordinates.

In general, artifacts caused by unknown velocity fluc-

tuations and receiver sampling overlap and, although the

two phenomena are not equivalent, their effect on the

reconstructed wavefields are analogous. As illustrated in

the following sections, the general character of those arti-

facts is that of random wavefield fluctuations. Ideally, the

imaging procedure should attenuate those random wave-

field fluctuations irrespective of their cause in order to

support automatic source identification.

Conventional imaging condition

Assuming data D x; tð Þ acquired at coordinates x function of

time t (e.g. in a borehole) we can reconstruct the wavefield

V x; y; tð Þ at coordinates y in the imaging volume using an

appropriate Green’s function G x; y; tð Þ corresponding to

the locations x and y (Fig. 2)

V x; y; tð Þ ¼ D x; tð Þ �t G x; y; tð Þ; ð1Þ

where the symbol *t indicates time convolution. The total

wavefield U y; tð Þ at coordinates y due to data recorded at

(a) (b) (c) (d)

Fig. 1 Schematic representation of focus constructions using time

reversal. Each line in the plots represents a wavefront reconstructed at

the source from a given receiver. The panels represent the following

cases: a dense acquisition, complete angular coverage and correct

velocity, b dense acquisition, partial angular coverage and correct

velocity, c dense acquisition, partial angular coverage and incorrect

velocity, and d sparse acquisition, partial angular coverage and

incorrect velocity. Panel d represents the worst case scenario for

micro-earthquake imaging

receivers

y

x seismic

in borehole

source

Fig. 2 Illustration of the variables x and y used for the description of

the conventional and interferometric imaging procedures


123

all receivers located at coordinates x is represented by the

superposition of the reconstructed wavefields V x; y; tð Þ:

U y; tð Þ ¼Z

x

dx V x; y; tð Þ: ð2Þ

A conventional imaging condition (CIC) applied to this

reconstructed wavefield extracts the image RCIC yð Þ as the

wavefield at time t = 0

RCIC yð Þ ¼ U y; t ¼ 0ð Þ: ð3Þ

This imaging procedure succeeds if several assumptions

are fulfilled: first, the velocity model used for imaging has to

be accurate; second, the numeric solution to the wave-

equation used for wavefield reconstruction has to be

accurate; third, the data need to be sampled densely and

uniformly on the acquisition surface. In this paper, I assume

that the first and third assumptions are not fulfilled. In these

cases, the imaging is not accurate because contributions to

the reconstructed wavefield from the receiver coordinates do

not interfere constructively, thus leading to imaging

artifacts. As indicated earlier, this situation is analogous to

the case of imaging with an inaccurate velocity model, e.g.

imaging with a smooth velocity of data corresponding to

geology characterized by rapid velocity variations.

Different image processing procedures can be employed

to reduce the random wavefield fluctuations. The procedure

advocated in this paper uses interferometry for noise can-

cellation. Interferometric procedures can be formulated in

various frameworks, e.g. coherent interferometric imaging

(Borcea et al. 2006) or wave-equation migration with an

interferometric imaging condition (Sava and Poliannikov

2008).

Interferometric imaging condition

Migration with an interferometric imaging condition (IIC)

uses the same generic framework as the one used for the

conventional imaging condition, i.e. wavefield reconstruc-

tion followed by an imaging condition. However, the dif-

ference is that the imaging condition is not applied to the

reconstructed wavefield directly, but it is applied to the

wavefield which has been transformed using pseudo-Wigner

distribution functions (WDF) (Wigner 1932). By definition,

the zero frequency pseudo-WDF of the reconstructed

wavefield U y; tð Þ is

W y; tð Þ ¼Z

thj j �T

dth

Z

yhj j � Y

dyhU y� yh

2; t � th

2

� �

� U yþ yh

2; t þ th

2

� �; ð4Þ

where Y and T denote averaging windows in space and

time, respectively. In general, Y is three dimensional and T

is one dimensional. Then, the image RIIC yð Þ is obtained by

extracting the time t = 0 from the pseudo-WDF, W y; tð Þ,of the wavefield U y; tð Þ:RIIC yð Þ ¼ W y; t ¼ 0ð Þ: ð5Þ

The interferometric imaging condition represented by Eqs.

4 and 5 effectively reduces the artifacts caused by the

random fluctuations in the wavefield by filtering out its

rapidly varying components (Sava and Poliannikov 2008).

In this paper, I use this imaging condition to attenuate noise

caused by sparse data sampling or noise caused by random

velocity variations. As suggested earlier, the interferomet-

ric imaging condition attenuates both types of noise at

once, since it does not explicitly distinguish between the

various causes of random fluctuations.

The parameters Y and T defining the local window of the

pseudo-WDF are selected according to two criteria (Cohen

1995). First, the windows have to be large enough to

enclose a representative portion of the wavefield which

captures the random fluctuation of the wavefield. Second,

the window has to be small enough to limit the possibility

of cross-talk between various events present in the wave-

field. Furthermore, cross-talk can be attenuated by select-

ing windows with different shapes, for example Gaussian

or exponentially decaying. Therefore, we could in principle

define the transformation in Eq. 4 more generally as

W y; tð Þ ¼Z

thj j �T

dthWT t; thð ÞZ

yhj j � Y

dyhWY y; yhð Þ

� U y� yh

2; t � th

2

� �U yþ yh

2; t þ th

2

� �; ð6Þ

where WT and WY are weighting functions which could

represent Gaussian, boxcar or any other local functions

(Artman 2011, personal communication). For simplicity, in

all examples presented in this paper, the space and time

windows are rectangular with no tapering and the size is

selected assuming that micro-earthquakes occur sufficiently

sparse, i.e. the various sources are located at least twice as far

in space and time relative to the wavenumber and frequency

of the considered seismic event. Typical window sizes used

here are 11 grid points in space and 5 grid points in time.

Example

I exemplify the interferometric imaging condition method

with a synthetic example simulating the acquisition

geometry of the passive seismic experiment performed at

the San Andreas Fault Observatory at Depth (Chavarria

et al. 2003; Vasconcelos et al. 2008). This numeric


123

experiment simulates waves propagating from three micro-

earthquake sources located in the fault zone (Fig. 3), which

are recorded in a deviated well located at a distance from

the fault. For the imaging procedure described in this

paper, the micro-earthquakes represent the seismic sources.

This experiment uses acoustic waves, corresponding to the

situation in which we use the P-wave mode recorded by the

three-component receivers located in the borehole

(Figs. 4b, 5b). The three sources are triggered 40 ms apart

and the triggering time of the second source is conven-

tionally taken to represent the origin of the time axis.

The goal of this experiment is to locate the source

positions by focusing data recorded using dense acquisition

in media with random fluctuations or by focusing data

recorded using sparse acquisition arrays in media without

random fluctuations. In the first case, the imaging artifacts

are caused by the fact that data are imaged with a velocity

model that does not incorporate all random fluctuations of

the model used for data simulation, while in the second

case, the imaging artifacts are caused by the fact that the

data are sampled sparsely in the borehole array. The third

case is a combination of acquisition with two sparse arrays,

and imaging with an inaccurate velocity model.

Figures 6a and b, 7a and b and 8a and b show the

wavefields reconstructed in reverse time around the target

location. From left to right, the panels represent the

wavefield at different times. As indicated earlier, the time

at which source 2 focuses is selected as time t = 0,

although this convention is not relevant for the experiment

and any other time could be selected as reference. The

experiment depicted in Fig. 6a and b corresponds to

modeling in a model with random fluctuations and

1 40ms

40ms

3

2

Fig. 3 Geometry of the sources used in the numeric experiment. The

horizontal and vertical separation between sources is 250 m. The

sources are triggered with 40 ms delays in the order indicated by their

numbers. Time t = 0 is conventionally set to the triggering moment

of source 2

(a)

(b)

Fig. 4 a Wavefields simulated in random media and b data acquired

with a dense receiver array. Overlain on the model and wavefield are

the positions of the sources and borehole receivers. The boxed areacorresponds to the images depicted in Fig. 6a and b

(a)

(b)

Fig. 5 a Wavefields simulated in smooth media and b data acquired

with a sparse receiver array. Overlain on the model and wavefield are

the positions of the sources and borehole receivers. The boxed areacorresponds to the images depicted in Fig. 7a and b


123

migration in a smooth background model. In this experi-

ment, the data used for imaging are densely sampled in the

borehole, i.e. there are 81 receivers separated by approxi-

mately 12 m. In contrast, the experiment depicted in

Fig. 7a and b corresponds to modeling and migration in the

smooth background model. In this experiment, the data are

sparsely sampled in the borehole, i.e. there are only six

receivers obtained by selecting every 16th receiver from

the original set. In all cases, panels (a) correspond to

imaging with a conventional imaging condition, i.e. simply

(a)

(b)

Fig. 6 Images corresponding to

migration of the denselysampled data (Fig. 4b) modeled

in the random velocity by

a conventional IC and

b interferometric IC using the

background velocity. The left-most panel shows focusing at

source 1, the middle panelshows focusing at source 2, and

the right-most panel shows

focusing at source 3. The

overlain dots represent the exact

source positions

(a)

(b)


migration of the sparselysampled data (Fig. 5b) modeled

in the background velocity by








source positions

(a)

(b)


migration of the dual sparselysampled data (Fig. 9b) modeled

in the random velocity by








source positions


123

select the reconstructed wavefield at various times, and

panels (b) correspond to imaging with the interferometric

imaging condition, i.e. select various times from the

wavefield transformed with a pseudo-WDF of 11 grid

points in space and 5 grid points in time. For this example,

WDF window corresponds to 44 m in space and 2 ms in

time.

Figure 6a shows significant random fluctuations caused

by wavefield reconstruction using an inaccurate velocity

model. The fluctuations caused by the random velocity and

encoded in the recorded data are not corrected during

wavefield reconstruction and they remain present in the

model. Likewise, Fig. 7a shows significant random fluc-

tuations caused by reconstruction using the sparse borehole

data. However, the pseudo-WDF applied to the recon-

structed wavefields attenuates the rapid wavefield fluctua-

tions and leads to sparser, better focused images that are

easier to use for source location. This conclusion applies

equally well for the experiments depicted in Fig. 6a and b

or 7a and b.

The final example corresponds to the case of acquisition

with two separate sparse arrays (Fig. 9a, b). As expected,

the wavefields are far less noisy after the application of the

WDF, and the focusing is increased due to the larger array

aperture. This facilitates an automatic procedure for

focusing identification, since most of the spurious noisy is

eliminated from the image.

Finally, I note that the 2D imaging results from this

example show better focusing than what would be expected

in 3D. This is simply because the 1D acquisition in the

borehole cannot constrain the 3D location of the micro-

earthquakes, i.e. the azimuthal resolution is poor, espe-

cially if scatterers are not present in the model used for

imaging. This situation can be improved using data

acquired in several boreholes or using additional informa-

tion extracted from the wavefields, e.g. polarization of

multicomponent data.

Conclusions

The interferometric imaging condition used in conjunction

with time-reverse imaging reduces the artifacts caused by

random velocity fluctuations that are unaccounted-for in

imaging and by the sparse wavefield sampling on the

acquisition array. The images produced by this procedure

are crisper and support automatic picking of micro-earth-

quake locations. Imaging with sparse arrays allows

increased aperture for identical acquisition cost with that of

a narrower but denser array. At the same time, a larger

aperture improves focusing of the events, thus facilitating

automatic event identification. The interferometric imaging

procedure has a similar structure to conventional imaging

and the moderate cost increase is proportional to the size of

the windows used by the pseudo-Wigner distribution

functions. The source positions obtained using this proce-

dure can be used to monitor fluid injection or for studies of

naturally occurring earthquakes in fault zones.

Acknowledgments This work is supported by the sponsors of the

Center for Wave Phenomena at Colorado School of Mines and by a

research grant from ExxonMobil. The reproducible numeric examples

in this paper use the Madagascar open-source software package freely

available from http://www.reproducibility.org.





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time-reverse imaging. Geophys Prospect 58:861–873

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imaging in clutter. Geopysics 71:SI165–SI175

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San Andreas Fault at Parkfield through vertical seismic profiling.

Sci Agric 302:1746–1748

Cohen L (1995) Time frequency analysis: Signal processing series.

Prentice Hall, Englewood Cliffs

(a)

(b)

Fig. 9 a Wavefields simulated in random media and b data acquired

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are the positions of the sources and borehole receivers. The boxedarea corresponds to the images depicted in Fig. 8a and b. The toptraces in b correspond to the vertical array, and the other traces

correspond to the sparse deviated array


123

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123

REVIEW PAPER - EXPLORATION GEOPHYSICS

Delineating deep basement discontinuitiesof Qarun Lake Area, Egypt

Ahmad S. Helaly • Ahmed A. El-Khafeef

Received: 12 December 2010 / Accepted: 3 October 2011 / Published online: 21 October 2011


Abstract The current study is mainly concerned with the

description and analysis of the available aeromagnetic

anomalies using different methodologies. Some structural

elements could be deduced from the qualitative interpre-

tation of such magnetic anomalies. The analysis of the

worked magnetic maps, which included the total intensity

magnetic map, reduced to-pole map, upward-continued

maps, downward-continued maps, anomaly separation

based on their wavelengths, or anomaly widths and

enhanced horizontal gradient filtering aided in divulging

the structural regime of the basement rocks, as well as the

shallower features. As a result of the investigation, a

basement tectonic map of the study area was constructed.

This map shows that the area is portrayed by the presence

of several major alternating basement swells and troughs in

belts trending ENE–WSW, N–S, NE–SW and E–W. These

major trends with the other minor trends dissected the

basement surface into several tilted fault blocks forming

anticlinal and synclinal zones with various depths and

directions. These structural elements are shown in the

basement tectonic map, and named Camel Pass-Abu Roash

high, El-Sagha high, El Faras-El faiym high and Qattrani-

El Gindi low trends.

Keywords Magnetic � Matching filtering �Horizontal gradient � Continuation

Introduction

The area under study is located to the west of the Nile

River, within the northeastern portion of the Western

Desert of Egypt. It lies between latitudes 29�000 and

30�000N and Longitudes 30�000 and 31�180E (Fig. 1),

covering a total surface area of about 14,350 km2.

The surface geology of the north Western Desert, in

general, is characterized by almost featureless terrain of

simple geologic nature. The exposed rocks are generally of

Tertiary age interrupted by some spots of Cretaceous out-

crops around Abu Roash area and Bahariya Oasis.

Because the north Western Desert tract is located within

the unstable belt of Egypt, there are a number of folding

and faulting structures within its sedimentary section that

caused lateral variations in compositions and thicknesses of

the affected sequences.

In general, the geophysical magnetic method is mainly

based on the measurements and analysis of small variations

in the earth’s magnetic field within any area. An aero-

magnetic map is a reflection of the distinctions in the

magnetic properties of the underlying rocks. Therefore,

these variations encountered in the measured magnetic

field are attributed to the distribution of the subsurface

magnetically polarized rocks.

The sedimentary rocks are of weaker magnetic proper-

ties than the underlying basement rocks, especially the

mafic rocks. Therefore, the magnetic methods are used to

delineate the structural and lithological configuration of the

basement rocks. Estimating the depths to the basement

surface with basement determination methods is compa-

rable to the calculation of the thicknesses of the overlying

sedimentary rocks. That is important for hydrocarbon

exploration, since the hydrocarbons can be found mainly in

the sedimentary section, where the configuration of the

A. S. Helaly

Department of Geophysics, Faculty of Science,

Ain Shams University, Abbassia, Cairo, Egypt

A. A. El-Khafeef (&)

Exploration Department, Egyptian Petroleum

Research Institute, Nasr City, Cairo, Egypt


123


DOI 10.1007/s13202-011-0012-8

basement rocks reflects the size and shape of any sedi-

mentary basin and ridge that form the source rocks and

trapping elements.

The main type of available geophysical data for the

current study is an aeromagnetic map showing the distri-

bution of the total intensity magnetic anomalies within the

study area (Fig. 3). The current study involves the quali-

tative analysis of the available aeromagnetic data.

Geologic setting

The distribution of the different rock types exposed in the

area under study is shown in the geological map (Fig. 2),

which was compiled from the Egyptian Geological Survey

and Mining Authority (1981). This map reveals that, the

exposed outcrops of this area range in age from Eocene to

Recent.

The Eocene rocks are composed of limestone with some

flints, mainly blanketing most of the southwestern portion

of the study area, around the Faiyum Depression. Mean-

while, the Miocene deposits mainly cover the northwestern

portion of the area. The Miocene deposits are separated

from the Eocene rocks by narrow belt of Oligocene rocks

outcropping north of Birket Qarun and are composed of

cross-bedded sandstones and gravels with interbeds of

shales and limestones. To the east, the Pleistocene–Recent

sediments mainly cover the narrow strip of the Nile Valley,

around the cultivated lands, with local Pliocene outcrops

covering the older rocks. Surficial deposits in the form of

sand dunes running generally in a north northwesterly

direction also represent the Pleistocene–Recent rocks.

Fig. 1 Locaion map of the

study area

Fig. 2 Geological map of the

study area (Geological Survey

of the Egypt 1981)


123

Basaltic flows and sheets, which are believed to be of Late

Oligocene–Early Miocene age, are exposed in some

localities in this area, e.g., Gabal Qatrani, south of Cairo,

and west of the Nile Valley. Gabal Qatrani is situated to the

north of the study area.

Geomorphologically, the studied area, as a part of the

north Western Desert of Egypt, is generally a rocky plat-

form of low altitude, which has been characterized through

its recent history by arid climatic condition. Therefore, its

main geomorphologic features are primarily due to the

wind action (Said 1962). The area exhibits a vast pene-

plain, which is covered in many places by wind-blown

sands, sand sheets, and gravels.

Generally, the main geomorphologic features of the

north Western Desert are: the absence of well marked

drainage lines, the presence of some parallel belts of sand

dunes of different lengths running mainly in a NNW

direction, the presence of plateaus that are capped by

resistant Eocene and Miocene limestone, and the presence

of numerous extensive and deep-in depression, e.g. Ba-

hariya Oasis, Faiyum and Wadi El-Rayian depressions.

The second and third depressions are located in the study

area.

Structurally, the north Western Desert has been exten-

sively described by many workers, e.g. Said (1962), You-

ssef (1968), Meshref and El-Sheikh (1973), El-Gezerry

et al. (1975), El-Sirafe (1985), Meshref (1980), Abu El-Ata

(1988), Hantar (1990), Meshref (1990), and others.

The north Western Desert, where the area under inves-

tigation lies, is dominated by faults, many of which are step

normal faults having a NE–SW, E–W, NW–SE and N–S

trends. Some of these faults suffered strike-slip movements

during a part of their history. There are also a large number

of hanging faults affecting the shallower parts of the sec-

tion and usually of limited throw. These faults are common

in the northern part of the region.

Most folds owe their origin to compressional movements,

which affected the area during the Late Cretaceous–Early

Tertiary tectonic event. These folds have an ENE–WSW trend

and a periclinal geometry. In addition, there are other folds,

which owe their origin to normal or horizontal displaced faults

(Hantar 1990).

Main concepts

There are some principles should be taken into consider-

ation when working with the magnetic data. The interpre-

tation of magnetic data is not unique, because it is

controlled by many factors; for example, depth to top of the

causative feature, its shape, its azimuth, its magnetic sus-

ceptibility, that is mainly related to its petrographical

2.5 0 2.5 5 7.5 10

Km.

-140.0

-120.0-100.0

-80.0

-70.0-60.0-50.0-40.0

-30.0-20.0-10.0

0.010.0

20.030.0

40.050.0

60.070.080.0

100.0110.0

120.0140.0

160.0180.0200.0220.0

nt

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

0 0 2 -

00

1-

00

1-

-100

- 10 0

-1

00

0

0

0

0

0

0

0

0

0

00 1

001

0 01

10

0

0 01

10

0

2 00

002

002

00 2

00

2

20

0

Fig. 3 Total intensity

aeromagnetic of the study area


123

composition. Such factors are related to the subsurface

anomalous features that produce their magnetic signatures

at the surface. The availability and use of some of these

factors during the interpretation reduce the ambiguity in the

magnetic interpretation. Such factors can be taken from

the available well data and regional geology of the area.

The available magnetic data for this study have been cor-

rected for the diurnal variations, instrument drift, and for

the errors in positioning and height keeping.

Insights on the original magnetic data

The close study of the total intensity aeromagnetic map

(Fig. 3) indicates that most of the observed anomalies show

ENE–WSW trend patterns with some sharp gradients at

varying locations. Since the magnetic maps are related

directly to the basement rocks’ features, therefore, this

indicates the presence of a basement relief change. This is

because any sudden change in the magnetic contour spac-

ing over a relative short distance suggests a discontinuity in

the basement rocks, lithological variations within the

basement rocks, or both.

The analysis of Fig. 3 (total intensity magnetic map)

shows the existence of a major ENE–WSW low magnetic

anomaly parallel to Birket Qarun, bounded between two

magnetic highs at the northwestern and southeastern por-

tions of the study area, with some superimposed smaller

anomalies. The magnetic gradient to the northwestern

portion is rather gentler than that of the southern one. The

effects of the sub-topographic relief of the dissected

basement surface and/or the small variations in suscepti-

bility of its composing rocks caused such magnetic highs

and lows. The occurrence of some basement intrusions into

the sedimentary cover of the study area complicated the

aeromagnetic pattern. The combined effect of these

anomalies with the regional field of the geomagnetic field

produced such observed aeromagnetic data. Therefore, the

aeromagnetic map can be described in terms of the fol-

lowing parameters, the anomaly’s areal extension, shape,

amplitude in gammas and the gradient.

Analysis of the magnetic data

The processing of the aeromagnetic anomalies is based on

the analysis of the computer-digitized information using

different processing techniques at different altitudinal

levels from the compiled aeromagnetic data shown in

Fig. 3. These techniques involve; first the reduction to the

north magnetic pole. The reduced to the north magnetic

pole digitized data were used for further investigative

techniques that helped integratively to deduce the structural

set-up for the basement of the considered area.

Reduction to the north magnetic pole

Since the study area is positioned within a low-latitude

region in the northern hemisphere, the original aeromag-

netic data subjected to reduction to the north-pole. A

reduction-to-pole (RTP) transformation is standardly

applied to the aeromagnetic data to minimize the polarity

effects. These effects are manifested as a shift of the main

anomaly from the center of the magnetic source and are

due to the vector inclination of the measured magnetic

field. The RTP transformation usually involves an

assumption that, the total magnetizations of most rocks

align parallel or anti-parallel to the Earth’s main field

(declination = 3.439�, inclination = 43.279�, and IGRF

total intensity value = 42,989 nT, for the study area). This

assumption probably works well for the Tertiary units in

the surveyed area, which are the focus of interpretation.

The RTP aeromagnetic data, computed from the grid of

total-field magnetic data, are shown in Fig. 4. This figure

shows a kind of general northward shift of the magnetic

anomalies, with the appearance of some sort of sharper

magnetic gradients in the central part of the study area with

a general ENE–WSW trend; in addition to a shorter N–S

trend at the middle-eastern side of the study area.

Upward continuation

Because of the potential nature of the potential fields (like

in Gravity and Magnetic), they can be calculated at any

elevation above (and in some cases below) the level of

measurements, that is, if there is neither gravity nor mag-

netic sources between these two levels. This procedure is

called the upward continuation of potential field. It is

generally a useful and physically meaningful filtering

operation. It allows smoothing the field and eliminating

small anomalies (noises) in the form of noises from the

near surface objects. In the spectral domain, upward con-

tinuation can be written as:

Fðu; vÞ ¼ sðu; vÞ � f u; vð Þ

Fðu; vÞ ¼ sðu; vÞ1þ asðu; vÞ2

� f ðu; vÞð1Þ

where f(u,v) is the spectrum of the field to be transformed.

F(u,v) is the spectrum of transformed (upward or down-

ward continued) field. s(u,v) is the spectrum of the trans-

formation and the small regularization parameter.

The upward continuation of the reduced to the pole data

to an altitude above the measurements level will eliminate

the effects of possible near-surface noises that may result in


123

misleading responses. In the same time, upward-continued

maps reflect the general configuration of the main sources

of the magnetic anomalies, which is mainly the surface of

basement rocks. This will, definitely, reduce the resolution

of the magnetic anomalies.

In the current study, the upward-continued magnetic

response was determined at three levels, 1 km (Fig. 5), 2 km

(Fig. 6) and 3 km (Fig. 7) above the level of measurements.

A closer look at those three maps showed that Fig. 5 exhibits

more resolvable anomalous features than in Figs. 6 and 7.

That is expected, since we are going further away from the

magnetic sources, the smaller sources will be reduced in

their responses. The upward-continued map at 1 km shows

relative smaller anomalies superimposed on the wider

regional magnetic responses. The two levels of 2 and 3 km

upward-continued maps are showing more general pattern

for the basement surface. This reflects that, there is a major

plutonic uplift trending ENE–WSW within the study area. In

addition, it can be noticed that, the big negative anomaly in

Fig. 5, at the northwestern part of the study area, is reduced

in its areal extension and amplitude, as shown in Fig. 7.

Downward continuation

Downward continuation highlights the high frequency

content of a gridded magnetic data set, just as if the data

had been acquired at a lower survey height. Theoretically,

the field can also be continued downwards until the con-

tinuation level does not cross any field sources. However, it

has been proved that, this operation is unstable because it

greatly magnifies the existing noise and makes the field

unusable.

To deal with this problem; some relaxation (regulari-

zation) techniques can be used. In the current study, that

can be done through the use of Tikhnonov regularization

parameter. The Tikhonov regularization parameter b(Tikhonov and Arsenin 1977) is important in the optimi-

zation process. Kristofer and Yaoguo (2007) explained

that, in order to find the optimal data misfit, a Tikhonov

parameter, b, is chosen based on the optimal model

weighting. The regularization parameter is chosen, so the

optimal solution is neither over-smoothing nor under-

smoothing the data (i.e. fitting the noise or the signal).

Several values for this parameter were tried to find the best

for the data under study. This parameter was chosen such

that the resulted data using the selected parameter’s value

show some sort of similarity (in its overall representation)

to the pattern of the original data to be downwardly

continued.

The reduced-to-pole data (Fig. 4) is subjected to the

downward continuation, with Tikhonov regularization

parameter of 10-4, to transform the studied data to be as

2.5 0 2.5 5 7.5 10

Km.

-190-160-140-130-120-110-100-90-80-70-60-50-40-30-20-10

0103040607090

110120140160180190220250310

nt

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

00

2-

0 0 1 -

001-

-1

00

- 1 0 0

-100

-100

-100

0

0

0

0

0

0

1 00

00

1

00

1

0 0 1

10

0

002

00

2

20

0

003

00

4

Fig. 4 Reduction to the Pole

(RTP) map for the study area


123

taken at lower levels. Downward-continued data to a rel-

atively shallow depth will emphasize the residual compo-

nents (of shallower sources) making the map noisier (as

shown in Fig. 8). While, downwardly continued data to

deeper depths will show less noisy-manifestations. Know-

ing that the average depth to the basement surface in the

study area is in the range of about 4.5 km as known from

some deep wells, the reduced-to-pole data were continued

downwardly to three levels 1, 3, and 5 kilometers, as shown

in Figs. 8, 9, and 10, respectively. As we are going deeper,

below the original level of measurement, such downward-

continued maps reflect the combined effect of the strikes of

the subsurface structural elements, direction of magneti-

zation, as well as the susceptibility contrasts between the

sedimentary section and the underlying/surrounding base-

ment. These structural features shown on such maps are

slightly different, and will be discussed separately.

For the downward-continued map to 1 km depth

This map (Fig. 8) shows that, a -125 gamma contour line

is located at the southeastern portion of the study area,

while a ?250 gamma contour lines are located within the

middle portion of the study area with an ENE–WSW trend

and accompanied by a number of smaller or local

anomalies in a scattered fashion. This reflects the irregular

nature of the closer-to-surface causative features; except

the northwestern portion of the study area which shows

some sort of less heterogeneity. The contour gradient is

sharper in the middle portion of the study area and towards

the south, but shows gentler behavior at the northern part of

the study area. Many smaller wavelength local anomalies

can be seen in this map, revealing the existence of limited

small subsurface features, in either their composition and/

or their altitude.


This map (Fig. 9) shows more relative regular contour lines

with local features of different trends and amplitudes. As

this map shows a downward-continued picture, it is clear

that as we approaching the basement surface, so the mag-

netic effect will get bigger (in its positivity and negativity).

Therefore, the middle portion of the study area shows

relative high magnetic values (up to ?750 gammas at the

eastern part), while also the negativity increased in the

northern part of the study area down to -250 gammas).

The many localized features, in some localities, are signs

that the basement surface still not reached yet. Sharper

contour gradients can be seen especially at the southern

-155.0-136.1-122.0-112.2-104.9-99.8-95.7-92.2-88.6-84.9-80.9-75.8-70.4-64.6-58.4-52.1-45.8-39.7-33.9-27.9-20.2-11.5-0.311.423.435.549.664.177.389.5

102.1120.9140.1157.0172.0191.9222.1264.4

nt

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

- 2 0 0

00

2-

00

1-

00

1-

- 1 0 0

- 1 0 0

-100

00 1 -

0

0

0

0

0

0

100

001

001

1 0 0

10

0

00

2

0 0 2

200

003

30

0

2.5 0 2.5 5 7.5 10

Km.

Fig. 5 Upward-continues RTP

map to 1-km level


123

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

00 1

-

001-

- 10 0

-1

00

0

0

0

0

0

0

100

001

00 1

10

0

002

2 00

00

3

-128.2-114.4

-104.4-95.9

-89.3-85.9

-82.9-80.2

-77.6

-74.4-70.4

-65.4-60.0

-54.3-48.4

-43.2-38.2

-33.5-28.7

-23.1-16.3

-8.5

-0.18.6

18.029.0

40.451.9

63.374.2

86.7102.8

119.2

135.9151.8

170.5195.2

231.2

nt

2.5 0 2.5 5 7.5 10

Km.

Fig. 6 Upward-continues RTP

map to 2-km level

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

0 01

-

- 1 0 0

-10

0

0

0

0

0

0

001

0 01

10 0

002

2 00

-108.3

-97.7

-90.1

-83.5-77.9

-74.5

-72.1

-70.0

-67.4

-64.4

-60.5-56.0

-51.3

-46.4

-41.3

-36.1

-32.4

-28.1-23.6

-18.9

-13.2

-7.1

-0.4

7.1

15.324.2

33.5

43.0

52.8

63.0

74.8

88.3103.0

118.8

134.3

151.4

173.0

203.3

nt

2.5 0 2.5 5 7.5 10

Km.

Fig. 7 Upward-continued RTP

map to 3-km level


123

Fig. 8 Downward Continued

RTP Map at Level 1-km




123

half of the study area. Such gradients illustrate the presence

of sharp contacts between the subsurface causative fea-

tures. These contacts are most likely of fracturing effect.


This map (Fig. 10) shows smoother contour lines with higher

amplitudes that reached ?750 gammas, while also the nega-

tive contours are showing amplitudes of -750 gammas and

less (down to -1,250 gammas). The smoothness of these

contours gives an indication that this level is within the

basement rocks and this reflects the combined effect of the

structural elements and/or the lithological variations within

the basement rocks. The gradients in those two maps are

gentler than the previous map (Fig. 8), reflecting more

homogeneity.

Extracting the magnetic sources using matching

band-pass filtering

The RTP magnetic data of the study area can be used to

illustrate this process. The shallow geologic units produce

weak, short wave length magnetic anomalies. The deeper

geologic units produce stronger magnetic anomalies with

longer wavelengths. This is reflected by varying slops in

the Fourier power spectrum of the aeromagnetic data,

which has been averaged for all azimuths as illustrated in

Fig. 11. The first step in designing a filter (using program

MFDESIGN of Phillips 1997), is to fit only the short

wavelength end of the spectrum with a straight line rep-

resenting the spectrum of a thin magnetic layer containing

a near-surface source layer (Fig. 11a). The effect of this

layer is subtracted from the spectrum, and the intermediate

wavelengths of the residual spectrum are fit with another

straight line representing the spectrum of the intermediate

source layer (Fig. 11b). This process is continued until the

long wavelength end of the spectrum is fit with the deepest

equivalent source layer (Fig. 11c). At this point, the com-

bined spectrum of all the equivalent layers should

approximately match the spectrum of the data (Fig. 11d).

Fourier bandpass filters for extracting the magnetic signals

of each of the equivalent layers are computed as the

spectrum of the individual equivalent layer divided by the

combined spectrum of all the equivalent layers (Fig. 11e).

The filters are applied to the observed data (using pro-

gram MFFILTER of Phillips 1997) to separate the mag-

netic anomalies by apparent source depth. Figure 12

contains RTP magnetic anomalies produced by shallow

geologic sources with equivalent dipole layer for this band-

pass located at 0.30 km. The intermediate wavelength map

(Fig. 13) involves RTP anomalies produced by geologic

sources at intermediate depths. The equivalent RTP




123

half-space for this band-pass is located at 1.18 km. Moreover,

the long wavelength map (Fig. 14) includes the anomalies

from the deepest and broadest features of the geology.

Therefore, the equivalent magnetic half space for this

band-pass is located at 3.9 km depth.

Horizontal gradient maps

The horizontal gradient (HG) method is considered as the

simplest approach to delineate the contact locations (e.g.

faults). It requires a number of assumptions about the

sources: (1) the regional magnetic field is vertical, (2) the

source magnetization is vertical, (3) the contacts are ver-

tical, (4) the contacts are isolated, and (5) the sources are

thick (Phillips 1998). In contrast, the method is the lease

susceptible to noise in the data, because it only requires the

two first-order horizontal derivatives of the magnetic field.

If T(x, y) is the magnetic field and the horizontal deriva-

tives of the field are (qT/qx and qT/qy), then the horizontal

gradient HG (x, y) is given by:

Fig. 11 In matched filtering,

the radial power spectrum, is fit

by series of linear curves

representing the power spectra

of simple equivalent magnetic

layers


123

-1.55

-1.10

-0.85-0.70

-0.60

-0.50

-0.45-0.40

-0.35

-0.30

-0.25

-0.20-0.15

-0.10

-0.05

0.000.05

0.10

0.15

0.200.25

0.35

0.40

0.450.55

0.65

0.80

1.001.30

1.85

nt

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

00

0

0

0

0

0

0

0

2.5 0 2.5 5 7.5 10

Km.

Fig. 12 Short-wave length

component of RTP magnetic

data using matching filtering

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

-1

0

01-

1 0

1 0

10

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

2.5 0 2.5 5 7.5 10

Km.

-15

-11

-10-9

-8

-7

-6-5

-4

-3

-2-1

0

1

23

4

56

7

8

910

12

14

1723

nt

Fig. 13 Medium-wave length




123

HG ðx; yÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffioT

ox

� �þ oT

oy

� �sð2Þ

Once the field is reduced to pole, the regional magnetic

field will be vertical and most of the source magnetizations

will be vertical, except for sources with strong remnant

magnetization such as basic volcanic rocks. This technique

has been carried out to the downward-continued data, along

the three depth levels, 1, 3, and 5 km, below the surface of

measurement. This resulted in three maps showing the

distribution of the HG features, as shown in Figs. 15, 16, and

29 0

030

00

29 0030 00

30 00 31 00

31 0030 00

- 20

0-

10

0

001-

00

1-

001-

-1

00

001-

001-

0

0

0

0

0

0

0

001

10

0

10

0

1 0 0

10

0

00

2

20

0

00

3

40

0

2.5 0 2.5 5 7.5 10

Km.

-182-157

-142-129

-120-112

-106-102

-98-94

-89-85

-79

-73-66

-59-53

-46-39

-31-22

-110

1429

4459

7590

104

119139

158174

186212

243301

nt

Fig. 14 Long-wave length



Fig. 15 Horizontal gradient map for 1-km downward-continued mapFig. 16 Horizontal gradient map for 3-km downward-continued map


123

17. These horizontal-gradient maps are vivid, simple, and

intuitive derivative products, which reveal the anomaly

texture and highlight anomaly-pattern discontinuities. These

maps contour the steepness of the anomaly relief’s slope.

Horizontal-gradient maxima occur over the steepest parts of

potential-field anomalies, and minima over the flattest parts.

Short-wavelength anomalies are also enhanced.

Tectonic inferences of the basement discontinuities

The results and information obtained from the fore-men-

tioned critical analysis and interpretation were integrated

with the general available geologic features to construct the

predominant tectonic elements affecting the basement

discontinuities of the study area (Fig. 18).

These tectonic features are either high trends (express-

ing anticlinal zones or swell-like belts) or low trends

(referring synclinal zones or trough-like belts) and fault

trends (throwing from the high trends to the low trends).

Accordingly, the basement surface is configured by

three major swell systems and two trough belts. The

northern high belt (swell) system trends mostly ENE–

WSW with N–S splitting at the west end, which represents

the Camel Pass–Abu Roash high (Abu El-Ata 1990).

While, the second swell orients mostly NE–SW (El

Faras–El Faiyum High trend), with mostly E–W bifurca-

tion at its western part (El-Sagha high trend) and other two

small E–W, NNE–SSW bifurcations at its central part. The

main trend of this belt represents the El Faras–El Faiym

high trend.

The southwestern small third high belt (Camel-Pass

belt), that starts in NW–SE direction and ends in the mostly

N–S with E–W bifurcation at its southern end.

Moreover, the major central trough zone (Qatrani-El

Gindi low trend) that run mostly ENE–WSW with N–S

split at its western part and NW–SE split at its central part

throughout Qarun lack. While, the southeastern trough belt

orients NE–SW with two N–S and NNW–SSE splits at its

southern end. In addition, a series of separated ENE–WSW

and N–S small troughs are observed at the northern and

southwestern parts of the map, beside a series of moderate

N–S and NE–SW swells observed at the northwestern and

southwestern corners.

These high and low trends are bounded and dissected by

major and minor faults, in the form of horst blocks, graben

blocks, or step-like blocks.

Horizontal gradient maps aided in defining the location

of linear features, which in turn are related to the trend of

the structural manifestations in the area. Faults can be

traced easily along these linear features.

Results and conclusions

Through the downward-continued maps, it can be deduced

that, some of the magnetic anomalies shown in Fig. 4, have

sources within the sedimentary section, overlying the deep-

seated basement rocks. The types, magnitudes, areal

extensions, and distributions of such sources are expected

to be in close relation with the basement rocks (i.e., supra-

basement features).

It seems that, the whole area is portrayed as a part of a

major sedimentary basin interrupted by several disconti-

nuities in the form of smaller highs and lows. This reveals

the complexity of the stress effects and directions exerted

Fig. 17 Horizontal gradient map for 5-km downward-continued map

Fig. 18 Map showing integrated basement structure discontinuities


123

on the area, in form of compressional and tensional stres-

ses. The predominant tectonic trends as delineated through

N60�E with intermittent N–S directions. Such basement

surface can be illustrated as being of several swells and

troughs with zones of displacement of different reliefs,

areal extensions and mainly oriented northeasterly. Block

faulting could be the most prominent structural style.

Through integrating the whole set of maps together with the

horizontal gradient maps, the faults were traced along these

maps. The resulting set of lineaments was compared with the

available well data that reached the basement surface, to

determine the relative highs and lows in the basement rocks.

Based on the integrated magnetic anomaly pattern from the

different processed techniques used in this work, a number of

magnetic highs (swells) and lows (troughs) features were

delineated. Such swells and troughs are in the form of uplifted

and down-faulted blocks within the basement. The illustra-

tions showed, the major trends of the basement features are

ENE–WSW, NE–SW, E–W and NNE–SSW trends. These

major trends are interrupted by number of minor N–S trending

faults with shorter areal extensions.

The fore-mentioned tectonic elements are shown in the

basement tectonic map, and named related to Abu El-Ata

(1990), Camel Pass–Abu Roash high, El-Sagha high,

El-Faras-El-Faiym High as well as Qatrani-El Gindi low trends.


Creative Commons Attribution License which permits any use, dis-

tribution and reproduction in any medium, provided the original

author(s) and source are credited.

References

Abu El-Ata ASA (1988) The relation between the local tectonics of

Egypt and the plate tectonics of the surrounding regions using

geophysical and geological data

Abu El-Ata ASA (1990) The role of seismo-tectonics in establishing

the structural foundations and starvation conditions of El-Gindi

Basin, Western Desert, Egypt. In: 8th E.G.S. Proceedings of the

6th annual meeting, Cairo, pp 150–169

El-Gezerry MN, Farid M, Taher M (1975) Subsurface geological

maps of northern Egypt. Unpublished maps. General Petroleum

Company, Cairo

El-Sirafe AM (1985) Application of aeromagnetic, aero-radiometric

and gravimetric survey data in the interpretation of the geology

of Cairo-Bahariya area, north Western Desert, Ph.D Thesis, Ain

Shams University, Egypt

Hantar G (1990) North Western Desert, Chap 15. In: Said R (ed) The

geology of Egypt. A.A. Balkema, Brookfield, pp 293–319

Jeffery DP (1998) Processing and interpretation of aeromagnetic data

for the Santa Cruz Basin-Patagonia mountain area, South central

Arizona, Open-File Report 02-98, USGS

Kristofer D, Yaoguo L (2007) A fast approach to magnetic equivalent

source processing using an adaptive quadtree mesh discretiza-

tion. ASEG, Perth, pp 1–4

Meshref WM, El-Sheikh MA (1973) Magnetic tectonic trend analysis

in northern Egypt. Egypt J Geol 17(2):179–184

Meshref WM (1980) Structural geophysical interpretation of base-

ment rocks of the northwestern Desert of Egypt. Annu Geol Surv

Egypt X:923–937

Meshref WM (1990) Tectonic framework, Chap 8. In: Said R (ed)

The geology of Egypt. A.A. Balkema, Rotterdam, pp 113–157

Phillips JD (1997) Potential-field geophysical software for the PC,

version 2.2, US Geological Survey Open-File Report 97-725.

ftp://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0725/

pfofr.htm

Said R (1962) The geology of Egypt. Elsevier, Amsterdam

Tikhonov AN, Arsenin VY (1977) Solutions of ill-posed problems.

V.H Winston and Sons, Washington, p 258

Youssef MI (1968) Structural pattern of Egypt and its interpretation.

AAPG Bull 52(4):601–614


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ftp://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0725/pfofr.htm

ftp://greenwood.cr.usgs.gov/pub/open-file-reports/ofr-97-0725/pfofr.htm

REVIEW PAPER - PRODUCTION ENGINEERING

Scientific research and field applications of polymerflooding in heavy oil recovery

Chang Hong Gao

Received: 6 August 2011 / Accepted: 17 October 2011 / Published online: 1 November 2011


Abstract The heavy oil resources worldwide are esti-

mated at 3,396 billion barrels. With depletion of light oil,

we have to face the technical and economical challenges of

developing heavy oil fields. Due to severe viscous finger-

ing, the recoveries of heavy oil reservoirs are often below

20% or even 10%. Thermal methods have been success-

fully applied in many heavy oil fields. However, reservoirs

at great depth or thin pay zones are not good candidates for

thermal methods.

According to past experiences, polymer flood was not

recommended for oil viscosity higher than 100 centipoises.

In recent years, polymer flood becomes a promising tech-

nology for heavy oil recovery thanks to the widespread use

of horizontal wells. This paper highlights the research

advances of polymer in heavy oil recovery since 1977. In

laboratory tests, polymer achieved tertiary recovery of

more than 20% for heavy oil. A few field cases in China,

Canada, Turkey, Suriname and Oman are also reviewed

and analysed. Some field pilots have shown positive

results. Field experiences indicate the major challenge

facing polymer flooding effectiveness is to maintain good

viscosity of polymer solution.

KeyWords Polymer � Oil recovery � Heavy oil � Review

Introduction

Heavy oil refers to the crude with high density (from 10� to

20� API) and high viscosity (more than 100 cP). Heavy oil

widely exists in many basins around the world, especially

in South America, North America and Middle East. The

heavy oil resources by region are given in Fig. 1 (Meyer

et al. 2007).

Due to high demand for energy and depletion of light

oil, we have to investigate technically and economically

feasible methods to produce heavy oil. Heavy oil presents

great challenges to oil producers. The drastic viscosity

difference between heavy oil and water causes injected

water to finger through the reservoir, leaving large quan-

tities of oil behind. As a result, recovery of heavy oil was

often less than 20% or even less than 10% (Meyer 2003).

Polymer flood is the most widely used chemical EOR

method. By adding polymers to water, the water–oil mobility

is lowered. Such a change can lead to better sweep efficiency.

It is generally believed that polymer flooding cannot reduce

the residual oil saturation, but it can help to reach residual oil

saturation in shorter time (Du and Guan 2004).

Polymer flood was proved technically and economically

successful in many EOR projects worldwide (Wang et al.

2009; Sheng 2011). In field applications, polymer floods

increased recovery by 12–15% (Wang et al. 2002). The

field experiences in China showed that polymer flood was

cheaper than water flood, due to increased oil output and

reduced costs in water injection and treatment (Wang et al.

2003).

Based on past experiences, polymer flood is recom-

mended for oil viscosity less than 100 cP under reservoir

temperature, and sandstone reservoir with oil saturation

higher than 30%, reservoir permeability greater than

20 mD, net thickness more than 3 m (10 ft), and reservoir

temperature less than 90�C or 200�F (Lake et al. 1992;

Alkafeef and Zaid 2007; Gao and Towler 2011).

Most commonly used polymers include polyacrylamids

(PAM), partially hydrolyzed polyacrylamide (HPAM) and

C. H. Gao (&)

School of Engineering, University of Aberdeen,

Aberdeen AB24 3UE, UK


123


DOI 10.1007/s13202-011-0014-6

Xanthan. HPAM can be synthesized to high molecular

weights and costs less than Xanthan, therefore more pop-

ular in field applications. However, HPAM is less tolerant

to salt (Morel et al. 2008).

According to a survey, thermal methods such as steam

flood and hot water flood are the successful strategy for

producing heavy oil (Koottungal 2010). However, thermal

methods are not suitable for thin layers and deep reservoirs.

Researchers have been studying polymer flood as a possi-

ble alternative for such scenarios.

Advances in scientific research

In 1977, two scientists at Marathon Oil Company pio-

neered the research on heavy oil recovery with polymer

(Knight and Rhudy 1977). Polymer solutions with various

PAM concentrations were injected into Ottawa sand packs.

The permeability of the sand packs ranged from 3,700 to

5,900 mD. The porosity of the sand packs was around

35%. Two heavy oils were tested. One was a crude oil from

Wyoming with viscosity of 220 cP and 19.8�API. The

other sample was very viscous synthetic oil (1,140 cP). The

mobility ratio with water flood was as high as 30. Polymer

flood reduced mobility ratio to 0.34 for the 220 cP oil, and

3.2 for the more viscous crude. Polymer achieved tertiary

recovery between 19 and 31%. The results clearly dem-

onstrated the potential of polymer flood in heavy oil EOR.

In recent years, polymer flooding attracted increasing

attention in heavy oil recovery, thanks to high oil prices.

This topic has been very active in Canada.

In western Canada, Water flood only recovered 10% of

the heavy oil reserves. Aiming to improve the heavy oil

recovery, researchers tested polymer solution on displacing

three oil samples with viscosity of 280, 1,600 and 780 cP

(Wassmuth et al. 2007b). The procedure was to inject

0.5 PV (pore volume) of water into high permeability core

until water cut reached 90%. Afterwards, 6 PV of polymer

solution was injected into the core, followed by 5 PV of

water. The tested polymer concentration was 1,500 ppm,

which produced an in situ viscosity of 18 cP. The incre-

mental recovery was 16, 22 and 23% for the three oil

samples, respectively. The test result in Fig. 2 clearly

shows the acceleration of recovery process with polymer

flood.

At University of Regina, HPAM solution was tested on

homogeneous and heterogeneous sand packs (Wang and

Dong 2007). The viscosity of test oil was 1,450 cP at room

temperature of 22.5�C. The homogeneous sand had

porosity of 0.35 and permeability of 7 Darcy. The sand

pack was first flooded with water till oil recovery of 42%,

and polymer solution was subsequently injected. The ter-

tiary recoveries ranged from 4% with polymer solution of

medium viscosity, to 19% with high-viscosity polymer

solution.

In a lab study in Alberta, 0.5 PV of polymer injection

lead to 20% of tertiary heavy oil recovery. The tested crude

had a viscosity of 600–2,000 cP and a gravity of 14�API.

The injected polymer solution produced a viscosity of

25 cP (Wassmuth et al. 2007a).

In another research project, PAM solutions of various

concentrations of 500, 1,000, 5,000 and 10,000 ppm were

tested against a heavy oil sample with viscosity of 1,450 cP

(Asghari and Nakutnyy, 2008). The test media were two

sand packs with permeability of 2 and 13 Darcy. It was

discovered that polymer concentration must exceed

5,000 ppm to mobilize the test oil.

At University of Calgary, heavy oil samples with vis-

cosities ranging from 430 to 5,500 cP were flooded with

polymer solutions with effective viscosities of

3.6–359.3 cP. It was discovered that the polymer solution

must exceed certain effective viscosity to achieve a tertiary

recovery of more than 10%. This can be seen in Fig. 3

(Wang and Dong 2009).

Fig. 2 Comparison of water flood and polymer flood on 1600 cP oil

Fig. 1 Heavy oil resources by region


123

The influence of oil saturation was also tested. The sand

pack was flooded till oil recovery of 35%, and polymer flood

was then initiated. It was discovered that polymer solution

with relatively low viscosity achieved good tertiary recovery

between 8 and 21%. This indicated that polymer flood could

be more effective when applied early. The tests on heteroge-

neous sand pack lead to much lower tertiary recovery, com-

pared with the results for homogeneous sands.

The heavy oil reservoirs in Saskatchewan are not suitable

for thermal methods or miscible CO2 flood. At Saskatchewan

Research Council, polymer flood was tested on heavy oil

recovery (Zhang et al. 2010). The heavy oil had a gravity of

18.3�API and a viscosity of 707 cP at 15�C. The molecular

weight of the test polymer was 8–20 million. The polymer

solution was prepared by adding 0.4 wt% of polymer to brine,

which produced a viscosity of 29 cP. Firstly, 4.7 PV of water

was injected into the sand pack with a permeability of

2.35 Darcy. Subsequently, 0.8 PV of polymer solution fol-

lowed, and finally chased by 2.85 PV of water flood. The

polymer flood recovered 13% of extra oil after initial water

flood. The test data are reproduced in Fig. 4.

For the laboratory research surveyed here, polymer flood

could lead to tertiary oil recovery of more than 10%.

However, high polymer concentration and viscosity were

required to mobilize heavy oil.

Field applications

Even though laboratory research demonstrated the poten-

tial of polymer flood in recovering heavy oil, most oil

companies are still reluctant to apply this technology in the

field. Five field cases are identified and reviewed here.

Bohai Bay, offshore China

It was estimated that more than 70% of the reserves in

Bohai Bay is heavy oil (Zhou et al. 2008). The recovery by

10 years of water flooding was only 13.5%. China National

Offshore Oil Company (CNOOC) started polymer flood in

Bohai offshore field since 2002 (Liu et al. 2010). The pilot

test on a single well lasted 500 days. The water cut drop-

ped from 95 to 54%. The incremental oil was 2,5000 m3

(157,250 bbl).

After the success of the single well treatment, polymer

was injected to four injection wells with six corresponding

production wells. The reservoir depth was 1,300–1,600 m,

and the average thickness of pay zone was 61.5 m. The

sands were poorly consolidated with porosity of 28–35%,

and average permeability of 2,600 mD (Han et al. 2006).

The reservoir temperature was about 65�C. The average

well spacing was 370 m. The water cut after polymer flood

reduced by 10%, and 17,700 m3 (111,330 bbl) of incre-

ment oil per well was produced. Till 2010, totally 53

operations of polymer flood have been conducted and the

incremental oil was about 636,000 m3 (4 MMSTB).

East bodo reservoir, Alberta Canada

The East Bodo sandstone reservoir is located in Alberta

and Saskatchewan in Canada. The reservoir had good

permeability (1,000 mD) and oil viscosity was high

(600–2,000 cP). The polymer injection with horizontal

wells was initiated in May 2006. The major challenge was

the quality of source water for mixing polymer solutions.

At the early stage, the maximum polymer viscosity pro-

duced was only 10 cP at 1500 ppm of polymer concen-

tration. No pressure resistance was observed. Later, the

water supply was changed to a fresher water source, and

the polymer solution achieved a much higher viscosity of

60 cP. The wellhead pressure increased to 6,000 kPa

(870 psi) at injection rate of 200 m3/day (1,258 bbl/day).

The production data after polymer flooding was not

reported (Wassmuth et al. 2009).

Fig. 3 Higher polymer viscosity lead to higher oil recoveryFig. 4 Oil Recovery with water flooding followed by polymer

flooding


123

Tambaredjo field, Suriname

The pilot was a sandstone reservoir at 387 m (1,270 ft)

with pressure of 1,724 kPa (250 psi). The net pay zone was

6.7 m (22 ft) thick with porosity of 33% and permeability

of 3–6 Darcy. The live oil viscosity was 400 cP at reservoir

temperature 36�C (97�F). Polymer flood started in Sep-

tember 2008. The polymer concentration in the injected

fluid was 1000 ppm, which produced a viscosity of

44–60 cP. The polymer injection rate was about 32 m3/day

(200 bbl/day), which was 7–10 times less than previous

water injection rate.

Till 2010, totally 0.22 PV of the well pattern has been

injected. Polymer breakthrough occurred at two of the five-

spot wells after approximately 1 year of injection. Analysis

of polymer fluid revealed 7% viscosity reduction from

mixing tank to wellhead. It was thus estimated that 40% of

polymer viscosity was already lost before entering forma-

tion rock. The production response to polymer flood was

not reported (Manichand et al. 2010).

Turkey case study

Bati Raman was a heavy oil field located in southeast

Turkey with oil gravity of 10–15�API. Primary recovery

was only 1.5%, and CO2 flooding improved recovery up to

5%. Polymer solution was injected to improve the sweep

efficiency of CO2. Three injection wells took 10,000 bar-

rels of polymer solution each, and pressure increases were

observed. After injection was complete, the wells were shut

in for a week, and CO2 injection resumed. Increased pro-

duction was observed in 16 production wells after

3 months of injection. The total cost of the polymer

treatment was USD 445,000. The payout time was 1 year

(Topguder 2010).

Oman case study

The Marmul Field in southern Oman was discovered in

1956 and brought on stream in 1980. The OOIP was esti-

mated at 390 million m3 (2,453 MMSTB). Like many

fields in the southern Oman, Marmul was characterised by

heavy, viscous crude oil that was difficult to extract.

The Kalata formation of Marmul field was located at

610 m (2,001 ft) deep with reservoir temperature of 46�C

(115�F). The oil is medium heavy with reservoir viscosity

of 80–110 cP. It was considered a good candidate for

polymer flood.

The first small-scale polymer flood pilot took place

between 1986 and 1988, with one injector well and four

producing Wells. The OOIP of the block was estimated at

190,000 m3 (1,195 MSTB). PAM solution of 1,000 ppm

was injected at a flow rate of 500 m3/day (3,145 barrel/

day). The polymer solution gave a viscosity of 15 cP at

surface under 46�C (115�F).

From May 1986 to September 1986, a water pre-flush of

0.23 PV was injected. A polymer slug of 0.63 PV followed

till August 1987. A water post flush of 0.34 PV was

completed in January 1988. The recovery was 12% at the

end of water pre-flush, 46% at the end of polymer

flood, and 59% at the end of the post flush (Koning et al.

1988).

Because of discoveries in Oman that promised cheaper

extraction costs than the tough Marmul field, the Marmul

polymer project was shelved. Today’s economic conditions

make the various EOR techniques more feasible. Recently

petroleum development Oman (PDO) announced the start

of a large-scale polymer flood project in southern Oman.

PDO estimated that by using polymer flooding it could

raise the total percentage of oil recovered from the reser-

voir to the high 20 s or even low 30 s.

Challenges facing polymer flooding operations

Polymer flood will be more effective if applied early, when

oil saturation is well above residual oil saturation. The

major challenge in polymer flood operations is to maintain

a good polymer viscosity. Water salinity, shear degrada-

tion, thermal degradation and adsorption can severely

damage viscosity of polymer fluid. Other issues facing field

applications included low injectivity, low productivity, and

polymer plugging formations (Thomas 2008).

At Daqing field in China, a field test was performed in

1998 to investigate the effect of water salinity. Waste water

with salinity of 3,800 ppm was used to prepare polymer

solution. The test was conducted in a 395-acre block with

45 wells and OOIP of 4.45 million m3 (28 MMSTB). The

tertiary recovery was much lower compared to adjacent

areas flooded with less saline water (Wang et al. 2002).

For offshore fields, sea water is usually available for

preparing polymer solution. Test data from Dalia field

offshore Angola showed that PAM viscosity decreased

rapidly with increase in water salinity. Moreover, shearing

at the wellhead chokes caused 25–50% of loss in polymer

viscosity (Morel et al. 2008).

Existence of oxygen in polymer solution can severely

degrade polymer viscosity. Therefore, oxygen must be

removed from the polymer solution. Polymers become

unstable at high temperature. Most field applications of

polymer flooding were under reservoir temperatures of less

than 75�C (Du and Guan 2004).

At Daqing field in China, injection wells suffered from

high injection pressure and low injection rate. Fracturing

could only improve injectivity for less than 3 months.

Improved fracturing technology with resin-coated proppant


123

enhanced well injectivity for up to 26 months (Wang et al.

2008).

The low permeability zones at the production wells were

also fractured to increase flow rate and recovery (Wang

et al. 2002). For example, 66 production wells were frac-

tured. After the treatments, the average fluid production

rate per well increased by 41%, and the average oil pro-

duction rate per well increased by 46%.

High polymer viscosity can improve conformance and

recovery. But polymer with too high molecular weight can

plug pore faces (Wang et al. 2002). In a field test, polymer with

molecular weight of 17 million plugged formations with

permeability ranging from 100–200 mD. But the same poly-

mer did not plug another reservoir with higher permeability.

Polymer flood in offshore fields faces more challenges

than that onshore (Raney et al. 2011). These challenges

include costs to transport chemicals, space for mixing

facilities on platform, large well spacing, and reduced

polymer viscosity when mixed with sea water.

In recent years, some operating companies started to

seriously consider EOR methods for offshore fields (Bon-

dor et al. 2005). For example, the Dalia field, 130 km

offshore Angola at water depth of 1,300 m (4,265 ft),

started to undergo polymer flood since February 2010

(Morel et al. 2010).

Conclusions

Past laboratory research showed that polymer could

increase heavy oil recovery by more than 20%. Field cases

in China, Turkey and Oman demonstrated the success of

polymer flooding in heavy oil fields.

In field applications, the major challenge is to maintain

polymer viscosity in surface injection facilities and under

reservoir conditions. Low salinity water should be used to

mix polymer solutions. Surface injection facilities should

be carefully designed to minimize shearing degradation.

It can be concluded that polymer flood is a promising

technology for recovering heavy oil. However, higher

polymer concentration will be required to mobilize heavy

oil. As a result, the cost of polymer will be significantly

higher when polymer flood is applied in heavy oil fields.





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123

ORIGINAL PAPER - PRODUCTION ENGINEERING

Mathematical modeling of geomechanical behavior of tarmatduring the depletion of giant oil reservoir-aquifer systems

Ayse Pamir Cirdi • Turgay Ertekin •

Luis F. Ayala H. • Ali H. Dogru

Received: 12 April 2011 / Accepted: 2 June 2011 / Published online: 28 June 2011


Abstract In this work, deformation and failure behavior

of tarmat layers during depletion of a giant reservoir–

aquifer system has been studied. Deformation response of

the tarmat to increasing pressure differential caused by

continuous depletion of reservoir is examined and a

mathematical model is developed for the study of this type

of composite systems. The geomechanical failure that takes

place when the pressure differential reaches a critical value

is also evaluated, along with the characterization of the

resulting fracture. Plate theory, maximum shear stress

failure criterion, conventional well test model, Perkins–

Kern–Nordgren (PKN) and Khristianovic–Geertsma–de

Klerk (KGD) models and flow through fractures models are

used. The developed sensitivity analysis proposes the

proper protocol to be followed in order to undertake pro-

duction design in such composite systems. The methodol-

ogy presented in this paper, ultimately, predicts fracture

width and fracture permeability that would be developed in

a system with a tarmat layer having a certain thickness and

a reservoir being produced at a certain production rate and

total depletion time.

Keywords Geomechanics � Tarmat � Numerical

modeling � Giant oil reservoir � Aquifer

List of symbols

A Cross-sectional area, L2

a, b Dimensions of the drainage area considered, L

B Formation volume factor, dimensionless

c Compressibility, Lt2/M

D Flexural rigidity coefficient, dimensionless

dx, dy, dz Incremental lengths, L

E Modulus of elasticity in tension and compression,

m/Lt2

G Shear modulus, m/Lt2

h Thickness, L

k Absolute permeability, L2

M Bending moment, mL

p Pressure, m/Lt2

q Applied load, m

q Volumetric flow rate, L3/t

rw Wellbore radius, L

t Time, t

V Shear forces, mL/t2

w Displacement (deformation), fracture width, L

x, y, z Coordinate directions

/ Porosity, dimensionless

l Viscosity, m/Lt

k Unit conversion constant (2.637 9 10-4 in

practical field units)

c Unit conversion constant (141.2 in practical

field units)

s Shear stress, m/Lt2

r Stress, m/Lt2

m Poisson’s ratio, dimensionless

Introduction

Oil resources are located in various types of reservoir

formations, varying with properties, dimensions and

A. P. Cirdi � T. Ertekin (&) � L. F. Ayala H.

Penn State University, University Park, PA, USA


Present Address:A. P. Cirdi

Halliburton, Houston, TX, USA

A. H. Dogru

Saudi Aramco, Dhahran, Saudi Arabia

123


DOI 10.1007/s13202-011-0008-4

architectures. Creating feasible production strategies with a

reasonable exploration and development plan is of great

importance in the production of these oil sources. The

process requires a good understanding of oil, reservoir

properties and existing geological architecture of the res-

ervoir of interest. Giant oil fields, being oil sources with

high production potentials, contain more than 500 million

barrels of recoverable oil as they constitute almost 75% of

the recoverable oil resources in the world.

This study focuses on a three-layered composite sys-

tem, typical of giant oil fields in the Middle East. Upper

layer contains mobile reservoir fluids, middle layer is

referred as the tarmat, and the bottom layer is a high

pressure water aquifer. Tarmat is an extremely viscous

hydrocarbon layer, mainly composed of tar or bitumen,

which exists between oil and water contact. In many

cases, the tarmat acts as a permeability barrier between

the reservoir and its aquifer. This composite system is

depicted in Fig. 1.

The main objectives of this study are: (1) the charac-

terization of the geomechanical behavior and eventual

failure of the tarmat layer as a response to hydrocarbon

production and the associated significant increase in pres-

sure differential between the depleting reservoir and its

aquifer; and (2) the evaluation of the system behavior after

geomechanical failure of the tarmat takes place. The latter

part of the analysis involves the characterization of the

fracture and its permeability and the resulting communi-

cation between the aquifer/reservoir system.

Tarmat deformation analysis

By recognizing the tarmat layer as a flat plate with a

thickness significantly smaller than its areal dimensions,

plate theory can be used for the analysis of tarmat defor-

mation. Plate theory extends the findings of the theory of

beams for these types of structural elements (Boresi and

Schmidt 2003; Bickford 1998; Timoshenko and Woi-

nowski-Krieger 1959). The tarmat plate is assumed to be

simply supported having rectangular shapes and lateral

dimensions that are perpendicular to x and y axes.

Deformations can take place in both x and y directions.

Tarmat response under uniform and non-uniform loading

has been studied, and the resulting forces are a conse-

quence of the developed normal and shear stresses. Fig-

ure 2 shows a deformed plate with the resulting forces, the

way they act and their relations with each other. These

forces include bending and twisting moments (M’s), and

shear forces (V), which occur throughout the plane due to

the load (q).

For this system, a balance of forces in x and y directions

yield the following equilibrium equation relating the

resulting moments generated by the applied load (Boresi

and Schmidt 2003):

o2Mx

ox2þ o2My

oy2þ o2Mxy

oyoxþ o2Myx

oxoy¼ q ð1Þ

where q = load applied to the system. A plate subjected to

transverse loading with certain distribution is displaced

perpendicular to its middle plane. Strain–displacement

relations can be derived following the definitions of normal

and shear stresses in terms of plane displacement or

deformation (w), as follows:

Fig. 1 Schematic representation of the system under consideration

Fig. 2 Bending moments, shear forces on deformed plate, force resultants acting on the plate element


123

rx¼�Ez

1�m2

o2w

ox2þm

o2w

oy2

� �; ry¼�

Ez

1�m2

o2w

oy2þm

o2w

ox2

� �

sxy¼�Ez

1�m21�mð Þ o2w

oxoy

� �

ð2Þ

These expressions, when substituted into definitions of

bending and twisting moments, yield:

Mx ¼�Zh=2

�h=2

zrxdz¼Do2w

ox2þ m

o2w

oy2

� �

My ¼�Zh=2

�h=2

zrydz¼Do2w

oy2þ m

o2w

ox2

� �; D¼ Eh3

12 1� m2ð Þ

Mxy ¼�Myx�Zh=2

�h=2

zsxydz¼D 1� mð Þ o2w

oxoy

ð3Þ

where D is referred as flexural rigidity. Expressions in

Eq. 3 can be substituted in Eq. 1 to allow the derivation of

the biharmonic equation, shown below as Eq. 4:

Do4w

ox4þ 2

o4w

ox2oy2þ o4w

oy4

� �¼ q; Dr2 r2w

� �¼ q ð4Þ

In this study, all of the edges of the plate are considered

to have simply supported boundary conditions. There are

two main conditions to be satisfied by simply supported

edges. First, the displacement (w) must be equal to zero at

the edges and any moment that coincides in direction with

the direction of the edge must be equal to zero. Therefore,

the following boundary conditions are to be satisfied by the

y = constant and x = constant edges:

y - constant: w ¼ 0; My ¼ Do2w

oy2þ m

o2w

ox2

� �¼ 0

x - constant: w ¼ 0; Mx ¼ Do2w

ox2þ m

o2w

oy2

� �¼ 0

ð5Þ

The biharmonic equation, the fourth degree differential

equation in Eq. 4, can thus be solved with these four boundary

conditions and a relevant loading expression, to obtain the

expression for transverse deformation w(x,y). For the case of a

uniform loading, for example, the following solution can be

found for plate transverse deformation:

wðx; yÞ ¼ 16q0

p6D

Xm;odd

Xn;odd

sin mpxa sin npy

b

mn ma

� �2þ nb

� �2� �2

ð6Þ

Once the transverse deformation is found, stresses and

bending and twisting moments and twisting moments

across the plate can be calculated using Eqs. 2 and 3.

Tarmat failure analysis

In order to evaluate the tarmat behavior at the moment of

geomechanical failure, tarmat deformation analysis should

be coupled with a failure criterion. There are a number of

theories that predict failure as a function of prevailing

stresses. For example, the maximum shear stress failure

theory, as originally developed by Charles Coulomb and

Henry Tresca, indicates that the failure point is reached

when the maximum shear stress in the material becomes

equal to the value of the shear stress at yielding. This point,

which indicates the occurance of failure is referred as yield

strength. Yield strenght is a property of the material which

needs to be experimentally determined by uniaxial com-

pression or uniaxial tension test. The Mohr–Coulomb

failure (internal friction) criterion is another common way

of evaluating failure by relating shearing resistance to

contact forces, friction and cohesion that is present among

the rock grains and it is deemed to be appropriate for the

prediction of failure in brittle materials. Other failure cri-

teria include the maximum normal stress failure criterion,

Hoek–Brown failure criterion, Von Mises failure criterion,

and the octahedral shear stress theory, among others.

If the maximum shear stress failure criterion is utilized,

principle stresses must be calculated for the material. They

can be estimated by implementing Eq. 7 below:

r1;2 ¼ �rx þ ry

2�

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirx � ry

2þ s2

xy

rð7Þ

In this equation, maximum values for the stresses must

be used. In a simply supported plate, these occur at the

center of the structure. At the center of the plate, maximum

stresses are given by the expressions:

rxð Þmax¼ �6Mx

h2; ry

� �max¼ � 6My

h2;

sxy

� �max¼ � 6Mxy

h2

ð8Þ

It can be shown that for the case of interest,

r2 r1h 0h ; r3 ¼ 0 ð9Þ

Therefore, if r2j j exceeds rYS of the material, failure

occurs (Gere 2001; Bickford 1998).

Fracture width and fracture permeability analysis

For the purpose of fracture width analysis, two different

hydraulic fracturing models have been used: the Perkins–

Kern–Nordgren (PKN) and the Khristianovich–Zheltov–

Geertsma–deKlerk (KGD) models. They relate fracture

width to properties of fluid and rock in the fractured sys-

tem. The working fluid in our model is the aquifer water

and the rock is represented by the tarmat. In both models,


123

the most influential fluid properties are viscosity and spe-

cific gravity and influential rock properties are Poisson’s

ratio, Young’s modulus of elasticty. Additional variables of

importance are fluid injection rate and fracture length.

Fracture thickness is a property that is not influential in

PKN model but is influential in KGD model. Inputs into the

analysis protocol used in this study are viscosity and spe-

cific gravity of water, Poisson’s ratio and Young’s Modulus

of Elasticiy of tarmat, reservoir production rate and

thickness of tarmat. Reservoir production rate is assumed

close to fluid injection/breakthrough rate since both are

expected to create a similar pressure differential in mag-

nitude and direction.

The problem is thus approached as an inverse problem,

in which fracture width is estimated as a function of res-

ervoir production rate. In this problem, thickness of tarmat

represents the fracture penetration length. In the hydraulic

fracturing analog, fracture length is the parameter that

helps to express the penetration of the crack created while

in the case of our interest, the target crack penetration is the

tarmat thickness. Fracture thickness in the KGD model is

assumed to correspond to this fracture length. Both the

PKN and KGD models are shown to be in agreement when

the fracture thickness is assumed to be as long as the line

that is drawn at the points on the plate where shear stress is

99% of the maximum shear stress.

The expressions for fracture width calculation for the

PKN and KGD models are presented below in Eq. 10,

respectively:

w ¼ 0:3ql 1� vð Þ h0=2ð Þ

G

1=4 p4

c� �

; G ¼ E

2 1þ vð Þ

w ¼ 0:29ql 1� vð Þ h0=2ð Þ2

Ghf

" #1=4p4

� �ð10Þ

In these expressions, G is the shear modulus. Figure 3

explains fracture thickness and fracture length orientation

for a hydraulic fracturing case and the problem studied

here.

Once fracture width is estimated, the associated fracture

permeability can be calculated. For example, fracture

permeability can be related to fracture width by equaling

the Poiseuille’s Law in parallel plates to Darcy’s law in

porous media (Craft and Hawkins 1959) which yields the

expression:

q ¼ P1 � P2ð ÞA0w2

12lh0

; k ¼ 54� 106w2 ð11Þ

A similar expression can be independently derived by

considering the case of the flow of hydraulic fracturing

fluids through induced fractures (Yew 1997). Yew (1997)

assumed that fractures have a narrow opening of constant

width all through the fracture thickness. If the flowing fluid

is assumed to be an incompressible Newtonian fluid, Yew

(1997) shows that fracture width and permeability can be

related by Eq. 12:

w2

12¼ k; k ¼ 5:45� 107w2 ð12Þ

Reservoir depletion and pressure transient model

At this stage of the analysis, reservoir depletion must be

considered in order to recreate the magnitude of the load

placed on the tarmat place. In order to relate pressure

depletion with time evolution, the standard computational

procedure of classical well test model is followed (Ear-

lougher 1977; Lee 1982). Reservoir is single phase and

square-shaped. Well is assumed to be located at the center

of the drainage area. In this procedure, dimensionless time

is converted to actual time and dimensionless pressure is

converted into actual pressure. Dimensionless production

rate is used as an intermediate step in these calculations.

The solutions for dimensionless pressure drop (pd) versus

Fig. 3 Fracture length, fracture width and fracture thickness in a hydraulic crack


123

dimensionless time (td) tabulated by Earlougher (1977) for

the case pressure variation at the center of the rectangular-

shape reservoirs are utilized. Equations 13, 14 and 15 give

the expressions for dimensionless production rate, dimen-

sionless pressure and dimensionless time, respectively:

qD ¼cBqplkhPi

ð13Þ

DPD ¼Pi � P

PiqD

ð14Þ

tD ¼kkt

/lcr2w

; tDA ¼ tD

r2w

A; tDA ¼

kkt

/lcAð15Þ

Results and discussions

Tarmat failure analysis

Figure 4 shows the expected deformation response as a

function of an uniformly applied loading along with the

associated failure envelope for two reservoir scenarios with

different properties. In these figures, deformation versus

loading behavior is investigated until the point where

maximum shear stress failure criterion predicts geome-

chanical failure. The rectangular plate deformation model

is used to model the behavior of the tarmat. In these figures,

it is readily seen that thicker the tarmat, the larger the

pressure drop required to trigger geomechanical failure. At

the same time, the thinner the tarmat, the larger the

deformation experienced by the tarmat prior to the onset of

failure. Inspection of Fig. 4 reveals that as the Young’s

modulus of elasticity and yield strength becomes larger, the

pressure differential required for the tarmat to fail increases

while its deformation is expected to slightly decrease.

Figure 5 displays the magnitude and nature of the

effects caused by the principal parameters of this analysis

on failure pressure including lateral dimensions, yield

strength and Poisson’s ratio of the tarmat. Each of the

figures is drawn considering critical pressures and

deformations that occur until critical pressure is reached. It

is observed that in smaller drainage areas, more pressure

differential is required to fail tarmat, tarmat having higher

yield strength, requires more pressure differential until

failure and tarmat with smaller Poisson’s ratios, requires

more pressure differential until the failure point. All of

these parameters indicate a direct proportionality with

tarmat thickness and magnitude of pressure required to fail

the tarmat.

Figure 6 displays a comparison between deformation

versus loading and associated failure envelope of uniform

loading (a) and non-uniform loading (b). For a tarmat with

a certain thickness, lateral dimensions, Young’s modulus of

elasticity, Poisson’s ratio and yield strength, more pressure

differential is required to observe failure in the case of non-

uniform loading. A comparison of Fig. 6a and b reveals a

slightly more deformation in the case of a uniform loading.

Figure 7 displays a comparison between loading versus

thickness for different lateral dimensions of tarmat in the

cases of uniform loading (a) and non-uniform loading (b);

respectively. A similar comparison can be made for yield

strength and Poisson’s Ratio effects. For a tarmat of certain

influential properties more pressure differential is required

to observe geomechanical failure in the case of non-uni-

form loading.

Reservoir depletion model

This study has been conducted for two different drainage

area assumptions. In each case, production rate has been

varied between 1,000 and 10,000 STB/day. Reservoir

properties assigned in this analysis are given in Table 1

below.

Figure 8 provides a comparison of different drainage

area assumptions while production rate influences on

pressure and time relationship can also be observed. Fig-

ure 8a and b represent the analysis with drainage area

assumption of 51.65 and 200 acres. As production rate

increases, a certain pressure differential is reached in a

shorter period of time. For reservoirs with smaller drainage

0

5

10

15

20

25

30

Δ P, psi

(a)

Δh

, ft

0

5

10

15

20

25

30

0 1,000 2,000 3,000 0 1,000 2,000 3,000

ΔP, psi

(b)

Δh

, ft

Fig. 4 Deformation versus

loading with associated failure

envelope. a E = 3,000,000 psi,

rYS = 30,000 psi,

a = b = 750 ft, v = 0.30,

b E = 5,500,000 psi,

rYS = 50,000 psi,

a = b = 750 ft, v = 0.30


123

areas, it takes less time to reach a certain pressure differ-

ential than it does for those with larger drainage areas.

Fracture permeability characterization

In PKN and KGD models, which are used to predict

fracture width, production rate from the reservoir above

that would make a similar effect as injection rate from the

aquifer below has been used as an input flow rate. The

production rates that have been used in the analysis with

conventional well test model is used in this part of the

study. The production rates are changed between 1,000 to

10,000 STB/day. The same analysis that is relating pro-

duction rate and width has been repeated for a possible

0

1,000

2,000

3,000

4,000

5,000

6,000

ho, ft

(a)

ΔP

, psi

a=b=500 ft

a=b=600 ft

a=b=750 ft

a=b=1,100 ft

a=b=1,500 ft

a=b=4,000 ft

E=4,000,000 psiσYS=40,000 psiv =0.30

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

ho, ft

(b)

Δ P, p

si

σYS=30,000 psi

σYS=15,000 psi

σYS=50,000 psi

σYS=75,000 psi

σYS =100,000 psi

E=4,000,000 psiv =0.3a=b=750 ft

0

500

1,000

1,500

2,000

2,500

3,000

20 40 60 80 100 120

20 40 60 80 100 120 20 40 60 80 100 120

ho, ft

(c)

ΔP

, psi

v =0.10

v =0.50v =0.40

v =0.30

v =0.20E=4,000,000 psiσYS=40,000 psia=b=750 ft

Corresponding Drainage Areas

(500 ft)2=5.75 acres (600 ft)2=8.28 acres (750 ft)2=12.94 acres (1,100 ft)2=27.83 acres (1,500 ft)2=51.65 acres (4,000 ft)2=368.00 acres

Fig. 5 a Loading versus thickness for various lateral dimensions

(E = 4,000,000 psi, rYS = 40,000 psi, v = 0.30). b Loading versus

thickness for various yield strengths (E = 4,000,000 psi, v = 0.30,

a = b = 750 ft). c Loading versus thickness for various Poisson’s

ratios (E = 4,000,000 psi, rYS = 40,000 psi, a = b = 750 ft)

0

10

20

30

Δ h, f

t

ΔP, psi

0

10

20

30

0 1,000 2,000 3,000 4,000 5,000 0 2,000 4,000 6,000 8,000

Δh

, ft

ΔP, psi

(a) (b)

Fig. 6 Comparison of deformation versus loading with associated failure envelope with a uniform, and b non-uniform loading assumption

(E = 8,000,000 psi, rYS = 75,000 psi, a = b = 750 ft, v = 0.30)


123

range of tarmat thicknesses varying between 30 and 100 ft.

Figure 9 includes the relationship between fracture width

and production rate for PKN and KGD models, for various

properties and relationship between fracture permeabil-

ity and fracture width. It should be noted that Eq. 1

refers to the first method and Eq. 2 refers to the second

method.

In both models, Young’s modulus of elasticity is

observed to be inversely proportional with fracture width.

A system with known properties encounters a wider

fracture width if the reservoir at the top of the system is

being produced with a higher production rate. Wider

fracture widths would be created in systems with thicker

tarmat layers. PKN model predicts larger widths than

KGD does. Difference in this prediction is largest in

systems with high reservoir production rates and thick

tarmat layers.

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

ho, ft

ΔP

, psi a=b=500 ft

a=b=600 ft

a=b=750 ft

a=b=1,100 fta=b=1,500 fta=b=4,000 ft 0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

9,000

20 40 60 80 100 120 140 20 40 60 80 100 120 140

ho, ft

ΔP

, psi

a=b=500 ft

a=b=600 ft

a=b=750 ft

a=b=1,100 ft

a=b=1,500 ft

a=b=4,000 ft

(a) (b)

Fig. 7 Comparison of loading versus thickness graphs for various lateral dimensions with uniform and non-uniform loading assumption

Table 1 Hydrocarbon reservoir properties

Property Value Unit

l 0.72 cp

Ø 0.25 fraction

B 1.3 rb/stb

k 400 md

h 200 ft

c 0.0000015 psi-1

rw 0.5 ft

Pi 9,000 psi

Fig. 8 Pressure differential versus time differential graphs for various flow rates. a Cross-sectional area = 51.65 acres, b cross-sectional

area = 200 acres


123

Coupled analysis protocol

This part of the section outlines the methodology followed

in this study coupling each individual step. Suggested

protocol is explained through the use of a composite sys-

tem. Properties of each layer of the composite system are

given in Table 2.

First step involves construction of deformation versus

loading with associated failure envelope. This relation is

dependent on Young’s modulus of elasticity, yield

strength, Poisson’s ratio and lateral dimensions of the

tarmat. Figure 10a represents the outcome of the study on

this relationship. By entering the chart at the 80 ft tarmat

thickness line, magnitudes of deformation and pressure

are found to be 15 ft and 432 psi, respectively, at the time

of failure. Second step involves the use of conventional

well test model to obtain the relationship between pres-

sure differential and time, for various flow rates within

the range chosen. Figure 10b represents the results of this

analysis (data used in this analysis are from the hydro-

carbon reservoir part of Table 2). Two different times

chosen are 3 and 7 days. In the analysis, the failure

pressure of 432 psi from the first stage is used with the

production rates for 3 and 7 days as 5,000 and

2,000 STB/day, respectively. This is followed with the

fracture width determination and permeability analysis

using the PKN and KGD models. A selected range of

production rates and tarmat thicknesses are considered.

Relation between fracture width and production rate is the

output of Figure 11 is the output (data is presented in

tarmat and fluid sections of Table 2). The 80 ft thickness

from family of thickness curves in PKN and KGD models

0.006

0.014

0.022

0.030

q, STB/d

w, i

n

0.006

0.014

0.022

0.030

q, STB/d

w, i

n

0.006

0.014

0.022

0.030

0 0q, STB/d

w, i

n

0

10,000

20,000

30,000

40,000

50,000

60,000

70,000

80,000

0 2,000 4,000 6,000 8,000 10,00

0 2,000 4,000 6,000 8,000 10,000 12,00 0 2,000 4,000 6,000 8,000 10,000 12,000

12,00 0.0000 0.0100 0.0200 0.0300 0.0400

w, in

k, d

arcy

equation 1 equation 2

(a)

(c) (d)

(b)

Fig. 9 Width versus production rate graphs for various tarmat

thicknesses for PKN and KGD models. a E = 3,000,000 psi,

v = 0.30, hf = 47.82 ft, b E = 5,500,000 psi, v = 0.30,

hf = 47.82 ft, c E = 3,000,000 psi, v = 0.30, hf = 47.82 ft, d frac-

ture permeability versus fracture width


123

is selected. Fracture widths for 2,000 STB/day are pre-

dicted to be 0.0140 and 0.0130 in. Fracture widths for

5,000 STB/day are predicted to be 0.0180 and 0.0165 in;

respectively. Final step of the analysis is determination of

the permeability as related to the fracture widths. Average

values of fracture widths of 0.0135 and 0.0173 in yield

fracture permeabilities of 10,500 and 16,000 darcy,

respectively (Fig. 12).

Summary and conclusions

In this study, we have examined the tarmat deformation

and failure behavior of a giant oil reservoir-aquifer system

undergoing a depletion process. The fracture that develops

after failure is characterized and its permeability is deter-

mined. In the analysis, plate theory, maximum shear stress

failure criterion, classical well test analysis theory, PKN

model, KGD model, and fracture flow models are used. A

sensitivity analysis is conducted by varying the reservoir,

rock and fluid properties. The proposed methodology,

predicts fracture width and fracture permeability that

would be created in a system with a tarmat layer of certain

thickness as a function of rate of depletion and total

depletion time. In the proposed analysis protocol, each

analysis step focuses on the behavior of a layer individu-

ally. As an alternative approach the composite system in its

entirety can be analyzed by coupling of each layer. This

will allow computation of the fracture penetration rate

through the tarmat layer as a function of time. Also, as a

continuation of the work presented in this paper, we would

like to take the proposed solution one step further by

integrating the formulated geomechanical model with the

fluid flow (and/or heat flow) models so that all of the

unknowns are solved simultaneously.

Within the bounds of the analysis protocol presented in

this paper, following conclusions are drawn:

1. As thickness of tarmat increases, total deformation that

occurs until the failure point decreases, and pressure

differential that is required to fail the tarmat increases.

2. As Young’s modulus of elasticity and yield strength of

tarmat increase, pressure differential that is required to

fail tarmat increases, and magnitude of deformation

that occurs until failure of tarmat decreases.

Table 2 Properties of composite system

Property Value Unit

Hydrocarbon reservoir

A 51.65 acres

2,250,000 ft2

l 0.72 c

Ø 0.25 fraction

B 1.3 rb/stb

k 400 md

h 200 ft

c 1.5E-06 psi-1

rw 0.5 ft

Pi 9,000 psi

Tarmat

v 0.3 –

E 8,000,000 psi

a 1,500 ft

b 1,500 ft

h 80 ft

rYS 30,000 psi

Fluid

c 1 –

l 1 cp

0

15

30

45

0 200 400 600 800

ΔP, psi

Δh,

ft

E=8,000,000 psiσYS=30,000 psiv =0.30

a=b=1 500 ft

h=30 ft

h=40 ft

h=50 ft

h=60 fth=70 ft

h=80 fth=90 ft

h=100 ft

0

100

200

300

400

500

600

011

Δ t, days

ΔP

, psi

q=1,000 STB/d

q=2,000 STB/d

q=3,000 STB/d

q=4,000 STB/d

q=5,000 STB/d

q=6,000 STB/d

q=7,000 STB/d

q=8,000 STB/d

q=9,000 STB/d

q=10,000 STB/d

1 2

(a) (b)

Fig. 10 a Deformation versus loading with associated failure envelope (E = 8,000,000 psi, rYS = 30,000 psi, a = b = 1,500 ft, v = 0.30).

b Pressure differential versus time differential graphs for various flow rates (cross-sectional area = 51.65 acres)


123

3. As lateral dimensions of tarmat increase, pressure

differential that is required to fail the tarmat decreases.

4. As yield strength of tarmat increases, pressure differ-

ential that is required to fail the tarmat increases.

5. As Poisson’s ratio of tarmat increases, pressure

differential that is required to fail the tarmat decreases.

6. A case of non-uniform loading requires more pressure

and the system experiences less deformation until

failure as compared to a similar case with uniform

loading configuration.

7. The PKN model predicts larger fracture widths than

the KGD model does. The difference in predictions

becomes more obvious in the presence of thick tarmat

layers and high production rates.

8. The PKN and the KGD models predict wider fracture

widths for higher reservoir production rates and thicker

tarmat layers.


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References

Bickford WB (1998) Advanced mechanics of materials. Addison-

Wesley, Menlo Park

Boresi AP, Schmidt RJ (2003) Advanced mechanics of materials.

Wiley, Hoboken

Craft BC, Hawkins MF (1959) Applied petroleum reservoir engi-

neering. Prentice Hall, Upper Saddle River

Earlougher RC Jr (1977) Advances in well test analysis, society of

petroleum engineers of AIME. Dallas, TX

Gere JM (2001) Mechanics of materials, 5th edn. Brooks-Cole,

Pacific Grove

Lee J (1982) Well testing, society of petroleum engineers of AIME.

Dallas, TX

Timoshenko S, Woinowski-Krieger S (1959) Theory of plates and

shells. McGraw Hill, Hightstown

Yew CH (1997) Mechanics of hydraulic fracturing. Gulf Publishing

Company, Houston

0.006

0.010

0.014

0.018

0.022

0.026

0.030

q, STB/d

w, i

n

PKN modelE=8,000,000 psiv =0.30hf =47.82 ft

2

1

0.006

0.010

0.014

0.018

0.022

0.026

0.030

0 4,000 8,000 12,000 0 4,000 8,000 12,000

q, STB/d

w, i

n

KGD modelE=8,000,000 psiv =0.30hf=47.82 ft

2

1

(a) (b)Fig. 11 Width versus

production rate graphs for

various tarmat thicknesses

(PKN and KGD model)

(E = 8,000,000 psi, v = 0.30,

hf = 47.82 ft)

0

10,000

20,000

30,000

40,000

50,000

60,000

0.0000 0.0100 0.0200 0.0300 0.0400

w, in

k, d

arcy

equation 1 equation 2

1 2

Fig. 12 Fracture permeability

versus fracture width


123


Prediction of reservoir performance in multi-well systems usingmodified hyperbolic model

Y. B. Adeboye • C. E. Ubani • O. Oribayo

Received: 29 March 2011 / Accepted: 13 August 2011 / Published online: 15 September 2011


Abstract Decline curve analyses are usually based on

empirical Arps’ equations: exponential, hyperbolic and

harmonic decline. The applicable decline for the purpose of

reservoir estimates is usually based on the historical trend

that is seen on the well or reservoir performance. This

remains an important tool for the reservoir engineer, so that

the practice of decline curve analysis has been developed

over the years through both theoretical and empirical

considerations. Despite the fact that the fundamental

principles are well known and understood, there are aspects

which can still lead to a range of forecast and reserve

estimates that until now have not been investigated. In this

work, a model was developed considering the effect of well

aggregation and interference in multi-well systems. This

approach accounts for the entire production history of the

well and the reservoir, and thus reduces the influence of

well interference effects on decline curve analysis. It pro-

vides much better estimates of reserves in multi-well sys-

tems. The models were validated with field data from

different wells. Production decline data from different

wells in a reservoir were analyzed and used to demonstrate

the application of the developed model.

Keywords Decline curve � Well aggregation �Interference � Forecast � Reserve estimates

List of symbols

NP Production (liter)

qi Initial oil production rate (liter/year)

b Constant

Di Constant

q Oil production rate (liter/year)

t Production time

NPx Cumulative oil production (liter)

qx Cumulative oil production rate (liter/year)

tx Cumulative production time (year)

DCA Decline curve analysis

Introduction

Production of hydrocarbons declines due to a decline in

reservoir energy and/or increases in producing water cut.

Graphical plots of performance data provide a time-tested,

frequently used technique known as ‘‘decline curve’’ for

estimating ultimate recovery and/or reserves to be expected

from a well, reservoir or field.

Decline curve analysis is used for analyzing declining

production rates and forecasting future performance of oil

and gas wells. Forecasting future production is essential in

economic analysis of exploration and production expendi-

tures. Hence, the analysis of production decline curves

represents a useful tool for forecasting future production

from wells and reservoirs. The basis of this procedure is

that factors which have affected production in the past will

continue to do so in future.

Y. B. Adeboye (&)

Department of Petroleum and Gas Engineering,

University of Lagos, Akoka, Yaba, Lagos, Nigeria


C. E. Ubani

Department of Petroleum and Gas Engineering,

University of Port-Harcourt, Port-Harcourt, Nigeria

O. Oribayo

Department of Chemical Engineering,

University of Lagos, Akoka, Yaba, Lagos, Nigeria

123


DOI 10.1007/s13202-011-0009-3

Most conventional decline curve analyses are based on

the classic works of Arps (1970) and Fetkovich (1980),

which illustrate the analysis of well performance data using

empirically derived exponential, harmonic and hyperbolic

functions. Although the study of Arps (1970) is completely

empirical, its simplicity and the fact that it requires no

knowledge of reservoir or well parameters make its use

widespread in the upstream petroleum industry, particu-

larly for production prediction and estimating reserves

from production decline behavior. However, our observa-

tion is that the Arps’ method completely ignores the

flowing pressure data, does not account for changing pro-

duction conditions and changing gas properties with time

(reservoir pressure); thus, it yields inconsistent results

(unreliable matches and poor extrapolation).

Regarding the research works of Fetkovich (1980) and

Fetkovich et al. (1998), we noticed that their works discuss

the use of Arps’ hyperbolic relations and that they do

provide a semi-analytical result for gas flow behavior

which, unfortunately, is never valid in practice. To address

the impact of pressure-dependent gas properties on the

evaluation of gas production data, Fraim and Watten

Barger (1987) presented a decline type curve for gas res-

ervoir systems. Although the Fraim and Watten Barger

(1987) approach is more rigorous than simply using the

hyperbolic model, the Fraim solution is not universal. The

decline type curves not only permit forecast of well per-

formance, but also estimate reservoir properties (i.e., flow

capacity in kh) as well as oil in place.

The Fetkovich method was improved upon by the

introduction of two additional type curves, which were

plotted concurrently with the normalized rate type curves:

the rate integral function and derivative function, which

help in smoothing the often noisy character of production

data and in obtaining a more unique match (Blasingame

et al. 1991). The Blasingame et al. (1991) method is similar

to that of Fetkovich in that they use type curves for pro-

duction data analysis. However, the primary difference is

that the modern method incorporates the flowing pressure

data along with production rates and use analytical solu-

tions to calculate hydrocarbons in place.

McCray (1990) developed a time function that would

transform production data for systems exhibiting variable

rate or pressure drop performance into an equivalent sys-

tem produced at a constant bottom-hole pressure, which

was extended by Blasingame et al. (1991) to an equivalent

‘‘constant rate’’ analysis approach. The issue of variable,

non-constant bottom-hole pressures in gas wells was

addressed by Palacio and Blasingame (1993). They intro-

duced new methods, which use a modified time function

for analyzing the performance of single phase liquid or gas

wells. One of the shortcomings of this method is that it

completely ignores the flowing pressure data; thus, when

applied, there is always underestimation or overestimation

of reserves. Besides, it does not account for changing

production conditions and thus cannot always provide a

reliable estimate of recoverable hydrocarbons in place, and

changing gas properties with time (reservoir pressure) are

not accounted for; thus, gas reserves are usually

underestimated.

Fetkovich et al. (1998) was the first to apply the concept

of using type-curves to transient production. The research

methodology of Fetkovich (1980) and Fetkovich et al.

(1998) was the same as that of Arps (1970) depletion for

the analysis of boundary-dominated flow and constant

pressure type curves originally developed by Van Everd-

ingen and Hurst for transient production. Type-curve

matching is essentially a graphical technique for visual

matching of production data using pre-plotted curves on a

log–log paper. The most valuable feature of type curves

lies not in the analysis, but in the diagnostics. Fetkovich

et al. (1998) presented the theoretical basis for Arps’ pro-

duction decline models using the pseudo-steady state flow

equation. The decline type curves not only permit forecast

of well performance, but also estimate reservoir properties

(i.e., flow capacity in kh) as well as oil in place.

The Fetkovich method was improved upon by the

introduction of two additional type curves, which were

plotted concurrently with the normalized rate type curves

that help in smoothing the often noisy character of pro-

duction data and in obtaining a more unique match

(Blasingame et al. 1989). McCray TL (1990) developed a

time function that would transform production data for sys-

tems exhibiting variable rate or pressure drop performance

into an equivalent system produced at a constant bottom-hole

pressure, which was extended by Blasingame et al. (1991) to

an equivalent ‘‘constant rate’’ analysis approach.

The issue of variable, non-constant bottom-hole pressures

in gas wells was addressed by Palacio and Blasingame

(1993). They introduced a new method which uses a modi-

fied time function for analyzing the performance of single

phase liquid or gas wells. The method of Blasingame et al.

(1991) is similar to that of Fetkovich in that they use type

curves for production data analysis. However, the primary

difference is that the modern method incorporates the

flowing pressure data along with production rates and use

analytical solutions to calculate hydrocarbons in place.

Rodriguez and Cinco-Ley (1993) developed a model for

production decline in a bounded multi-well system. The

primary assumptions in their model are that the pseudo-

steady state flow condition exists at all points in the res-

ervoir and that all wells produce at a constant bottom-hole

pressure. They concluded that the production performance

of the reservoir was shown to be exponential in all cases, as

long as the bottom-hole pressures in individual wells were

maintained constant. Camacho et al. (1996) improved the


123

Rodriguez–Cinco-Ley model by allowing individual wells

to produce at different times.

Valko et al. (2000) presented a ‘‘multi-well productivity

index’’ concept for an arbitrary number of wells in a

bounded reservoir system. Li and Home (2005) and Guo

et al. (2007) proposed semi-analytical, direct solutions for

determining average reservoir pressure, rate and cumula-

tive production for gas wells produced at a constant bot-

tom-hole flowing pressure. These authors also assumed the

existence of pseudo-steady state flow, but proved that the

concept was valid for constant rate, constant pressure or

variable-rate/variable pressure production.

Despite the wide use of decline curve analysis and type-

curve matching of oil well, they sometimes over-predict or

underestimate reserves. The subjectivity of other methods

along with the need for pressure data necessitates the

development of our model, which does not require pressure

data and also eliminates the subjectivity of the analysis.

The specific objectives of this paper are to:

• develop a model to estimate reserve and predict

reservoir performance for multi-well reservoir system

using production data analysis;

• demonstrate the applicability of the newly developed

model by validating it with existing models and field

data.

Model development

The new model is a modification of that used by Arps.

The basic assumptions are:

1. Whatever causes controlled the trend of a curve in the

past will continue to govern its trend in the future in a

uniform manner.

2. According to Fetkovich, if production from each well

in a reservoir or field followed the exponential decline

solution, the total decline curve analysis production

from the reservoir or field would be better estimated

using hyperbolic decline model.

A hyperbolic decline occurs when the decline rate is no

longer constant. Compared to exponential decline, the

following two hyperbolic decline curve equations estimate

a longer production life of the well.

For hyperbolic decline

NP ¼qb

i

ðb� 1ÞDifðq1�b � q1�b

i Þg ð2:1Þ

and

q ¼ qi

ð1þ bDitÞ1b

ð2:2Þ

Combining Eq. 2.1 with 2.2 yields the expression given

as

NP ¼qb

i

ðb� 1ÞDi

qi

ð1þ bDitÞ1b

!1�b

�q1�bi

8<:

9=; ð2:3Þ

Further simplification of Eq. 2.3 yields the equations:

NP ¼qb

i

ðb� 1ÞDiðqiÞ1�b ð1þ bDitÞ

b�1b � 1

� �n oð2:4Þ

NP ¼qi

ðb� 1ÞDið1þ bDitÞð1þ bDitÞ

�1b

h i� 1Þ

n oð2:5Þ

NP ¼qi

ðb� 1ÞDifð1þ bDitÞð

q

qi� 1Þg ð2:6Þ

NP ¼1

b� 1ð ÞDi1þ bDitð Þðq� qiÞf g ð2:7Þ

NP ¼1

ðb� 1ÞDifðqþ qbDit � qiÞg ð2:8Þ

NPðb� 1ÞDi ¼ fðqþ qbDit � qiÞg ð2:9ÞNPðb� 1ÞDi þ qi ¼ qf1þ bDitg ð2:10Þ

q� NPðb� 1ÞDi þ qi

f1þ bDitgð2:11Þ

Equation 2.11 is derived from the hyperbolic solution,

but can be used for both the exponential and harmonic

solution; thus, the developed equation is a general

equation.

When cumulative production (Np) is expressed in terms

of the previous cumulative production (Npx) and production

rate q over a period of time, the equation obtained is given

as

Np ¼ NPx þ qðt � txÞ ð2:12Þ

Substituting for Np in Eq. 2.11 gives

q� ðNPx þ qðt � txÞÞðb� 1ÞDi þ qi

f1þ bDitgð2:13Þ

qf1þ bDitg ¼ ðNPx þ qðt � txÞÞðb� 1ÞDi þ qi ð2:14Þqf1þ bDitg ¼ NPxðb� 1ÞDi þ qðt � txÞðb� 1ÞDi þ qi

ð2:15Þqf1þ bDitg � qðt � txÞðb� 1ÞDi ¼ NPxðb� 1ÞDi þ qi

ð2:16Þqfð1þ bDitÞ � ½ðt � txÞðb� 1ÞDi�g ¼ NPxðb� 1ÞDi þ qi

ð2:17Þ


123

Rearranging Eq. 2.17 yields

q ¼ NPxðb� 1ÞDi þ qi

fð1þ bDitÞ � ½ðt � txÞðb� 1ÞDi�gð2:18Þ

By simplifying the denominator and if t - tx & t, then

q ¼ qi þ NPxðb� 1ÞDi

1þ tDið2:19Þ

In the case of forecast or prediction of reservoir

performance for a multi-well system, Eq. 2.19 can be

used, but Di is replaced by Dt

Then Eq. 2.19 is the modified hyperbolic model that can

be used to calculate the future production rate based on the

initial production rate qt, previous cumulative production

Npx, and constants Dt and b for a multi-well reservoir

system. The procedure for determining model parameters,

i.e., Di- and b-values is the same as that in the hyperbolic

model and is shown in Appendix A

Model validation

In this study, the basic principle/fundamental concept used

is that of Arps’ model; hence, result from the developed

model is validated with Arps’ exponential and hyperbolic

model using the production data from reservoirs (A and B)

given below as case study.

Reservoir A: case study

This reservoir is an integrated oil and gas reservoir with

major oil reserves with two wells drilled through it and still

producing up to date. The off-take built up rapidly from

2001 and reached a peak of 4852.64 stb/d by August 2001.

Subsequently, off-take has shown natural decline from the

wells. The predominant drive mechanism is both the aquifer

and gravity; hence the values of b ranging from 0.5–0.8 will

be acceptable for DCA. There is currently pressure main-

tenance and artificial lift scheme in this reservoir due to the

high viscosity of the oil. In this multi-well reservoir, the

producing drainage points do not display any visible decline

trend that can be useful for DCA; thus it is recommended to

carry out the DCA first on reservoir basis, and then on the

drainage points with established trends. Due to the inter-

connectivity test carried out, it was discovered that there

was possibility of interference between these wells; hence

reservoir is suitable for use as case study.

Reservoir B: case study

This is an oil reservoir with little gas reserves. It has three

wells drilled through it and two are still producing to the

present. The off-take built up rapidly from 1974 and

reached a peak of 6763.88 stb/d by April 1994. Subse-

quently, the off-take has shown a natural decline, with

beaning down of the wells. The predominant drive mech-

anism is aquifer. The well that has quit production is due to

depletion of reservoir energy. There is currently neither

pressure maintenance nor artificial lift in this reservoir.

Presently, there is poor production allocation in terms of

well performance, hence reservoir B is a suitable multi-

well reservoir system for case study.

Data analysis

The production data from reservoir A and B were analyzed

using conventional Arps’ exponential and hyperbolic

decline models, juxtaposing the results obtained to validate

the developed model. The production curves shown in

Figs. 1, 2, and 3 were plotted using each of the model for

reservoirs A and B, respectively. From each plot, the model

parameters shown in Tables 1 and 2 for exponential,

hyperbolic and developed models were determined using

the procedure shown in Appendix A. Having substituted

the obtained parameters shown in Tables 1 and 2 in

Fig. 1 Exponential decline production plot for reservoir A

Fig. 2 Hyperbolic decline production plot for reservoir A


123

exponential, hyperbolic and developed models, the pro-

duction rate decline curves shown in Figs. 4, 5 6 and 7

were obtained.

Results and discussions

The basic principle/fundamental concept used is that of

Arps’ model; hence, results from the developed model are

compared with those of Arps’ exponential and hyperbolic

model. The comparison demonstrated in Fig. 4, 5, 6 and 7

reveals that the exponential model tends to underestimate

reserves and production rates, while the hyperbolic model

over-predicts the reservoir performance. The accurate

prediction, using the developed model, is achieved due to

the fact that: the use of cumulative production rate in the

Fig. 3 Hyperbolic decline production plot for reservoir B

Table 1 Model parameters

Parameters obtained

from graph

For multi-well

reservoir system A

For multi-well

reservoir system B

Slope -0.668 -0.302

Nominal decline factor

Di (/year)

-0.2438 -0.1102

Effective decline factor (d) 0.21637 0.10437

Table 2 Model parameters

Parameters obtained

from graph

For multi-well

reservoir system

A

For multi-well

reservoir system

B

Hyperbolic exponent (b) 0.765 0.945

Nominal decline factor

Di (/year)

0.07024 0.0484

Decline rate factor, Dt (/year) 0.06667 0.0463

Decline rate factor, Dt (/year) 0.000183 0.000127

Fig. 4 Production rate decline comparison of the three models

Fig. 5 Production comparison of the three models

Fig. 6 Production rate decline comparison of the three models

Fig. 7 Production comparison of the three models


123

new model takes into cognizance the effect of well inter-

ference (volumetric mass influx) by new wells, which steal

from other wells. The pressure data are not used in this

case. Also, the adverse effects of downtime experienced

using a model that only relates the rate and time are

reduced, because ‘gaps’ in the production data during

periods of no production disappear when cumulative pro-

duction is integrated in the developed modified hyperbolic

model.

The consequence of underestimating or over-predicting

reserves is that it will affect the investment decisions. This

is because production forecasts, together with product

prices, operating costs and investments, are used to deter-

mine the project economics. Revenue is then predicted

when pricing forecasts are combined with the volumes

forecast. Production forecast data are also used to develop

expense forecasts. These forecasts are made on the basis of

production volumes and the forecasts of active completions

and related operational considerations. In turn, profit can be

predicted based on expected revenue and expenses. Profit

predictions will be used for work planning and project

justification.

However, the forecasts have direct dollar impacts far

beyond an organization. Based upon these forecasts, a

company can supply and coordinate marine and pipeline

transportation resources required to get the oil and gas to

market. On the other hand, forecasting too low may lead to

purchase of expensive spot capacity to handle the extra

production. In the longer term, forecasts affect more stra-

tegic decisions such as whether a producing property

should be kept or sold, the long-term availability of capital

for new projects, and whether a company should adjust its

pipeline or marine transportation capacity.

Conclusion

Based on the present study, the following conclusions may

be drawn in the cases studied:

1. The limitations of the Arps’ hyperbolic decline model

have been corrected by taking into cognizance the

effect of well aggregation and interference in multi-

well systems using high level reservoir data.

2. The comparison of model predictions using the

reservoir production data demonstrated that the devel-

oped modified hyperbolic model had the best predic-

tion compared to the exponential and the harmonic

models in the cases studied.

3. The study also revealed that decline analysis and

reserve estimation based on decline analysis must be

carried out with good understanding of the factors that

control the decline.





Appendix A: Determination of the hyperbolic exponent,

initial nominal and effective decline constant

for hyperbolic decline as stated in the economic analysis

and investment decision by Ikoku (1985), University

of Port Harcout, Nigeria

This is a curve-fitting procedure based on reading three

points from a smooth curve representing a set of data points

in the most direct method of analyzing hyperbolic decline

curves. The procedure is as follows

For multi-well system A

From Fig. 2,

a. Select points (t1, q1) and (t2, q2)

t1 = 1 year, q1 = 4475 bbl/day

t2 = 7 years, q2 = 2750 bbl/day

b. Read t3 at q3 ¼ffiffiffiffiffiffiffiffiffiq1q2p

q3 ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi4475� 2750p

¼ 3508 t3 = 3.8 years

c. Calculate Did

� �¼ t1þt2�2t3

t23�t1t2

= 0.0537

d. Find q0 at t = 0, q0 = 4800 bbl/day

e. Pick up any point (t*, q*) say t* = 2 years,

q* = 4200 bbl/day

f. q� ¼ qo

1þ Didð Þt�ð Þ ) d ¼ log

qoq�ð Þ

log 1þ Didð Þt�ð Þ ¼ 1:308

g. Finally, Di ¼ Di

d

� �d

h. (0.0537 9 1.308) = 0.07024/year

where d ¼ 1=b, b = 0.765.

The hyperbolic decline constant at some future time, t, is

defined by the following equation Dt:


123

Dt ¼Di

1þ bDit

Therefore,

Dt ¼0:07024

1þ ð0:765� 0:07024� 1ÞDt ¼ 0:06667=year

Dt ¼0:06667

year� 1 year

365 days¼ 0:000183=day

Appendix B: Illustrating the applicability

of the modified hyperbolic model using a case study

It is required to forecast the production rate of a reservoir in

2 years’ time using DCA by Arps’ model and the modified

Arps’ model. The analysis is to be carried out at the end of

2008 after the well had produced 9 MMstb. The analysis of

the production data gave a nominal exponential decline rate

of 0.11023 pa and an estimate for the initial rate for the

forecast of 1374.17 stb/day and the hyperbolic exponent of

0.945 with an initial nominal decline rate of 0.0463/year.

This can easily be done because the equations are not of

a complex form. Using Arps’ model:

For the exponential DCA,

q ¼ q1e�Dt

Therefore,

q ¼ 1374:17e�0:11023�2 ðandÞq ¼ 1102:29 bbl/day

For the Arps’ hyperbolic DCA,

q ¼ qt

ð1þ bDttÞ1b

Therefore,

q ¼ 1374:17ð1þ ð0:945� 0:0463� 2ÞÞ�1

0:945

q ¼ 1257:44 bbl/day:

Using the modified hyperbolic model given by

q ¼ qi þ NPxðb� 1ÞDi

1þ tDi

q¼1374:17þ 9� 106�ð0:945� 1Þ� 0:0463� 1

365

� �� 1þð2� 0:0463Þ

q ¼ 1200:24 bbl/day:

This illustrated that when the multi-well system

production forecast is done using the three models, the

exponential model underestimates the reservoir

performance while the hyperbolic overestimates the

reservoir performance, but the modified hyperbolic model

gives a better result that is higher than the value of the

exponential but lower than that of the hyperbolic model.

This is because the modified model makes use of the entire

cumulative oil production data of wells in the multi-well

system, and hence gives a better result.

References

Arps, JJ (1970) Oil and gas property evaluation and reserve estimates,

vol. 3, Reprint Series, SPE, Richardson, TX, pp 93–102

Blasingame TA, Etherington JR, Hunt EJ, Adewusi A (1989) Decline

Curve Analysis Using Type-Curves. SPE 110927

Blasingame TA, McCray, TC, Lee, WJ (1991) Decline curve analysis

for variable pressure drop/variable flowrate system. SPE 21513

Camacho VR, Rodriguez, F, Galindo-NA, Prats M (1996) Optimum

position for wells producing at constant wellbore pressure. SPE,

vol 1, pp 155–168

Fetkovich, MJ (1980) Decline curve analysis using type curves. JPT,

1065–1077

Fetkovich MJ et al (1998) Decline curve analysis using type-curves.

SPE 13169

Fraim ML, Watten Barger RA (1987) Gas reservoir decline analysis

using type curves with real gas pseudo-pressure and normalized

time. SPEFE (Dec. 1987)620

Guo B, Lyons WC, Ghalambor A (2007) Petroleum production

engineering—a computer-assisted approach. Elsevier Science &

Technology Books Publishers, Amsterdam, pp 98–105

Ikoku CU (1985) The economic analysis and investment decision, 3rd

edn. University of Port Harcourt, Nigeria

Li K, Home RN (2005) Verification of decline curve analysis models

for production prediction. SPE 93878

McCray, TL (1990) Reservoir analysis using production decline data

and adjusted time. MS Thesis, Texas A & M University College

Station, TX

Palacio JC, Blasingame TA (1993) Decline curve analysis using type

curves. SPE 25909

Rodriguez F, Cinco-Ley H (1993) A new model for production

decline. SPE 25480

Valko PP, Doublet, LE, Blasingame TA (2000) Development and

application of the multiwell productivity index (MPI). SPEJ


123


How to improve poor system efficiencies of ESP installationscontrolled by surface chokes

Gabor Takacs

Received: 16 April 2011 / Accepted: 28 September 2011 / Published online: 21 October 2011


Abstract Electrical submersible pumping is the most

inflexible of any artificial lift system because a specific

ESP pump can only be used in a definite, quite restricted

range of pumping rates. If it is used outside the specified

range, pump and system efficiencies rapidly deteriorate and

eventually mechanical problems leading to a complete

system failure develop. When serious deviation from the

design production rate is experienced, the possible solu-

tions are (a) running a different pump with the proper

recommended operating range, or (b) using a variable

speed drive (VSD) unit. However, in case the ESP system

produces a higher than desired liquid rate, a simple and

frequently used solution is the installation of a wellhead

choke. The wellhead choke restricts the pumping rate and

forces the ESP pump to operate within its recommended

liquid rate range. This solution, of course, is very detri-

mental to the economy of the production system because of

the high hydraulic losses across the choke that cause a

considerable waste of energy. The paper utilizes NODAL

analysis to investigate the negative effects of surface pro-

duction chokes on the energy efficiency of ESP systems as

compared to the application of VSD drives. The power

flow in the ESP system is described and the calculation of

energy losses in system components is detailed. Based on

these, a calculation model is proposed to evaluate the

harmful effects of wellhead choking and to find the proper

parameters of the necessary VSD unit. By presenting a

detailed calculation on an example well using the proposed

model the detrimental effects of wellhead choking are

illustrated and the beneficial effects of using a VSD drive

are presented. Using data of a group of wells placed on ESP

production a detailed investigation is presented on the

field-wide effects of choking. The energy flows and the

total energy requirements are calculated for current and

optimized cases where VSD units providing the required

electrical frequencies are used. Final results clearly indi-

cate that substantial electric power savings are possible if

production control is executed by VSDs instead of the

present practice of using surface chokes.

Keywords Electrical submersible pumping � ESP �Oil well � Production � Optimization � Wellhead choke �Energy � Efficiency � System analysis � NODAL analysis

Introduction

The objective of any artificial lift design is to set up a lift

system with a liquid producing capacity that matches the

inflow rate from the well it is installed in. Since the

mechanical design of the lifting equipment is only possible

in the knowledge of the probable liquid rate, the designer

needs a precise estimate on the production rate attainable

from the given well. Design inaccuracies or improperly

assumed well rates can very easily result in a mismatch of

the designed and actually produced liquid volumes (Brown

1980; Takacs 2009). The main cause of discrepancies

between these rates, assuming proper design procedures are

followed, is the improper estimation of possible well rates,

i.e. inaccurate data on well inflow performance. The con-

sequences of under-, or over-design of artificial lift systems

can lead to the following:

• If the artificial lift equipment’s capacity is greater than

well inflow then the operational efficiency of the

G. Takacs (&)

University of Miskolc, Miskolc, Hungary


123


DOI 10.1007/s13202-011-0011-9

system cannot reach the designed levels; mechanical

damage may also occur.

• In case the well’s productivity is greater than the

capacity of the lifting system, one loses the profit of the

oil not produced.

Over-, and under-design of artificial lift installations

happens in the industry very often and professionals know

how to deal with them. Some lifting methods such as gas

lifting or sucker rod pumping are relatively easy to handle

since their lifting capacity can be adjusted in quite broad

ranges after installation. ESP installations, however, do not

tolerate design inaccuracies because any given ESP pump

can only be used in a specific, quite restricted range of

pumping rates. If used outside its recommended liquid rate

range, the hydraulic efficiency of the pump rapidly dete-

riorates; efficiencies can go down to almost zero. In addi-

tion to the loss of energy and the consequent decrease in

profitability the ESP system, when operated under such

conditions, soon develops mechanical problems that can

lead to a complete system failure. The usual outcome is a

workover job and the necessity of running a newly

designed ESP system with the proper lifting capacity.

One common solution for over-designed ESP systems is

the use of production chokes at the wellhead. Installation of

the choke, due to the high pressure drop that develops

through it, limits the well’s liquid rate so the ESP pump is

forced to operate in its recommended pumping rate range.

This solution eliminates the need for running a new ESP

system of the proper capacity into the well and saves the

costs of pulling and running operations. At the same time,

however, the system’s power efficiency decreases consid-

erably due to the high hydraulic losses occurring across the

surface choke.

The paper investigates the detrimental effects of surface

chokes on the power efficiency of ESP systems and dis-

cusses an alternative solution. The analysis is provided for

wells producing negligible amounts of free gas and is based

on the application of NODAL analysis principles to

describe the operation of the ESP system.

The effects of using wellhead chokes

Why use chokes

Most ESP installations are designed to operate using

electricity at a fixed frequency, usually 60 or 50 Hz. This

implies that the ESP pump runs at a constant speed and

develops different heads for different pumping rates as

predicted by its published performance curve. When

designing for a constant production rate, a pump type with

the desired rate inside of its recommended capacity range is

selected. The number of the required pump stages is

found from detailed calculations of the required total

dynamic head (TDH), i.e. the head required to lift well

fluids to the surface at the desired pumping rate. Thus, the

head versus capacity performance curve of the selected

pump can easily be plotted based on the performance of a

single stage.

For an ideal design when all the necessary parameters of

the well and the reservoir are perfectly known the pump

will produce exactly the design liquid rate since it will

work against the design TDH (1997; 2001; 2002). In this

case the head required to overcome the pressure losses

necessary to move well fluids to the separator is covered by

the head available from the pump at the given pumping

rate. This perfect situation, however, is seldom achieved;

very often inaccuracies or lack of information on well

inflow performance cause design errors and the well pro-

duces a rate different from the initial target.

The problem with the conventional design detailed

above is that the ESP installation is investigated for a single

design rate only and no information is available for cases

when well parameters are in doubt. All these problems are

easily solved if system (NODAL) analysis principles are

used to describe the operation of the production system

consisting of the well, the tubing, the ESP unit, and the

surface equipment. NODAL analysis permits the calcula-

tion of the necessary pump heads for different possible

pumping rates and the determination of the liquid rate

occurring in the total system, This will be the rate where

the required head to produce well fluids to the separator is

equal to the head developed by the ESP pump run in the

well.

Figure 1 shows a schematic comparison of the conven-

tional design with that provided by NODAL analysis.

Conventional design calculates the TDH at the design rate

only and selects the type of the ESP pump and the neces-

sary number of stages accordingly. After selecting the rest

of the equipment the ESP unit is run in the well and it is

only hoped that actual conditions were properly simulated

resulting in the well output being equal to the design liquid

rate. If well inflow performance data were uncertain or

partly/completely missing during the design phase then the

ESP system’s stabilized liquid rate is different from the

design target. NODAL calculations, however, can predict

the required head values for different liquid rates, shown in

Fig. 1 by the curve in dashed line. The well’s actual pro-

duction rate will be found where the required and the

available (provided by the pump) heads are equal, at

Point 1 in the figure.

In typical cases the actual liquid production rate is

greater than the target value. This clearly indicates inac-

curacies in the well performance data assumed during the

design process. Since the well’s required production is


123

usually dictated by reservoir engineering considerations

production of a greater rate is not allowed. The problem is

caused, as shown in Fig. 1, by the fact that the actual head

requirement (actual TDH) is much less than the calculated

design TDH.

The solution of the problem, if pulling the ESP equip-

ment and replacing it with a properly designed one is not

desired, is to place a production choke of the proper

diameter at the wellhead to restrict the liquid rate to the

design target. At this rate, however, the installed pump

develops the designed operating head as shown by Point 2.

Since the actual head required for lifting the well fluids to

the surface, as found from NODAL calculations, is less

than this value, a sufficient head loss across the choke is

needed. This head loss, found between Points 2 and 3 must

be sufficient to supplement the system’s actual TDH to

reach the TDH that was used for the original design. As a

result, the head requirement of the production system is

artificially increased and the ESP pump is forced to pro-

duce the desired liquid rate.

Estimating the energy loss across wellhead chokes

The detrimental effect of choking an ESP unit is clearly

indicated by the amount of power wasted through the

surface choke. This (in HP units) can be calculated from

the pumping rate and the amount of head loss across the

choke:

Pwasted ¼ 7:368� 10�6 ql DHchoke cl; ð1Þ

where ql is the pumping rate (bpd), DHchoke the head loss

across surface choke (ft), and cl is the specific gravity of the

produced liquid.

The above power, of course, must be supplied by the

electric motor to drive the submersible pump that is being

subjected to a higher than necessary load. Since this power

is wasted, the ESP system’s power efficiency as well as the

profitability of fluid production will decrease.

Calculation of the ESP pump’s required head

by NODAL methodology

Since choking of the ESP well at the wellhead is clearly

detrimental to the lifting performance, proper design and

installation of the ESP equipment is highly important. In

case sufficiently accurate inflow performance data are

available, the use of NODAL analysis techniques allows

for an accurate installation design and eliminates the need

for using wellhead chokes (Takacs 2009).

In order to apply systems (NODAL) analysis to the ESP

installation, the variation of flowing pressures in the well

should be analyzed first. Figure 2 depicts the pressures

along the well depth (a) in the tubing string, and (b) in the

casing-tubing annulus. The well is assumed to produce

incompressible liquids at a stabilized flow rate, found from

the well’s inflow performance relationship (IPR) curve.

From the depth of the perforations up to the setting depth of

the ESP pump, pressure in the casing changes according to

the flowing pressure gradient of the well fluid which is

approximated by the static liquid gradient. This assumption

is acceptable when medium flow rates are produced

through large casing sizes; otherwise, a pressure traverse

including all pressure losses should be calculated. The

calculated casing pressure at the pump setting depth is the

pump intake pressure (pintake).

Pump Capacity

Dev

elo

ped

Hea

d

60 Hz

65 Hz

55 Hz

50 Hz

45 Hz

40 Hz

1

2

3

Head Dropthru Choke

ActualTDH

DesignTDH

Required Head

Available Head

Fig. 1 Explanation of the need for a wellhead choke

Fig. 2 Pressure distributions in an ESP installation


123

At the depth of the pump discharge (which is practically

at the same depth as the intake), the pump develops a

pressure increase denoted as Dppump in the figure. The

pressure available at the ESP pump’s discharge, therefore,

can be calculated as follows:

pd ¼ pwf � Lperf � Lset

� �gradl þ Dppump; ð2Þ

where pwf is the flowing bottomhole pressure (psi), gradl

the liquid gradient (psi/ft), Dppump the pressure increase

developed by the pump (psi), Lset = pump setting depth

(ft), Lperf is the depth of perforations (ft).

Calculation of the pressure at the pump’s setting depth

required to produce the given rate is started from the sur-

face separator. The wellhead pressure pwh is found by

adding the flowing pressure losses in the flowline to the

separator pressure psep. For the single-phase liquid pro-

duction case studied in this paper, the pressure distribution

in the tubing string starts at the wellhead pressure and

changes linearly with tubing length. Tubing pressure has

two components: (1) the hydrostatic pressure, and (2) the

frictional pressure loss. By proper consideration of the

terms described we can define the required discharge

pressure of the ESP pump as follows:

p�d ¼ psep þ Dpfl þ Lsetgradl þ Dpfr; ð3Þ

where psep is the surface separator pressure (psi), Dpfl the

frictional pressure drop in the flowline (psi), Dpfr is the

frictional pressure drop in the tubing string (psi).

Since the available and the required pressures must be

equal at the ESP pump’s discharge, the simultaneous

solution of the two formulas results in the following

expression that describes the pressure increase to be

developed by the ESP pump:

Dppump ¼ psep þ Dpfl þ Lperfgradl þ Dpfr � pwf : ð4Þ

Since the ESP industry uses head instead of pressure, the

previous equation is divided by the liquid gradient to arrive

at the necessary head of the pump:

DHpump ¼ Lperf þ DHfl þ DHfr �2:3 1

cl

pwf � psep

� �; ð5Þ

where DHfl is the frictional head drop in the flowline (ft),

DHfr is the frictional head drop in the tubing string (ft).

The previous formula, if evaluated over an appropriate

range of liquid flow rates, represents the variation of the

necessary head that the pump must develop to produce the

possible liquid rates from the given well, see the curve in

dashed line in Fig. 1. For an accurate installation design the

ESP pump’s operating point must fall on this curve at its

intersection with the desired liquid rate. Based on this, the

required pump can be properly selected and no wellhead

choke will be needed to control the flow rate. This scenario,

of course, can only be followed if sufficiently accurate

inflow performance data on the given well are available.

Use of variable speed drive (VSD) units to eliminate

wellhead chokes

If, for any reason, the installation design is inaccurate and

the ESP system, after installation, produces a higher rate

than desired the use of wellhead chokes is a common

solution to control the well’s production. If a VSD is

available, however, the elimination of the choke and its

associated disadvantages can be accomplished (Divine

1979). As shown in Fig. 1, by reducing the electrical fre-

quency driving the ESP system to a level where the head

developed by the pump is equal to the head required to

produce the desired rate (Point 3) the choke is no more

needed to adjust the pumping rate.

When a VSD unit is used to control the ESP system’s

liquid rate the different components of the system behave

differently as the driving frequency is adjusted. The cen-

trifugal pump will develop different head values and will

need different brake horsepowers from the electric motor.

All these changes are described by the pump performance

curves valid at variable frequencies usually available from

manufacturers. In case such curves are missing, the Affinity

Laws (Takacs 2009; 1997) and the performance curves at a

constant frequency may be used to calculate the required

parameters at the reduced frequency: heads, efficiencies,

and brake horsepowers.

The performance parameters of the ESP motor at vari-

able frequency operation are described by two basic for-

mulae that express the change of (a) the nameplate voltage,

and (b) the power developed, both with the changes in the

electrical frequency. Actually, nameplate voltage of the

motor is adjusted by the surface VSD unit so that the

voltage-to-frequency ratio is kept constant. This is to

ensure that the motor becomes a constant-torque, variable

speed device. The applicable formula is the following:

U2 ¼ U1

f2f1

� �; ð6Þ

where f1, f2 are the AC frequencies (Hz), U1, U2 are the

output voltages at f1 and f2 (Hz, V).

The power developed by the ESP motor is linearly

proportional with the electrical frequency as shown by the

next formula:

HP2 ¼ HP1

f2f1

� �; ð7Þ

where f2, f1 are the AC frequencies (Hz), HP1, HP2 are the

motor powers available at f1 and f2 (Hz, HP).


123

As described previously, the use of a VSD unit sub-

stantially modifies the power conditions of the ESP pump

and the motor. In order to fully understand the changes and

to demonstrate the beneficial effects of removing wellhead

chokes the next section details the power conditions in the

ESP system.

Power conditions in ESP installations

Power flow in the ESP system

The ESP installation’s useful output work is done by the

centrifugal pump when it lifts a given amount of liquid

from the pump setting depth to the surface. This work is

described by the useful hydraulic power, Phydr, and can be

calculated from the power consumed for increasing the

potential energy of the liquid pumped. The following for-

mula, recommended by Lea et al. (1999), can be applied to

any artificial lift installation and gives a standardized way

to compare the effectiveness of different installations:

Phydr ¼ 1:7� 10�5ql 0:433clLpump � pintake

� �; ð8Þ

where Phydr is the hydraulic power used for fluid lifting

(HP), ql the liquid production rate (bpd), Lpump the pump

setting depth (ft) and pintake is the pump suction pressure,

called pump intake pressure (psi).

The total power consumed by the system comprises, in

addition to the energy required to lift well fluids to the

surface (i.e. the hydraulic power Phydr), all the energy

losses occurring in downhole and surface components.

Thus, the required electrical energy input at the surface is

always greater than the useful power; the relation of these

powers defines the ESP system’s power efficiency.

Classification of the energy losses in ESP systems can be

made according to the place where they occur; one can thus

distinguish between downhole and surface losses (Takacs

2010). Another way to group these losses is based on their

nature and categorizes them as hydraulic and electrical.

Energy losses in the ESP system

Hydraulic losses

The sources of energy losses of hydraulic nature are the

tubing string, the backpressure acting on the well, the ESP

pump, and the optional rotary gas separator.

Tubing losses Flow of the produced fluids to the surface

involves frictional pressure losses in the tubing string; the

power wasted on this reduces the effectiveness of the ESP

installation. In case a single-phase liquid is produced, the

frictional loss in the tubing string is determined from the

total head loss, DHfr, usually taken from charts or appro-

priate calculation models. The power lost, DPfr in HP units,

is found from the following formula:

DPfr ¼ 7:368� 10�6qlDHfrcl; ð9Þ

where DHfr is the frictional head loss in the tubing (ft).

Backpressure losses The ESP unit has to work against the

well’s surface wellhead pressure and the power consumed

by overcoming this backpressure is not included in the

useful power. The necessary power to overcome the well-

head pressure (in HP units) is found from:

DPbp ¼ 1:7� 10�5qlpwh; ð10Þ

where ql is the liquid production rate (bpd) and pwh is the

wellhead pressure (psi).

Pump losses Energy losses in the ESP pump are mostly

of hydraulic nature, and are represented by published pump

efficiency curves. In most cases the pump efficiencies, as

given by the manufacturer, include the effect of the addi-

tional power required to drive the ESP unit’s protector.

Based on the actual pump efficiency, the power lost in the

pump (in HP units) is easily found:

DPpump ¼ BHP 1�gpump

100

� �; ð11Þ

where BHP is the pump’s required brake horsepower (HP)

and gpump is the published pump efficiency (%).

Electrical losses

Electrical power losses in the ESP installation occur,

starting from the motor and proceeding upward, in the ESP

motor, in the power cable, and in the surface equipment.

Motor losses The ESP motor converts the electrical energy

input at its terminals into mechanical work output at its shaft;

the energy conversion is characterized by the motor effi-

ciency. Based on published efficiency values, the power lost

in the ESP motor (in HP units) is calculated as follows:

DPmotor ¼ HPnpLoad 1� gmotor

100

� �; ð12Þ

where HPnp is the motor’s nameplate power (HP), Load is

the motor loading, fraction, and gmotor is the motor effi-

ciency at the given loading (%).

Cable losses Since the ESP motor is connected to the

power supply through a long power cable, a considerable

voltage drop occurs across this cable. The voltage drop

creates a power loss proportional to the square of the

current flowing through the system, as given here in kW

units:


123

DPcable ¼3I2RT

1; 000; ð13Þ

where I is the required motor current (Amps) and RT is the

resistance of the power cable at well temperature (Ohms).

Surface electrical losses The ESP installation’s surface

components are very efficient to transmit the required

electric power to the downhole unit, their usual efficiencies

are around gsurf = 0.97. The energy wasted in surface

equipment can thus be found from:

DPsurf ¼ P1� gsurfð Þ

gsurf

; ð14Þ

where P is the sum of the hydraulic power and the power

losses, and gsurf is the power efficiency of the surface

equipment.

Example problem

In the following, a detailed calculation model is proposed

and illustrated through an example well. Energy flow in the

ESP system is determined for current conditions when a

surface choke is used to control the well’s liquid flow rate.

Then the use of a VSD unit is investigated and the required

operational frequency is determined; the energy conditions

of the modified installation are compared to the original

case.

Well data

Production data of an example well are given in Table 1.

Common calculations

First calculate those parameters that are identical for the

original, choked conditions and for the case without the

choke.

The flowing bottomhole pressure from the Productivity

Index formula is found as:

pwf ¼ pws � q=PI ¼ 1; 527� 2; 600=15:4 ¼ 1; 358 psi:

Now the pump intake pressure is calculated:

pintake ¼ pwf � 0:433cl Lperf � Lpump

� �¼ 1; 358� 0:433 0:876 4; 070� 2; 965ð Þ ¼ 939 psi:

Knowledge of these parameters permits the calculation

of the system’s useful hydraulic power from Eq. 8

Phydr ¼ 1:7 E� 5 Q ð0:433clLpump � pintakeÞ¼ 1:7E� 5 2; 600 0:433 0:876 2; 965� 939ð Þ¼ 8:2 HP ¼ 6:1 kW:

At pump suction conditions there is no free gas present,

as can be found from the Standing correlation; the oil’s

volume factor at the same pressure is found as

Bo = 1.115 bbl/STB. The total liquid volume to be

handled by the ESP pump is thus:

ql ¼ 2; 600 1:115 ¼ 2; 900 bpd; or 461m3=day:

In order to find the frictional head loss due to the flow of

the current liquid rate through the well tubing the Hazen-

Williams formula or the use of the proper graph gives a

head loss of 42 ft/1,000 ft of pipe. The total head loss in

the tubing is thus:

DHfr ¼ 42 2; 965=1; 000 ¼ 124 ft:

The energy loss corresponding to tubing frictional losses

can be calculated from Eq. 9:

DPfr ¼ 7:368E� 6 QDHfrcl

¼ 7:368E� 6 2; 600 124 0:876 ¼ 2:1 HP ¼ 1:5 kW:

Energy conditions of the current installation

This section contains calculations for the original, choked

condition and evaluates the energy conditions of the cur-

rent ESP installation.

Table 1 Production and ESP

dataWell data ESP installation data

Depth of perforations 4,070 ft Pump setting depth 2,965 ft

Tubing size 3 � in. ESP pump type GN4000

Static bottomhole pressure 1,527 psi Number of stages 99

Productivity index 15.4 bpd/psi Electrical frequency 50 Hz

Production GOR 82 scf/STB Motor NP power 104.2 HP

Production data Motor NP voltage 1,095 V

Liquid rate 2,600 STB/day Motor NP current 60 Amps

Water cut 0% ESP cable size AWG 2

Producing wellhead pressure 745 psi

Pressure downstream of choke 130 psi


123

The hydraulic losses due to the backpressure at the

wellhead pressure of 745 psi are calculated from Eq. 10 as

follows:

DPbp ¼ 1:7E� 5 Q pwh ¼ 1:7E� 5 2; 600 745 ¼ 33 HP

¼ 25 kW:

From the performance curve of the GN4000 pump

operated at 50 Hz, the following parameters of the pump

are found at the current liquid rate of 461 m3/day:

HBP=Stage ¼ 0:84 HP:

Pump efficiency ¼ 66%:

Since there are 99 stages in the pump, the pump’s power

requirement is:

99 0:84 cl ¼ 99 0:84 0:876 ¼ 73 BHP:

Based on these parameters the power lost in the pump

can be calculated from Eq. 11:

DPpump ¼ 73 1� 66=100ð Þ ¼ 24:8 HP ¼ 18:5 kW:

The existing ESP motor’s rated power (see input data)

being 104.2 HP, the motor is only 70% loaded by the pump

power of 73 BHP. From motor performance data, motor

efficiency at that loading is 89%. Now the power loss in the

electric motor can be found from Eq. 12:

DPmotor ¼ 104:2 0:70 1� 89=100ð Þ ¼ 8 HP ¼ 6 kW:

In order to find the electrical losses in the downhole

cable, first the resistance of the well cable has to be found.

The installation uses an AWG 2 size electrical cable with

an electrical resistance of 0.17 Ohm/1,000 ft. The total

resistance of the downhole cable, considering well

temperature, is found as 0.658 Ohms.

The actual current flowing through the cable is equal to

the motor current found from the motor load and the

nameplate current as:

I ¼ 0:70 Inp ¼ 0:70 60 ¼ 42 Amps:

Now the electrical power lost in the cable is calculated

from the basic 3-Phase power formula (Eq. 13):

DPcable ¼ 3 I2R=1; 000 ¼ 3 4220:658=1; 000 ¼ 3:5 kW:

Finally, the power lost in the ESP system’s surface

components is to be found from Eq 14 with a surface

efficiency of 97%.

DPsurf ¼ ðPhydr þ DPfr þ DPbp þ DPpump þ DPmotor

þ DPcableÞ 1� 0:97ð Þ=0:97

¼ 1:9 kW:

Energy conditions of the modified installation

This section presents the calculations required to describe

the conditions when a VSD unit is used to control the

pumping rate instead of choking the well.

In this case the operating wellhead pressure is reduced to

the flowline intake pressure; this was measured downstream

of the wellhead choke as 130 psi. The hydraulic losses due to

the backpressure are calculated from Eq. 10 as follows:

DPbp ¼ 1:7E� 5 Q pwh ¼ 1:7E� 5 2; 600 130 ¼ 6 HP

¼ 4:4 kW:

Next the required electrical frequency is calculated

using the head performance curve of the pump for multiple

frequencies. Since the current case uses 50 Hz, metric

performance curves have to be used.

• The head developed by the pump at 50 Hz operation is

found at the current liquid rate of 461 m3/day and is

designated as Point 1.

• The head drop across the wellhead choke, corrected for

one stage, is calculated in metric units:

Drop ¼ 0:3048 2:3 pwh � Pdownstreamð Þ=cl=no: of stages

¼ 0:3048 2:3 745� 130ð Þ=0:876=99 ¼ 5 m:

• From Point 1, a vertical is dropped by the calculated

distance of 5 m; this defines Point 2.

• The frequency valid at Point 2 is read; this should be

used on the VSD unit to drive the ESP motor.

The process described here resulted in a required fre-

quency of 37 Hz for the example case.

Next the operational parameters of the GN4000 pump at

37 Hz service have to be determined. Since detailed per-

formance curves for this frequency are not available, the

use of published 50 Hz curves and the Affinity Laws is

required.

The required rate of 461 m3/day at 37 Hz operation

corresponds to the following rate at 50 Hz, as found from

the Affinity Laws:

Rate ¼ 461 50=37 ¼ 623 m3=day:

The power requirement and the efficiency of the pump

at this rate at 50 Hz operation are read from the 50 Hz

performance curves as:

BHP=stage ¼ 0:83 HP=stage; and

Pump efficiency ¼ 65%:

From these data and using the Affinity Laws again, the

power requirement of the pump at 37 Hz operation is

calculated:

BHP=stage ¼ 0:83 37=50ð Þ3¼ 0:34 HP=stage:

The efficiency of the pump remains at 65%.

Now the power needed to drive the 99 pump stages at an

electrical frequency of 37 Hz has decreased to:

99 0:34cl ¼ 99 0:34 0:876 ¼ 29 HP:


123

Based on these parameters the power lost in the pump

can be calculated as (Eq. 11):

DPpump ¼ 29 1� 65=100ð Þ ¼ 10:2 HP ¼ 7:6 kW:

The operating conditions of the ESP motor change at the

modified frequency. Its nameplate power decreases from

that at 50 Hz according to Eq. 7:

Pnp ¼ 104:2 37=50ð Þ ¼ 77 HP:

Motor voltage is adjusted by the VSD unit from the

nameplate value valid at 50 Hz to the following voltage,

according to Eq. 6:

Umotor ¼ 1; 095 27=50ð Þ ¼ 810 V:

The ESP motor’s loading is found from the pump power

requirement and the modified motor power:

Loading ¼ 29=77 ¼ 38%:

The efficiency of the motor at this loading is 87%, as

found from motor performance curves. The power loss in

the electric motor can now be found from Eq. 12:

DPmotor ¼ 77 0:38 1� 87=100ð Þ ¼ 3:9 HP ¼ 2:9 kW:

When finding the electrical losses in the downhole cable,

the resistance of the cable is identical to the previous case at

0.658 Ohms. Since the nameplate current of the ESP motor at

the new frequency does not change the actual motor current is

found from the motor load and nameplate current as:

I ¼ 0:38 Inp ¼ 0:38 60 ¼ 23 Amps:

The power loss in the cable is calculated from Eq. 13:

DPcable ¼ 3 I2R=1; 000 ¼ 3 2320:658=1; 000 ¼ 1 kW:

Finally, the power lost in the ESP system’s surface

components is to be found from Eq. 14 with a surface

efficiency of 97%:

DPsurf ¼ ðPhydr þ DPfr þ DPbp þ DPpump þ DPmotor

þ DPcableÞ 1� 0:97ð Þ=0:97

¼ 0:7 kW:

Final results

Table 2 summarizes the energy conditions of the two cases.

As seen, the use of a VSD unit has increased the system

efficiency to more than twofold and system power

decreased to less than 40% of the original requirement.

Application to a group of wells

In order to evaluate the model proposed in the paper for

increasing the efficiency of ESP wells on surface choke

control, calculations were performed using the data of

several wells from the same field. The wells produced

API 40 gravity oil with low water cuts from relatively

shallow depths. Original installation designs were far from

ideal and most wells had downhole equipment capable of

Table 2 Energy conditions of the two cases

Component 50 Hz case 37 Hz case

Useful hydraulic power (kW) 6.1 6.1

Wellhead loss (kW) 25.0 4.4

Tubing friction (kW) 1.5 1.5

ESP pump losses (kW) 18.5 7.6

ESP motor losses (kW) 6.0 2.9

ESP cable losses (kW) 3.5 1.0

Surface losses (kW) 1.9 0.7

Total (kW) 61.5 24.2

System efficiency (%) 10 25.2

Table 3 Comparison of original and modified cases for an example field

Well no. Liquid rate pwh (psi) Line Pr. (psi) Original Modified

STB/day bpd Power (kW) Eff. (%) Freq. (Hz) Power (kW) Eff. (%)

1 1,444 1,629 805 165 53.8 3 33 13.1 12.1

2 2,000 2,132 960 120 62.7 3 31 13.5 13.7

3 1,700 1,824 700 100 57.1 6.9 38 21.6 18.3

4 3,000 3,340 920 100 73.7 9 33 26.2 25.4

5 3,000 3,340 1,180 120 73.7 9 33 26.2 25.4

6 2,600 2,900 745 130 61.5 9.9 37 24.2 25.2

7 2,400 2,642 700 150 57.3 4.6 39 23.2 11.3

8 2,700 3,007 670 175 59.9 8.1 35 25.1 19.4

9 1,600 1,749 860 120 55.4 2.5 33 13 10.7

10 1,600 1,761 540 100 50.7 7.4 41 24.9 15.0

Total power (kW) 605.8 211.0


123

much higher production rates than those permitted by

reservoir engineering management and had to be choked

back. This is the reason why wellhead pressures are much

higher than the required line pressure in the gathering

system.

The most important input and calculated data are given

in Table 3. Most of the wells indicate quite high pressure

drops across the wellhead chokes that obviously involve

lots of energy wasted in the ESP system. The surface power

requirements for the original cases, of course, include these

wasted power components and the overall system effi-

ciencies are accordingly very low.

After re-designing the installations according to the

procedure proposed in this paper, application of VSD

units was assumed and the required operational fre-

quencies were determined. The modified cases, as seen

in Table 3, have much lower total energy requirements

mainly due to the removal of the wellhead choke’

harmful effect; overall system efficiencies have substan-

tially increased.

Total electrical power requirement of the well group

investigated has decreased to almost one-third of the ori-

ginal, from 606 to 211 kW. This clearly proves that using

VSDs to control the production rate of ESP wells is a much

superior solution to wellhead choking adopted in field

practice.

Conclusions

The paper investigates the power conditions of ESP

installations where the pumping rate of oversized ESP units

is reduced by placing chokes on the wellhead. Power flow

in the system with the description of possible energy losses

is presented and system efficiency is evaluated. In order to

reduce the harmful effects of wellhead chokes on system

efficiency NODAL analysis principles are used to describe

the operation of the ESP system. A detailed calculation

method is developed and example cases are presented to

find the proper frequency setting of a VSD unit to be used.

Main conclusions derived are as follows.

• The practice of controlling the pumping rate of ESP

installations by wellhead chokes can very substantially

reduce the energy efficiency of the system.

• NODAL analysis can be used to properly design an

ESP installation and/or rectify the situation without a

need to change downhole equipment.

• The proposed calculation model provides a much more

energy-efficient solution to production rate control

using VSD units.

• Several field examples are shown to prove that very

substantial energy savings can be realized by following

the proposed model.

Acknowledgments This work was carried out as part of the

TAMOP-4.2.1.B-10/2/KONV-2010-0001 project in the framework of

the New Hungarian Development Plan. The realization of this project

is supported by the European Union, co-financed by the European

Social Fund.





References

Submersible pump handbook (1997) 6th edn. Centrilift-Hughes Inc.,

Claremore

The 9 step (2001) Baker-Hughes Centrilift, Claremore

Recommended practice for sizing and selection of electric submer-

sible pump installations (2002) API RP 11S4, 3rd edn. American

Petroleum Institute

Brown KE (1980) The technology of artificial lift methods, vol 2b.

PennWell Books, Tulsa

Divine DL (1979) A variable speed submersible pumping system. In:

Paper SPE 8241 presented at the 54th annual technical confer-

ence and exhibition held in Las Vegas, September 23–26

Lea JF, Rowlan L, McCoy J (1999) Artificial lift power efficiency. In:

Proceedings of 46th Annual Southwestern Petroleum Short

Course, Lubbock, pp 52–63

Takacs G (2009) Electrical submersible pumps manual. Gulf Profes-

sional Publishing, USA

Takacs G (2010) Ways to obtain optimum power efficiency of

artificial lift installations. In: Paper SPE 126544 presented at the

SPE oil and gas India conference and exhibition held in Mumbai,

20–22 January


123


Prediction of asphaltene precipitation using artificial neuralnetwork optimized by imperialist competitive algorithm

Mohammad Ali Ahmadi

Received: 23 August 2011 / Accepted: 17 October 2011 / Published online: 1 November 2011


Abstract One of the most important phenomena in petro-

leum industry is the precipitation of heavy organic materials

such as asphaltene in oil reservoirs, which can cause diffu-

sivity reduction and wettability alteration in reservoir rock

and finally affect oil production and economical efficiency.

In this work, the model based on a feed-forward artificial

neural network (ANN) optimized by imperialist competitive

algorithm (ICA) to predict of asphaltene precipitation is

proposed. ICA is used to decide the initial weights of the

neural network. The ICA–ANN model is applied to the

experimental data reported in the literature. The performance

of the ICA–ANN model is compared with Scaling model and

conventional ANN model. The results demonstrate the

effectiveness of the ICA–ANN model.

Keywords Asphaltene � Precipitation � Artificial neural

network � Imperialist competitive algorithm � Prediction

List of symbols

R Solvent to oil ratio (g/mol)

M Molecular weight (g/mol)

W Amount of precipitated asphaltene (weight percent)

Y Function defined by Eq. 1

X Function defined by Eq. 2

x Function defined by Eq. 4

y Function defined by Eq. 5

ANN Artificial neural network

PSO Particle swarm optimization

ICA Imperialist competitive algorithm

Introduction

The precipitation and deposition of crude oil polar fractions

such as asphaltenes in petroleum reservoirs reduce consid-

erably the rock permeability and the oil recovery. So, many

researchers studied this important subject. They introduced

experimental procedures or even analytical models, but a

fully satisfactory interpretation is still lacking. The avail-

able models for description of asphaltene precipitation are

divided into two general groups. The first group consists of

thermodynamic models, which need asphaltene properties

such as density, molecular weight and solubility parameter

for prediction of asphaltene phase behavior. All those

models consider asphaltene as a pure pseudo-component,

but this assumption causes much deviation in the prediction

of asphaltene phase behavior (Pedersen et al. 1989); the

second group of models is based on the scaling approach

which explained separately. In this paper, the ability of the

artificial intelligence in establishing and predicting amount

of asphaltene precipitation is to be investigated. Artificial

intelligence have been widely used and are gaining atten-

tion in petroleum engineering because of their ability to

solve problems that previously were difficult or even

impossible to solve. One example of ability neural network

in well-log analysis. This technique has been increasingly

applied to predict reservoir properties using well-log data

(Doveton and Prensky 1992; Balan et al. 1995).

A soft sensor is a conceptual device whose output or

inferred variable can be modeled in terms of other

parameters that are relevant to the same process (Rallo

et al. 2002). According to Rallo et al. (2002), artificial

M. A. Ahmadi (&)

Department of Petroleum Engineering,

Ahwaz Faculty of Petroleum Engineering,

Petroleum University of Technology,

Kut Abdollah, Ahwaz, Iran

e-mail: [email protected];

[email protected]

123


DOI 10.1007/s13202-011-0013-7

neural network (ANN) could be used as soft sensor

building approach.

The determination of network structure and parameters

is very important; some evolutionary algorithms such as

genetic algorithm (GA) (Qu1 et al. 2008), back propagation

(BP) (Tang and Xi 2008), pruning algorithm (Reed 1993),

simulated annealing (de Souto et al. 2002) can be used for

this determination. Recently, a new evolutionary algorithm

has been proposed by Atashpaz-Gargari and Lucas (2007)

which has inspired from a socio-political evolution, called

imperialist competitive algorithm (ICA).

In the present work, we propose ICA for optimizing the

weights of feed-forward neural network. Then simulation

results demonstrate the effectiveness and potential of the

new proposed network for asphaltene precipitation pre-

diction compared with scaling model (Hu and Guo 2001)

using the same data.

Scaling model

The three variables involved in the scaling equation are the

weight percent of precipitated Asphaltenes, W (based on the

weight of feed oil), the dilution ratio, R (defined as the ratio

of injected solvent volume to weight of crude oil), and the

molecular weight of solvent, M. Rassamdana et al. (1996)

combined the three variables into two (X, Y) as follows:

X ¼ R

MZð1Þ

Y ¼ W

RZ0 ð2Þ

Z and Z0 are two adjustable parameters and must be

carefully tuned to obtain the best scaling fit of the

experimental data. They suggested Z0 is a universal constant

of -2 and Z = 0.25 regardless of oil and precipitant used. The

proposed scaling equation is expressed in terms of X and Y

through a third-order polynomial function

Y ¼ A1 þ A2X þ A3X2 þ A4X3 X [ Xcð Þ ð3Þ

where Xc is the value of X at the onset of asphaltene

precipitation.

Hu et al. (2000) performed a detailed study on the

application of scaling equation proposed by Rassamdana

et al. (1996) for asphaltene precipitation. They examined

the universality of exponents Z and Z0 and found that Z0 is a

universal constant (Z0 = -2) while exponent Z depends on

the oil composition and independent of specific precipitant

(n-alkane) used. For the experimental data used, they found

also that the optimum value of Z is generally within the

range of 0.1 \ Z \ 0.5.

Despite the simplicity and accuracy of the scaling equa-

tion mentioned above, it is restricted to use at a constant

temperature and since temperature is not involved in the

scaling equation as a variable, it is not adequate for corre-

lating and predicting the asphaltene precipitation data

measured at different temperatures. Due to this issue, Ras-

samdana et al. modified their scaling equation by implanting

temperature parameter in the scaling equation. Based on the

previous equation, they defined two new variables x and y:

x ¼ X=TC1 ð4Þ

y ¼ Y=XC2 ð5Þ

in which X and Y are variables defined as in Eqs. (1) and (2)

and constant C1 and C2 are adjustable parameters. They

reported that the good fit of their experimental data can be

achieved by setting C1 = 0.25 and C2 = 1.6.

Again the new scaling equation is a third-order poly-

nomial in general form of:

y ¼ b1 þ b2xþ b3x2 þ b4x3 x [ xcð Þ ð6Þ

Hu et al. (2001) studied the effects of temperature,

molecular weight of n-alkane precipitants and dilution ratio

on asphaltene precipitation in a Chinese crude oil

experimentally. The amounts of asphaltene precipitation at

four temperatures in the range of 293–338 K were measured

using seven n-alkanes as precipitants. They found that their

experimental data could not be well correlated by setting

C1 = 0.25 and C2 = 1.6 as recommended by Rassamdana

et al. (1996). They reported that their experimental data

could be correlated successfully by choosing C1 = 0.5 and

C2 = 1.6. Regression plot of predicted asphaltene

precipitation using scaling model (Hu and Guo 2001)

against experimental data is shown in Fig. 1.

Artificial neural networks

Artificial neural networks are parallel information pro-

cessing methods which can express complex and nonlinear

relationship use number of input–output training patterns

from the experimental data. ANNs provides a non-linear

mapping between inputs and outputs by its intrinsic ability

(Hornik et al. 1990).

Fig. 1 Movement of colonies toward their relevant imperialist


123

The most common neural network architecture is the

feed-forward neural network. Feed-forward network is the

network structure in which the information or signals will

propagate only in one direction, from input to output. A

three layered feed-forward neural network with back

propagation algorithm can approximate any nonlinear

continuous function to an arbitrary accuracy (Brown and

Harris 1994; Hornick et al. 1989).

The network is trained by performing optimization of

weights for each node interconnection and bias terms until

the output values at the output layer neurons are as close as

possible to the actual outputs. The mean squared error of

the network (MSE) is defined as:

MSE ¼ 1

2

XG

k¼1

Xm

j¼1

YjðkÞ � TjðkÞ� �2 ð7Þ

where m is the number of output nodes, G is the number of

training samples, YjðkÞ is the expected output, and TjðkÞ is

the actual output. The data are split into two sets: a training

data set and a validating data set. The model is produced

using only the training data. The validating data are used to

estimate the accuracy of the model performance.

Imperialist competitive algorithm

The ICA is a new evolutionary algorithm in the evolu-

tionary computation field based on the human’s socio-

political evolution (Atashpaz-Gargari and Lucas 2007).

Like other evolutionary algorithms, the ICA starts with

initial populations called countries. There are two types of

countries: colony and imperialist (in optimization termi-

nology, countries with the least cost) which together form

empires. In the imperialistic competition process, imperi-

alists try to attempt to achieve more colonies. So during the

competition, the powerful imperialists will be increased in

the power and the weak ones will be decreased in the

power. When an empire loses all of its colonies, it is

assumed to be collapsed. At the end, the most powerful

imperialist will remain in the world and all the countries

are colonies of this unique of this empire. In this stage,

imperialist and colonies have the same position and power.

The implementation procedures of our proposed

matching strategy based on ICA are described as follows.

Generating initial empire

A country formed as an array of variable values to be

optimized. In a Nvar dimensional optimization problem, this

array defined by:

Country ¼ P1;P2;P3; . . .;PNvar½ � ð8Þ

The cost of a country is found by evaluating the cost

function f :

Cost ¼ f countryð Þ ¼ f ð½P1;P2;P3; . . .;PNvar�Þ ð9Þ

The algorithm starts with the number of initial countries

(Ncountry), number of imperialist (Nimp) and number of the

remaining country are colonies that each belongs to an

empire (Ncol) the initial number of colonies of an empire in

convenience with their powers. To divide the colonies

among imperialists proportionally, the normalized cost of

an imperialist is defined by:

Cn ¼ cn �maxifcig ð10Þ

where cn is the cost of nth imperialist and Cn is its

normalized cost. Having the normalized cost of all

imperialist, the power of each imperialist is calculated by:

Pn ¼CnPNimp

i¼1 Ci

�� ð11Þ

In the other hand, the normalized power of an

imperialist is determined by its colonies. Then, the initial

number of an imperialist will be:

NCn ¼ roundfPn � Ncolg ð12Þ

where NCn is the initial number of colonies of nth empire

and Ncol is the number of all colonies. To divide the col-

onies among imperialists, NCn of the colonies is selected

randomly and assigned them to each imperialist. The col-

onies together with the imperialist form the nth empire.

Moving colonies of an empire toward the imperialist

The imperialist countries try to improve their colonies and

make them a part of themselves. This fact is modeled by

moving all colonies toward their relevant imperialist. Fig-

ure 1 (Atashpaz-Gargari and Lucas 2007) shows this move-

ment. In this figure, the colony moves toward the imperialist

by x (is a random variable with uniform distribution) units.

x�Uð0; b� dÞ ð13Þ

where b is a number greater than 1 and d is the distance

between a colony and an imperialist. In the moving pro-

cess, a colony may reach a position with lower cost than

that of its imperialist. In this case, the imperialist and the

colony change their positions. Then, the algorithm will

continue by the imperialist in the new position and then

colonies start moving toward this position.

The total power of an empire

The total power of an empire depends on both the power of

the imperialist country and the power of its colonies. This

fact is modelled by defining the total cost by:


123

TCn ¼ Cost imperialistnð Þþ nmeanfcostðcolonies of impirenÞg ð14Þ

where TCn is the total cost of then th empire, and n is a

positive number which is considered to be less than 1. A

small value for n implies that the total power of an empire

to be determined by just the imperialist and increasing it

will increase the role of the colonies in determining the

total power of an empire. The value of 0.1 for n is a proper

value in most of the implementations.

Imperialistic competition

All empires try to take the possession of colonies of other

empires and control them. The imperialistic competition

gradually brings about a decrease in the power of weaker

empires and an increase in the power of more powerful

ones. This competition is modelled by just picking some

Table 1 Compositions (mol%) and properties of the degassed Cao-

qiao crude oil and separator gas

Component Degassed oil Separator gas

CO2 0.0 2.96

N2 0.0 1.18

C1 0.0 89.37

C2 0.0 3.34

C3 0.0 2.10

i-C4 0.0 0.32

n-C4 0.0 0.26

i-C5 0.16 0.22

n-C5 0.58 0.15

n-C6 1.2 0.12

C7? 98.06

C11? 87.16

C7? molecular weight (g/mol) 503.6

C7? density (at 293 K) 0.9526

Reservoir temperature 343

Bubble point pressure at 343 K (MPa) 9.8

Gas oil ratio (GOR, m3/m3) 30.2

Saturates (wt%) 38.0

Aromatics (wt%) 47.6

n-C5 asphaltenes (wt%) 7.26

Resins (wt%) 18.6

Table 2 Comparison between the performances of ICA–ANN and

scaling model

ICA–ANN ANN Scaling

MSE 0.0032749 0.83759 0.69396

R2 0.99367 0.95586 0.96413

Fig. 2 Regression plot of prediction by scaling equation (Hu and

Guo 2001)

(a)

(b)

20 40 60 80 100 120-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Training Data

time (samples)

5 10 15 20 25 30 35 40 45 50 55 60-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1Testing Data

time (samples)

Fig. 3 Comparison between measured and predicted asphaltene

precipitation (ICA-ANN): a training, b test


123

(usually one) of the weakest colonies of the weakest

empires and making a competition among all empires to

possess this colonies.

To start the competition, first, the possession probability

of each empire is found based on its total power. The

normalized total cost is obtained by:

NTCn ¼ TCn �maxifTCig ð15Þ

where, TCn and NTCn are the total cost and the normalized

total cost of nth empire, respectively. Having the

normalized total cost, the possession probability of each

empire is given by:

10-5

100

105

grad

ient

Gradient = 0.005049, at epoch 19

10-4

10-3

10-2

mu

Mu = 0.001, at epoch 19

0 2 4 6 8 10 12 14 16 180

5

10

val f

ail

19 Epochs

Validation Checks = 6, at epoch 19

Fig. 4 Training state plot of

ICA-ANN

10-5

100

105

grad

ient

Gradient = 0.85593, at epoch 50

10-4

10-2

100

mu

Mu = 0.001, at epoch 50

0 5 10 15 20 25 30 35 40 45 500

5

10

val f

ail

50 Epochs

Validation Checks = 6, at epoch 50

Fig. 5 Training state plot of

ANN


123

PPn¼ NTCnPNimp

i¼1 NTCi

�� ð16Þ

To divide the mentioned colonies among empires,

vector P is formed as

P ¼ PP1;PP2

;PP3; . . .;PPNimp

h ið17Þ

Then the vector R with the same size as P whose

elements are uniformly distributed random numbers is

created,

R ¼ r1; r2; r3; . . .rNimp

� �ð18Þ

Then vector D is formed by subtracting R from P

D ¼ P� R ¼ D1;D2;D3; . . .;DNimp

� �ð19Þ

Referring to vector D, the mentioned colony (colonies)

is handed to an empire whose relevant index in D is

maximized.

Powerless empire will collapse in the imperialistic

competition and their colonies will be divided among other

empires. At the end, all the empires except the most

powerful one will collapse and all the colonies will be

under the control of this unique empire. In this stage,

imperialist and colonies have the same position and power.


In this study, an ANN was used to build a model to predict

asphaltene precipitation using the data reported in literature

Fig. 6 Regression plot of ICA-

ANN


123

(Hu and Guo 2001). The best ANN architecture was: 3-4-

10-1 (3 input units, 4 hidden neurons in first layer, 10

hidden neurons in second layer, 1 output neuron). ANN

model trained with back propagation network was trained

by Levenberg–Marquardt using three parameters: (1)

molecular weight, (2) dilution ratio, and (3) temperature as

inputs. The transfer functions in hidden and output layer

are sigmoid and linear, respectively. Physical and ther-

modynamic properties of oil used for generating experi-

mental data by Hu and Guo (2001) are shown in Table 1.

ICA is used as neural network optimization algorithm

and the MSE used as a cost function in this algorithm. The

goal in proposed algorithm is minimizing this cost func-

tion. Every weight in the network is initially set in the

range of [-1, 1]. In these simulations, the number of

imperialists and the colonies is considered 4 and 40,

respectively; parameter b is set to 2. The number of

training and testing data is 130 and 60, respectively.

0 2 4 60

1

2

3

4

5

6

Experimental

AN

N O

utpu

t

Training: R2=0.90418

Data

FitY = T

0 2 4 60

1

2

3

4

5

6

7

Experimental

AN

N O

utpu

t

Validation: R2=0.93718

Data

FitY = T

0 2 4 60

1

2

3

4

5

6

Experimental

AN

N O

utpu

t

Test: R2=0.95586

Data

FitY = T

0 2 4 60

1

2

3

4

5

6

7

Experimental

AN

N O

utpu

t

All: R2=0.92419

Data

FitY = T

Fig. 7 Regression plot of ANN

0 2 4 6 8 10 12 14 16 1810

-4

10-3

10-2

10-1

100

101

Best Validation Performance is 0.0032749 at epoch 13

Mea

n S

quar

ed E

rror

(m

se)

19 Epochs

TrainValidationTestBest

Fig. 8 Performance plot of ICA-ANN


123

The simulation performance of the ICA–ANN model

and ANN model were evaluated on the basis of MSE and

efficiency coefficient R2. Table 2 gives the MSE and R2

values for the three different models of the validation

phases. Prediction of asphaltene precipitation by scaling

model is shown in Fig. 2 and prediction of asphaltene

precipitation in the training and test phase is shown in

Fig. 3. The simulation performance of the ICA–ANN

model and ANN model were evaluated on the basis of

MSE and efficiency coefficient R2. Table 2 gives the MSE

and R2 values for three different models of the validation

phases. Training state and regression plot and performance

of ICA–ANN and ANN models are shown in Figs. 4, 5, 6,

7, 8 and 9, respectively. It can be observed that the per-

formance of ICA–ANN model is better than scaling model

and ANN model.

Conclusions

The idea of ICA algorithm is that each initial point of the

neural network is selected by ICA and the fitness of the

ICA is determined by a neural network. The experiment

with experimental data reported in literature (Hu and Guo

2001) has showed that the ICA–ANN model is successfully

demonstrated on prediction of asphaltene precipitation also

predictive performance of the proposed model is better

than that of scaling model (Hu and Guo 2001) and con-

ventional ANN model. One problem when considering the

combination of neural network and ICA for prediction of

asphaltene precipitation is the determination of the optimal

neural network structure. Proposed neural network struc-

ture described in this work is determined manually.

A substitute method is to apply the ICA or another evo-

lutionary algorithm for neural network structure optimiza-

tion, which will be a part of our future work. The proposed

asphaltene precipitation prediction model may be com-

bined with existing asphaltene precipitation modeling

softwares to speed up their performance, reduce the

uncertainty and increase their prediction and modeling

capabilities.





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0 5 10 15 20 25 30 35 40 45 5010

-1

100

101

102Best Validation Performance is 0.83759 at epoch 44

Mea

n S

quar

ed E

rror

(m

se)

50 Epochs

TrainValidationTestBest

Fig. 9 Performance plot of ANN


123

SHORT COMMUNICATION - PRODUCTION ENGINEERING

Experimental setup for performance characterization of a jetpump with varying angles of placement and depth

Rit Nanda • Shashank Gupta • Ajit Kumar N Shukla

Received: 5 August 2011 / Accepted: 18 September 2011 / Published online: 5 October 2011


Abstract In an oil field, when the crude cannot come to

the surface on its own due to either low pressure differ-

ential or the fluid properties like high viscosity, artificial

lift technology has to be used. The jet pump is one of the

artificial lift techniques considered to be better than other

lift systems because of no moving parts and simple

working principle. This makes it easy to monitor and

regulate. It works on the fluid power hence it can be placed

at greater depths and at varying angles with respect to the

horizontal. In a field, some wells are deeper than the others,

while some are deviated. The performance of a jet pump is

different for different cases as the parameters affecting it

are the depth and the angle of placement. These aspects

with respect to the working of the jet pump need to be

investigated and demonstrated. Hence, an effort has been

made in this paper to design an experimental setup by

which the pump efficiency with respect to depths and

angles of placement can be easily determined. The exper-

imental setup uses a jet pump driven by an electric motor

of 2.5 kW along with a measurement setup. The jet pump

was mounted on a hinged fixture and injection fluid from a

centrifugal pump was used. The gate valve was used to

throttle the flow for injection and create resistance across

the delivery line of the jet pump as a measure of increasing

depth. These flow rates were used to characterize the per-

formance of the jet pump.

Keywords Artificial lift � Jet pump � Discharge flow rate �Injection flow rate

List of symbols

Qi Injection flow rate, m3/s

Qs Suction flow rate, m3/s

Q0 Discharge flow rate, m3/s

Pd Discharge pressure, bar

g Efficiency, %

Introduction

Artificial lift is a system that lifts the fluid from bottom of

the well to the surface artificially. In a self flowing well, the

pressure at the bottom is sufficient to naturally lift the fluid

to the surface. But once the crude is produced the pressure at

the bottom of the wellbore decline makes it unable to come

to the surface of its own. High viscosity of the crude is

another reason due to which the wells do not self flow

(Takacs 2005).

One of the artificial lift techniques is to use jet pump.

Here, the fluid is circulated through a chamber, housing a

foot valve and a venturi which causes the pressure drop when

the fluid is injected before the venturi. It sets the flow in the

pipeline housing the foot valve. Armstrong (2010) in his

study has documented the working of jet pump in terms of

principle and applications. Kwon et al. (2002) has evaluated

the chamber shape effect on the efficiency of jet pump.

Irrespective of the chamber shape, it is important to

check the performance of a jet pump for wellbore deviation

and depth parameters, as the well bore is seldom vertical. To

characterize the performance of the jet pump, various tests

have been suggested by Lal (2000). The performance

characterization of jet pump for various nozzle angles has

been studied before (New 2009), but the effect of angle of

R. Nanda � S. Gupta � A. K. N. Shukla (&)

School of Petroleum Technology, Pandit Deendayal Petroleum

University, Gandhinagar, Gujarat, India


123


DOI 10.1007/s13202-011-0010-x

placement for a vertical nozzle has not been reported. This

can be checked by the experimental setup and recommen-

dation can be made to study the effect on pump performance

by angle and depth.

In the following sections, an experimental setup has

been explained to measure the efficiency of a jet pump with

varying angles of placement and depth. The effect of

diameter and nozzle–throat area ratio and its effects have

been studied before by Lima Neto 2011 and the same has

not been reported here.

Assembly of a jet pump test rig (JPTR)

The following procedure was followed while assembling a

jet pump test rig. The materials and equipments used have

been detailed in relevant steps as follows:

• A 2.5 kW powered jet pump was installed on a tank of

200 l capacity. The tank was filled to the level of

400 mm for testing purpose as shown in Fig. 1.

• A collecting tank of approximately 43 l capacity was

installed for measurement of flow rate from the jet

pump. Transparent graded tubing was used to see the

level of water in the collecting tank and simultaneous

measurement for time duration was done to calculate

the discharge flow rate.

• A hinged fixture was developed with slots for 90�, 60�,

45�, 30� and 0� hold angles. The jet pump was mounted

on the hinged arm and the fixed arm was kept as base.

Initially, the hinged arm was kept perpendicular to the

fixed arm, so that the jet pump was positioned vertical

to perform the test.

• The pump was primed and electric motor powering the

injection line was switched on.

• The gate valve fitted on the injection line was used to

control flow rates. The flow rate was measured by the

pressure drop across the orifice plate fitted in the

injection line as shown in Fig 1. Mercury manometer

was used to measure the pressure drop across the orifice.

• The discharge valve in the discharge line was used to

control the discharge flow rate and pressure gauge was

used to measure the discharge pressure. Similarly,

suction pressure gauge was used to measure the

pressure in the delivery line of the jet pump.

• The performance characteristic of jet pump was

obtained in vertical position at constant injection rates

by varying discharge flow rates. Similarly, the perfor-

mance test was done at two other angles of placement,

45� and at horizontal position.

Experimentation and computation

To evaluate the performance characteristics, values of flow

rates are calculated for various angles of placement and

depths. The computation process was carried out as under:

• The efficiency was calculated at five different points of

opening of gate valve at set injection rate. The point of

best efficiency was obtained through this which signi-

fies the operating point at given injection rate. Simi-

larly, the test was repeated for other positions.

• Now the angle of placement was changed and the

efficiency was calculated for the above injection flow

rate and the corresponding point of best efficiency was

determined. It was found that the efficiency dropped

when the angle of placement was changed from vertical

to horizontal position.

• When the gate valve fitted on delivery line was closed,

a reduction in discharge pressure signified the effect of

increased depth and the values of efficiencies were

measured at each angle of placement. It was found that

by increasing the head over the pump the efficiency

increased.

• The above steps were checked for repeatability and the

operating point was found at the nearly same point in

each case.

• Furthermore, the range of efficiency in each measure-

ment showed repeatability with previous measurements

for the same operating conditions.


The performance characteristics of jet pump are reported at

two conditions:

a. Various angles of placement

b. Various depths of placement at different anglesFig. 1 Schematic of the experimental setup


123

Table 1 shows that at constant injection flow rate and

discharge head the efficiency of jet pump is higher when it

is placed vertically than when it is placed horizontally.

The flow rate at vertical position is around 9% greater than

when it is placed in horizontal position. The reason to this

is attributed to greater buoyancy force due to submergence

but having dead weight of the valve same. This follows

the linear relationship as at 450, midway the corresponding

increase is around 5% only. It further shows that suction

flow rate is greater when it is positioned vertically and the

magnitude is around 22% higher while at 450, again it

follows the linear relationship reducing to 11% rise from

the minimum flow rate. Corresponding to this, there is a

5% difference in efficiency when the jet pump is placed in

vertical position and horizontal position. The analyses here

consider single phase fluid with no dissolved gas in it. As

the main flow take the fluid upward beyond the venturi,

the pressure remains positive and is sufficient for main-

taining only the flow. It does not carry any hydrodynamic

action as at fully closed position of delivery valve the

injection line act as the circulating line without harming

the pump.

Table 2 shows that at vertical position of the jet pump

the efficiency of the pump decreases if the depth of the

pump is decreased. It also shows that the discharge flow

rate increases when depth is increased. A 10% increase in

flow caters to 15% increase in head over the pump. This is

explained as with larger head it provides larger length of

the pipe which carries kinetic energy of the fluid for

longer time. Hence, jet pump works better at higher depth

and deliver large amount of fluid. At this condition, the

corresponding increase in suction flow rate is of order of

30–38%. This means that at greater depth in this case 15%

increase the force due to buoyancy make the valve

opening easy accommodating larger flux of fluid to get in.

This leads to 6 to 7 basis point increase in efficiency from

its base point. Likewise, the efficiency and discharge flow

rate curiously have nearly the same magnitude at hori-

zontal position and vertical position. It is because once the

flow commences through the foot valve, of the two

components: vertical and horizontal flows, one component

of flow becomes zero while the other is active. But when

the jet pump is at 450 both the component remains and

there is less fluid loss. This ensures that efficiency is

marginally better for 450 at greater depth. In this case it is

around 4% better. All throughout the experiment, the

injection rate is kept constant so its influence is not

accounted here with. Nevertheless, it is expected that at

larger injection power the above outcome will be

magnified.

Conclusion

The experimental setup so assembled was successful in

creating a system by which the performance of the jet

pump was characterized at different angles of placement

and depth. To enable this, unique fixture is designed. The

stress of the work is on experimental setup for performance

evaluation of a jet pump where in practical field it is dif-

ficult to make such an analysis. The success of work lies in

creating a system of arrangement through which influence

of varying angle of placement and depth is evaluated. The

range of variation of flow at vertical position to horizontal

position changed the discharge flow rate from 0.308 to

0.252 l/s which is order of 22% increase. The efficiency

was a maximum of 46% when jet pump was placed ver-

tically. It dropped to 42% at 45� when placed at greater

depth. When there was 15% decrease in discharge pressure,

there was around 10% decrease in the flow rate. The above

variations are calculated at constant operating injection

flow rates. The facility so generated can be used for future

research work on various aspects of jet pump by experi-

mentation. This study presents two interesting outcomes as

a result of testing the influence of angle of placement and

depth over jet pump: at constant depth jet pump works

better at vertical position but when it is under the influence

of both depth and angle of placement, incline position is

better once flow is commenced. It is also being an exper-

imental experience that jet pump performance is a function

of valve seating design and active pressure control is

expected to work better than the gravity and buoyancy

settled valve. At shallow depth, jet pump is expected to

perform better and the maximum limit for immersion will

be checked against vapour pressure for the working fluid.

Table 1 Influence of angle of placement on pump performance

Angle of

placement

Total

head

(bar)

Qo

(m3/s 9 103)

Qi

(m3/s 9 103)

Qs

(m3/s 9 103)

g(%)

Vertical 0.51 0.669 0.361 0.308 46

45� 0.51 0.641 0.361 0.280 44

Horizontal 0.51 0.612 0.361 0.252 41

Table 2 Influence of depth and positions on pump performance

Angle of

placement

Total

head

(bar)

Qo

(m3/s 9 103)

Qi

(m3/s 9 103)

Qs

(m3/s x 103)

g(%)

Vertical 1 0.583 0.361 0.222 38

0.85 0.521 0.361 0.160 31

450 1 0.625 0.361 0.264 42

0.85 0.563 0.361 0.202 36

Horizontal 1 0.585 0.361 0.224 38

0.85 0.531 0.361 0.171 32


123

The experimental aspect of the setup developed is expected

to be extensible used for future work and create snow ball

effect in terms of the arrangement for varying angle of the

placement and depth. The authors propose that further

research can be carried out by varying the angle of place-

ment and depth for the following parameters: different

nozzle angles, different chambers shapes, varying diame-

ters, area ratio and positive and negative suction heads

(Hammoud 2006).

Acknowledgments The authors wish to acknowledge the use of

facility and technical help provided by the personnel at the fabrication

technology laboratory, Pandit Deendayal Petroleum University,

Gandhinagar, India, without whom this experiment could not have

been performed.





References

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123

http://www.wseas.us/e-library/conferences/2006elounda2/papers/538-122.pdf

http://www.wseas.us/e-library/conferences/2006elounda2/papers/538-122.pdf

http://dx.doi.org/10.1007/BF03182599

http://dx.doi.org/10.1007/s00348-009-0622-9

Documents

Journal of Petroleum Exploration and Production Technologies - Vol. 1, Numbers 1-4, 2011