SPE-135587

The Effect of Drillstring Rotation on Equivalent Circulation Density: Modeling and Analysis of Field Measurements Ramadan Ahmed, Majed Enfis, Hamza Miftah-El-Kheir, SPE, University of Oklahoma; Morten Laget, SPE, AGR Petroleum Services; and Arild Saasen, SPE, Det norske oljeselskap ASA and the University of Stavanger

Copyright 2010, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Annual Technical Conference and Exhibition held in Florence, Italy, 19–22 September 2010. This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contents of the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflect any position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations may not be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract A number of field and laboratory studies have been carried out to accurately predict the effect of drillstring rotation on

downhole pressure and equivalent circulating density (ECD). Field studies indicated that drillstring rotation often results in an

increased ECD. This is in contradiction with the results obtained from number of laboratory studies and other field studies.

Consequently, there is no comprehensive model that accounts for the effect drillstring rotation on wellbore hydraulics.

Recently, simple empirical models have been developed based on field measurements alone. Although these models can be

very useful as they are based on field measurements, they have no physical basis and are limited to specific ranges of field

parameters.

This article presents results of field studies and theoretical analysis conducted on the effect of drillstring rotation on

wellbore hydraulics. Field measurements during actual drilling operation were obtained from four different wells. Key drilling

parameters such as flow rate, drillstring rotation speed, rate of penetration, ECD and return density, were recorded as a

function of measured depth.

Selected published field measurements were analyzed systematically using dimensional analysis techniques. After

correlating different dimensionless groups, a new semi-empirical model was developed. The model was rigorously tested for

its accuracy. Model predictions were compared with new field measurements and predictions of an existing model. Model

predictions show good agreement with field measurements. The new model exhibits appreciably better accuracy than the

existing one.

The model developed in this investigation is relevant to manage ECD in slim holes, deepwater wells, and extended-reach

wells where the increased wellbore length results in excessive pressure loss and limits the operating window for bottom hole

pressure. In deepwater applications, ECD management becomes critical due to the narrow operating window between the pore

and fracture pressure gradients.

1. Introduction Research on ECD management and wellbore hydraulics has received an increased attention in the last few years as new

technologies such as slim-hole and casing drilling have emerged in the industry. Despite their technical and economical

benefits, these technologies have presented several hydraulic challenges as a result of the narrow annular clearance that

substantial increase in pressure loss. Moreover, in recent years, deep-water drilling has been pursed as a mean to satisfy the

increasing oil demand. Deep-water drilling presents several drilling challenges associated with downhole pressure

management because of the narrow margin between pore pressure gradient and fracture gradient. It is very critical to assess the

accuracy of downhole pressure prediction and thoroughly understand the effect of drillstring rotation on BHP and ECD.

Accurate predictions optimize of wellbore hydraulics and avoid excessive annular pressure losses that occur frequently in the

field. Also, accurate prediction is needed for planning of drilling fluid density prior to drill out. Failure to accurately predict

the ECD may in the end result in fracturing of the formation, lost circulation, excessive loss of drilling fluid, loss of well

control and increased drilling cost

The rotation of the drillpipe can substantially increase the annular pressure loss resulting in higher bottom hole pressure

(BHP) and ECD. The relationship between the drillpipe rotation speed and friction pressure loss is complex and often

influenced by fluid properties (rheology and density), flow regime, diameter ratio and eccentricity. For simple annular flows

such as Newtonian laminar flow in concentric annulus, the axial and radial momentum equations are fully decoupled. This

indicates theoretically the disassociation of these two key drilling parameters for Newtonian fluids. However, for laminar flow

2 SPE 135587

of Non-Newtonian fluid in concentric annuli, the equations of motion are fully coupled through the shear rate dependent

apparent viscosity function. Hence, for shear thinning fluids, theoretically the pressure loss is expected to reduce due to the

rotation of the inner pipe. Despite this expectation, both experimental and field studies predominately show an increased

annular pressure loss with drillstring rotation. The increase in the pressure loss is attributed to different flow phenomena

including: i) pipe eccentricity and/or geometric irregularities (pipe wobbling and eccentricity fluctuations) that generate

additional losses; ii) formation of secondary flows like Taylor vortices; and iii) increase in annular cuttings concentration.

In inclined and horizontal wellbores, the drillstring settles on the low side of the wellbore forming eccentric annulus that

changes the flow pattern. Without the drillstring rotation, eccentricity can reduce the annular pressure by as much as 60%

(Haciislamoglu and Langlinais 1990). In addition, as the drillstring rotates, due to its extensive length, it moves from one end

to the other end of the wellbore, producing wobbling motion and eccentricity fluctuations that create very complicated flow

patterns in the annulus. Furthermore, in 1880, Lord Rayleigh discovered that the existence of flow instability in annular flow

with inner string rotation. Secondary flows such as Taylor vortices can be formed in the annulus because of centrifugal and

shear instabilities. A recent numerical study (Jeng and Zhu 2010) shows the formation Taylor vortices in helical flow of

Bingham fluids in concentric annulus. These conditions result in substantial increase in pressure losses. As the flow patterns

become more complex, mathematical modeling becomes very difficult, if not impossible. Experimental approach is more

realistic option to develop predictive models. However, experiments conducted in small-scale laboratory setups may not

represent the conditions in the field. For instance, laboratory tests cover only low Taylor number flows whereas field

measurements indicate high Taylor number flow conditions in the wellbore. Therefore, although they are expensive, field

studies are preferable in this case to provide practical and useful solutions.

2. Literature Review Numerous laboratory studies (Nouri and Whitelaw 1994; Hansen and Sterri 1995; Hansen et al. 1999; Ahmed and Miska

2008; Yamada 1962; Walker and Al-Rawi 1970; Wei 1997; Woo et al. 2005) were carried out to evaluate the effect of pipe

rotation on annular pressure loss. Most of these studies demonstrate both negative and positive effects of the rotation speed.

An earlier study (Nouri and Whitelaw 1994) conducted in a concentric annulus (0.79ʺ x 1.59ʺ) showed an increase in the

friction factor with inner pipe rotation compared to a non-rotating case in laminar flow regime. The experiments were

conducted using Newtonian and non-Newtonian fluids. Aqueous solution of Glycerol (Newtonian) and 0.2% aqueous solution

of CMC (power-law fluid) were used in the experiments. A year later, another experimental study (Hansen and Sterri 1995)

was undertaken to determine the effect of pipe rotation and pipe eccentricity on pressure losses in narrow annuli. The fluids

used in this experiment were non-Newtonian and best fit the power law model. The results of this experiment have shown

unexpected pressure loss patterns. The study confirmed that pressure loss could eventually increase or decrease as pipe

rotation increases. Similar results were obtained from a more recent study (Hansen et al. 1999) conducted by the same authors.

Analogous to their previous study (Hansen and Sterri 1995), one of the main objectives of this experiment was to examine the

effect of drillpipe rotation and pipe eccentricity on annular pressure loss. A series of tests were conducted using a 13-ft long

narrow annular test section (2ʺ x 1.75ʺ). These tests were run using the following three types of fluids: water, three different

solutions of CMC, and two different solutions of Xanthan gum. The CMC solutions best fit the power law model whereas the

Xanthan gum solutions fit the Herschel-Bulkley model. For the CMC solution, a combined circulation and rotation tests were

undertaken in a fully concentric annulus. As the inner pipe was rotated from 0 to 600 RPM at 100 RPM increments the

pressure loss increased almost linearly as the pipe rotation increased for all flow rates. Similar tests conducted using

eccentricity annulus (relative eccentricity of 0.7) showed a small decrease in pressure loss for low flow rates (below 75 l/min)

as pipe rotation increased. However, once the flow rate exceeded this value, there was a relatively higher increase in pressure

losses with increase in pipe rotation speed. For Xanthan gum solutions in a concentric annulus, results are to some extent

similar to the data obtained using the CMC solutions. There was a substantial decrease in the pressure loss as pipe rotation

increased at low flow rates (below 100 l/min). Once the flow rate exceeded this value, there was a slight pressure loss increase.

Another study (Sterri et. al 2000) conducted in partially (50%) eccentric annulus with diameter ratio of 80% showed

consistently increased annular pressure loss with the increase in inner pipe rotation speed. A more recent study (Ahmed and

Miska 2008) corroborated the results obtained from previous laboratory investigations by concluding that indeed annular

pressure loss could increase or decrease with increasing drillpipe rotation speed.

In addition to the laboratory investigations, a number of numerical studies (Wan et al. 2000; Escudier et al. 2002; Fang and

Manglik 2002) were carried out to analyze helical flow of both Newtonian and non-Newtonian fluids in annuli. Simulation

results for Newtonian fluid in eccentric annuli showed increased pressure gradients as the rotation speed increases. This

phenomenon is attributed to the inertial effect that arises from the coupling of Navier–Stokes equations as the flow becomes

three-dimensional. For power-law fluid, results indicated the influences of both inertial effect and shear thinning. In a slightly

eccentric annulus, shear thinning dominates, whereas in a highly eccentric annulus, inertial effect becomes predominate. In an

annulus of intermediate eccentricity, shear thinning and inertial effect become comparable and the influence of rotational

speed becomes minimal.

Unlike the results from the majority of the laboratory studies, most of the field measurements (Delwiche et al. 1992; Ward

and Andreassen 1998; Isambourg et al. 1998; Charlez et al. 1998; Green et al. 1999; Hemphill et al. 2007; Hemphill et al.

2008) have shown a significant increase in pressure loss as the pipe rotation increases. The discrepancy between lab

observations and field measurements can be attributed to several factors, such as drillpipe wobbling or instability, the irregular

SPE 135587 3

geometry of the wellbore, tool joint effect, or a combination of these factors. Delwiche et al. (1992) carried out a field study in

several narrow-annuli wells. Different tests were carried by changing the flow rate and pipe rotation speed and recording the

pressure loss. The results (Fig. 1) show considerable increase in pressure loss with the increase in pipe rotation. In fact, in

slim-hole applications it is expected that the drillpipe rotation would produce larger increases in annular pressure drop

compared to conventional drilling because of the small annular clearance. Another field study conducted in North Sea

(Isambourg et al. 1998) reported similar increase in pressure loss as the rotation increases. The measurements were obtained

from an 8.5ʺ well with 5ʺ drillpipe. At low rotational speeds (below 60 RPM) pressure loss slightly increased. Above 60 RPM,

the pressure loss increased linearly with the rotation speed

In general, field measurements show similar response

of annular pressure loss with the change in drillstring

rotation speed. A series of Pressure-while-Drilling (PWD)

measurements (Charlez et al. 1998) obtained from North

Sea wells agree closely with the results of earlier studies

(Delwiche et al. 1992; Isambourg et al. 1998). Another

field study (Green et al. 1999) was conducted in several

wells in the Niakuk field in the North Slope, Alaska. These

tests were run after several problems were encountered

while drilling 8.5ʺ sections of several Extended-Reach-

Drilling (ERD) wells. In order to overcome these

challenges, it was necessary to develop new operational

guidelines to help prevent future drilling problems.

Therefore, a set of different tests was carried to examine

several wellbore hydraulics aspects. One of the tests

conducted involved recording PWD measurements while

varying the drillpipe rotation speed and drilling fluid flow

rate. The tests were carried out in cased (9.625ʺ ID casing)

section of a well inside while rotating a 5.5ʺ drillpipe.

Tests were performed using oil based mud, which fit the

Herschel-Bulkley model very well. The results show the

existence of two regions in the pressure loss curve. The first region (below 50 RPM) where there is slight linear increase in the

pressure loss occurs with increase in the angular speed of the pipe, and a second region (above 50 RPM) where there is a

moderate linear increase in annular pressure loss. The overall trend of these curves shows that annular pressure loss increases

as the drillpipe rotates at higher angular velocities. However, a recent field study (Hemphill et al. 2007) conducted two years

ago in the North Sea reported a sharp increase in annular pressure loss at the lower drillpipe rotation speeds, and a slower

increase at the higher rotation speeds.

3. Field Data Analysis The aim of the data analysis is to develop a model that can predict pressure loss variations as a function of drillpipe rotation

speed. Published data from a number of field studies (Delwiche et al. 1992; Isambourg et al. 1998; Charlez et al. 1998; Green

et al. 1999; Hemphill et al. 2007; Bode et al. 1991; Marken et al. 1992) were considered in the initial stage of the analysis. All

the data were extracted and converted to dimensionless variables. Some field studies were omitted due to the lack of key test

information required for the analysis. After applying dimensional analysis techniques, we found that some of the field data do

not correlate well. The poor correlation could be due to the discrepancy resulting from measurements inaccuracies since most

of the pressure losses were determined indirectly from bottom hole pressure measurements. In order to improve the quality of

the correlation, some of the field data were removed and the analysis was repeated numbers of times until satisfactory results

were obtained. Finally, data points (Table 1) from three field studies (Delwiche et al. 1992; Isambourg et al. 1998; Charlez et

al. 1998) were correlated well. Except two data points, all the measurements were taken under laminar for conditions. In the

effort to manipulate the field data in a convenient form, a dimensionless parameter (pressure loss ratio) is introduced. The

pressure loss ratio (PLR) is defined as:

0)/(

)/(

dLdP

dLdPPLR ..….………………………………………………………………………….……...….……. (1)

Using dimensional analysis, the following model has been developed to predict the PLR as:

0.0152-0.0420.03190.0540.1580.428

2)1

1(Re)5.31(36.0 k

kTanU

PLR effave

y

, …………..…………………. (2)

Fig. 1 Pressure losses as function of RPM for different flow rates

(Delwiche et al. 1992)

0

50

100

150

200

250

300

350

400

450

500

0 50 100 150 200 250 300 350 400

Pre

ssu

re lo

sses

(psi

)

RPM

Q= 200 l/min Q= 300 l/min Q= 400 l/min Q= 500 l/min

4 SPE 135587

where is density of the fluid. y and n are the Herschel-Bulkley yield stress and fluid behavior index, respectively. U and

are mean annular velocity and diameter ratio Dp/Dh, respectively. Average dimensionless eccentricity eave of a well is

expressed as:

n

i

i

ph

i

aveMD

L

DD

Ee

1 )(

2 , …………….…………………..……………………………………………………..…. (3)

where Li and MD is length of a wellbore section and total measured depth of the well, respectively. Ei is effective eccentricity

of a wellbore section that represents the offset distance between the centers of the drillpipe and casing/hole. Theoretically, a

vertical section of a well is expected to have zero eccentricity. However, due to slight inclination and other geometric

irregularities, a vertical section may have a certain level of eccentricity. After analyzing number of field data and considering

the observations from previous studies (Wan et al. 2000; Escudier et al. 2002; Fang and Manglik 2002) that for intermediate

eccentricity, rotation effects are minimal, we recommend an effective eccentricity value of 50% for a vertical wellbore (i.e. for

a section with inclination less than 1°). In inclined and horizontal sections, the drillpipe lays on the low side of the wellbore.

Hence, the effective eccentricity is estimated as:

ph

TJh

DD

DDE

, …………………………………………………………………………………………………….. (4)

where DTJ is the diameter of a tool joint. The Taylor number (Ta) presented in Eq. (1) is expressed as:

23

16

)(

app

php DDDTa

, …………….………………….…………………………………………..……… (5)

where app is the apparent viscosity evaluated at the total shear rate 22

z . The tangential shear rate (

) and axial

shear rate (z ) are estimated using methods presented elsewhere (Ahmed and Miska 2008). The effective Reynolds number is

calculated as (White 2002):

lamw

eff

U

,

28Re

, …………………………………………………………………………………………………….. (6)

where w,lam is the average wall shear stress for a concentric annulus, which is predicted from a laminar flow hydraulic model

such as narrow slot method.

4. Model Validation Model validation has been carried out in two stages. First,

the predictions of the model have been compared (Fig. 2)

with the published field data from five field studies

(Delwiche et al. 1992; Isambourg et al. 1998; Charlez et al.

1998; Green et al. 1999; Bode et al. 1991; Marken et al.

1992). Even though the data points were obtained under

different drilling conditions (i.e. different drilling

parameters, fluid properties, wellbore configurations and

profiles), most of the predictions are between ±12.5% error

bars. Predicted and measured pressure loss ratio values are

between 1.0 and 1.6. Some measurements are out of these

bars. But they are not significantly far from the lines. The

scattering of the data points could be due measurements

error as field experiments are not often carried out under

fully control conditions. Be side this, bottom hole pressure

and ECD measurements could be affected by drilling

parameters (tool joint, wellbore quality, annular cuttings

concentration, rate of penetration and well profile) that are not included in the dimensional analysis. Desipte the minor effects

of the omitted parameters, their contributions could be substantial in some special situations. For example, the pressure loss

0.0

0.4

0.8

1.2

1.6

0.0 0.4 0.8 1.2 1.6

Measured

Pre

dic

ted

Charlez et al.

Green et al.

Isambourg et al.

Bode et al.

Delwiche et al

Marken et al.

Fig. 2 Predicted vs. measured pressure loss ratio

+12.5%

-12.5%

SPE 135587 5

across a tool joint can be negligible for conventional wells; however, for narrow clearance wellbores, tool joint geometry could

be critical.

0

500

1000

1500

2000

2500

-100 100 300 500 700 900

HD (m)

TV

D (

m)

(a)

0

500

1000

1500

2000

2500

3000

3500

4000

-100 0 100 200 300

HD (m)

TV

D (

m)

(b)

0

500

1000

1500

2000

2500

3000

3500

-100 0 100 200 300

HD (m)

TV

D (

m)

Well C

Well D

(c)

Fig. 3 Wellbore profiles of test wells: a) Well A; b) Well B; and c) Well C & D

To further validate the developed model, model predictions were compared with recent field measurements that are

obtained from four North Sea wells (Well A, Well B, Well C and Well D) drilled by Det norske oljeselskap ASA. The wells

have the same wellbore geometry (8.5ʺ × 5ʺ). Rheological properties of drilling fluids used during the field test are presented

in Table 2. Wellbore profiles of the wells are shown in Fig. 3. All tests were conducted by measuring bottom hole pressure

(BHP) while varying the pipe rotation speed.

Due to operational difficulties, tests performed in

directional wells (Well A and Well B) were not conducted

at zero rotation speed. As a result, it was not possible to

determine the PLR. The comparisons between

measurements and predictions have been made using

pressure loss instead of PLR. During the field test, the

rotational speed was varied from 80 rpm to 140 rpm. The

measured BHP data is used to determine the pressure loss.

Measured and predicted pressure losses are presented in

Fig. 4. The data points exhibit a higher degree of scattering

than the pressure loss ratio (Fig. 2). The source of the

scattering shown in Fig. 4 could be attributed to the

additional error resulting from the prediction of annular

pressure loss in addition to the pressure loss ratio. This is

exacerbated due to the fact that the well profiles include

inclined sections that can form cuttings beds, which

partially block the annulus and reduce the accuracy of

hydraulic calculations. Moreover, measurements were taken in actual drilling conditions, in which other drilling parameters

such as annular cuttings concentration (annular cuttings load) could have substantial effect on the bottom hole pressure. Hence,

the conversion of the bottom hole pressure measurements to friction pressure loss could introduce additional error. As a result,

discrepancies become relatively high for these data points. However, most of the measurements are within ±25% error bars;

and they are scattered on both sides of the perfect-fit line (i.e. zero error line). For Well A, the predictions are higher than

measured values for the sidetrack section while the pressure loss is under-predicted for the mainbore.

Flow in vertical wellbores is less complicated than in deviated wells. Field tests were carried out in two vertical wells

(Well C and Well D) to validate the model. Flow rates and pipe rotation speeds were varied from 1700 l/min to 2200 l/min and

0 rpm to 150 rpm, respectively. Predictions of the new model (Fig. 5) are in good agreement with the field measurements. The

Fig. 4 Predicted vs. measured pressure loss for Well A and Well B

0.0

0.4

0.8

1.2

1.6

0.0 0.4 0.8 1.2 1.6

Measured (kPa/m)

Pre

dic

ted

(kP

a/m

)

Well A SidetrackWell A MainboreWell BPerfect-fit Line+25%-25%

Mainbore

Sidetrack

6 SPE 135587

maximum error is approximately 10%. The measured and predicted pressure loss ratios vary from 1.05 to 1.23 indicating

significant increase in annular pressure loss with the increases in the rotation speed. Furthermore, the accuracy of the new

model is compared with the existing model developed by Hemphill et al. (2008). When tested with the data from Well C, the

new model shows better accuracy than the existing one (Fig. 5a). The predictions of the two models are very similar in

predicting the data from Well D (Fig. 5b).

1.0

1.2

1.4

1.6

1.8

1.0 1.1 1.2 1.3

Measured

Pre

dic

ted

Hemphi l l et a l . 2008

Present Study

Perfect-fi t Line

(a)

1.0

1.1

1.2

1.3

1.4

1.0 1.1 1.2 1.3 1.4

Measured

Pre

dic

ted

Perfect-fi t Line

Hemphi l l et a l . 2008

Present Study

(b)

Fig. 5 Predicted vs. measured pressure loss ratio: a) Well C; and b) Well D

5. Results and Discussion The relationship between annular pressure loss and drillstring rotation speed depends on number drilling parameters such as

wellbore geometry (diameter ratio and eccentricity), flow regime, and fluid properties. After validating the model, sensitive

analysis was carried out to study the influence of these parameters on the pressure loss under laminar flow conditions. Two

base cases (Table 3) with different borehole geometries are considered for the analysis. Figure 6 presents predictions of the

model showing the effect of yield stress on the PLR. As anticipated, with an increase in the yield stress the PLR decreases

indicating the shear thinning effect. At high yield stress (YS) values, the PLR becomes insensitive to YS. Although the

annular velocities are approximately the same for both cases, the slim hole (Base Case 2) has relatively higher PLR agreeing

with previous field measurements (Bode et al. 1991).

The annular velocity is expected to have strong influence on the PLR. Predictions (Fig. 7) indicate that the increase in

velocity raises PLR as the velocity tends to amplify the inertial effects. At low velocities, the PLR appeared to very sensitive to

the change in velocity. Moreover, the relationship between the velocity and PLR depends on drilling parameters such as the

diameter ratio and drillpipe rotation speed. The increase in these two parameters raises the PLR.

1.1

1.2

1.3

1.4

1.5

0 2 4 6 8 10

Yield Stress (Pa)

PLR

RPM = 100

RPM = 200

RPM = 300

(a)

1.1

1.2

1.3

1.4

1.5

0 2 4 6 8 10

Yield Stress (Pa)

PLR

RPM = 100

RPM = 200

RPM = 300

(b)

Fig. 6 Predicted pressure loss ratio versus yield stress: a) Base Case 1; and b) Base Case 2

SPE 135587 7

1.0

1.1

1.2

1.3

1.4

1.5

0.0 0.2 0.4 0.6 0.8

Annular Velocity (m/s)

PLR

RPM = 100

RPM = 200

RPM = 300

(a)

1.0

1.1

1.2

1.3

1.4

1.5

0.0 0.2 0.4 0.6 0.8

Annular Velocity (m/s)

PLR

100 RPM

200 RPM

300 RPM

(b)

Fig. 7 Predicted pressure loss ratio versus annular velocity: a) Base Case 1; and b) Base Case 2

The above simulation results (Fig. 7) are obtained considering practical flow rate ranges used in the field that produce

predominately laminar flow conditions in the annulus (i.e. Low Reynolds number). As the drillpipe rotates the flow becomes

complex. It produces an oscillatory flow pattern which requires additional dimensionless parameter (i.e. Strouhal number) to

properly describe the flow regime. The Strouhal number can be expressed for annular flow as:

U

)( ph DDSt

The Strouhal number compares the tangential velocity to the linear velocity. In other word, it weighs the tangential shear force

against axial shear force. Figure 8 presents PLR predictions as a function of the Strouhal number for different rotation speeds.

The data is generated by vary the flow rate at a constant rotation speed. The Strouhal number tends to strongly affect the PLR.

At low Strouhal number, as the flow rate increases at a constant rotational speed, there is a sharp increase in the PLR

indicating weakening of the shear thinning relative to other phenomena that intensify viscous losses.

Streamlines in concentric annular flow form perfectly helical pattern. This means that the magnitude of axial fluid velocity

is only a function of radial distance from the center. However, a rotating eccentric pipe generates very complicated flow

pattern, resulting in substantial variation of fluid velocity along the streamline. This creates additional mechanisms for viscous

losses that are counteracted by the effect of shear thinning. Both field and laboratory studies indicate a modest increase in PLR

with the increase in eccentricity. This can be perceived from the high-power exponent (0.158) of effective eccentricity in the

model (Eq. (2)), which confirms the experimental observations. Even though it has moderate influence on the PLR,

eccentricity has limited range. In this study, the range of effective eccentricity is considered to be between 0.5 and 1.0. Hence,

the increase in the effective eccentricity from 0.5 to 1.0 could raise the PLR at most by about 12%. It is important to note that

higher PLR doesn’t translate to a higher annular pressure loss

dLdp because the increased eccentricity also reduces the

pressure loss of an annulus with non-rotating drillpipe 0

dLdp and according to Eq. (1): PLRdLdpdLdp 0

.

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0 5 10 15 20

Strouhal number

PLR

RPM = 100

RPM = 200

RPM = 300

(a)

1.0

1.1

1.2

1.3

1.4

1.5

1.6

0.0 1.0 2.0 3.0 4.0 5.0

Strouhal number

PLR

RPM = 100

RPM = 200

RPM = 300

(b)

Fig. 8 Predicted pressure loss ratio versus Strouhal number: a) Base Case 1; and b) Base Case 2

8 SPE 135587

Helical flows between rotating cylinders may form translating or propagating spiral vortices (Taylor vortices). The vortices

could be complete or only partial. Two mechanisms are believed to be responsible for destabilizing a helical flow: i)

centrifugal instability resulting from the curved streamlines; and ii) shear instability due the axial flow. The formation of

Taylor vortices increases viscous dissipation and the PLR. Using perturbation method, Chandrasekhar (1981) showed that the

stability characteristic of helical flow of Newtonian fluid is determined using two dimensionless groups (Taylor number and

Reynolds number). High Reynolds number tends to improve the stability of the flow. Nonetheless, the improvement is often

small. The model developed in this study is strictly applicable to the ranges of Taylor and Reynolds numbers that are covered

in the original field data (Table 2). When the model is used out of these ranges (721 ˂ Reff ˂ 2397 and 479 ˂ Ta0.5

˂ 1602), care

must be taken to avoid any excessive extrapolation that may produce unexpected results.

6. Conclusions After studying the field measurements in conjunction with the semi-empirical model, the following conclusions are drawn:

- pressure loss ratio is affected by different drilling parameters including drillpipe rotation speed, fluid properties, pipe

eccentricity, diameter ratio and flow regime;

- the increase in pipe rotation speed raises the PLR and bottomhole pressure;

- Higher annular velocity tends to increase the PLR and amplifies the effect of pipe rotation on the bottom hole

pressure;

- PLR predictions are in good agreement with field measurements and remarkably close to the data obtained from

vertical wells;

- discrepancies between field measurements and predictions are observed from some of the directional wells; possible

explanations for the discrepancies could be increased annular cuttings concentration and cuttings bed buildup that are

not accounted in the determination of pressure loss from bottomhole pressure measurements; and

- PLR prediction trends are in agreement with previous field and laboratory results and theoretical analysis.

Acknowledgements We wish to express our appreciation to the University of Oklahoma, Det norske oljeselskap ASA and AGR Petroleum

Services for their support.

References Ahmed, R. and Miska, S. 2008. Experimental Study and Modeling of Yield Power-Law Fluid Flow in Annuli with Drillpipe

Rotation”, SPE paper 112604 presented at the SPE/IADC Drilling Conference, 4-6 March, , Orlando, Florida.

Bode, D.J., Noffke, R.B., Nickens, H.V. 1991. Well-Control Methods and Practices in Small-Diameter Wellbores, paper SPE

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Nomenclature BHP = bottom hole pressure, Pa

ECD = Equivalent circulation density

D = diameter, m

e = relative eccentricity

E = absolution eccentricity, m

L = length, m

MD = measured depth, m

p = pressure, Pa

PLR = pressure loss ratio

Re = Reynolds number

St = Strouhal number

Ta = Taylor number

U = mean fluid velocity, m/s

YS = Yield stress

Greek Letters

= shear rate

= viscosity

= diameter ratio

= fluid density

= stress

= angular speed

Subscripts

app = apparent

ave = average

eff = effective

h = hole

p = pipe

TJ = toll joint

y = yield

w = wall

lam = under laminar flow condition

= tangential

z = axial

Tables

Table 1 Summary of field data used to develop the model for pressure loss ratio

Reference

Geometry

Q ΔP/ΔL Reeff (Ta)0.5

y n K e

gpm

(l/sec) RPM Psi/ft (Pa/m) - - lbf/100.ft2 (Pa) -

lbf.Sn/ft2

(Pa.Sn) -

Charlez et al. 1998

5" X 8.5"

317 (20) 150 0.0028 (63) 721 819 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

317 (20) 200 0.0031 (70) 721 1095 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

370 (23) 100 0.0030 (67) 922 585 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

370 (23) 150 0.0033 (74) 922 879 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

370 (23) 200 0.0035 (80) 922 1174 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

10 SPE 135587

Reference

Geometry

Q ΔP/ΔL Reeff (Ta)0.5

y n K e

gpm

(l/sec) RPM Psi/ft (Pa/m) - - lbf/100.ft2 (Pa) -

lbf.Sn/ft2

(Pa.Sn) -

423 (27) 100 0.0034 (77) 1141 622 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

423 (27) 150 0.0037 (84) 1141 934 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

423 (27) 200 0.0040 (91) 1141 1248 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

476 (30) 100 0.0038 (87) 1371 656 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

476 (30) 150 0.0042 (94) 1371 985 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

476 (30) 200 0.0046 (104) 1371 1315 8.053 (3.86) 0.662 0.00603 (0.29) 0.570

Delwiche et al. 1992

5.5" X 9.6"

400 (25) 50 0.0244 (552) 1437 479 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

400 (25) 100 0.0270 (611) 1437 960 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

400 (25) 150 0.0292 (661) 1437 1445 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

500 (32) 50 0.0311 (704) 1904 508 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

500 (32) 100 0.0336 (760) 1904 1017 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

500 (32) 150 0.0362 (820) 1904 1529 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

600 (38) 100 0.0405 (916) 2397 1066 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

600 (38) 150 0.0438 (988) 2397 1602 0.0 (0.0) 0.738 0.00309 (0.15) 0.700

Isambourg et al. 1998

5" X 8.5"

423 (27) 120 0.0369 (835) 1379 831 9.272 (4.44) 0.921 0.00180 (0.09) 0.550

423 (27) 180 0.0416 (941) 1379 1250 9.272 (4.44) 0.921 0.00180 (0.09) 0.550

375 (24) 120 0.0329 (744) 1157 802 9.272 (4.44) 0.921 0.00180 (0.09) 0.550

375 (24) 180 0.0370 (838) 1157 1207 9.272 (4.44) 0.921 0.00180 (0.09) 0.550

Table 2 Rheological properties of drilling fluids used in the field test

Parameter Unit Well A Main Well A Side Well B Well C Well D

n - 0.63 0.63 0.68 0.76 0.76

Pa.sn 0.32 0.32 0.90 0.14 0.14

lbf sn/100 ft2 0.66 0.66 1.89 0.29 0.29

y Pa 4.82 4.82 2.75 3.5 3.5

lbf/100 ft2 10.09 10.09 5.76 7.3 7.3

Table 3 Base case inputs for sensitivity analysis

Inputs Base Case1 Base Case 2 Unit

Annular Geometry 8.5" X 5" 5" X 3.7" -

Flow Rate 272.6 63.8 gal/min

1.06 0.25 m3/min

Density 8.5 8.5 ppg

1020 1020 kg/m3

Consistency Index

0.145 0.145 lbfsn/100 ft2

0.069 0.069 Pa.sn

Yield Stress 0 0 lbf/100 ft2

0 0 Pa

Fluid Behavior Index 0.75 0.75 -