SPE-39714-MS

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Copyright 1998, Society of Petroleum Engineers, Inc.

This paper was prepared for presentation at the 1998 SPE Asia Pacific Conference on IntegratedModelling for Asset Management held in Kuala Lumpur, Malaysia, 23–24 March 1998.

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AbstractA new approach to the estimation of reserves in a fractured

limestone reservoir is presented and verified with a lookback

analysis over the past five years of production from the field.

This approach uses a filtered Monte Carlo method to integrate

independent reserves calculations based upon volumetric,

material balance, well pressure survey analysis, and well decline

estimates of oil in place and recovery. For the Waihapa-Ngaere

field, two estimates of oil in place are available: a volumetric

estimate obtained from mapped gross reservoir volume and

formation parameters; and a material balance estimate obtained

from pressure decline and production data. Independent

estimates of oil recovery can be obtained from estimation of

recovery factors based upon areal and vertical sweep in the

fractured reservoir, and recovery obtained from extrapolation of

well decline. The approach taken, that is to integrate all of the

available information and only accept parameter sets which are

consistent, led to an estimate of reserves and production

potential from the field which has proved remarkably accurate as

a predictor of field performance and recovery over the past five

years.

BackgroundThe Waihapa Field lies at the southern end of the Tarata Thrust

zone, within the eastern edge of the Taranaki Basin, New

Zealand (Figure 1). The field was discovered in February 19

with flows of up to 3124 bopd and gas up to 3.2 MMscf/d fro

the fractured Tikorangi Limestone during drillstem testing of t

Waihapa-1B well. The Toko-1 well, to the north of the Ngae

area of the field, was the first well to be drilled in the area

November 1978 but a test of the top section of the Tikoran

formation was inconclusive. Following the success of tWaihapa-1B well, Waihapa-2, 4, 5, 6, 6A were drilled in t

structure from the period 1988-1989 with all but Waihapa

(which was tight) being successful. Northern extension we

Ngaere-1, -2 and –3 were successfully drilled from March 19

through February 1994.

Geological Setting. The Waihapa structure is the southe

termination of a west-directed thrust sheet which formed as

result of movement along the NS-trending Taranaki Fault. At t

Tikorangi level the structure develops from a simple lo

amplitude, symmetrical fold in the south to an overthru

structure in the north. A major tear fault, with a weste

displacement of approximately 2 km, lies between the Ngaereand Ngaere-3 wells. A schematic top depth map showing w

locations and the major faults, as seen on seismic, is shown

Figure 2.

The Tikorangi Formation is an interbedded foraminife

limestone, siltstone and mudstone sequence averaging 230

thickness in the Waihapa area. Diagenetic features in t

limestone matrix include extensive pressure solution a

concomitant calcite cementation reducing the original prima

porosity to the typically observed 5 to 7%. The matrix, althou

of reasonable measured porosity, is of low permeability (< 0.

mD), is water saturated and is currently postulated to make

contribution either to oil production or to pressure support to t

field. The significant secondary porosity development for the accumulation is from post-burial fracturing of the formatio

Fracturing is common over the entire thickness of the Tikoran

Formation and extensive over a wide area.

SPE 39714

Probabilistic Reserves Assessment Using A Filtered Monte Carlo Method In AFractured Limestone ReservoirL.R. Stoltz SPE, Fletcher Challenge Energy Taranaki, M.S. Jones SPE, Fletcher Challenge Energy Canada,A.W. Wadsley, Optimiser Consulting

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2 L.R.STOLTZ, M.S.JONES, A.W.WADSLEY SPE 397

Based on a field wide correlation, four units have been

defined within the Tikorangi Formation. Unit A, the uppermost,

appears as a relatively uniform interval with a blocky GR and

sonic response, both indicating massive moderately clean

carbonate. Unit B has a more irregular log response, indicative

of an interbedded lithology, most likely limestone and shale.

Unit C, directly beneath this, has a blocky appearance indicating

relatively clean carbonate. This generally grades to a more shalylithology towards the top of unit D. The lowermost unit, unit D,

has a more uniform character and appears as a more silty/shaly

lithology.

IntroductionNo reservoir parameter in the Waihapa field is known with any

confidence: fracture porosity and areal distribution is not known;

fracture compressibility can not be measured directly; the

reservoir closure has not been mapped or the nature of the

closure identified; the initial oil-water contact was not

penetrated; and the reservoir top structure is uncertain outside of

well control because of large uncertainty in seismic velocity

trends in the field. Thus it is extremely difficult to obtain reliableestimates of oil initially in place (OIIP) and reserves for the

field. However, a large body of data has been gathered over

time, including well and average reservoir pressures, oil and

water production trends, interference and transient pressure

analyses, core analyses, interpretation of 3-D seismic, and results

of specialist studies. Much of this data appeared only marginally

consistent. For example, the CO2 concentration for the produced

gas was 7% in the Waihapa-1B well and 12% in the Waihapa-2

well implying different oil compositions and possible reservoir

compartmentalisation. Notwithstanding this, these are the closest

wells in the field (600m apart) and are in pressure

communication (as unequivocally shown by interference test

analysis).The approach taken was to integrate all of the quantitative

data observations into a single Monte Carlo estimation

procedure for oil in place and reserves. For the field, two

independent estimates of oil in place are available: a volumetric

estimate obtained from mapped gross reservoir volume and

formation parameters; and a material balance estimate obtained

from pressure decline and production data. Independent

estimates of oil recovery can be obtained from recovery factors

based upon areal and vertical sweep in the fractured reservoir

and, and recovery obtained from extrapolation of well decline.

Each reservoir parameter is estimated independently and only

those sets of parameters which lead to consistent estimates of

OIIP and recovery are accepted. This methodology filters out theinconsistent sets of reservoir parameters and is referred to in this

paper as the filtered Monte Carlo method.

In 1989, just after the start of field production, it was

uncertain as to the nature of the fractured reservoir and whether

or not the matrix was contributing to flow. At this time t

filtered Monte Carlo method was used to differentiate betwe

alternative reservoir models. Following further drilling a

production a revised analysis was undertaken in 1993 which h

proven to be a robust estimator of reserves to the present time.

Fractured Reservoir Models

After Nelson1

we can distinguish four types of fracturreservoir model: Type 1, fractures provide the essent

(hydrocarbon) reservoir porosity and permeability; Type

fractures provide the essential reservoir permeability; Type

fractures assist permeability in an already producible reservo

Type 4, fractures provide no additional porosity or permeabil

but create significant reservoir anisotropy.

Classification of the Waihapa Tikorangi Formation. T

Tikorangi formation is a Type 1 reservoir under th

classification. That is, the fracture network provides the whole

the hydrocarbon storage. This interpretation is based upon co

observations and wire-line log interpretation: very low matr

permeabilities were measured in core plugs (<0.01mD); oil wnot observed in solvent extracted core plugs; and hydrocarb

saturations were not interpreted in logs.

Matrix Fracture Communication. Identification of the degr

of matrix fracture communication in the reservoir is importa

notwithstanding that the potential for oil storage in the matrix

small. Even at the low permeabilities measured in the Tikoran

core plugs, there is potential for water movement from the matr

into the fractures because of the large surface area available

flow. At permeabilities of <0.001mD water influx from t

matrix can still make a substantial contribution to mater

balance and pressure support.

Both cemented and slickenside fractures have been observin Waihapa cores. Calcite cementation provides an impermeab

barrier between the fracture channels and matrix porosity, whi

slickensiding gives rise to a zone of compacted and crush

grains along the fracture planes which can significantly redu

permeability and hence matrix-fracture communication. It

consistent with these observations to propose that the Waiha

Tikorangi formation is a non-porous fractured reservoir with

fracture-matrix interaction.

In 1989, when the first filtered estimates of OIIP were ma

for the Waihapa Field, pressure surveys were interpreted

classic dual porosity systems. Thus, at that time, the poro

fractured reservoir model was considered more likely in whi

the matrix can provide pressure support (albeit water only) to tfractures. Subsequently, in November 1990, reanalysis of t

transient pressure test trends showed that a conventional, sing

porosity model (fluid storage and permeability assigned solely

the fracture system) with boundary gave better agreeme

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SPE 39714 RESERVES IDENTIFICATION IN THE FRACTURED LIMESTONE, WAIHAPA FIELD, NEW ZEALAND

between observed and calculated pressure trends than did the

dual porosity model. Notwithstanding this the analysis presented

below also includes a term for fracture-matrix interaction.

Dual Fracture Model. The dual fracture model consists of a

primary fracture network of large open fractures in

communication with a secondary fracture system of smaller, less

extensive micro-fractures or fissures. Large extensional fractureshave been observed with fracture widths up to 16mm that could

constitute the primary fracture system. There are numerous

conjugate shear fractures on a smaller scale. Shear fractures (and

their conjugates) may exist on all scales, from fractured grains in

the matrix to reservoir wide fractures across the whole

formation. These fractures may be fold related2, and can be

associated with faulting. The relationship of fractures to faults

exists on all scales: Friedman3 used the orientation of

microscopic fractures from oriented cores in the Saticoy Field to

determine the orientation and dip of a nearby fault. In a Triassic

limestone, a frequency analysis4 of widths of open fractures was

interpreted to arise from several sets of fracture distributions

superimposed upon each other: the first was due to initialtectonic stresses; the second to weathering and exfoliation, and

other sets to karstic and strongly faulted zones.

In the Waihapa Tikorangi no evidence exists for sub-aerial

exposure (that is, weathering) and detailed core analysis failed to

find evidence of micro-fractures or fissures. However, there is

evidence of different fracture regimes in the field which could

possibly lead to a dual fracture flow regime. There is a dominant

NE to ENE striking trend with an apparent but less dominant N

to NW striking trend. The NE-ENE striking sets are generally

near vertical and the N-NW sets have shallow to moderate dips

(20 to 50o). Many fractures seen in Waihapa-2 and Ngaere-2 are

highly shattered with pieces of host rock being incorporated in

the mineralising calcite. In the Ngaere-2 well these are northerlystriking which is consistent with the trend of reverse faulting

observed in the seismic interpretation.

Complex Porosity Model. The complex reservoir model is

similar to the dual fracture model with the additional assumption

that both fracture sets are in communication with a porous and

permeable matrix.

Dual Porosity Model. The dual porosity reservoir model

assumes that there is a single dominant fracture system in

communication with a porous and permeable matrix.

Non-Porous Fracture Model. The non-porous fracture model,or single porosity fracture model, is equivalent to a conventional

single porosity model in which the fracture system provides all

of the reservoir storage and permeability.

Fracture Continuity and Permeability. Calculations5

effective fracture permeability for a 10mm opening based up

(laminar) Poiseiulle flow between the fracture walls gave valu

ranging from 1000mD for 80m spacing between fractures

greater than 80000mD for a fracture spacing of 1m. The

calculated permeabilities are significantly higher than t

permeability interpreted from pressure test analyses of betwe

27mD and 158mD. The most likely explanation for thdiscrepancy between observed permeability and theoretic

calculation is that the large extensional fractures observed

core are not continuous or connected over large distances. Th

may be en echelon with fluid flow from fracture to fracture bei

through lower permeability matrix or, more likely, through

network of smaller fissures. Alternatively, the degree

cementation in these fractures may vary, with some sectio

being almost completed cemented with paths for flow bei

either extremely tortuous or disconnected.

Components of Material Balance and VolumetricsThe reservoir model used for the material balance calculations

based upon a Type 1, complex porosity, fractured reservoir wgas cap and aquifer, no hydrocarbon saturation in the matrix, a

constant bubble-point pressure in the oil column,

The reservoir is naturally zoned into gas, oil and water zon

with boundaries at the initial gas-oil and water-oil contac

respectively. Subzones also develop during production of t

reservoir: in particular, a gassing zone6 develops below t

original gas-oil contact (OGOC) as the reservoir pressure drop

Initially, the pressure at the original gas-oil contact equals t

bubble-point pressure, with an increase in pressure with dep

due to the oil density gradient down to the original oil-wa

contact (OOWC). As the average pressure in the reservo

declines, both the gas-cap and the water-leg will expand (t

latter due also to aquifer influx) to new contact levels, being tcurrent gas-oil contact (GOC) and the current oil-water conta

(OWC). Because there are assumed to be no capillary forc

present in the fracture networks, there will be no water-transiti

zone above the OWC and no residual oil saturation in the ga

invaded and water-invaded zones behind the new contac

However, there could be oil saturations trapped in dead-e

fractures.

As the reservoir pressure declines, the pressure at the GO

will not equal the initial bubble-point pressure of the oil, but w

be in equilibrium with oil at a lower bubble-point. Because t

oil column was everywhere at the same initial bubble-point (s

PVT discussion below), we can define a current bubble-po

level (BPL) as that depth where the oil pressure equals the initbubble-point pressure. The zone between the current bubb

point level and the current gas-oil contact is called the gassi

zone. In this zone, the oil pressure is everywhere below t

initial bubble-point pressure and gas is being liberated fro

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solution. This gas percolates vertically upwards to form either

secondary gas caps or merge with the expanded original gas cap

of the reservoir.

The following zones can be identified: original gas-cap, gas

invaded zone, gassing zone (saturated oil), under-saturated oil

column, water-invaded zone, and original water-leg.

Volume Contributions to Reservoir Voidage. Oil production fora depleting reservoir is a result of volume changes for all of the

communicating components of the reservoir system:

Shrinkage of total reservoir volume

primary fracture volume (1+m+w)cf ϕf

secondary fracture column (1+m+w)cdϕd

matrix volume (1+m+w)cmϕm

Expansion of water in matrix

(1+m)ϕmSwcw

Expansion of oil in undersaturated zone

(1-s)( ϕm(1-Sw)+ϕf +ϕd)co

Shrinkage of oil in gassing zone

s (ϕm(1-Sw)+ϕf +ϕd) (Bob /Boi-1)

Expansion of gas cap

m(ϕm(1-Sw)+ϕf +ϕd)(Bg /Bgi-1)

Liberation of gas from gassing zone

s(ϕm(1-Sw)+ϕf +ϕd) Rsbp(Bg /Bgi)

Expansion of water-leg

w(ϕm+ϕf +ϕd)cw

Expansion of aquifer

BwWe

Material Balance Estimate of Oil in Place. At the start of

production the gassing zone has not formed, therefore s=0; and

the aquifer has not been activated, therefore We=0. Thus the

general material balance equation, at the start of production, is:

Nmat = (dN/dP)/( { (1+m+w)(cf ϕf +cdϕd+cmϕm)

+(1+m)ϕmSwcw

+(ϕm(1-Sw)+ϕf +ϕd)co

+m(ϕm(1-Sw)+ϕf +ϕd)cg

+w(ϕm+ϕf +ϕd)cw }/{ ϕm(1-Sw)+ϕf +ϕd } )

The decline rate, dN/dP, is defined as the cumulati

production per unit pressure decline at the start of productioThus it is unaffected by pressure support arising from creation

the gassing zone or from aquifer influx.

The components of material balance included in this compl

porosity reservoir model are: shrinkage of total fracture volum

expansion of oil in primary fractures, expansion of oil

secondary fractures, expansion of water in matrix, expansion

water below oil-water contact, and expansion of gascap. T

components of material balance excluded from the model a

shrinkage of oil in gassing zone (0 @ t=0), gas liberated

gassing zone (0 @ t=0), aquifer influx (0 @ t=0), expansion

oil in matrix (0 in this model, Sw=1), expansion of gas in matr

(0 in this model).

Volumetric Estimate of Oil in Place. Initial oil in place can

related to gross rock volume of the oil column by the equation

Nvol = f openf map(ϕm(1-Sw)+ϕf +ϕd)(V(zowc)-V(zgoc))/Boi

Calculation of Oil in Place and ReservesTwo estimates of oil in place are calculated during the Mon

Carlo simulation. These are the volumetric estimate, N

obtained from the mapped gross reservoir volume and formati

parameters, and the material balance estimate, Nmat. In order

obtain a consistent estimate of oil in place, both the volumet

and material balance estimates were rejected if they were n

sufficiently close:

Nvol and Nmat rejected if |1-Nmat /Nvol| > ε

where ε is fractional tolerance, set to 0.1 in this analysis.

Recovery. Recovery can be estimated from a volumetric swe

efficiency and oil remaining in the reservoir between t

abandonment gas-oil contact, zagoc, and the abandonment o

water contact, zaowc. Total remaining oil in the reservoir

abandonment is

Na = f openf map{ (ϕm(1-Sw)+ϕf +ϕd)(V(zaowc)-V(zagoc))

+ (1-EaEv)( V(zagoc)-V(zogoc) + V(zoowc)-V(zaowc) ) }/Boa

Volumetric recovery is defined by Rvol = 1-Na /Nvol.

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A further constraint is applied to the recovery obtained from

the oil in place estimate by application of the recovery

efficiency. The volumetric recovery is rejected if it is not

sufficiently close to the recovery estimate, Rwell, obtained from

well decline curve analysis:

Rvol and Rwell rejected if |1-Rwell /Rvol| > ε.

This criterion also ensures that the volumetric estimate is

realistic and can be tied to a proper well development sequence.

In particular, extremely low or high estimates will be rejected if

they cannot be realised by at least one well sequence.

Storativity. Consistency can also be realised with respect to well-

test analysis in the case of dual porosity or dual fracture

reservoir models. The ratio of primary fracture storativity to

volumetric system storativity, ω vol, is defined by:

ω vol = sf /stot

where

sf = ϕf (cf +co),

stot = ϕf (cf +co)+ϕd(cd+co)+ϕm(cm+Swcw+(1-Sw)co).

The Monte Carlo trial is rejected if the volumetric storativity

ratio is not consistent with the storativity ratio, ω pre, calculated

from pressure test analysis:

ω vol and ω pre rejected if |1-ω vol / ω pre| > ε.

Based on the analysis of interference tests, an independent

constraint can be also imposed on primary fracture storativity

calculated volumetrically, sf , and from interference test analysis,

spre:

sf and spre rejected if |1-sf /spre| > ε.

Further, fracture storativity is the product of fracture

compressibility and porosity. Thus a further constraint can be

applied to the independently sampled storativity, compressibility

and porosity values:

ϕf , cf and sf rejected if |1-ϕf cf /sf | > ε.

Reservoir ParametersNo reservoir parameter is known with any confidence in the

Waihapa Field. The following discussion highlights the

difficulties encountered in defining or measuring these values

and, by implication, explains the necessity of using the filtered

Monte Carlo method for reserves estimation.

Areal Closure. Neither the areal extent of fractures nor t

nature of the reservoir closure to the north of the field is know

with any confidence. A separate pressure regime is known

exist to the north and updip of the Toko-1 and Toko-2 wells. T

Waihapa reservoir closure could be due to faulting or lack

fracturing but no feature has been observed which clearly defin

the reservoir extent. In the analysis, separate depth volume tabl

were derived for both the Waihapa/Ngaere area to the Ngaerewell, VWN ,and for the undeveloped Toko area to the north of t

field, VTK. A combined depth volume table for the whole fie

was defined by

V(z) = VWN(z)+θVVTK(z)

where θV ⊂ U(0,1) was a parameter selected from a unifor

distribution between 0 and 1.

Mapping Uncertainty. Because of the significant veloc

gradients in the field, depth conversion of seismic time ma

outside of well control is uncertain but is likely to

systematically in error in the flanks of the field. This uncertainwas expressed by multiplying the total depth volume relation f

the field by a parameter, f map, where

f map ⊂ Cum(0.6,0.7,0.8,1.0,1.2,1.3,1.4).

(Cum specifies a standard cumulative probability distributi

defined in Appendix I.)

Average Fracture Porosity. Effective fracture porosity in t

area of open fractures is not known. The total of all analys

core from the Waihapa well has been calculated to avera

0.13% porosity. However, this value excludes the absence

open fractures in the Waihapa-6 well (porosity=0%) and teffective linear porosity of 1% observed during the drilling

Waihapa-6a and Toko-1. (During the drilling of both of the

wells the bit was observed to fall by 2m ~ porosity=1% in 200

of Tikorangi limestone). Fracture aperture imaging (FMS) in t

borehole is generally limited to calculating apertures of less th

1mm in size. The fractures contributing the most porosity in t

Waihapa wells are much larger than this with oil stained op

fractures of greater than 16mm being observed in co

Generally, core derived fracture porosity is dominated

relatively few fractures. In Waihapa-2, four fractures have

individual porosity contribution greater than 0.01% porosity, b

these four fractures account for around 68% of the total porosi

The largest frequency of occurrence is the size class 0.000.0001% porosity, but these fractures contribute less than 5%

the total porosity. Core porosity ranged from 0% to 0.198%

FMS porosity ranged from 0.12% to 0.56%; drilling porosi

ranges from 0% to 1% based upon drilling breaks. Vario

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calculations based upon fracture density, orientation and well

sampling ranged from 0.6% to 0.75%. There is extremely low

confidence in any of these porosity estimates. Fracture porosity,

ϕf , and secondary fracture porosity, ϕd, used in the Monte Carlo

analysis were defined by

ϕf ,ϕd⊂ Cum( 0,0.0005,0.0015,0.005,0.0085,0.0095,0.01).

Extent of Open Fractures. Various fracture models have been

proposed to define the extent of the open fractures both areally

and with respect to the layering of the limestone. None of these

models lead to quantitative predictions. Problems arise using

curvature models because of the significant changes in curvature

at all points in the formation during thrust development, and lack

of well-defined time-depth conversion on the flanks of the

structure. Although there is some evidence that fracturing in the

limestone has a stratigraphic control, recent determination of

formation storativity based upon interference test analysis (which

calculates cϕh) and Earth-Tide analysis7 (which calculates cϕ)

shows that all of the Tikorangi is contributing to formation

storativity and hence any stratigraphic control on effectivefracture porosity is weak. Of the twelve wells drilled and tested

in the Waihapa Tikorangi, nine have been productive (>2000

bpd), one has been of low productivity although in

communication with the rest of the field, one has been tight, and

one gave an inconclusive production test although losses were

noted during drilling. The areal extent of open fractures, f open,

used in the analysis was defined by

f open ⊂ Cum(0.5,0.55,0.7,0.85,0.9,0.95.1).

Fracture Storativity. A major uncertainty in the material balance

estimate of oil in place is fracture storativity. Numerous

interference tests have been completed with storativities, basedupon the full Tikorangi interval contributing to flow from

0.23x10-6

to 0.75x10-6

psi-1

. These calculated storativities are

assumed to apply to the fracture system only (that is, the primary

fracture system for the single porosity and dual porosity model,

and the primary and secondary fracture systems for the complex

porosity and dual fracture systems). A difficulty in applying the

interference test data, which was obtained assuming a single

porosity system in the analysis, is that it may not apply to the

fracture storativity concept applied in the material balance. It is

not universally agreed as to whether the interpreted storativity

applies to just the fracture system, or to both the fracture and

matrix systems combined. This difficulty in interpretation is not

a problem for the 1993 analysis which assumed that the reservoirconsists of a single porosity system with only the primary

fracture system contributing to flow.

Direct rock stress measurements were obtained from core

data for two plugs which gave storativities of 0.277x10-6

and

0.081x10-6

psi-1

for plugs with measured porosities of 0.77% a

0.25%. However, it is uncertain as to the relevance of the

measurements as the plugs will have undergone stress rel

during coring and mechanical estimates of fractu

compressibility are difficult to interpret unambiguously. T

storativities used in the Monte Carlo analysis were defined by

sf ⊂ Cum( 0.02,0.05,0.10,0.27,0.35, 0.40,0.75)x10-6.

Fracture Compressibility. Fracture compressibility can

calculated from published correlations, notably that of Jone

and Reiss5. Jones’s correlation gave a value of 100x10

-6 psi

-1 f

an initial Waihapa reservoir pressure of 4257 psia and gro

overburden pressure of 8857 psia. The method of Reiss ga

values in the range 7x10-6

to 70x10-6

psi-1

. The difference

compressibility estimates arises from different assumptions as

the compressibility of the matrix-matrix interaction at t

fracture planes. If these are mainly grain supported as in the ca

of slickensided fractures, then the effective surfa

compressibility can be very large (due to the elastic compressi

of the surface asperities which are bearing a large load oversmall area). In the case of vuggy or calcite cement support

fractures, the compressibility will tend to that of the country ro

or cement, leading to low values. Fracture compressibility w

measured in two core plug samples (the same samples for whi

storativity was calculated) with values of 32.4x10-6

and 35.9x16 psi

-1. Both these samples were 50% cemented open fracture

The compressibilities used in the Monte Carlo analysis we

defined by

ϕf , ϕd ⊂ Cum(0,0.05,0.15,0.50,0.85,0.95,1.0)x10-6

.

Oil-Water Contract. None of the Waihapa wells penetrated

oil-water contact (OWC). The lowest known oil in the field wproduced from fractures at 2838m TVSS in the Waihapa-2 we

However, in October 1989, water production (at a water-cut

40%) was observed from an interval 2751m to 2773m TVSS

the nearby Waihapa-5 well at the south of the field. A spinn

survey showed that the water was being produced from the low

part of this interval. Coning analysis of multi-rate producti

tests, using both the method of Aguilera and Acevedo9 (whi

assumed flow in a single fracture plane) and an analysis bas

upon equations of Dake10

(which assumes segregated flow on

gave an OWC at 2848m. Recently, an analysis of pressu

changes in the Ahuroa Gas Field, which is completed in t

Tariki sandstone, indicated that a breach of the reservoir h

occurred and that it is in communication with the Tikoranlimestone. The Ahuroa field is to the north of the Waihapa Fie

in the overthrust, with the Tariki sandstone bei

stratigraphically some 400m below the Tikorangi limeston

Tikorangi-Tariki juxtaposition occurs at the main tear fau

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between the Ngaere-2 and Ngaere-3 wells. If these fields are in

communication or in the same pressure regime, then a contact at

2835m TVSS can be established from the intersection of the

water gradient in the Ahuroa field with the oil gradient in the

Waihapa Field. This contact is consistent with that obtained from

the coning analysis for the Waihapa-5 well. However, the nearby

Hu Road well in the Tikorangi formation drilled to the south of

the Waihapa field, which encountered water, gives an OWC at3090m TVSS via extrapolation of gradients. In the Toko-1 well

to the north of the field, a kick occurred at 2891m TVSS and oil

was reported in the pits. Provided the oil came from the bottom

of the hole, this supports an oil down to of 2891m TVSS with an

OWC greater than this. In the Monte Carlo analysis, the oil-

water contact for the field was sampled as

zowc ⊂ Cum(2780,2800,2840,2880,2890,2920,3090).

Gas-Oil Contact. No gas-oil contact (GOC) was intersected by

any well. Highest known oil was observed in Waihapa-4 at

2579m TVSS. A sub-surface oil sample taken in Waihapa-1B

from a producing interval 2679m to 2736m TVSS and sampledat 2677m TVSS had a bubble point pressure, when measured in

the laboratory, of 3971 psia. This is some 285 psi below the

initial reservoir pressure at 2700m TVSS. Based on an oil

gradient of 0.9 psi/m this gives an equilibrium gas-oil contact at

2443m TVSS, but an error of just 50 scf/bbl in recombination

GOR leads to an error of 125m in GOC depth. Initial GOR was

1100 scf/bbl which remained constant until the average field

pressure went through the bubble point during 1994. In the

Monte Carlo analysis the gas-oil contact was defined by

zgoc ⊂ Cum(2280,2300,2380,2450,2500,2580,2600)

Initial Pressure Decline. The initial pressure decline as afunction of cumulative production gives the rate of oil in place

change with pressure, dN/dP. This can be derived by

extrapolating the slope of the initial pressure-cumulative

production decline to time, t=0.

An alternative method, which also provides a

characterisation of the aquifer, is to use the initial slope of the

self influence function11

of the field. The influence function (IF)

gives the rate of pressure decline with time for unit fluid

withdrawal rate. The reciprocal of the initial slope gives the

volumetric compressibility (rb/psi) in the immediate vicinity of

the production wells (the “local accumulation”), whereas the

reciprocal of the final slope of the function gives the volumetric

compressibility of the total field. The advantage of using thismethod is that the extrapolation to time zero is straightforward

and automatically excludes any early aquifer influx. The

calculated aquifer influence function for the Waihapa field is

shown in Figure 4. The rate of pressure decline of the local

accumulation (with respect to cumulative oil production) w

defined by

dN/dP ⊂ Cum(3000,5000,5500,7500,9500,10000,12000).

Local Accumulation Factor. Because the pressure decline in t

field is extrapolated to time zero, the volume of the loc

accumulation must be related to map volumetrics. In may not the case that all of the initial oil in place is contributing to t

initial pressure decline. To model this, a fraction of the mapp

oil volume, f local, was selected as the volume of the loc

accumulation which defines the initial pressure decline. In t

Monte Carlo analysis this was defined by

f local ⊂ Cum( 0.3,0.4,0.55,0.7,0.85,1.0,1.1).

Areal Sweep Efficiency. A review of recoveries of simi

fractured reservoirs6 gave total recovery efficiencies in the ran

60% to 66%. These recoveries were adjusted to compensate f

vertical sweep effects. The areal sweep efficiency, Ea, used in t

analysis was defined by

Ea ⊂ Cum(0.5,0.55,0.65,0.75,0.85,0.95,1.0).

Vertical Sweep Efficiency. Evidence for vertical percolation

Waihapa-4 and inverse coning of water in Waihapa-6A sugge

there is good vertical communication in the producing fractu

sets. Production testing of the Waihapa-5 well, which had be

closed in for a year (water-cut a time of shut in was 60%

produced 100% water with no oil production, suggesting that t

oil had been swept from the area of the well, at least from the t

of the structure. Vertical sweep efficiency, Ev, used in t

analysis was defined by

Ev ⊂ Cum(0.6,0.75,0.8,0.85,0.9,0.95,1.0).

Well Decline. The analysis carried out in 1989 did not inclu

estimates of individual well recovery. The 1993 analysis us

decline curve analysis to estimate remaining reserves for ea

current producer and reserves for future development and inf

wells based upon analogue production. Reserves for t

Waihapa wells (-1 to 6A) were lumped together into a sing

distribution, with reserves for the Ngaere-1 well, which h

recently been drilled, and the planned Ngaere-2, Ngaere

Toko-2 and Waihapa-8 infill wells separately represented. At t

time of the 1993 analysis, 14 MMbbl of oil had been produce

Distributions of remaining reserves for the existing Waihawells and the planned wells are given in Table 1. The historic

oil production rate and water-cut for the field to end 1997

shown in Figure 4.

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Other Reservoir Parameters. Distributions for the abandonment

oil-water contact, the abandonment gas-oil contact, the

abandonment final pressure, oil formation volume factor, water

compressibility, oil compressibility, matrix porosity and matrix

compressibility are given in Table 1.

The Monte Carlo analysis was carried out using the E&P

Workbench program12

.

Oil in Place Estimates for Different Reservoir ModelsThe 1989 study was initiated when approximately 3 MMbbl of

oil had been produced. At that time, the reservoir dynamics were

still being interpreted using dual porosity models, although these

had been extended to encompass the dual fracture and complex

porosity models. In 1991, a further analysis was carried out

using the single fracture porosity model. Significantly different

estimates of OIIP were obtained. Mean estimates of OIIP for

each model are tabulated in Table 2 together with the mean

estimates of primary and secondary fracture porosity. These

estimates range from 18.8 MMbbl for the dual porosity model,

50.6 MMbbl for the single fracture porosity model, 73.4 MMbblfor the complex porosity model, and 112.0 MMbbl for the dual

fracture model.

The complex porosity, dual fracture and dual porosity

models of the Tikorangi formation were introduced primarily to

be compatible with the interpretation of the wells tests as

exhibiting classical dual porosity behaviour. The low OIIP

calculated for the dual porosity model (with only one fracture

regime) is determined by the storativity ratio between fracture

and matrix calculated in the well test analysis. In this cases, since

the matrix contains no oil but has a high porosity (~5%)

compared to fracture porosity (~.2%) there is little room for

hydrocarbon storage. The high OIIP in the dual fracture model

arises because the secondary fracture set is oil filled and has ahigh effective porosity required to match the storativity ratio.

The complex porosity model is intermediate between these

cases.

These results show that determination as to whether the true

nature of the flow regime is that of a dual porosity system is

critical to determination of OIIP in the reservoir. Secondly,

determination of whether a secondary fracture systems exists is

also critical to the OIIP determination.

Further detailed core analysis, following on from the 1989

study, showed that the matrix permeabilities were extremely low

(<0.01mD) and that calcite cementation and surface gouge

would further reduce effective matrix-fracture communication.

The core analysis also found no evidence for micro-fracturingwhich could constitute a secondary fracture system. A re-

analysis of the pressure test data using conventional, single

porosity models in a bounded reservoir gave good agreement

between observed and calculated pressure trends in the well

tests. This view of the reservoir, as a single porosity, bound

system was also supported by analysis of the results of t

Waihapa Production Testing Programme which took place ov

two years from the middle of 1989 to the middle of 1991, a

included a full field shut in for 30 days to monitor pressu

response in the field.

Oil in Place Estimates for Single Porosity SystemUp until the end of 1991 there had been no significant wat

production from the field (apart from Waihapa-5 well which h

watered out after only 50,000 bbl of oil production). From 19

the field shows a steady increase in water production through

1993, when the Ngaere-1, -2 and –3 wells were drilled and tot

field water-cut drops. The water-cut at the end of 1997 w

almost 90%.

In 1993, the filtered recovery estimate was updated

include recovery estimates for each well. From the filter

Monte Carlo analysis, mean OIIP was calculated at 45.

MMbbl with a recovery of 27.5 MMbbl. Mean fracture porosi

was 0.51% and fracture compressibility 56x10-6

psi-1

. Figure

presents a cumulative frequency diagram for Waihapa ultimarecovery. Maximum recovery is 49.7 MMbbl, P50 recovery 26

MMbbl, and P90 recovery (at 1993) was 18.9 MMbbl.

Lookback Analysis Reserves. At the end of 1997, current production from t

Waihapa Field was 22.4 MMbbl of oil, with remaining reserve

under the “do nothing” scenario, of 0.8 MMbbl leading to

ultimate recovery of 23.2 MMbbl of oil. Development sin

1993 included the successful Ngaere-2 and Ngaere-3 wells, t

unsuccessful Toko-2 and Toko-2A northern extension we

(Toko-2 encountered hydrocarbons but was tight, and Toko-2

encountered 100% water in a separate pressure regime), and t

unsuccessful Waihapa-8 infill well which was 140m deep prognosis (due to unfavourable velocity trend) and was water

out at the drilled location.

Detailed analysis of the results of the 1993 study show

that, of the 27.5 bbl total recovery, 4.0 MMbbl of oil w

expected from up to three infill/extension wells drilled in t

Waihapa/Ngaere structure. These wells have not been drilled

were unsuccessful at the drilled locations. Subtracting t

anticipated 4.0 MMbbl of oil from the estimate of 27.5 MMb

obtained in 1993, leaves 23.5 MMbbl estimated from the th

existing production wells and the planned Ngaere wells. Th

recovery is very close to the currently booked ultimate recove

from field of 23.2 MMbbl. This result, which shows that t

1993 filtered Monte Carlo method is an excellent predictor future field performance, could be a mere coincidence but it

supported by recent work using Earth Tide analysis of reservo

storativity, and a detailed study of sweep in the field.

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Porosity and Compressibility. Earth Tide analysis calculates

formation storativity from pressure response due to the

gravitational pull of the moon and sun on the Earth’s crust13

. The

results presented in [7] are in close accord with those obtained

from interference test analysis. However, because storativity is

the product of fracture porosity with total compressibility (cf +co),

it is not possible to obtain a direct estimate of fracture porosity

from the analysis. Recall that the estimates of fracturecompressibility ranged from 5x10

-6 to 100x10

-6 psi

-1 as discussed

above. However, at the crest of the overthrust a new well

penetrated the Tikorangi limestone reservoir and flowed

hydrocarbons with a high GOR. Because of the inferred presence

of free gas in the reservoir, the effective fluid compressibility in

the fractures is much higher than that in the Waihapa reservoir

(which are oil or water filled) with the gas compressibility

(~360x10-6

psi-1

) dominating the fracture compressibility.

Calculated storativity for the well was 2.06x10-6

psi-1

leading to

porosity estimates in the range 0.55% down to 0.48% for

fracture compressibilities of 5x10-6

and 100x10-6

psi-1

respectively. Assuming both fracture porosity and

compressibility are, on average, the same for each reservoir,leads to estimates of 0.49% for fracture porosity and 47x10

-6 psi

-

1 for fracture compressibility for the Waihapa Field (based upon

average storativities). These are in excellent agreement with the

mean values of 0.51% and 56x10-6

psi-1

calculated in the 1993

study.

Infill Drilling. A study was instigated at the end of 1997 to

review the potential for further recovery from the Waihapa Field

with two infill wells, drilled as side-tracks from existing

wellbores, to be completed in the first half of 1998. A detailed

study of sweep in the field has shown that significant potential

for additional reserves exists in the north of the field, in line with

predictions from the 1993 study. Figure 6 presents a

stochastically generated bubble-map showing the areal sweep for

each production well with 70% areal sweep efficiency. Potential

for infill wells exists in the Ngaere-2 location and north of the

Ngaere-3 well.

Conclusions1. The filtered Monte Carlo method is straightforward to apply

and provides excellent estimates of OIIP and recovery even

when there is large uncertainty in the underlying reservoir

parameters.

2. For the Waihapa Field, use of the method leads to good

estimates of fracture porosity and compressibility in

agreement with recent deterministic estimates obtained by

Earth Tide analysis.3. Lookback analysis shows that the 1993 estimates of total oil

recovery from the Waihapa Field were correct.

4. The results of the 1993 filtered Monte Carlo study are being

used to identify further infill potential in the Waihapa Field.

AcknowledgmentsThe authors wish to thank Fletcher Challenge Energy and Bli

Oil and Minerals (NZ) Ltd for permission to publish this paper

NomenclatureBoa = oil formation volume factor at abandonment

pressure, rb/stb

Bob = oil formation volume factor at bubble point

pressure, rb/stbBoi = initial oil formation volume factor, rb/stb

Bg = gas formation volume factor, rb/scf

Bgi = initial gas formation volume factor, rb/scf

Bw = water formation volume factor, rb/stb

cd = secondary fracture compressibility, psi-1

cf = primary fracture compressibility, psi-1

cm = matrix compressibility, psi-1

dN/dP = rate of change of oil in place with respect to

pressure decline, stb/psi

Ea = areal sweep efficiency

Ev = vertical sweep efficiency

f open = fraction of reservoir volume with open fractures

f map = mapping factor applied to gross reservoir volumeuncertainty

Na = volume of oil in place at abandonment, stb

Nmat = material balance estimate of oil in place, stb

Nvol = volumetric estimate of oil in place, stb

m = ratio of gas cap volume to oil column volume

Rvol = volumetric estimate of oil recovery, stb

Rwell = well decline estimate of oil recovery, stb

s = fraction of oil column in gassing zone

sf = primary fracture storativity, psi-1

stot = total formation storativity, psi-1

spre = estimate of formation storativity from interference

test analysis, psi-1

Sw = matrix water saturationV(zaowc) = gross rock volume from top structure to

abandonment OWC

V(zagoc) = gross rock volume from top structure to

abandonment GOC

V(zowc) = gross rock volume from top structure to OWC

V(zgoc) = gross rock volume from top structure to GOC

w = ratio of water-leg volume to oil column volume

We = aquifer influx, stb

ε =rejection tolerance, 0.1

ϕd = secondary fracture porosity

ϕf = primary fracture porosity

ϕm = matrix porosity

θV = fraction of Toko reservoir volume includedreservoir volume

ω vol = volumetric estimate of storativity ratio

ω pre = estimate of storativity ratio from transient pressure

test analysis

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References1. Nelson, R.A.: Geological Analysis of Naturally Fractured

Reservoirs, Gulf Publishing Co., Houston (1985).

2. Murray, G.H.: “Quantitative Fracture Study – Sanish Pool,

McKenzie County, North Dakota”, AAPG Bull., Vol 52 (1968)

57-65.

3. Friedman, M.: “Structural Analysis of Fractures in Cores from

Saticoy Field, Ventura County, California”, AAPG Bull., Vol 53

(1969), 367-398.4. Kovacs, G.: Seepage Hydraulics, Elsevier Scientific Publishing

Company, Amsterdam (1981), 461.

5. Reiss, L.H.: Reservoir Engineering in Fractured Reservoirs,

French Institute of Petroleum (1976).

6. Van Golf-Racht, T.D.: Fundamentals of Fractured Reservoir

Engineering, Elsevier Scientific Publishing Company, Amsterdam

(1982), 587.

7. Wadsley, A.W. and Stoltz, L.R.: “Earth Tide Determination of

Porosity in a Fractured Limestone Reservoir, Waihapa Field, New

Zealand”, to be published , (1998).

8. Jones, F.O.: ”A Laboratory Study of the effects of confining

Pressure on Fracture Flow and Storage Capacity in Carbonate

Rocks”, JPT (1975), 21-27.

9. Aguilera, R. and Acevedo, L.: “Coning and Fingering of Oil andGas”, The Technology of Artificial Lift Methods, Volume 4,

Kermit E. Brown et al., Pennwell Books (1984).

10. Dake, L.P.: Fundamentals of Reservoir Engineering, Elsevier

Scientific Publishing Company, Amsterdam (1978), 372-379.

11. K.H. Coats, L.A. Rapoport, J.R. McCord and W.P. Drews,

“Determination of Aquifer Influence Functions from Field

Data”, JPT (1964), 1417-1424.

12. The E&P Workbench User Guide, Exploration and Production

Consultants (Australia) Pty Ltd, Hobart (1990).

13. Bredehoeft, J.D.: “Response of Well-Aquifer Systems to Earth

Tides”, J Geophys. Res. Vol.72 No.12 (1967), 3075-3087.

Appendix - Cumulative Probability Distribution

f ⊂ Cum(x100,x95,x85,x50,x15,x5,x0)

samples from a cumulative probability distribution with values

specified at 100%, 95%, 85%, 50%, 15%, 5% and 0%

cumulative probability. Thus the factor f takes a minimum value

of x100, a maximum value of x0, and has a 95% change of

exceeding x95, an 85% chance of exceeding x85, a 50% chance of

exceeding x50, a 15% chance of exceeding x15 and a 5% chance

of exceeding x5.

SI Metric Conversion Factors

psi × 6.894 757 E+00 = kPastb × 1.589873 E-01 = m3

TABLE 1 RESERVOIR PARAMETERSx100 x95 x85 x50 x15 x5 x0

ExistingWells

0 0.1 0.3 2.5 4.0 5.0 8.0

Ng-1 0 0.1 0.3 2.5 4.5 5.5 6

Ng-2 0 0 0 .5 1. 2.5 5

Ng-3 0 0.1 0.2 2.0 3.0 4.0 5.0

Infill Well 0 0 0 1.0 2.0 3.0 5.0

Bo 1.5 1.53 1.55 1.62 1.69 1.72 1.75

cw 2.3 2.5 2.73 3.23 3.73 4 4.2

co 14 15 15.5 17 18.5 19 20

zaowc U( 2600, zgoc)

zagoc U( zgoc,zgoc+100)

TABLE 2 OIIP & Porosity EstimatesOIIP(MMbbl)

TotalPorosity

PrimaryPorosity

SecondaryPorosity

Complex Porosity 73.42 .00822 .00197 .00624

Dual Fracture 111.97 .01104 .00186 .00917

Dual Porosity 18.83 .00193 .00193 na

Single Fracture 50.55 .00681 .00681 na

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Figure 1 Location of Waihapa Field, Onshore Taranaki

Figure 2 Location of Waihapa Wells and Top Structure Map

WH 1WH 2

W H 4

W H 5

W H 6W H 6 A

WH 8

NG 1

NG 2

NG 3

TK 1TK 2 T K 2 A T e a r F a u l t

O v e r t h r u s t

2 5 5 0 m TV S S

3 3 0 0 m T VS S

2 4 3 0 m TV S S

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Figure 3 Self Influence Function for the Waihapa Field

Figure 4 Production History for Waihapa Field

0 1 0 0 2 0 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1 0 0 0T i m e ( D a y s )

0

. 0 0 5

. 0 1

. 0 1 5

. 0 2I n f l u e n c e F u n c t i o n ( p s i . d / r b )

1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8Y e a r

0

4 0 0 0

8 0 0 0

1 2 0 0 0

1 6 0 0 0

2 0 0 0 0O i l - R a t e

1 9 8 8 1 9 9 0 1 9 9 2 1 9 9 4 1 9 9 6 1 9 9 8Y e a r

0

. 1

. 2

. 3

. 4

. 5

. 6

. 7

. 8

. 9

1W a t e r - C u t

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Figure 5 Cumulative Frequency Diagram for Waihapa Ultimate

Figure 6 Schematic Swept Area of Waihapa Field at End 1997

0 1 0 2 0 3 0 4 0 5 0R e c o v e r y ( MM b b l )

0

1 0

2 0

3 0

4 0

5 0

6 0

7 0

8 0

9 0

1 0 0C u m u l a t i v e P r o b a b i l i t y %

WH 1WH 2

WH 4

WH 5

WH 6W H 6 A WH 8

NG 1

NG 2

NG 3

T K 1T K 2 T K 2 A

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