Dr Harding4TH-SPE Paper 79695

8/13/2019 Dr Harding4TH-SPE Paper 79695

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Copyright 2003, Society of Petroleum Engineers Inc.

This paper was prepared for presentation at the SPE Reservoir Simulation Symposium held inHouston, Texas, U.S.A., 35 February 2003.

This paper was selected for presentation by an SPE Program Committee following review ofinformation contained in an abstract submitted by the author(s). Contents of the paper, aspresented, have not been reviewed by the Society of Petroleum Engineers and are subject tocorrection by the author(s). The material, as presented, does not necessarily reflect anyposition of the Society of Petroleum Engineers, its officers, or members. Papers presented atSPE meetings are subject to publication review by Editorial Committees of the Society ofPetroleum Engineers. Electronic reproduction, distribution, or storage of any part of this paperfor commercial purposes without the written consent of the Society of Petroleum Engineers isprohibited. Permission to reproduce in print is restricted to an abstract of not more than 300words; illustrations may not be copied. The abstract must contain conspicuousacknowledgment of where and by whom the paper was presented. Write Librarian, SPE, P.O.Box 833836, Richardson, TX 75083-3836, U.S.A., fax 01-972-952-9435.

AbstractProduced water re-injection at high rates presents a coupled

problem of reservoir flow, formation damage, stress alteration

around the injector, and fracture propagation. Accurateprediction of permeability changes, fracture propagation

pressure, and fracture dimensions is required for minimization

of disposal costs and design of surface equipment. The paper

presents the formulation and numerical implementation of acoupled reservoir, damage and geomechanical model which

includes the above couplings. Details of the model are first

described. A simple empirical damage model, calibrated tofield data is then presented. Finally, application of the

complete model to high rate reinjection in the Masila Block in

Yemen is presented. The model predictions show that it is

feasible to sustain over 100,000 BWPD in a single Masiladisposal well by injecting above fracture pressure.

Introduction

Oil production operations often produce large volumes ofwater and high rate produced water re-injection (PWRI) isusually the best method of water disposal. However, injection

wells can experience large reduction of injectivity due to

plugging caused by solids and oil in water1,2. In particular, thecombination of total suspended solids (TSS) and oil-in-water

(OIW) is particularly damaging2 and can cause equivalent

skins on the order of 200 or more. Consequently, injection

pressures increase with time and induced fracturing may takeplace.

The prediction of injectivity and fracture propagation in

injectors experiencing damage is a complex coupled problem

including multiphase flow, geomechanics (stress changes)

formation plugging, and fracture mechanics. This paper

describes the formulation and numerical implementation of a

model, which treats all of the above phenomena. The model isan extension of a previous coupled reservoir and

geomechanics model3,4, combined with a dynamic fracture

propagation feature and permeability reduction model. Thereare several possible approaches to fracture propagation

modeling, which will be discussed in detail. The plugging

mechanics is based on a simple, yet realistic model that can beeasily implemented in any conventional simulator.

The formulation described here has been implemented in the

GEOSIM modeling system and also in the Open Eclipse

environment. The software has been used to model the PWRIinjection in the Masila block in Yemen, operated by Nexen

Inc. Although the details of the engineering study are beyondthe scope of this paper, the methodology of conducting suchstudies and the consequences of the plugging mechanics for

history matching will be presented in detail. The model shows

in particular the importance of the coupling between theplugging, which generates increased pressure gradients, the

associated poroelastic and thermoelastic stress changes, and

the resulting fracture propagation pressure.

Formulation of the modelThe coupled model consists of four main components:

Fluid flow model

Deformation and stress modelDynamic fracture model

Permeability damage model

Because the formulation of the first two components has been

described previously3,4, this Section will give only a brief

overview and highlight the couplings between them, followed

by a detailed discussion of the fracturing and the damage

model in the following Sections.

Reservoir flow.

This part of the system is a conventional 3-dimensional 3-phase black oil simulator. This model is the host or master

SPE 79695

Coupled Simulation of Reservoir Flow, Geomechanics, and Formation Plugging WithApplication to High-Rate Produced Water Reinjection

R.C. Bachman, TAURUS Reservoir Solutions Ltd., T.G. Harding, Nexen Inc., A. (Tony) Settari, U. of Calgary and D.A.Walters, TAURUS Reservoir Solutions Ltd.


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2 R.C. BACHMAN, T. HARDING, A. SETTARI AND D.A. WALTERS SPE79695

for the other components. In the actual implementation, of the

software, the host reservoir model can be either Eclipse 100 or

the DE&S thermal reservoir simulator TERASIM.

Deformation/stress model

The model used is a continuum finite element code which

solves the classical poro and thermoelasticity equations for

nonlinear elasticity in an incremental fashion. The model alsohas elasto-plastic capabilities (discussed in Ref. 3) which have

not been used in this work.

In typical geomechanical applications, the main couplings

between the flow and stress are through the changes in

porosity (pore volume coupling) and through stress dependentpermeability (flow properties coupling). The first is dominant

in compaction problems5, while the second is important in

problems such as waterfloods in jointed media6.

In PWRI problems, both of these couplings are of minorimportance until formation failure is induced around the

fracture. However, there are additional couplings arising fromfracturing and damage mechanisms:

Permeability reduction due to damage can be verylarge (especially close to the injector), and will

completely overshadow any stress-dependent

changes.

Stress changes around the injector due to pressureand temperature changes cause time-dependent

changes in fracture initiation and propagation

pressure.

Because the pressure gradients are a strong functionof the damage, there is a strong coupling between thedamage, time of the start of fracturing, and fracturing

pressures.

Modeling of induced fracturing in geomechanicsFracture modeling can be approached from either the fracture

mechanics side, or the reservoir flow side.

a) The conventional hydraulic fracturing models (intendedprimarily for stimulation treatments) focus on details of

fracture geometry and other fracturing physics, and decouple

the reservoir flow by the use of analytical leak-off models. Itis well known that this approach becomes inaccurate as the

leak-off increases. The analytical reservoir treatment can be

improved considerably7and incorporate the plugging effects8,9

but ultimately such models are limited in generality.

b) The alternative approach is to build a model of fracturing

into a reservoir simulator to treat the leak-off implicitly. Such

models have been known since the 1980s. Early examples10,11

coupled 2-D analytical or pseudo-3D fracture geometrymodels with 3-D, 2-phase, thermal reservoir models.

However, the coupling with stress was still not included andconsequently the fracture propagation pressure had to be

specified.

For PWRI problems, the stress coupling and its effect on

fracture mechanics is significant. Therefore, the ultimate

PWRI fracturing model consists of three fully coupled

components: 1) Fracture mechanics model (computingfracture geometry, flow and heat transfer inside the crack), 2)

reservoir model (computing flow, heat transfer and damage in

the reservoir) and 3) geomechanics (computing stress-strain

response of the reservoir and its surroundings to pressure and

temperature changes, and loading on fracture face).

Some of the important couplings between the components are:

Pressure in the fracture is a boundary pressure forreservoir flow (leak-off)

Fracture width and pressure are equal, respectivelyto the displacement and normal stress on the crack

boundary in the stress model

Pressure and temperature in the reservoir are loadsfor the stress solution

Effective stress and volumetric strain determinereservoir permeability and porosity

The modeling approach can be either to formulate the entire

problem in a fully coupled manner, or in a modular fashion. In

a fully coupled model, the couplings become internal

compatibility conditions and are satisfied automatically, bu

require internal iterative process. In the modular approachused in this work (see Fig. 2 of Ref. 4), the compatibility

conditions can be satisfied by external iteration between the

modules, or approximated. We will now describe two existing

methods of implementing fracture modeling in the context of amodular system and discuss the outstanding issues for

rigorous coupling. Both methods are based on the assumption

that the primary interest in the modeling is to predict welproductivity or injectivity under fracturing conditions, and the

fracture geometry details are not as critical.

Partially coupled approach

The first is an extension of the partially coupled concept for

modeling stimulation treatments (Settari et al. 1990). The

fracture propagation is pre-computed using an uncoupled

fracture mechanics model (such as the models discussed undera) above). For the coupling with reservoir, the fracture must

lie in a grid plane of the flow model and it is represented in the

flow model by increased transmissibilities, which arecalculated from the local fracture width. The stress model

shares the mesh with the flow model; but the fracture width is

typically not used as a displacement boundary condition in

fracture plane. Since the transmissibilities are re-computed intime, the model can represent the dynamic process of fracturegrowth, or the propped or acidized fracture after the treatmen

(essentially static except for the conductivity changes due to

stress).

This approach also ignores the effect of created fracture

storage on pressure (this effect is however significant only

when the fluid efficiency is high). Since the leak-off duringthe fracture propagation calculations is computed

independently, there is no guarantee that it will be correct

This will show up as a mismatch in computed injection

pressures from the fracture mechanics and reservoir model: if


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SPE 95695 COUPLED SIMULATION OF RESERVOIR FLOW, GEOMECHANICS AND FORMATION PLUGGING 3

the predicted fracture growth rate is too small, coupling this

fracture into the reservoir model will produce pressures which

are too high and vice versa. Similarly, the poro andthermoelastic back stresses (also referred to as back

stresses) are computed independently in the fracture model,

and do not necessarily agree with the stresses on the fracture

face computed by the stress model. In spite of these

limitations, this method has been used extensively and can beapplied successfully to a number of problems if the models are

tuned to produce the same pressure history13,14.

Fully coupled approach with simplified fracture mechanics

The second approach is similar to that presented recently for

modeling waterfracs15. The idea is to use stress-dependentpermeability functions, which can represent the flow behavior

of the fracture in a fully coupled manner. In the potential

fracture plane (normal to the minimum effective stress), the

permeability (or directly the flow transmissibility) is increased

by several orders of magnitude as the effective stress normalto the fracture decreases. A typical function (permeability

multiplier) is shown in Fig. 1.

Fig. 1 Typical stress-dependent transmissibility functions

to represent fracture in the flow model

The shape of the curve can be related to the fracture width

versus net pressure (i.e., stiffness) and its position to net

pressure in the fracture. Imposing a maximum is necessary tomaintain the stability of the model. The coupled reservoir and

stress model is then run without any reference to a fracture

mechanics model, and the region where the flowtransmissibilities have reached large values is deemed to

represent the fracture.

This approach provides implicit coupling between reservoir

stress and fracture propagation pressure (i.e., the back stress is

implicit), However, the model lacks the fracture mechanicsfeatures. First, the crack opening is not included as a boundary

condition on the stress model. In soft formations with small

modulus and low fracture net pressure, the additional stress

from the opening will be small. Second, the fracture volume is

not represented. Again, this will not be a problem in high leak-

off situation, but this aspect can be modeled rigorously byeffective stress dependent porosity of the fracture blocks

Finally, the tip growth variables need to be introduced. This

may be important in hard rock, if fracture propagates through

a layered stress system (as it is usually the case), vertica

growth through stress barriers may be poorly represented if thefracture opening is not included in the stress model. In the

example of Fig. 2, where high stress layer is present within theperforated interval, the approach may produce two separate

fractures while the true solution may be a single fracture

Therefore the model will tend to exaggerate the confinement

of the fractures.

Confining

stress

Fracture mechanics

model

Stress dependent k

model

Fig. 2 Possible fracture geometry differences

On balance, our experience indicates that for PWRI fracturing

the reservoir flow and coupling with stress are more importanthan the fracture mechanics features, and therefore the coupled

method was used in this work. Its most significant advantage

for field applications is that it can model fractures in differentdirections (in Cartesian as well as in Corner Point Geometry

grid), and within local grid refinement, as shown in Fig. 3.

Fig. 3 Possible fracture representations using the

transmissibility modifier method

Further work is ongoing to remove some of its limitations andto make it a fully coupled solution for general applications.

1

10

100

1000

10000

100000

-600 -400 -200 0 200 400 600

Effective stress normal to fracture

Transmissibilitymultiplier

Increasing net

pressure in fracture


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The damage modelRigorous modeling of formation damage involves solving the

equations for particle transport and entrainment in porousmedia. While such models have been developed16,17, they are

currently too complex for full-field application and require

parameters directly describing the physics, which are usually

not readily available. For modeling purposes, it is desirable to

have a simple model with few parameters, which can becalibrated directly against field injection data.

Several authors18,19,20 postulated a model in which the

permeability reduction at a given point in the media is

expressed in a form:

)1(

1/ 0

+=kk (1)

where is some measure of the concentration of the particlesat that location. We now make an assumption that can berelated to the amount of the water that passed through thislocation. In a one-dimensional setting, this is simply

=t

dttQAtVt0

)(/)()( (2)

In a finite difference form, at the end of time step K,

nK

n

nKK tQAVt = =1

/)( (3)

where Qnis the computed water flow rate through the area A

during the time step n. Based on testing on field data described

later, the above formula was further generalized to thefollowing:

))/(1(1

1/

min

min0nAVR

Rkk+=

(4)

where , n and Rminare the three parameters of the model.The parameter represents the intensity of the damage and is

primarily related to the water quality (TSS and OIW) in

combination with reservoir permeability. Increasing accelerates damage as shown on Fig. 4. The exponent n

changes the shape of the damage curve as shown in Fig. 5.The factor Rminwas introduced because of field evidence that

the damaged permeability does not decrease to zero but

reaches an asymptotic minimum value, which in Eqn. (4)

becomes kmin= k0Rmin(see Fig. 6).

Laboratory tests on cores21 and field tests in the Masila

Block22suggest that there is also a dependence of damage onflow velocity. Fines migration testing in the lab has indicated a

dependence of permeability on flow velocity. In the field,

there is little or no damage observed during production tests

conducted immediately after drilling and completing disposal

wells nor during low rate injection tests, while damage isdefinitely observed even in short duration high rate injection

tests. This aspect is being investigated further.

Damage model with constant n=1, Rmin=0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100

Volume througput/Area

(k)d

amaged/(k)initial

alpha=0.01

alpha=0.1

alpha=1.0

Fig. 4 Effect of on damage function

Damage model with constant =0.5, Rmin=0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100


(k)damaged/(k)initial

n=1.0

n=0.6

n=1.4

Fig. 5 Effect of exponent non damage function

Damage model with constant alpha=0.5, n=1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.1 1 10 100


(k)dam

aged/(k)initial

Rmin=0.0

Rmin=0.1

Rmin=0.2

Fig. 6 Effect of residualRminon damage function

Implementation

Equation (4) was extended to 3-D flow and implemented in

the flow calculation via another set of transmissibility

multipliers (which are cumulative to those arising from

fracture propagation). It should be noted that, in the use ofEqn. (4), a distinction must be made between in-situ reservoir

water flow and injected water flow, because it is assumed that

the flow of the in-situ water does not create damage. Trackingthe difference can be accomplished in two ways:

a) Defining two water components in the model (e.g., by using

the oil component for in-situ water and water componenfor injected water). This is often sufficient as the injection

usually takes place into a water zone.

b) Using a tracer tracking capability in the reservoir modelThis is more general as it retains all model capabilities and


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allows injecting several produced water types with distinct

plugging properties.

The first method is used in the TERASIM based model, and

the second in the Eclipse based one.

Validation Gulf of Mexico data

As an example, consider the data for the Gulf of Mexico(GOM) wells reported in Ref. 1. All wells were limited to

injecting below fracture pressure, and temperature effects aresmall. This allows the testing of the damage model in a simple

setting without stress or fracture coupling. The reservoir data

is found in Ref. 1. Well A39 started injecting at 5000 BWPD

but the injectivity decreased to below 1000 BWPD in less than

a year. The decline was matched with the overall value of =0.12 (1/ft)n and n=1 as shown in Fig. 7. The value wasdecreased temporarily at early times to account for the acid

jobs. At late times, damage was limited byRmin= 0.0002.

Bullwinkle A39

7400

7600

7800

8000

8200

8400

8600

8800

9000

0 50 100 150 200 250 300 350 400 450

time (days)

BHP(psia)

0

1000

2000

3000

4000

5000

6000

7000

8000

InjRate(BWPD)

BHP data

Inj rate data

Model match

Fig. 7 Match of productivity decline GOM Well A39

Well A42 has similar history and its match, shown in Fig. 8,

was obtained with the same parameters as for A39. The well

Bullwinkle A42

7400

7600

7800

8000

8200

8400

8600

8800

9000

0 50 100 150 200 250 300 350

time (days)

BHP

(psia)

0

1000

2000

3000

4000

5000

6000

7000

8000

InjRate(BWPD)

BHP data

Inj rate data

Model match

Fig. 8 Match of productivity decline GOM Well A42

had a high initial skin, which was accounted for by initialpermeability reduction close to the well. Matches of similar

quality have been obtained for all other wells. The effect of

the acid treatments performed in some of the wells can be

modeled by the removal of the damage around the well.

The method of treating the damage, although very simplified

is remarkably realistic. Due to its empirical nature, the damage

parameters must be obtained by history matching of field data

or laboratory experiments. However, when the field injectioninvolves fracturing, the matching process is more complex, as

will be shown next on the example of the Haru 4 well of theMasila project.

Application high rate injection in the Masila Block

The Masila injection project

Canadian Nexen Petroleum Yemen Ltd. operates the Masila

project in the Republic of Yemen on behalf of its partner

Occidental Petroleum Ltd., Consolidated Contractors

Company S.A.L. and the Government of the Republic ofYemen. Oil production comes mainly from the high porosity

and permeability Upper Qishn sandstones of LowerCretaceous age. Currently, the operation produces 230,000

BOPD and over 1,000,000 BWPD. The produced water is

reinjected at matrix injection pressures mainly into the Upper

Qishn section below the original oil-water contact in each

field. The target injection horizon is the S2/S3 zone, which isconnected to the large regional aquifer, which underlies the

producing areas. Despite the high quality of the reservoirs

injectivity problems have hampered the project since inception

and have prompted the investigation of causes of theseproblems and the development of remedies. Further details o

the Masila operation and the analysis of water injectivity in

the laboratory and field have been reported earlier21, 22.

Produced water is currently reinjected into 24 vertical plus 4horizontal wells. These wells experience poor initia

injectivity that decreases further as a result of impurities in the

water that are impractical to remove through well headfiltration. Well acidizing or proppant fracturing the injectors

provided only temporary increases in injectivity. Additiona

disposal wells will be needed as water production continues toincrease. To meet future needs, Nexen plans to drill 4 to 6

injection wells to allow for the additional wastewater disposal

of approximately 500,000 BWPD. The present work wasundertaken to evaluate high rate produced water reinjection

above formation parting pressure.

A simulation study was conducted (and is currently beingupdated) to provide insight into the damage mechanism in theQishn sands, determine the injectivity and required wel

spacing at fracture conditions, and ultimately predict the

surface injection pressures at various target rates. In this way

the injection project can be optimized with respect to numberof wells needed versus the cost for the surface equipment.

In this paper, we only present the parts of this work thaillustrate the particular features of the coupled modeling and

its results. The results of the engineering study including the

details of the geomechanics will be published in a future

article.


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Calibrating the model

Two wells were used to calibrate the model: Camaal 30 andHaru 4.

The Camaal 30 well was completed in the S2 zone, with net

pay of 102 ft and permeability of 1307 md. Injection began

June 26, 1999 and continued with some interruptions untilFeb.4, 2001. During that time a number of workovers took

place, including filter changes, acid jobs and a propped fracjob. Conventional analysis using Hall plots and equivalent

skin calculations clearly showed the temporary nature of

injectivity improvement from these interventions. History

matching established the damage parameters, but becauseCamaal 30 is a low injectivity well, more emphasis was

placed on the Haru 4 calibration.

The Haru 4 well is more representative of future injectors. The

well is completed in water bearing S2 zone with net pay of 96ft and average permeability of 4300 md. The injection history

from February 1, 1999 to January 6, 2001 is in Fig. 9, togetherwith an interpreted skin due to damage, assuming radial flow.

Haru-4 - Injection Rate and BHP and interpreted damage skin

0

500

1000

1500

2000

2500

3000

0 100 200 300 400 500 600 700 800

Time (days)

BHP(psia),damageskinx10

30000

40000

50000

60000

70000

80000

90000

InjectionRate(stb/d)

BHP

skin from damageInjection Rate

Fig. 9 Field data for Haru 4 and interpreted damage skin

It was modeled with a single layer reservoir model coupled

with a 5-layer geomechanical model, using a Cartesian grid.Permeability damage model was used and fracture propagation

(if predicted by the model) could take place. Highly refined

grid was used in the potential fracture path and the model wasset up to act in an infinite manner. Water was injected at a

temperature of T = 27 deg F below reservoir temperature in

all cases. A total of 701 days of injection was modeled. Itbecame quickly apparent that the couplings present in the

physical system allow non-unique interpretation, if the

pressure is the only data matched. Three major factors were

identified:

a) Thermal expansion coefficient aL. Its value controls the

thermal stress component Twhich is added to the far-fieldconfining stress c. This in turn changes the fracture initiationand propagation pressure.

b) Damage strength (parameters , n and Rmin). Increaseddamage accelerates fracturing, but also increases the

poroelastic stress change pe, which increases fracturepressure.

c) Friction pressure loss in the fracture pfric (part of the nepressure), directly related to fracture conductivity. In PWR

injection, plugging occurs inside the fracture as well and can

significantly increase injection pressures. If the fracture

conductivity is finite, pfric increases significantly with

fracture length xf.

Thus, the observed injection pressure pfduring fracturing can

be written in a simplified manner as

pf= c- T(T) + pe(dam) + pfric(dam, xf) (5)

which illustrates the competing nature of these parameters. ForHaru 4, thermal expansion coefficient was not measured at the

time. Based on literature data, a median value of a L= 0.648 x

10-51/0F and a high value of 1.6 x 10-51/0F were selected

The cases of low and high fracture conductivity wereconstructed by choosing the maximum of the fracture

multipliers shown in Fig. 1 as 104

and 105

. The damageparameters were then varied to obtain a match for each caseFig. 10 shows the comparison of the pressure match for three

cases:

Case 1: Median aL= 0.648 x 10-5, low frac conductivity

Case 2: High aL= 1.6 x 10-5, low frac conductivity

Case 3: High aL= 1.6 x 10-5, high frac conductivity

1500

1700

1900

2100

2300

2500

2700

0 100 200 300 400 500 600 700 800

time (days)

BHP,

dataandsimulated(psia)

40000

50000

60000

70000

80000

90000

100000

Observed BHP

case 1

Case 2

Case 3

inj rate

Fig. 10 Comparison of pressure matches with three sets o

coupling parameters

These matches required different damage parameters as shown

in Table 1. Case 1 had the lowest amount of thermal stress andtherefore required the smallest amount of damage (see Eqn

(5)). In fact, the damage was not sufficient to initiate afracture. To maintain the match at late times, it was necessary

to increase Rmin with time (reduce cumulative damage)

Although we do not have a physical explanation for this

phenomenon, it is in agreement with the conventional skin

analysis shown in Fig. 9 where the skin decreases from 100 to65 during the second year. Case 2 had larger thermal stress

Tand required more damage (pe) to match pf. Howeverbecause of the low fracture conductivity, the friction pressure


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pfricwas significant, and the altered stress (i.e., c - T +pe) required was lower than pf. This resulted in a smallfracture of about 9 ft. Case 3 required much more damage asthe friction pressure was small and the altered stress needed to

be higher than in Case 2 and close to the injection pressure.

The effect of higher damage was to accelerate fracture

propagation; the length at the end was 366 ft.

Case (1/ft) n Rmin1 - median aL 0.0005 1 0.1

2 - high aL,high conductivity 0.002 1 0.035

3 - high aL,low conductivity 0.2 1 0.003

Table 1 Damage parameters for the 3 matches

The damage in the first two cases is localized close to the

injector, while in Case 3 it reaches far into the reservoir. Inthis respect, Case 3 is considered less realistic. Apart from the

oscillations due to fracture crossing block boundaries (which

could be reduced by still finer gridding), the three matches are

of similar quality, yet they produce a very different picture of

the process. This demonstrates the danger of using coupled (orany) modeling with too little data. The ambiguity can be

however dealt with as discussed below.

Predictions for typical future injectors

At this preliminary stage, all three scenarios were used to

generate forecasts for injection rates up to 150,000 BWPD,

and with different T, with the aim to determine the safesurface injection pressure (THP) specifications. At higher

rates, all scenarios produced fracturing, but the predictedsurface pressures were somewhat different.

For Case 1, the damage is low such that even the low

fracture transmissibility results in high dimensionless fractureconductivity. The predicted BHP is insensitive to rate as

shown on Fig. 11 for the case of T =27 oF. Therefore THP isprimarily a function of wellbore friction. For Case 2 there is a

significant dependency on rate as well as on fracture length,

and the BHP as well as THP continues to increase with time,

as shown on Fig. 12 T =27 oF. For Case 3 the pressure alsoclimbs with time. In all cases, injection temperature has a

large effect on BHP as shown in Fig. 13 for Case 1.

Case 1 Forecast - Infinite Reservoir, BHP for Various Rates for DT=27 deg F

2000

2200

2400

2600

2800

3000

3200

3400

0 200 400 600 800 1000 1200 1400 1600 1800 2000

time (days)

BHPinjpressure(psia)

Q=100,000, BH inj pressure



Fig. 11 BHP dependence on rate for Case 1, T =27

oF

Case 2 Forecast, infinite reservoir, BHP for various rates, DT=27 deg F

2000

2200

2400

2600

2800

3000

3200

3400

0 200 400 600 800 1000 1200 1400 1600 1800 20

time (days)

BHPinjpress

ure(psia)




Fig. 12 BHP dependence on rate for Case 2, T =27oF

Case 1 Forecast - Infinite Reservoir, BHP for Various DT, Qw=150,000 stb/d

2000

2200

2400

2600

2800

3000

3200

3400

0 200 400 600 800 1000 1200 1400 1600 1800 20

time (days)

BHPinjpressure(psia)

DT=17 Deg F, BH inj pressure



Fig. 13 BHP dependence on T, Case 1, Q=150,000 BWPD

Design consequences

It is obvious that due to the complexity of the process, as

many uncertainties as possible must be eliminated to design

high rate re-injection projects. First, data for aLcan be easilymeasured. Second, the damage can be calibrated by matching

injection tests below fracture pressure where the fracture

aspects do not interfere (like in the GOM example above)

Finally, for injection in fracture mode, analysis of steprate/fall-off tests and fracture diagnostics methods can be used

to determine fracture dimensions and conductivity by other

means, thus leaving only the damage as a matching parameter.

The above principles were followed in a subsequent study. Asa result, an essentially unique match for Haru 4 was obtained

and the uncertainties of the THP predictions were significantly

reduced. As a result, it was possible to recommend ANSI 600standard for the surface equipment design that will result in

significant cost savings for the operator.

Conclusions1) A numerical model solving in a coupled fashionmultiphase flow, geomechanics (stress changes), formation

plugging, and fracture mechanics has been developed.2) A simple, flexible model of permeability damage was


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formulated and implemented in the reservoir flow part of the

system. It is capable of reproducing the injectivity loss

observed in Gulf of Mexico and Masila Block wells.3) The factors controlling injection pressure match are thefracturing, the degree of reservoir permeability damage and

thermal stresses, which are dependent on the rock thermal

expansion coefficient (T).

4) Multiple interpretations of the field injection pressures arepossible, with trade-off between the thermal stress magnitude,poroelastic stress induced by permeability damage, and

fracture conductivity. However, if laboratory data on T isavailable, history match can be used to characterize the

plugging mechanics.

5) Accurate prediction of injection pressure is critical as itdirectly impacts facilities and pipeline design specifications.Forecasting with the calibrated model indicated that 100,000

BWPD injectors should be possible without exceeding ANSI

600 standard for surface equipment design.

6) Due to the cumulative permeability damage, the onlyfeasible method of maintaining injectivity in high rate

produced water re-injection is sustained fracturing.

NomenclatureA = flow area (m2)

aL = linear thermal expansion coefficient (1/deg C)

k = permeability (md)

k0 = undamaged permeability (md)n = exponent in damage equation

pf = fracture propagation pressure (kPa)

Q = injection rate (m3/d)Rmin = maximum damage parameter in Eqn. (4)

V = cumulative water flow through area A (m3)

= damage strength parameter in Eqn. (4) = coefficient in Eqn. (1)T = thermal stress (kPa)pe = poroelastic stress (kPa)pfric = friction pressure in the fracture (kPa)T = temperature difference (reservoir-inj) (deg C)c = undisturbed confining stress on fracture (kPa) = particle concentration (kg/m3)

AcknowledgementsThe authors wish to thank Nexen Inc. and its partners in the

Masila Project, Occidental Petroleum Ltd., Consolidated

Contractors Company S.A.L. and the Government of the

Republic of Yemen, for the permission to publish this paper.

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Dr Harding4TH-SPE Paper 79695

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