Dr Harding4TH-SPE Paper 79695
Transcript of Dr Harding4TH-SPE Paper 79695
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
1/9
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.
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
2/9
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
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
3/9
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
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
4/9
4 R.C. BACHMAN, T. HARDING, A. SETTARI AND D.A. WALTERS SPE79695
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
Volume througput/Area
(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
Volume througput/Area
(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
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
5/9
SPE 95695 COUPLED SIMULATION OF RESERVOIR FLOW, GEOMECHANICS AND FORMATION PLUGGING 5
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.
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
6/9
6 R.C. BACHMAN, T. HARDING, A. SETTARI AND D.A. WALTERS SPE79695
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
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
7/9
SPE 95695 COUPLED SIMULATION OF RESERVOIR FLOW, GEOMECHANICS AND FORMATION PLUGGING 7
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
Q=125,000, BH inj pressure
Q=150,000, 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)
Q=100,000, BH inj pressure
Q=125,000, BH inj pressure
Q=150,000, BH inj pressure
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
DT=27 Deg F, BH inj pressure
DT=37 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
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
8/9
8 R.C. BACHMAN, T. HARDING, A. SETTARI AND D.A. WALTERS SPE79695
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.
References1. Sharma, M.M., Pang, Shutong, Wennberg, K.E. and
Morgenthaler, L. : Injectivity Decline in Water InjectionWells: An Offshore Gulf of Mexico Case Study, Paper
SPE 38180, 1997 SPE European Formation DamageConference, The Hague, Netherlands, 2-3 June 1997.
2. Martins, J.P., Murray, L.R., Clifford, P.J., McLelland,W.G, Hanna, M.F and Sharp, J.W.: Produced Water Re-
Injection and Fracturing in Prudhoe Bay, SPE Reservoir
Engineering, August 1995, 176-182.3. Settari, A. and Walters, D.A.: Advances in Coupled
Geomechanical and Reservoir Modeling With
Applications to Reservoir Compaction, SPE Journal
Vol. 6, No. 3, Sept. 2001, pp. 334-342.4. Settari, A. and Mourits, F.M.: A Coupled Reservoir and
Geomechanical Simulation System", SPE Journal
September 1998, pp. 219-226.
5. Settari, A.: Reservoir Compaction, Dist. Author Series
J. Pet. Technol., August 2002, pp. 62-69.6. Heffer, K.J., Last, N.C., Koutsabeloulis, N.C., Chan
H.C.M., Gutierrez, M. and Mukarat, A.: The Influence oNatural Fractures, Faults and Earth Stresses on Reservoi
Performance Geomechanical Analysis by Numerica
Modelling, North Sea Oil and Gas Reservoirs III, pp
201-211, Proceedings 3rdInt. Conf. On North Sea Oil andGas Reservoirs, Trondheim, Kluwer Acad. Publ., 1994.
7. van der Hoek, P.J.: A Simple and Accurate Description oNon-linear Fluid Leak-off in High Permeability
Fracturing, paper SPE 63239, SPE Annual Tech. Conf.
Dallas, TX. 1-4 Oct., 2000.8. Gheissary, G., Fokker, P.A., Egberts, P.J.P., Floris, F.J.T.
Sommerauer, G. and Kenter, C.J.: Simulation ofFractures Induced by Produced Water Re-Injection in a
Multi-Layer Reservoir, paper SPE 54735, SPE European
Formation Damage Conf., The Hague, Netherlands, 31
May-1 June, 1999.
9. Saripalli, K.P., Gadde, P.B., Bryant, S.L. and SharmaM.M.: Role of Fracture Face and Formation Plugging in
Injection Well Fracturing and Injectivity Decline, paper
SPE 52731,SPE/EPA E&P Environm. Conf., Austin, TX
28 Feb-3 March, 1999.10. Settari, A.: Simulation of the Hydraulic Fracturing
Processes, SPEJ, (Dec. 1980). pp. 487-500.
11.Nghiem, L.X., Forsyth, Jr. P.A., and Behie, A.: A FullyImplicit Hydraulic Fracture Model, J. Pet. Tech., 1984
pp. 1191.12. Settari, A., Puchyr, P.J. and Bachman, R.C.: Partially
Decoupled Modelling of Hydraulic Fracturing
Processes', SPE PE, February 1990, pp.37-44.13. Settari, A. and Warren, G.M. : Simulation and Field
Analysis of Waterflood Induced Fracturing, Paper
SPE/ISRM 28081, Proceedings, SPE/ISRM Meeting"Rock Mechanics in Petroleum Engineering", Delft
Aug.29-31, Balkema Publ., 1994, pp. 435-445.
14. Settari, A., Warren, G.M. Jacquemont, , J., Bieniawski, Pand Dussaud, M.: Brine Disposal into a Tight Stress
Sensitive Formation at Fracturing Conditions: Design and
Field Experience, SPE Reservoir Eval. & Eng., Vol 2
No. 2, April 1999, pp.186-195.15. Settari, A., Sullivan, R.B., and Bachman, R.C.: The
Modeling of the Effect of Water Blockage and
Geomechanics in Waterfracs, Paper SPE 77600
presented at the Annual Techn. Conf. of SPE, San
Antonio, TX., Sept. 29 Oct. 2, 2002.16. Pang, S. and Sharma, M.M.: A Model for Predicting
Injectivity Decline in Water Injection Wells, SPE Form
Eval., pp. 194-201, Sept., 1997.17. Wennberg, K. E.: Particle Retention in Porous Media
Applications to Water Injectivity Decline, PhD Thesis
Dept. of Petroleum Engineering and Applied Geophysics
The Norwegian University of Science and Technology
-
8/13/2019 Dr Harding4TH-SPE Paper 79695
9/9
SPE 95695 COUPLED SIMULATION OF RESERVOIR FLOW, GEOMECHANICS AND FORMATION PLUGGING 9
Trondheim, Feb. 1998.
18. Soo, H. and Radke, C.J.: A Filtration model for Flow ofDilute, Stable Emulsions in Porous Media 1. Theory,Chem. Eng. Sci., Vol. 41, No. 2, 1986, 261-272.
19. Sharma, M. M. and Yortsos, Y.C.: Transport ofParticulate Suspensions in Porous Media: Model
Formulation, AIChE J., Vol. 33, Oct. 1987, 1636-1643.
20. Bedrikovetsky, P., Marchesin, D., Shecaira, F.S., Souza,Antonio Luiz S., Milanez, Paulo V. and Rezende,
Emerson: Injectivity Decline Caused by Injection ofSea/Produced Water: Applications to Waterflood
Management, Paper IBP 43300, Rio Oil and Gas
Conference, Rio de Janeiro, Oct. 16-19, 2000.
21. Harding, T G., Smith, K.H., Al-Hakimi, E., Al-Seyani,A., Wilkie, D, and Willson, N.D.: Produced Water
Management: Masila Block Yemen, presented at the 2nd
International Yemen Oil & Gas Conference, Sanaa,
Republic of Yemen, 24-25 June 2002.
22. Harding, T.G., Smith, K.H., and Norris, B.: HorizontalWater Disposal Well Performance in a High Porosity and
Permeability Reservoir, paper SPE 79007, presented atthe International Thermal Operations and Heavy Oil
Symposium and International Horizontal Well
Technology Conference, Calgary, 4-7 November 2002.