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Copyright 2000, Society of Petroleum Engineers Inc.

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AbstractThis paper presents a new history matching methodology toconstraint 3-D geostatistical reservoir model to well and

production data. This methodology is a general inversion

procedure based upon the gradual deformation method. It

allows for constraining simultaneously petrophysical,

geostatistical and reservoir parameters to dynamic production

data.The gradual deformation algorithm creates realizations, which

evolve smoothly while preserving the global statistical features

of the model. The deformation process is coupled with anoptimization algorithm to automatically match production

history. After validating the inversion process on synthetic

data, we focused on real data. The inversion process involvesup to fourteen parameters constrained through a fifteen-year

production history. A coarse geostatistical model conditioned

to rock-types and porosities observed at well locations

describes the geological uncertainties. The petrophysical

uncertainties are summarized within the permeability-porositylaws considered for the two dominant rock-types in the

reservoir. The main reservoir uncertainties are the strengths of

the edge aquifers and the critical gas saturations for each rock-

type. The final match is obtained after several inversions and

is quite satisfactory with respect to well pressure, oil and waterflow rates.

IntroductionGeostatistical model enables fine geological interpretations

of the reservoir. But, they are seldom used during the history

match thus leading to a loss of geological information during

the match. However, reservoir characterization could beimproved through conditioning of the geological model to

dynamic production data. Moreover, the geological model

should be preserved and updated during the history match.

This lead to the development of a new history ma

methodology to constrain 3-D geostatistical reservoir m

to well and production data. This methodology is a ginversion procedure based upon the gradual deform

method1. It allows for constraining simultan

petrophysical, geostatistical and reservoir paramete

dynamic production data. This paper presents the method

and its application, first to a synthetic case and, then to

field.

General inversion procedureThe Gradual Deformation Method

1 (GDM) and the

Fourier Transform-Moving Average (FFT-MA) algo

yield the main components of the general inversion proc

FFT-MA algorithm

The FFT-MA algorithm is used to produce uncond

Gaussian realization y with stationary covariance func

from:

zgyy += o

where yo is the mean of y and z is a Gaussian white

Function g results from the decomposition of the cova

function as:

ggC =

Determining g and calculating the convolution produ

may be an arduous task. Translating the problem in

spectral domain makes it much easier.

Gradual Deformation Method

The GDM is a geostatistical parameterization techni

perturb a realization from a few parameters, tdeformation parameters, while preserving the

variability. It can be applied to the Gaussian white noisas input into the FFT-MA algorithm:

( ) ( ) sincos 21 zzz +=

This relation ensures that zis a Gaussian white nois

and z2 are two independent Gaussian white noises. V

deformation parameter allows for describing a ch

SPE 62922

History Matching Geostatistical Reservoir Models with Gradual Deformation MethodY. Le Gallo, SPE, M. Le Ravalec-Dupin, SPE, Institut Franais du Ptrole, and the HELIOS Reservoir Group

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2 Y. LE GALLO, M. LE RAVALEC-DUPIN SPE

Gaussian white noises. As the deformation rule is periodic, ranges from 1 to 1. When it is 0.0 (0.5), zis the same as z1(z2). Introducing z into Eq. 1 yields a Gaussian realization y.

Thus, smooth variations in induce smooth variations in y. In

other words, realization ycan be modified, whatever its size,from a single deformation parameter. All along the

deformation process, the spatial variability of yis unchanged.

Because of these properties, it is attractive to integrate theGDM into optimization processes. Thus, the search process is

designed to assess an optimal deformation parameter to

minimize a given objective function. However, consideringsolely the realization chain derived from z1and z2restricts our

investigation of the realization space. To explore other

directions, the building of realization chains is repeated. Each

of them is sequentially screened to estimate the corresponding

optimal deformation parameter. The Gaussian white noise

built from the optimal deformation parameter defined at step

(i) is used in place of z1 at step (i+1). Additionally, a new

Gaussian white noise z2 is randomly drawn for every new

chain.

This gradual deformation scheme could be extended to the

combination of more than two realizations3. The number of

deformation parameters equals the number of combined

realization minus one.

General Inversion Scheme

An objective functionJis defined prior to any optimization

process. It measures the suitability of the suggested reservoir

model. Since the GDM preserves the spatial variability, the

objective function considered here is reduced to the mismatch

between the measured data and the ones simulated for the

studied reservoir model:

( ) ( )( )( ) ( )( )( )obs1

Dt

obs2

1dzCdzPg =

ff,,J ...(4)

z is the Gaussian white noise vector characterizing the

reservoir model. dobsis the vector of measured data and CDis

the covariance matrix quantifying the experimental and

theoretical uncertainties. The objective function Jdepends on

the deformation parameters that define the Gaussian white

noise z (Eq. 3), on the structural (geostatistical) parameters g

depending on function g and mean yo (Eq. 1), and on theproduction parameters Pinvolved in the fluid flow simulation.

Parameters gand Pare not explicitly written on the right-hand

side of Eq. 4: they are integrated into the operator f mappingthe Gaussian white noise space into the data space.

The main steps of the general inversion procedure4 are

depicted in Fig. 1.They are as follows:

1. Generate an initial Gaussian white noise z1.2. Generate a complementary Gaussian white noise z2.3. Gradual deformation of z1(Eq. 3).4. Compute the corresponding realization y(Eq. 1).5. Compute the fluid flow simulation.6. Determine the objective function.

7. Minimize the objective function by varying , gand P.

8. Update the initial Gaussian white noise and ostructural and production parameters.

9. Return to step 2 as long as the match is not satisfact

ApplicationField and reservoir model

The method is applied to an offshore oil field wit

main reservoirs. They are produced through seven wellof which are perforated in both reservoirs. The sediment

deposited along an east-west direction. The upper reserv

two main layers with clean sand and feldspar-rich sand

Two-edge aquifers provide some pressure support o

eastern and western flanks. The lower reservoir has alsmain layers: one, which is mainly fine-grained sandston

some interbedded clay, the other one, which is m

dolomite. Active edge aquifers on the eastern and w

flanks support pressure in the former. The latter is a

quality reservoir except in its central zone. Clay and

dolomite barriers isolate the two reservoirs. However, flow may occur between the reservoirs through th

common production wells.Field production started in mid 1982 through n

depletion up to early 1983 when water injection took

The water injection was quite limited with respect to a

water influx especially in the upper reservoir. By mid 19production wells were gas-lifted.

A no-flow barrier models the inter-reservoir. Henc

numerical model only includes four reservoir layers (tw

each of the reservoirs). A full-field 66x67x4 regular res

grid is used. Carter and Tracy analytical approach is u

model the aquifer behavior.

2-D seismic interpretations highlighted two main fau

east-west sealing fault, a major northeast-southwest s

fault. However, several minor faults could exist. The resmodel only considered the two major faults.

Reservoir models were established considering sole

two main rock-types, referenced as the "good" one an

"bad" one. Their mean porosities are 25% and 15% (Ta

respectively. The reservoir models were constrained to

types and porosities at well locations, when these data

available. The distributions of the rock-types within the

exhibit different trends (Table 2). The main trend obser

the upper reservoir is that rock-type proportions vary alo

east-west depositional axis. For the lower reservoir, this

is submitted to a depth correlation. Thus, the good roc

is prominent in the upper reservoir model while

essentially observed in the central area of the lower res

Permeabilities (K) are correlated to porosities () with r

to the relations ( ) 65.05.6Klog += for the good roc

and ( ) 8012log ..K = for the bad one.As the four layers are modeled independently, we pr

as follows to build a reservoir model (Fig. 2):

1. Twelve Gaussian white noises were generated.2. Four Gaussian white noises were turned into

stationary Gaussian realizations (Eq. 1) usin

structural properties reported in Table 1 for the roc

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SPE 62922 HISTORY MATCHING GEOSTATISTICAL RESERVOIR MODELS WITH GRADUAL DEFORMATION METHOD

distributions.

3. These distributions were conditioned to the rock-typesobserved at well locations.

4. These four realizations were truncated with respect toproportion maps accounting for the observed trends, thus

yielding rock-type realizations.

5. The other Gaussian white noises were used as input to

create porosity realizations (Eq. 1). The structuralproperties for the good and bad porosity distributions

are detailed in Table 1. There are two porosity

realizations per layer, one for the good rock-type, and

the other one for the bad rock-type.

6. The porosity realizations were conditioned to porositymeasurements at well location.

7. The generated porosity values were used to fill the rock-type realizations.

The main fluid properties are summarized in Table 3. The

upper reservoir oil in place (STOOIP) is about 5.5 106 Sm3

while the lower reservoir oil in place (STOOIP) is about4.2 106Sm3.

Synthetic case

Before applying the general inversion scheme to real data,

we focused on a synthetic case. A reference reservoir model,

characterized by the same geological features as above, wasbuilt (Fig. 3). The fluid flow simulation was computed over a

15-year production history. The computed pressures, flow

rates, water cuts and gas oil ratios were considered as the

reference data. Then, we aimed at determining a reservoir

model capable to duplicate the reference dynamic behavior. At

this stage, the rock-type distribution, the porosity distributions,

the average porosities as well as the activity multiplier

coefficients for the two aquifers are assumed to be unknown.

History match parameters. Two experiments were planned.For the first one, we considered 5 parameters to be optimized:

the two mean porosities, the two aquifer activity coefficients,

and one deformation parameter. The porosity and aquifer

parameters were submitted to constraints (inequalities) during

the optimization process (Table 4). The deformation

parameter was used to modify the rock-type distributions for

the four layers. For the second experiment, we considered 8

parameters to be optimized: again, the two mean porosities

and the two aquifer activity coefficients, plus 4 deformation

parameters instead of one. These 4 deformation parameters

allowed for varying the rock-type distributions for the four

layers independently. Every layer was attributed a deformation

parameter. Adding new deformation parameters increases the

number of degrees of freedom and makes the inversion

process more flexible. In both cases, we used porosity

distributions different from the reference ones, but we did not

try to constrain them. That way, we introduced some noise

into the inversion process.

Results. For the two experiments, the initial reservoirmodels (Fig. 2), mean porosities and aquifer activity

coefficients were identical. With 5 parameters, satisfactory

match for the pressures (Fig. 5), oil flow rates (Fig. 6) and

water cuts (Fig. 7) was achieved after the succ

investigation of five realization chains. However, the gratios obtained for the final reservoir model did not pr

reproduce the reference ones (Fig. 8). The mean po

parameters converge towards their reference values (Fi

Unlike the east aquifer coefficient, the west one d

converge towards its reference value: it was stopped b

upper bound (Fig. 9b). Its value turned out to be correlathe water cut in well 127.

When eight optimization parameters were used inst

5, the match improves significantly (Fig. 5,Fig. 6 and F

especially for the gas oil ratios (Fig. 8). Again, we ob

that the reference mean porosity values were reached (Fwhile the behavior of the aquifer activity coefficients w

longer restricted by the bounds (Fig. 9b). After screening

realization chains, the objective function decreases bel

(Fig. 9c). With 5 parameters, it was about 25 aft

investigation of 10 realizations.

This better match is due to additional deformparameters. For the first experiment, the roc

distributions for the four layers were controlled by a deformation parameter. This deformation parameter

evolve only if its variation improved the whole res

model. Thus, its influence on the inversion process was l

by the size of the reservoir. With 8 parameters, eachdepends on a deformation parameter. They can be mo

independently, which increases the flexibility of the inv

process. Fig. 9 shows the influence additional deform

parameters. With one deformation parameter, the

reservoir model was not very different from the initia

With four deformation parameters, differences appear c

That way, we had more degrees of freedom to determine

type distributions consistent with the reference ones. It w

longer necessary to boost the west aquifer coefficient to the water cut at well 127.

Real Case

The method is used to improve the geological res

model with dynamic production constraint. The goal

work is to obtain a history match of the reservoir produ

especially oil and water, by adjusting the reservoir para

and the geological model while maintaining the

constraints (porosity and rock-type proportions at the we

History match parameters. The general inversion s

is applied to the same reservoir but with the actual 1

field production history: pressure, gas oil ratio, and wate

To model the field gas production, gas r

permeabilities are used in the history match. The r

permeabilities are modeled as function of the fluid satu

e.g. Corey model. The Corey exponents of the gas r

permeability for each rock-type are added to the inv

parameters as well as gas critical saturation for each

rock-type.The different water production behaviors of two n

wells (127 and 137) indicate there may be a sealing

somewhere between the wells. Thus, a fault was

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midway between the two wells. The fault transmissivity

coefficient was added to the inversion parameters to test ifsuch a fault may be justified by the production history.

To reproduce the different dynamic behavior of the two

reservoirs, each aquifer influence was modeled separately

using multiplier coefficient of the aquifer transmissivity.

As in the synthetic case and due to computational

constraints, only one global deformation parameter is used tomodify the rock-type distribution for the whole reservoir. The

average porosity of each rock-type is still used in the match, as

well as the intercept of the porosity-permeability relationship

for each of the rock-type.

All the above lead to 14 inversion parameters summarizedin Table 5.

The objective function (Eq. 4) used to quantify the match is a

cumulative weighted least-square function between simulation

and measurement. In this real case approach, oil production

and pressure measurements were the most important parameter

to match (heaviest weights). Given measurement uncertainties,gas production was assigned the lightest weight. The water

production was assigned an intermediate weight. The choice ofweights affects the history match and influences the absolute

value of the objective function. However, this absolute value is

not important. Only its relative evolution indicates the quality

of the match: when the objective function decreases the matchquality improves as shown in Table 5.

Results. Table 5 summarizes the parameter evolutions with

the number of realization chains. In this case, seven realization

chains were computed. However, the main parameter

adjustments were obtained at the end of the second realization

chain. The following realization chains only resulted in minor

improvements (see Table 5). The seven realization chains

implied 164 reservoir simulations whereas only 91 reservoir

simulations were used to screen the first two realizationchains. It is important to note that 15 reservoir simulations are

required to compute the gradients with respect to each of the

14 inversion parameters, which lead us to only use one global

deformation parameter.

During the screening of realization chains, the overall

reservoir oil and water productions improve significantly (as

in Fig. 10). The fit between field data and model is quite good

(see left and middle graphs in Fig. 10). The gas production is

not so well predicted by the model (see the right graph in Fig.

10) due to the low weight assigned to these measurements in

the objective function. However, the match varies from well to

well since we use a single deformation parameter for the

whole reservoir.

To reproduce the very different water breakthroughs

between well 127 and 137, the waterfront must be slowed

down between the two wells. The history match indicates that

a partially sealing fault is necessary (a 0.29 transmissivity

multiplication coefficient is used in Table 5).

The average rock-type porosity (see Fig. 11 and Fig. 13)converge towards 29 % for the good rock-type and 14 % for

the bad one as shown in Table 5. The intercepts of the

porosity-permeability law converge towards values quite

different from those obtained in the synthetic case: 1.3

0.65 for the good rock-type in the real and synthetirespectively and, 0.98 and -0.8 for the bad rock-type

real and synthetic case respectively. These differences a

to the production history used in the match. Obvious

permeability are significantly increased during the h

match as illustrated in Fig. 12and Fig. 14.

To best match the gas production profiles, the criticsaturations of the two rock-types have been switch b

inversion process (see Table 5). The Corey exponent of t

relative permeability of the bad rock-type does not pl

significant role in this match: its values do not change

the match. The Corey exponent of the gas rpermeability of the good rock-type is slightly lower.

gas relative permeability parameters play a significan

towards improving the model match of the gas productio

During the history match, the eastern aquifers are

slightly changed from their initial value (see Tab

However, the western aquifers are increased between 22 % depending on the reservoir. This suggested th

initial western aquifer were not insuring enough prsupport.

The well pressures (Fig. 15)are not well matched d

the weight assigned to pressure measurements. The

pressure match explains the large absolute value objective function even after seven realization c

However, for some wells, e.g. 127 and 238, the match is

good. For most of them, the match is quite approx

especially those exhibiting a pressure increase combine

a GOR increase towards the end of the available history

18), e.g. 137, 254 and 467. The model could not display

behavior using the parameter chosen for the match

pressure match may be improved using several deform

parameters instead of one global deformation parametthe whole reservoir as in the synthetic case.

The standard oil rates (Fig. 16) are well matche

compensate for the other phase (gas and water) rate mFig. 17and Fig. 18)since in the reservoir simulator, th

fluid flow rate was imposed for each well. Water cu

correctly predicted for wells 137 and 344. But

breakthrough (Fig. 17)is too large in 254 well and too

the other wells. With the exception of 238 and 467

where no water production was computed, the h

matching improved significantly the model fit even i

well.

The GOR match is even more difficult than the wa

match. In some wells, GOR increases despite a pr

increase towards the end of the history. Thus, the goal

match is only to model the GOR trend. As illustrated i

18, the model fit is quite improved using the g

deformation history match.

ConclusionsThe inversion methodology was successfully applie

synthetic case built from an actual field. In this case, th

matching was pretty good. With the real field production

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the match quality is not as good. It could be improved by

increasing the number of gradual deformation parameters assuggested by the synthetic study. We observed that with one

deformation parameter per layer, we gave more flexibility to

the inversion process. In such conditions, the rock-type

distributions evolved clearly. Anyway, an automatic match

was reached using several parameters. An exact match was

beyond the scope of this work. Additionally, the results couldhave been refined performing some local deformation

parameters especially around 127 and 137 wells4.

NomenclatureC = covariance

dobs= measured data

K = permeability, mD

J = objective function

g= structural (geostatistical) parameters

P= production parameters

z = Gaussian white noise

y = Gaussian realization

= porosity

=deformation parameter

AcknowledgementsThe authors wish to thank Elf Exploration Production

(EEP) and Institut Franais du Ptrole (IFP) for their

permission to publish this paper and financial support. This

work was only possible through discussions and exchanges

with all the participants to the HELIOS reservoir group project

especially G. Vincent (EEP). All reservoir simulations were

carried out using ATHOS reservoir simulator, which is jointly

developed between IFP and BEICIP-FRANLAB.

References1. Hu, L. Y., Gradual deformation and iterative calibration of

Gaussian-related stochastic models, Math. Geol., 32(1): 87-108

(2000).

2. Le Ravalec, M., B. Noetinger, and L. Y. Hu, The FFT moving

average (FFT-MA) generator: An efficient tool for generating

and conditioning Gaussian simulations,Math. Geol., 32(6): 701-

723 (2000).

3. Roggero, F., and L. Y. Hu, Gradual deformation of continuous

geostatistical models for history matching, SPE 49004, New

Orleans, LA, 27-30 September 1998.

4. Le Ravalec, M., L. Y. Hu, and B. Noetinger, Stochastic

reservoir modeling constrained to dynamic data: Local

calibration and inference of the structural parameters, SPE

56556, Houston, TX, 3-6 October 1999.

SI Metric Conversion Factorscp x 1.0 E-03 = Pa.s

ft x 3.048 E-01 = m

ft2x 9.290 304 E-02 = m2

ft3x 2.831 685 E-02 = m3

mD x 9.869 233 E-04 = m2

psi x 6.894 757 E+00 = kPa

bbl/d x 1.589 873 E-01 = m3/d

scf/bbl x 1.801 175 E-01 = St m3/ m3

Table 1 Structural properties of the reservoir model

Layer Rock-type

distributions

Porosity distributions

1 anisotropic

Gaussian variogram

1stmain axis:(0;1;0)

1stmain correlation

length: 1000m

2ndmain axis:

(1;0;0)

2ndcorrelation

length: 500m

mean: 0.

variance: 1.

anisotropic Gaussian

variogram

1stmain axis: (0;1;0)1stmain correlation leng

500m

2ndmain axis: (1;0;0)

second correlation leng

250m

good rock-type mean

good rock-type varian

6.25 10-4

bad rock-type mean:

bad rock-type varianc

6.25 10-4

2 isotropic Gaussian

variogramcorrelation length:

1000m

mean: 0.

variance: 1.

isotropic Gaussian vario

correlation length: 500mgood rock-type mean


6.25 10-4

bad rock-type mean:


6.25 10-4

3 isotropic Gaussian

variogramcorrelation length:

750m

mean: 0.

variance: 1.

isotropic Gaussian vario

correlation length: 375mgood rock-type mean


6.25 10-4

bad rock-type mean:


6.25 10-4

4 isotropic Gaussianvariogram

correlation length:

750m

mean: 0.

variance: 1.

isotropic Gaussian variocorrelation length: 375m

good rock-type mean


6.25 10-4

bad rock-type mean:

bad rock-type varianc6.25 10-4

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Table 2 Geological rock-type evolution in the reservoir

Reservoir upper upper lower lower

Layer 1 2 3 4

Rock-type drift NE SW E W E W +

depth

depth

proportion goodrock-type (%)

50 50 30 10

Table 3 Fluid properties

Depth (m) 1100

Water oil contact upper reservoir (m) 1145

Water oil contact lower reservoir (m) 1190

Initial reservoir pressure (kPa) 119 102

Bubble point pressure (kPa) 80 102

Gas gravity 0.88

Gas dissolution ratio (Rm3/Sm

3) 42

API 29

Oil formation volume factor @ bubble point

pressure (Rm3/Sm3)

1.12

Oil viscosity @ bubble point pressure (cp) 3.8

Table 4 Optimized parameters (*estimated from 5 parameters;**estimated from 8 parameters)

Parameter Initial

value

Constraint Predicted

value

Reference

value

Mean ofthe good

rock-type

porosity

0.29 29.021.0

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z1 z2

z()

g

K

flowsimulation

,g,P

Gradual Deformation

FFT-MA

optimization

P

Fig. 1 Flow chart of the general inversion loop.

Fig. 2 Porosity maps for the initial synthetic case.

Fig. 3 Porosity maps for the reference synthetic case.

Fig. 4 Porosity maps for the final synthetic case.

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0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 1 2 7

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l

5 p a r a m e t e r s


0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 1 3 7

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 2 5 4

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 2 3 8

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 3 4 4

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 3 4 7

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 4 6 7

W

atercut

T im e ( d a y s)

r e f e r e n c e

i n i t i a l

5 p a r a m e t e r s8 p a r a m e t e r s

Fig. 7 - Water cut variations: The black dots describe thereference case, the solid thin lines are the initial simulationresults, the dashed lines are the final simulation results with 5inversion parameters, the solid thick lines are the final simulation

results with 8 inversion parameters.

0 1 5 0 0 3 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 1 3 7

GasOilR

atio(m

3/m3)

T im e ( d a y

r e f e r e n c e

i n i t i a l

5 p a r a m e t e r

8 p a r a m e t e r

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 1 2 7

GasOilR

atio(m

3/m3)

T im e (d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 2 3 8

GasOilRatio(m

3/m3)

T im e (d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 2 5 4

GasOilRatio(m

3/m3)

T im e ( d a y

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 3 4 7

GasOilRatio(m

3/m3)

T im e ( d a y

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 3 4 4

GasOilRatio(m

3/m3)

T im e (d a y s)

r e f e r e n c e

i n i t i a l



0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 5

4 0

4 5

5 0

5 5

6 0

6 5

7 0

7 5

W e l l 4 6 7

GasOilRatio(m3

/m3)

T im e (d a y s)

r e f e r e n c e

i n i t i a l

5 p a r a m e t e r s8 p a r a m e t e r s

Fig. 8 - Gas oil ratio variations: The black dots descrireference case, the solid thin lines are the initial simresults, the dashed lines are the final simulation results inversion parameters, the solid thick lines are the final sim

results with 8 inversion parameters.

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Fig. 9 - Parameter evolution during the inversion for the initial synthetic case.

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

I N F & S U P R e s e r v o ir s

G

asOilRatio(m3/m3)

T im e (d a y s)

f i e l d

i n i t i a l

f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0 .0

0 .2

0 .4

0 .6

0 .8

1 .0

1 .2

1 .4

1 .6

1 .8

2 .0


Cumu

lativeOilProduction(10

6 m3)

T im e (d a y s)

f i e l d

i n i t i a l

f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0


W

atercut

T im e (d a y s)

f i e l d

i n i t i a l

f i n a l

Fig. 10 Reservoir parameter variations during history matching (left: standard cumulative oil production, center: water cut, right: ratio). The black dots describe the field measurements, the solid thin lines are the initial simulation results, and the solid thick lines afinal simulation results.

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Fig. 11 Initial porosity maps for the real case.

Fig. 12 Initial permeability maps for the real case

Fig. 13 - Final porosity maps for the real case

Fig. 14 - Final permeability maps for the real case

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0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 1 2 7

Pressure(kPa

)

T im e (d a y s)

f i e l d

i n i t i a l

2nd i t e r a t i on

f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 1 3 7

Pressure(kPa

)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 2 5 4

Pressure(kPa)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 2 3 8

Pressure(kPa)

T im e (d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 3 4 4

Pressure(kPa)

T im e (d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 3 4 7

Pressure(kPa)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

3 0 0 0

4 0 0 0

5 0 0 0

6 0 0 0

7 0 0 0

8 0 0 0

9 0 0 0

1 0 0 0 0

1 1 0 0 0

1 2 0 0 0

W e l l 4 6 7

Pressure(kPa)

T im e (d a y s)

f i e l d

i n i t i a l


f i n a l

Fig. 15 - Pressure variations during history matching. The black

dots describe the field measurements, the solid thin lines are theinitial simulation results, the dashed lines are the second iterationsimulation results, and the solid thick lines are the finalsimulation results.

0 1 5 0 0 3 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W

StandardOilRate(m3/d)

T im e

0 1 5 0 0 3 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W


T im e

0 1 5 0 0 3 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W


T im e

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W e l l 3 4 4


T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W e l l 4 6 7


T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W e l l 2 3 8


T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

W e l l 1 2 7


T im e (d a y s)

f i e l d

i n i t i a l


f i na l

Fig. 16 - Standard oil flow variations during history matchinblack dots describe the field measurements, the solid thi

are the initial simulation results, the dashed lines are the siteration simulation results, and the solid thick lines are thsimulation results.

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0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 1 2 7

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 1 3 7

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 2 3 8

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 2 5 4

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 3 4 7

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 3 4 4

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

2 0

4 0

6 0

8 0

1 0 0

W e l l 4 6 7

W

atercut

T im e ( d a y s)

f i e l d

i n i t i a l

2nd i t e r a t i onf i n a l

Fig. 17 - Water cut variations during history matching. The blackdots describe the field measurements, the solid thin lines are theinitial simulation results, the dashed lines are the second iterationsimulation results, and the solid thick lines are the final

simulation results.

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 4 6 7

GasOilRatio(m3

/m3)

T im e (d a y s)

f i e l d

i n i t i a l

2nd i t e r a t i on f i na l

0 1 5 0 0 3 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 3 4 7

GasOilRatio(m3/m3)

T im e ( d a y

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 3 4 4

GasOilRatio(m3/m3)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 2 3 8

GasOilRatio(m3/m3)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

0 1 5 0 0 3 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 2 5 4

GasOilRatio(m3/m3)

T im e ( d a y

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0W e l l 1 3 7

GasOilR

atio(m3/m3)

T im e ( d a y

f i e l d

i n i t i a l


f i n a l

0 1 5 0 0 3 0 0 0 4 5 0 0 6 0 0 0

0

5 0

1 0 0

1 5 0

2 0 0

2 5 0

3 0 0

3 5 0

4 0 0

4 5 0

5 0 0

W e l l 1 2 7

GasOilR

atio(m3/m3)

T im e (d a y s)

f i e l d

i n i t i a l


f i na l

Fig. 18 - GOR variations during history match. The blacdescribe the field measurements, the solid thin lines are thesimulation results, the dashed lines are the second itsimulation results, and the solid thick lines are the

simulation results.

SPE62922.PDF

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