PROCEEDINGS, Twenty-Eighth Workshop on Geothermal Reservoir EngineeringStanford University, Stanford, California, January 27-29, 2003SGP-TR-173

OPTIMIZATION OF REINJECTION IN GEOTHERMAL RESERVOIRS

Irtek Uraz and Serhat Akin

Middle East Technical UniversityDepartment of Petroleum and Natural Gas Engineering

Ankara, 06531 TURKEYe-mail: serhat@metu.edu.tr

ABSTRACT

Re-injection of produced geothermal water forpressure support is a common practice in geothermalfield management. The location selection of the re-injection well and the rate of injection is achallenging subject for geothermal reservoirengineers. The goal of optimization for this type ofproblem is usually to find one or more combinationsof geothermal re-injection well locations that willmaximize the production and the pressure support atminimum cost and minimum temperature decrease.Although the number of well combinations ispotentially infinite, it has been customary to pre-specify a grid of potentially good well locations andthen formulate the search to locate the most time- orcost-effective subset of those locations that meetsproduction goals. To achieve this goal neuralnetwork technology is proposed. First, a knowledgebase of representative solutions for a geothermal fieldlocated in Turkey was developed using a simulator.Then artificial neural networks to predict selectedoutcomes was trained and tested. In the next stepwell combinations and injection rates of these wellsto predict outcomes with a given number of injectionwells were generated.

INTRODUCTION

One of the methods used in geothermal reservoirmanagement is to reinject geothermal fluid back intothe reservoir. Initially started as a disposal method,reinjection has become a common practice forincreasing the amount of energy that can berecovered from a geothermal reservoir (Goyal, 1999;Axelsson and Dong, 1998). Several parameters needto be considered for a successful reinjection process(Stefansson, 1997):

1. Disposal of waste fluid2. Cost3. Reservoir temperature (thermal

breakthrough)4. Reservoir pressure or production decline5. Temperature of injected fluid6. Silica scaling7. Location of reinjection wells

8. Chemistry changes in reservoir fluid9. Recovery of injected fluid10. Subsidence

The proper selection of reinjection location, isperhaps the most important factor affecting thesuccess of the reinjection and it has long been acontroversial subject in the geothermal literature.There are differing opinions regarding the locationselection from injecting outside the field (Einarssonet al, 1975) which is the most common reinjectionconfiguration (Stefansson, 1997) to injection somefraction of the waste water near the center of thereservoir (Bodvarsson and Stefansson, 1988). Yetanother reinjection strategy is to consider productionand injection wells are interchangeable and that theyare distributed uniformly in the field (James, 1979).A ramification of intermixed reinjection model is tointerchange the injection and production wells atdifferent parts of the reservoir for different times(Stefansson, 1986). Sigurdsson et al (1995)concluded that the peripheral injection is better if themaximum thermal sweep is of greater importancethan pressure maintenance.

Artificial Neural NetworksWithin recent years there has been a steady increasein the application of neural network modeling inengineering. ANNs have been used to address someof the fundamental problems, as well as specific onesthat conventional computing has been unable tosolve, in particular when engineering data for design,interpretations, and calculations have been less thanadequate. Also with the recent strong advances inpattern recognition, classification of noisy data,nonlinear feature detection, market forecasting andprocess modeling, neural network technology is verywell suited for solving problems in the petroleumindustry. Within the last five years, work has beenpublished covering the successful and potentialapplication of ANNs in different areas of thegeosciences (Yilmaz et al, 2002).

Neural computing is an alternative to programmedcomputing which is a mathematical model inspired

by biological models. This computing system ismade up of a number of artificial neurons and a hugenumber of interconnections between them.According to the structure of the connections, weidentify different classes of network architectures(Figure 1).

Figure1. a) Layered feed-forward neural network, b)Non-layered recurrent neural network

In feed-forward neural networks, the neurons areorganized in the form of layers. The neurons in alayer get input from the previous layer and feed theiroutput to the next layer. In this kind of networksconnections to the neurons in the same or previouslayers are not permitted. The last layer of neurons iscalled the output layer (right column) and the layersbetween the input and output layers are called thehidden layers. The input layer (left column) is madeup of special input neurons, transmitting only theapplied external input to their outputs. In a networkif there is only the layer of input nodes and a singlelayer of neurons constituting the output layer thenthey are called single layer network. If there are oneor more hidden layers (middle column), suchnetworks are called multilayer networks. Thestructures, in which connections to the neurons of thesame layer or to the previous layers are allowed, arecalled recurrent networks.

The lines represent weighted connections (i.e., ascaling factor) between processing elements. Theperformance of a network as shown in Figure 1 ismeasured in terms of a desired signal and an errorcriterion. The output of the network is comparedwith a desired response to produce an error. Analgorithm called back-propagation (Haykin, 1994) isused to adjust the weights a small amount at a time ina way that reduces the error. The network is trainedby repeating this process many times. The goal ofthe training is to reach an optimal solution based onthe performance measurement.

In order to tackle the optimum reinjection locationselection for a given geothermal field, an alternativesolution approach using the power of back-propagation artificial neural networks (ANN) isproposed. First, the training of the ANN with

simulator generated data for a geothermal field ispresented. Then using the ANN optimum reinjectionlocation, depth and rate for the given conditions areobtained. Advantages and disadvantages of theproposed method are discussed using a case study. Itwas observed that the proposed technique providedsatisfactory results.

METHODOLOGY

Simulation–optimization, a term that refers to thecoupling of models to optimization drivers, hasreceived extensive attention in the petroleumliterature (Johnson and Rogers, 2001). The goal ofoptimization for this type of problem is usually tofind one or more combinations of injection welllocations that will maximize the production atminimum cost. Although the number of wellcombinations is potentially infinite, it has beencustomary to pre-specify a simulation grid ofpotentially good well locations and then formulatethe search to locate the most time- or cost-effectivesubset of those locations that meets production goals.Nonlinear optimization algorithms extend fromgenetic algorithm and hybrid versions of geneticalgorithm (Guyaguler, 2002) to artificial neuralnetworks (Centilmen et al, 1999 McNichol et al,2001).

In this study, STARS thermal simulator (CMG, 2002)was used. Dual porosity simulation model wascalibrated using historical production, temperatureand pressure data from Kizildere geothermal field,Turkey (Yeltekin et al, 2002). The developedsimulation model (Table 1) consisted of 8x12x6rectangular grids (Fig. 1) with equal areal dimensions(60x60 m). The depth of the blocks (Fig. 2) matchedthe depth of the producing reservoir (Igdecikformation) divided into five equal parts. The last zblock was thick (5000 m) and was supported by athermal aquifer. The developed simulation model isin accord with hydrogeological models (Satman andSerpen, 2000; Dominco, 1974) that considerinfiltration of meteoric water into deeper sections ofthe Earth and up-flow of it after heating. Samplepressure and temperature history matches for wellsKD-6, KD-13 and KD-20 are provided in Figures 3through 5. The permeability data initially derivedfrom well test analysis (Kappa, 2001) was modifiedto achieve a reasonable match (Fig. 6). The initialand final temperature and pressure distributions at theend of 14 years of history match are given in Fig. 7and 8 respectively.

Table 1. Simulation model properties

Property ValueFracture spacing 20 m.Shape factor Gilman - KazemiFracture relative permeability Power law n = 2.8Matrix permeability 1 md.Fracture porosity 0.08

13

14

15

16

20

2122

23

24

6

7

8

0 100 200 300 400 500 600

100

200

300

400

500

600

700

800

+ Production well

+ Observation wellInjection well

N

Figure 1. Reservoir model grid diagram

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

520

540

560

580

600

620

640

660

680

700

720

740

760

780

800

820

Figure 2. Grid tops (m) distribution for the producinglayer.

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

0 1000 2000 3000 4000 5000

TIME (Day)

PR

ES

SU

RE

(kP

a)

KD-6 MODEL

190

192

194

196

198

200

202

204

18.2.1982 11.8.1987 31.1.1993 24.7.1998 14.1.2004

Date

Tem

pera

ture

(C

)KD-6 Model

Figure 3. Pressure (top) and temperature (bottom)match for well KD-6.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000

TIME (Day)

PR

ES

SU

RE

(kP

a)

KD-13 MODEL

190

192

194

196

198

200

202

204

29.3.1986 19.9.1991 11.3.1997 1.9.2002

Date

Tem

pera

ture

(C

)

KD-13 Model

Figure 4. Pressure (top) and temperature (bottom)match for well KD-13.

0

1000

2000

3000

4000

5000

6000

7000

8000

0 1000 2000 3000 4000 5000

TIME(Day)

PR

ES

SU

RE

(kP

a)

KD-20 MODEL

200

201

202

203

204

205

206

207

208

209

29.3.1986 19.9.1991 11.3.1997 1.9.2002

Date

Tem

pera

ture

(C

)

KD-20 Model

Figure 5. Pressure (top) and temperature (bottom)match for well KD-13.

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

Figure 6. Permeability (md) distribution.

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

194195196197198199200201202203204205206207208209210211212213214215

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

188

189

190

191

192

193

194

195

196

197

198

199

200

201

202

203

Figure 7. Temperature (°C) distribution. Initial -01/01/1988 (top), final - 01/09/2002(bottom)

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

7400

7600

7800

8000

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

800.00

4800

5000

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

7200

7400

7600

7800

Figure 8. Pressure (kPa) distribution. Initial-01/01/1988 (top), final-01/09/2002(bottom)

RESULTS AND DISCUSSIONS

A knowledge base of 126 simulations sampling 85possible injection locations and three different rates(2500, 3750, 4911 m3/day) was generated using thefinal simulation model by opening an injection wellat each empty grid block skipping one grid block in achessboard fashion at 10 years after thecommencement of injection at 150°C. The maximumflow rate was selected based on operating company’spump capacity. The knowledgebase data consisted ofpressure and temperature data of the production andobservation wells at different time steps. As ageneral observation for high injection rate (4911

m3/day) overall temperature decrease was lesspronounced (usually less than 4°C per grid block)with corner injections; however, pressure drop wasthe highest (more than 130 kPa per grid block). Onthe other hand, injections near the center of the fieldresulted in better pressure support (less than 117 kPaper grid block) but cooling was somewhat more(about 5 and 6 °C per grid block). Theseobservations were valid also for the lower injectionrates; however, the magnitudes of the pressure dropand the temperature decrease were somewhat less.

Then using this knowledgebase several differentANN’s were trained. During the training process fordetermining the weights, some simulation data shouldbe withheld for later verification of networkaccuracy. These data are often referred to as test orvalidation data. Once the weights have beendetermined through back propagation, the test datawere used as network inputs for determining thenetwork’s accuracy in predicting unprocessed datasets. The quality or goodness of training was judgedbased on the closeness of the prediction of theremaining “testing” data (i.e. simulated injection datathat was not used for training). This process wasrepeated for various networks and the network withthe highest accuracy was used as the model. Ratherthan randomly selecting the initial weight matrix,previously generated successful matrices were usedat the start. This feature decreased the iterationsapproximately 30% and also guaranteed training of a“good” network (Yimaz et al, 2002).

Several networks with varying degree of complexityhave been trained with no success. A two hiddenlayer network composed of 4 and 13 hidden nodesresulted in the lowest error among the single anddouble layer networks tried. Although use of morethan a single layer can lead to a very large number oflocal minima and make the training extremelydifficult (Hornik et al; 1989) this network resulted inthe best error.

The rapid estimates of temperature and pressure dataprovided by the ANN were fed into calculationswhere minimum temperature decrease – maximumpressure support is sought, which in turn were usedby a search algorithm to evaluate the effectiveness ofdifferent injection well locations and injection rates.Several dimensionless surface plots (see for examplefigures 9 and 10) were generated for evaluating theoptimum reinjection location. In these plots ANNtemperature and pressure outputs are scaled withmaximum values and then averaged by dividing tototal number of wells to find a representative number(dimensionless decrease per well) for the injectionlocation. Thus, high values of this number (hotcolors like red) correspond to relatively small

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.60

0.61

0.62

0.63

0.64

0.65

0.66

0.67

0.68

0.69

0.70

0.71

0.72

0.73

0.74

0.75

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.22

0.22

0.23

0.23

0.24

0.24

0.25

0.25

0.26

0.26

0.27

0.27

0.28

0.28

0.29

0.29

0.30

Figure 9. ANN dimensionless pressure decrease perwell (top) and ANN dimensionlesstemperature decrease per well (bottom)plots for high injection rate (4911m3/day).

decreases of the corresponding parameter (i.e.temperature or pressure).

When two extreme injection rates are considered,high injection rate results in better pressure supportespecially at the southeast of the reservoir. Theoverall pressure decrease is considerably less thanthat of the low injection rate. On the other hand,when low injection rate is preferred, the reservoircools faster. If maximum enthalpy is the overallobjective then lower injection rates need to beselected (see Fig. 10). In all cases bottom lowquadrant or southeast of the reservoir seems to be theideal location for reinjection. This location also hostsa fault named as southern fault zone and connects to

another geothermal reservoir namely Tekkehamamregion located approximately 4 km from the nearestwell in the area.

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.200.210.21

0.220.22

0.230.230.24

0.240.250.25

0.260.260.27

0.270.28

0.280.29

0.00 100.00 200.00 300.00 400.00 500.00 600.000.00

100.00

200.00

300.00

400.00

500.00

600.00

700.00

0.40

0.41

0.42

0.43

0.44

0.45

0.46

0.47

0.48

0.49

0.50

0.51

0.52

Figure 10. ANN dimensionless pressure decrease perwell (top) and ANN dimensionlesstemperature decrease per well (bottom)plots for low injection rate (2500 m3/day).

CONCLUSIONS

Optimization of reinjection well placement andreinjection rate by simulation-optimization viaartificial neural networks is proposed. The use of thedeveloped technology is demonstrated through awater dominated geothermal field located in Turkey.The performance of the reinjection location isevaluated by means of dimensionless temperatureand pressure drop per well plots obtained for thewhole field. With these plots it is possible to

pinpoint locations that will result in maximumpressure or maximum enthalpy support. For thewater dominated geothermal system studied here, thebest reinjection location is the southeast of thereservoir.

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