hydraulic fracture design and optimization of gas storage ... · conventional hydraulic fracture...

$: Hydraulic fracture design and optimization of gas storage ... · Conventional hydraulic fracture design and optimization involves the use of two- or three-dimensional hydraulic fracture$
Ž .Journal of Petroleum Science and Engineering 23 1999 161–171www.elsevier.comrlocaterjpetscieng

Hydraulic fracture design and optimization of gas storage wells

Shahab Mohaghegh a,), Bogdan Balanb b, Valeriu Platon c, Sam Ameri a

a Petroleum and Natural Gas and Engineering Department, West Virginia UniÕersity, P.O. Box 6070, Morgantown, WV 26506, USAb Schlumberger Austin Product Center, 8311 North FM 620 Road, Austin, TX 78726, USA

c Baker Atlas, 10201 Westheimer Rd., Houston, TX 77042, USA

Received 8 April 1998; accepted 19 May 1999

Abstract

Conventional hydraulic fracture design and optimization involves the use of two- or three-dimensional hydraulic fracturesimulators. These simulators need a wealth of reservoir data as input to provide users with useable results. In many cases,such data are not available or very expensive to acquire. This paper provides a new methodology that can be used in caseswhere detail reservoir data are not available or prohibitively expensive to acquire. Through the use of two virtual intelligencetechniques, namely neural networks and genetic algorithms, hydraulic fracture treatments are designed using only theavailable data. The unique design optimization method presented here is a logical continuation of the study that was

wpresented in two previous papers McVey et al., 1996. Identification of parameters influencing the response of gas storagewells to hydraulic fracturing with the aid of a neural network. SPE Computer Applications Journal, Apr., 54–57; Mohagheghet al., 1996b. Predicting well stimulation results in a gas storage field in the absence of reservoir data, using neural networks.

xSPE Reservoir Engineering Journal, Nov., 54–57. . A quick review of these papers is included here. This method will usethe available data on each well, which includes basic well information, production history and results of previous frac jobtreatments, and provides engineer with a detail optimum hydraulic fracture design unique to each well. The expectedpost-hydraulic fracture deliverability for the designed treatment is also provided to assist engineers in estimating incrementalincrease in recovery to be used in economic calculations. There are no simulated data throughout this study and all data usedfor development and verification of all methods are actual field data. q 1999 Elsevier Science B.V. All rights reserved.

Keywords: hydraulic fracturing; gas storage; neural networks

1. Introduction

Identifying under-performing wells and selectingcandidate wells for treatment is a challenging pro-

) Corresponding author. Tel.: q1-304-293-7682 ext. 405; Fax:q1-304-293-5708; E-mail: [email protected]

cess. This paper addresses this challenge for a gasstorage field with very little reservoir data and pro-vides a means for optimum design of hydraulicfractures for such wells. The background of thisstudy is presented followed by a quick review of themain technology used to achieve the objective. Themethodology that has been used will then be intro-duced in detail in order to make reproduction of the

0920-4105r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.Ž .PII: S0920-4105 99 00014-5

( )S. Mohaghegh et al.rJournal of Petroleum Science and Engineering 23 1999 161–171162

process possible for interested readers. Results anddiscussion follow the procedure and a few notes onthe application of this methodology to other fieldsŽ .where different sets of data may be available arepresented.

The new methodology being introduced in thispaper is a hybrid technique that tightly integratesmodel-building abilities of neural networks with in-telligent and powerful search and optimization func-

Žtionality of genetic algorithms. Available data previ-ous hydraulic fracture design details coupled with

.production data are used to construct and train aneural model of the hydraulic fracturing procedure ina particular field. Upon successful completion of thisstep, a genetic algorithm is used to search through allpossible combinations of the hydraulic fracture pa-rameters in order to find the most promising combi-nation of the parameters.

ŽIn applying this methodology instead of detail.reservoir data , historical data on prior hydraulic

fracture treatments are used to develop a neuro-modelof the stimulation characteristics in a particular for-mation. Historical data of past hydraulic fracturetreatments can usually be found in well files. Themost challenging part of using such data is theirconversion into electronic format. Some companieshave invested substantial resources in converting theirwell files into electronic format. These companiesare candidates for application of the methodologypresented in this paper. An application to a gasstorage field in Ohio is discussed.

The new methodology presented here is not aŽ .substitution for conventional physics-based ap-

proaches. This methodology is a tool that can beemployed when conventional methods can not beused due to lack of necessary data such as detailstress, thickness, porosity, and permeability profiles.This method also can be used in conjunction withconventional tools such as two- or three-dimensionalhydraulic fracture simulators to enhance productiv-ity.

2. Background

ŽIn two previous papers McVey et al., 1996;.Mohaghegh et al., 1996b , a systematic approach for

neuro-modeling of a hydraulic fracturing process

using a three-layer, back propagation neural network,was introduced. The approach assisted engineers inpredicting post-stimulation well performance and se-lecting candidate wells for stimulation treatment. Inthose papers, it was mentioned that this approachcould also be extended to optimize the stimulationdesign parameters. The optimization of hydraulicfracture design is the subject of this paper.

3. Genetic algorithm

The model being investigated has 17 parameters,which have been encoded into a 74-bit long chromo-some. 1 All the possible combinations of genes withinthis chromosome produce 1021 distinct, possible,solutions. If one could examine 106 solutions per

15 Žsecond, it would take 10 seconds about 300 mil-.lion years to exhaustively search the model space.

In the past, making intelligent guesses about thevalues of the parameters, and use of trial and errorwas used to solve problems like this.

Ž .Holland 1975 proposed an optimization tech-nique that exploited an analogy between functionoptimization and the biological process of evolution-ary adaptation. Genetic algorithms maintain a popu-

Ž .lation of individuals potential solutions and act in away that favors the ‘‘creation’’ and ‘‘survival’’ ofbetter individuals. This innovative technique solvescomplex problems by imitating Darwinian theoriesof evolution on a computer. In biological evolution,only the winners survive to continue the evolutionaryprocess. Note that one does not need to know whataspect of the organism makes it a winner, nature justassumes that if it lives, it must be doing somethingright. Genetic algorithms apply the same evolution-ary technique to a wide variety of real-world prob-lems like scheduling, adaptive control, optimalcontrol, database query optimization, gas pipelineoperation, inverse modeling in geophysics, etc.

By setting the parameters randomly throughoutthe search space, a population of chromosomes —each representing a potential hydraulic fracture de-sign — is created. This is the first step in implemen-

1 A chromosome is the binary representation of all parametersconcatenated to form one member of the genetic population.

( )S. Mohaghegh et al.rJournal of Petroleum Science and Engineering 23 1999 161–171 163

Table 1List of the parameters used in the genetic algorithm for optimiza-tion

Fracture parameters being optimized

Ž .Maximum sand concentration lbrgalŽ .Average injection rate BPM

Ž .Sand laden fluid viscosity cpŽ .Water amount bbl

Ž .Nitrogen amount bblŽ .Sand amount sacks

Sand mesh sizeŽ .Acid amount gal

Fluid typeAcid typeIron controlBacteria controlParaffin dispersing agentClay stabilizerSurfactantMethanolContractor

tation of a genetic algorithm. From this population ofsolutions, the worst are discarded and the best solu-tions are then ‘‘bred’’ with each other by mixing the

Ž .parameters genes from the most successful organ-

isms, thus creating a new population. During repro-duction, the chromosomes undergo different geneticoperation such as selection, cross-over, mutation and

Ž .inversion Michalewicz, 1992 . The selection opera-tor is responsible for choosing two organisms tobecome parents.

As in real life, this type of continuous adaptationcreates a very robust individual. The whole processcontinues through many ‘‘generations’’, with thebest genes being handed down to future generations.The result is typically a very good solution to theproblem. By continually cycling these operators, asurprisingly powerful search engine is constructed,which inherently preserves the critical balance neededwith any search: the balance between exploitationŽ .taking advantage of information already obtained

Ž .and exploration searching new areas . Althoughsimplistic from a biologist’s viewpoint, these algo-rithms are sufficiently complex to provide robust andpowerful search mechanisms.

Table 1 is the list of 17 parameters being opti-mized during this study. These parameters can bedivided into two general categories. First are parame-ters that have distinct and discrete values, or mem-bers, such as contractor, acid type, and sand meshsize. Therefore, selecting one member for each pa-

Fig. 1. Field results and network predictions for 48 treatments in Clinton sand.


Fig. 2. Schematic diagram of the methodology developed in this study.

rameter in this category requires random selection.Parameters in the second category have continuousvalues such as average injection rate, water amountand sand concentration. Any value between somedesignated minimum and maximum can be chosenfor these parameters.

A potential solution to the hydraulic fracture opti-mization problem includes a combination of valuesof these 17 parameters. A gene represents eachparameter and when combined together the 17 genesform a chromosome. Each chromosome is a potentialsolution.

As mentioned earlier one of the keys to a success-ful genetic algorithm is having a way of rankingsolutions. This is done using a ‘‘fitness function’’. 2

In this study, the neural network that has beendeveloped, trained and successfully tested as theneural model of the hydraulic fracture treatment in

Ž . Žthis field Mohaghegh et al., 1996b neural module

2 A fitness function in any problem is the model or the functionthat is being optimized.

.a2 — as it will be explained later is the fitnessfunction.

4. Methodology

A tool, which is able to predict post-hydraulicfracture deliverability of the gas storage wells in theClinton sand with 95% accuracy was described in

Žtwo previous papers McVey et al., 1996; Mo-.haghegh et al., 1996b .

The developed tool was trained on more that 570different hydraulic fracture treatments. It was shownthat this tool could predict post-hydraulic fracture

Ždeliverability even on new hydraulic fractures i.e.,.hydraulic fractures it had not been trained on . Fig. 1

shows the neural network’s predictions vs. field re-sults for three consecutive years: 1989, 1990 and1991.

The robustness of the neural model was estab-lished by successfully predicting the post-hydraulicfracture deliverability of the treatments for the years1989 through 1991. This neuro-model was used asthe fitness function for the genetic algorithm topredict the outcome of hydraulic fractures. This


makes the ranking and selection process of the ge-netic algorithm possible.

A two-stage process was developed to achieveoptimized hydraulic fracture design of gas storagewells in the Clinton sand that is the main objectiveof this study. A detail, step by step procedure ispresented in this section; Fig. 2 is a schematic dia-gram of the procedure.

ŽFor the first stage, a new neural network neural.module a1 is designed and trained specifically for

this study. No information on the hydraulic fracturedesign parameters are presented to this neural net-work. The only data available to this neural net isbasic well information and production history. Thiswill be all the information that will be available ineach well that is being considered for a hydraulicfracture treatment. This neural network is trained touse the data as input and estimate a post-hydraulicfracture deliverability as output. This process is arapid screening of all the wells to ‘‘weed-out’’ thewells that should not be considered for further study.This module will identify and separate the so-called‘‘dog wells’’ that would not be enhanced consider-ably even after a hydraulic fracture.

The wells that have passed the rapid screeningtest will enter the second stage of the process that isthe actual hydraulic fracture design stage. A second

Ž .neural net neural module a2 has been trained forthis stage with more than 570 different hydraulicfracture treatments that have been performed on gasstorage wells in the Clinton sand. During the trainingprocess, the network has learned how the wellsrespond to hydraulic fractures by building an internalrepresentation of the hydraulic fracturing process inthe Clinton sand. This internal representation is inthe form of connection-weights between neurons.This network is capable of providing post-hydraulicfracture deliverability with high accuracy using wellinformation, historical data and hydraulic fracturedesign parameters as input. Fig. 3 shows how thisneural network is being used in conjunction with thegenetic algorithm.

The input to neural module a2 can be divided toŽ . Ž .three categories: 1 basic well information, 2 pro-

Ž .duction history and 3 hydraulic fracture parameters.Ž .The objective is to optimize the third last category.

Each chromosome in the genetic population is anŽ .individual solution frac job design for a particular

Fig. 3. Schematic diagram of neural module a2, the fitnessfunction.

well. Therefore, for each well the first two parts ofŽthe input namely basic well information and produc-.tion history remains constant while the third part

enters the genetic algorithms. Fig. 1 illustrates theaccuracy of this neural network.

The output of the genetic algorithm is the opti-mized hydraulic fracture design for each well. Thetool also will provide the engineer with expectedpost-hydraulic fracture deliverability once the sug-gested design is used for a hydraulic fracture treat-ment. This result may be saved and printed. Thedesign parameters can then be given to any servicecompany for implementation.

5. Detail procedure

The well selection and hydraulic fracture designtake place in two stages.

5.1. Stage one: rapid screening

In this stage, a criterion is set for rapid screeningof all wells in the database. A screen display of thispart of the software is shown in Fig. 4.

Neural module a1, that has been trained on basicwell information and production history, is used toscreen the wells and selects those that meet a certainpost-hydraulic fracture deliverability criterion thresh-old, set by the design engineer. Those wells thatmeet or exceed the threshold will be identified andwill go for further analysis and hydraulic fracture


Fig. 4. A screen display of the first window of the software’s user interface.

design. A preliminary post-hydraulic fracture deliv-erability for each well will be calculated and dis-played. The post-hydraulic fracture deliverability thatis presented at this stage is expected as a result of ageneric hydraulic fracture design for this well, i.e.,with no optimization.

Note that if the actual threshold is, for example,500 MCFD then 400 MCFD should be used at thispoint. This is due to the fact that the optimizationprocess has an average post-hydraulic fracture deliv-erability enhancement of 20% in this field.

At this point, the design engineer is presentedwith a list of candidate wells that meet androrexceed the post-hydraulic fracture deliverability

Ž .threshold set previously Fig. 4 . The engineer mustselect one well at a time and enter the second stagefor optimization.

5.2. Stage two: optimization

The following steps are taken in this stage.ŽStep 1: One of the four fracturing fluids water,

.gel, foam, foamrwater is selected. Note that these

four procedures were chosen because they have beenroutinely performed in the aforementioned field in

Žthe past. In a previous paper Mohaghegh et al.,.1996b , it was demonstrated that if a new hydraulic

Žfracture procedure is used, a procedure that this.software has not been trained for , the software will

provide the user with a reasonable answer. This isdue to the fact that virtual intelligence paradigms donot undergo complete breakdown, once they en-counter new and unfamiliar environments and infor-mation. They ‘‘degrade gracefully’’. Actually it wasshown that once the software has been exposed tothe new procedure, it will learn the new procedurequickly and therefore its performance returns to its

Žnormal accuracy refer to Fig. 6 of Mohaghegh et al.,.1996b .

Step 2: One hundred random combinations ofŽ .input variables hydraulic fracture parameters are

generated. This is called the original population.Step 3: Neural module a2 that has been proven to

have high accuracy in predicting post-hydraulic frac-ture deliverability for this particular field is used toforecast post-frac deliverability for 100 cases gener-

Ž .ated in step 1 Fig. 3 .


Fig. 5. A screen display of optimization process.

Step 4: The outcome of neural module a2 will beranked from 1 to 100, 1 being the highest post-hy-draulic fracture deliverability.

Step 5: The highest-ranking combination of pa-Ž .rameters design is compared with the last highest-

ranking design and the better of the two is saved inthe memory as the optimum design.

Step 6: The top 25 designs of step 4 will beselected for the next step and the rest will be dis-carded.

Step 7: Cross-over, mutation, and inversion opera-tors are used on the top 25 designs of step 6 and anew population of 100 designs is generated.

Step 8: the procedure is repeated from step 3.Fig. 5 shows a graphical representation of the

design optimization process.One may stop the process at any time if a better

design can not be achieved. Two different conver-gence criteria are suggested. The software providesthe design engineer with information to make thisdecision. During the optimization process, the high-est post-hydraulic fracture deliverability everachieved is displayed along with number of genera-

tions that have passed without any enhancement inpost-hydraulic fracture deliverability. One may de-cide that if, after so many generations no enhance-ment is taken place, it is time to stop the process. Asa second convergence criteria, the engineer may lookat the cumulative post-hydraulic fracture deliverabil-ity curve for each generation that is displayed on realtime. The slope of this curve determines whetherevery new generation is an improvement over thelast generation. A positive slope indicates overallimprovement of one generation compared to theprevious generation and suggests that the optimiza-tion should continue. A zero or negative slope, onthe other hand, suggest no improvement has takenplace.

6. Results and discussions

In order to demonstrate the application of thismethod, it was decided to perform design optimiza-tion on wells that were treated during 1989, 1990


Fig. 6. Post-hydraulic fracture deliverability enhancement due to optimization.

and 1991. Since the actual results of hydraulic frac-ture treatments on these wells were available, itwould provide good comparisons. We used the soft-

Ž .ware to: a predict the hydraulic fracture treatmentŽ .and compare it with the actual field results and, b

see the enhancement that would have been achievedif this software were used to design the treatment.

Neural module a2 in the software is responsibleŽfor prediction of output hydraulic fracture treatment

. Žresults from new sets of input data hydraulic frac-




.ture designs for particular wells . It would be reason-able to expect that if this module predicts hydraulicfracture treatment results within a certain degree ofaccuracy for one set of the input values, it shouldpredict the results of another set of input valueswithin the same degree of accuracy.

Figs. 6–8 show the results of this demonstration.In these figures, circles show actual field results.Squares show software’s prediction for the same fracdesigns. It is expected that circles and squares shouldbe close to one another. Fracture treatment parame-ters that have been generated by the software itselfusing the combined neuro-genetic procedure resultedin the hydraulic fracture treatment results shown bytriangles. Note that the same module in the softwarethat has produced the triangles has produced thesquares, and in both cases from a set of input datawhich is new to the module.

From these figures, one can observe that by usingthis software to design a hydraulic fracture treatmentfor this field, one can enhance treatment results byan average of 20%. It should also be noted that thesewells were chosen from among 100 candidate wells.If the software were available at the time of theselection process, one would expect some of the

restimulated wells to have been substituted withcandidate wells with better potentials.

Table 2 shows the result of this process on oneparticular well. Well a1166 was treated and itspost-hydraulic fracture deliverability was determinedto be 918 MCFD. The software predicted that thiswell’s post-hydraulic fracture deliverability would be967 MCFD, which is within 5.5% of the actualvalue. Using the neuro-genetic optimization processintroduced here, the software predicts a post-hydra-ulic fracture deliverability of 1507 MCFD. Using the5.5% tolerance for the software’s accuracy for thiswell, this method could have enhanced this well’spost-frac deliverability by 55% to 73%.

After the optimization process is completed, thesoftware provides the engineer with proposed hy-

Table 2Software results for the well a116

Data source Field result Neural net Optimized

Ž . Ž . Ž .Post-frac 918 MCFD 967 MCFD 1507 MCFDdeliverability


Fig. 9. A screen display of the software’s output.

draulic fracture parameters for the well. Fig. 9 is ascreen display of the software output.

7. Application to other fields

This method can be applied, not only to gasstorage operation, but to other types of operations aswell. This is true as long as production history andhistorical data on prior treatments are available.

With some modifications, this method can also beapplied to new fields where no hydraulic fractureswere performed in the past. In such cases, it isnecessary that reservoir data be available. If perme-ability profile for the wells in the field is not avail-able, well logs can be used to generate themŽ .Mohaghegh et al., 1996a . The reason why a spe-

Žcific number of wells is not suggested for logs,.cores and stress profiles is because it is a function

of the size of the field under investigation.

8. Conclusions

Reservoir data such as permeability, porosity,thickness and stress profiles are among the essential

data that make conventional hydraulic fracture simu-lation possible. The success of the simulation andfracture design process is directly related to theaccuracy of such data. Acquisition of the abovementioned data can be very expensive, especially forolder fields. The methodology introduced in thispaper, uses available data such as well completion,production data, and past hydraulic fracture treat-ment data. The hybrid system developed in this studyis able to forecast gas storage well deliverability witha high degree of accuracy. This system is also capa-ble of assisting practicing engineers in the design ofoptimum hydraulic fractures. This software is cur-rently being used for candidate well selection andhydraulic fracture design optimization in the Clintonsand.

A hybrid system that is made up of two neuralnetworks and a genetic algorithm routine is devel-oped for design and optimization of hydraulic frac-turing procedures in a gas storage field in Ohio. Themajor difference between this system with conven-tional two- or three-dimensional hydraulic fracturesimulators is that the developed hybrid system pro-vide a solution for hydraulic fracture treatment de-sign and optimization in the absence of conventionalreservoir data that are an absolute necessity when


Ž .using conventional 2D or 3D simulators. The maincomponent of the hybrid system has been success-fully tested.

References

Holland, J., 1975. Adaptation in Natural and Artificial Systems.University of Michigan Press.

McVey, D.S., Mohaghegh, S., Aminian, K., Ameri, S., 1996.Identification of parameters influencing the response of gas

storage wells to hydraulic fracturing with the aid of a neuralnetwork. SPE Computer Applications Journal, Apr., 54–57.

Michalewicz, Z., 1992. Genetic AlgorithmsqData StructuresEvolution Programs. Springer-Verlag, ISBN 3-540-55387-8,1992.

Mohaghegh, S., Ameri, S., Arefi, R., 1996a. Virtual measurementof heterogeneous formation permeability using geophysical

Ž .well log responses. The Log Analyst 37 2 , 32–39.Mohaghegh, S., Aminian, K., Ameri, S., McVey, D.S., 1996b.

Predicting well stimulation results in a gas storage field in theabsence of reservoir data, using neural networks. SPE Reser-voir Engineering Journal, Nov., 54–57.

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