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Hydraulic fracture design and optimization of gas storage wells
Journal of Petroleum Science and Engineering 23 Ž1999. 161–171 www.elsevier.comrlocaterjpetscieng
Hydraulic fracture design and optimization of gas storage wells Shahab Mohaghegh a
a,)
, Bogdan Balanb b, Valeriu Platon c , Sam Ameri
a
Petroleum and Natural Gas and Engineering Department, West Virginia UniÕersity, P.O. Box 6070, Morgantown, WV 26506, USA b 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 fracture simulators. 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 cases where detail reservoir data are not available or prohibitively expensive to acquire. Through the use of two virtual intelligence techniques, namely neural networks and genetic algorithms, hydraulic fracture treatments are designed using only the available data. The unique design optimization method presented here is a logical continuation of the study that was presented in two previous papers wMcVey et al., 1996. Identification of parameters influencing the response of gas storage wells to hydraulic fracturing with the aid of a neural network. SPE Computer Applications Journal, Apr., 54–57; Mohaghegh et al., 1996b. Predicting well stimulation results in a gas storage field in the absence of reservoir data, using neural networks. SPE Reservoir Engineering Journal, Nov., 54–57.x. A quick review of these papers is included here. This method will use the available data on each well, which includes basic well information, production history and results of previous frac job treatments, and provides engineer with a detail optimum hydraulic fracture design unique to each well. The expected post-hydraulic fracture deliverability for the designed treatment is also provided to assist engineers in estimating incremental increase in recovery to be used in economic calculations. There are no simulated data throughout this study and all data used for 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 selecting candidate 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 gas storage field with very little reservoir data and provides a means for optimum design of hydraulic fractures for such wells. The background of this study is presented followed by a quick review of the main technology used to achieve the objective. The methodology that has been used will then be introduced in detail in order to make reproduction of the
0920-4105r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 4 1 0 5 Ž 9 9 . 0 0 0 1 4 - 5
162
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
process possible for interested readers. Results and discussion follow the procedure and a few notes on the application of this methodology to other fields Žwhere different sets of data may be available. are presented. The new methodology being introduced in this paper is a hybrid technique that tightly integrates model-building abilities of neural networks with intelligent and powerful search and optimization functionality of genetic algorithms. Available data Žprevious hydraulic fracture design details coupled with production data. are used to construct and train a neural model of the hydraulic fracturing procedure in a particular field. Upon successful completion of this step, a genetic algorithm is used to search through all possible combinations of the hydraulic fracture parameters in order to find the most promising combination of the parameters. In applying this methodology Žinstead of detail reservoir data., historical data on prior hydraulic fracture treatments are used to develop a neuro-model of the stimulation characteristics in a particular formation. Historical data of past hydraulic fracture treatments can usually be found in well files. The most challenging part of using such data is their conversion into electronic format. Some companies have invested substantial resources in converting their well files into electronic format. These companies are candidates for application of the methodology presented in this paper. An application to a gas storage field in Ohio is discussed. The new methodology presented here is not a substitution for conventional Žphysics-based. approaches. This methodology is a tool that can be employed when conventional methods can not be used due to lack of necessary data such as detail stress, thickness, porosity, and permeability profiles. This method also can be used in conjunction with conventional tools such as two- or three-dimensional hydraulic fracture simulators to enhance productivity.
2. Background In two previous papers ŽMcVey 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 in predicting post-stimulation well performance and selecting candidate wells for stimulation treatment. In those papers, it was mentioned that this approach could also be extended to optimize the stimulation design parameters. The optimization of hydraulic fracture 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 chromosome. 1 All the possible combinations of genes within this chromosome produce 10 21 distinct, possible, solutions. If one could examine 10 6 solutions per second, it would take 10 15 seconds Žabout 300 million years. to exhaustively search the model space. In the past, making intelligent guesses about the values of the parameters, and use of trial and error was used to solve problems like this. Holland Ž1975. proposed an optimization technique that exploited an analogy between function optimization and the biological process of evolutionary adaptation. Genetic algorithms maintain a population of individuals Žpotential solutions. and act in a way that favors the ‘‘creation’’ and ‘‘survival’’ of better individuals. This innovative technique solves complex problems by imitating Darwinian theories of evolution on a computer. In biological evolution, only the winners survive to continue the evolutionary process. Note that one does not need to know what aspect of the organism makes it a winner, nature just assumes that if it lives, it must be doing something right. Genetic algorithms apply the same evolutionary technique to a wide variety of real-world problems like scheduling, adaptive control, optimal control, database query optimization, gas pipeline operation, inverse modeling in geophysics, etc. By setting the parameters randomly throughout the search space, a population of chromosomes — each representing a potential hydraulic fracture design — is created. This is the first step in implemen-
1
A chromosome is the binary representation of all parameters concatenated to form one member of the genetic population.
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171 Table 1 List of the parameters used in the genetic algorithm for optimization Fracture parameters being optimized Maximum sand concentration Žlbrgal. Average injection rate ŽBPM. Sand laden fluid viscosity Žcp. Water amount Žbbl. Nitrogen amount Žbbl. Sand amount Žsacks. Sand mesh size Acid amount Žgal. Fluid type Acid type Iron control Bacteria control Paraffin dispersing agent Clay stabilizer Surfactant Methanol Contractor
tation of a genetic algorithm. From this population of solutions, the worst are discarded and the best solutions are then ‘‘bred’’ with each other by mixing the parameters Žgenes. from the most successful organ-
163
isms, thus creating a new population. During reproduction, the chromosomes undergo different genetic operation such as selection, cross-over, mutation and inversion ŽMichalewicz, 1992.. The selection operator is responsible for choosing two organisms to become parents. As in real life, this type of continuous adaptation creates a very robust individual. The whole process continues through many ‘‘generations’’, with the best genes being handed down to future generations. The result is typically a very good solution to the problem. By continually cycling these operators, a surprisingly powerful search engine is constructed, which inherently preserves the critical balance needed with any search: the balance between exploitation Žtaking advantage of information already obtained. and exploration Žsearching new areas.. Although simplistic from a biologist’s viewpoint, these algorithms are sufficiently complex to provide robust and powerful search mechanisms. Table 1 is the list of 17 parameters being optimized during this study. These parameters can be divided into two general categories. First are parameters that have distinct and discrete values, or members, such as contractor, acid type, and sand mesh size. Therefore, selecting one member for each pa-
Fig. 1. Field results and network predictions for 48 treatments in Clinton sand.
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Fig. 2. Schematic diagram of the methodology developed in this study.
rameter in this category requires random selection. Parameters in the second category have continuous values such as average injection rate, water amount and sand concentration. Any value between some designated minimum and maximum can be chosen for these parameters. A potential solution to the hydraulic fracture optimization problem includes a combination of values of these 17 parameters. A gene represents each parameter and when combined together the 17 genes form a chromosome. Each chromosome is a potential solution. As mentioned earlier one of the keys to a successful genetic algorithm is having a way of ranking solutions. This is done using a ‘‘fitness function’’. 2 In this study, the neural network that has been developed, trained and successfully tested as the neural model of the hydraulic fracture treatment in this field ŽMohaghegh et al., 1996b. Žneural module
2
A fitness function in any problem is the model or the function that is being optimized.
a2 — as it will be explained later. is the fitness function. 4. Methodology A tool, which is able to predict post-hydraulic fracture deliverability of the gas storage wells in the Clinton sand with 95% accuracy was described in two previous papers ŽMcVey et al., 1996; Mohaghegh et al., 1996b.. The developed tool was trained on more that 570 different hydraulic fracture treatments. It was shown that this tool could predict post-hydraulic fracture deliverability even on new hydraulic fractures Ži.e., hydraulic fractures it had not been trained on.. Fig. 1 shows the neural network’s predictions vs. field results for three consecutive years: 1989, 1990 and 1991. The robustness of the neural model was established by successfully predicting the post-hydraulic fracture deliverability of the treatments for the years 1989 through 1991. This neuro-model was used as the fitness function for the genetic algorithm to predict the outcome of hydraulic fractures. This
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
makes the ranking and selection process of the genetic algorithm possible. A two-stage process was developed to achieve optimized hydraulic fracture design of gas storage wells in the Clinton sand that is the main objective of this study. A detail, step by step procedure is presented in this section; Fig. 2 is a schematic diagram of the procedure. For the first stage, a new neural network Žneural module a1. is designed and trained specifically for this study. No information on the hydraulic fracture design parameters are presented to this neural network. The only data available to this neural net is basic well information and production history. This will be all the information that will be available in each well that is being considered for a hydraulic fracture treatment. This neural network is trained to use the data as input and estimate a post-hydraulic fracture deliverability as output. This process is a rapid screening of all the wells to ‘‘weed-out’’ the wells that should not be considered for further study. This module will identify and separate the so-called ‘‘dog wells’’ that would not be enhanced considerably even after a hydraulic fracture. The wells that have passed the rapid screening test will enter the second stage of the process that is the actual hydraulic fracture design stage. A second neural net Žneural module a2. has been trained for this stage with more than 570 different hydraulic fracture treatments that have been performed on gas storage wells in the Clinton sand. During the training process, the network has learned how the wells respond to hydraulic fractures by building an internal representation of the hydraulic fracturing process in the Clinton sand. This internal representation is in the form of connection-weights between neurons. This network is capable of providing post-hydraulic fracture deliverability with high accuracy using well information, historical data and hydraulic fracture design parameters as input. Fig. 3 shows how this neural network is being used in conjunction with the genetic algorithm. The input to neural module a2 can be divided to three categories: Ž1. basic well information, Ž2. production history and Ž3. hydraulic fracture parameters. The objective is to optimize the third Žlast. category. Each chromosome in the genetic population is an individual solution Žfrac job design. for a particular
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Fig. 3. Schematic diagram of neural module a2, the fitness function.
well. Therefore, for each well the first two parts of the input Žnamely basic well information and production history. remains constant while the third part enters the genetic algorithms. Fig. 1 illustrates the accuracy of this neural network. The output of the genetic algorithm is the optimized hydraulic fracture design for each well. The tool also will provide the engineer with expected post-hydraulic fracture deliverability once the suggested design is used for a hydraulic fracture treatment. This result may be saved and printed. The design parameters can then be given to any service company for implementation.
5. Detail procedure The well selection and hydraulic fracture design take place in two stages. 5.1. Stage one: rapid screening In this stage, a criterion is set for rapid screening of all wells in the database. A screen display of this part of the software is shown in Fig. 4. Neural module a1, that has been trained on basic well information and production history, is used to screen the wells and selects those that meet a certain post-hydraulic fracture deliverability criterion threshold, set by the design engineer. Those wells that meet or exceed the threshold will be identified and will go for further analysis and hydraulic fracture
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Fig. 4. A screen display of the first window of the software’s user interface.
design. A preliminary post-hydraulic fracture deliverability for each well will be calculated and displayed. The post-hydraulic fracture deliverability that is presented at this stage is expected as a result of a generic 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 this point. This is due to the fact that the optimization process has an average post-hydraulic fracture deliverability enhancement of 20% in this field. At this point, the design engineer is presented with a list of candidate wells that meet andror exceed the post-hydraulic fracture deliverability threshold set previously ŽFig. 4.. The engineer must select one well at a time and enter the second stage for optimization. 5.2. Stage two: optimization The following steps are taken in this stage. Step 1: One of the four fracturing fluids Žwater, gel, foam, foamrwater. is selected. Note that these
four procedures were chosen because they have been routinely performed in the aforementioned field in the past. In a previous paper ŽMohaghegh et al., 1996b., it was demonstrated that if a new hydraulic fracture procedure is used, Ža procedure that this software has not been trained for., the software will provide the user with a reasonable answer. This is due to the fact that virtual intelligence paradigms do not undergo complete breakdown, once they encounter new and unfamiliar environments and information. They ‘‘degrade gracefully’’. Actually it was shown that once the software has been exposed to the new procedure, it will learn the new procedure quickly and therefore its performance returns to its normal accuracy Žrefer to Fig. 6 of Mohaghegh et al., 1996b.. Step 2: One hundred random combinations of input variables Žhydraulic 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 fracture deliverability for this particular field is used to forecast post-frac deliverability for 100 cases generated in step 1 ŽFig. 3..
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
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Fig. 5. A screen display of optimization process.
Step 4: The outcome of neural module a2 will be ranked from 1 to 100, 1 being the highest post-hydraulic fracture deliverability. Step 5: The highest-ranking combination of parameters Ždesign. is compared with the last highestranking design and the better of the two is saved in the memory as the optimum design. Step 6: The top 25 designs of step 4 will be selected for the next step and the rest will be discarded. Step 7: Cross-over, mutation, and inversion operators are used on the top 25 designs of step 6 and a new 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 convergence criteria are suggested. The software provides the design engineer with information to make this decision. During the optimization process, the highest post-hydraulic fracture deliverability ever achieved is displayed along with number of genera-
tions that have passed without any enhancement in post-hydraulic fracture deliverability. One may decide that if, after so many generations no enhancement is taken place, it is time to stop the process. As a second convergence criteria, the engineer may look at the cumulative post-hydraulic fracture deliverability curve for each generation that is displayed on real time. The slope of this curve determines whether every new generation is an improvement over the last generation. A positive slope indicates overall improvement of one generation compared to the previous generation and suggests that the optimization should continue. A zero or negative slope, on the other hand, suggest no improvement has taken place.
6. Results and discussions In order to demonstrate the application of this method, it was decided to perform design optimization on wells that were treated during 1989, 1990
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Fig. 6. Post-hydraulic fracture deliverability enhancement due to optimization.
and 1991. Since the actual results of hydraulic fracture treatments on these wells were available, it would provide good comparisons. We used the software to: Ža. predict the hydraulic fracture treatment and compare it with the actual field results and, Žb.
see the enhancement that would have been achieved if this software were used to design the treatment. Neural module a2 in the software is responsible for prediction of output Žhydraulic fracture treatment results. from new sets of input data Žhydraulic frac-
Fig. 7. Post-hydraulic fracture deliverability enhancement due to optimization.
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
169
Fig. 8. Post-hydraulic fracture deliverability enhancement due to optimization.
ture designs for particular wells.. It would be reasonable to expect that if this module predicts hydraulic fracture treatment results within a certain degree of accuracy for one set of the input values, it should predict the results of another set of input values within 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 frac designs. It is expected that circles and squares should be close to one another. Fracture treatment parameters that have been generated by the software itself using the combined neuro-genetic procedure resulted in the hydraulic fracture treatment results shown by triangles. Note that the same module in the software that has produced the triangles has produced the squares, and in both cases from a set of input data which is new to the module. From these figures, one can observe that by using this software to design a hydraulic fracture treatment for this field, one can enhance treatment results by an average of 20%. It should also be noted that these wells were chosen from among 100 candidate wells. If the software were available at the time of the selection process, one would expect some of the
restimulated wells to have been substituted with candidate wells with better potentials. Table 2 shows the result of this process on one particular well. Well a1166 was treated and its post-hydraulic fracture deliverability was determined to be 918 MCFD. The software predicted that this well’s post-hydraulic fracture deliverability would be 967 MCFD, which is within 5.5% of the actual value. Using the neuro-genetic optimization process introduced here, the software predicts a post-hydraulic fracture deliverability of 1507 MCFD. Using the 5.5% tolerance for the software’s accuracy for this well, this method could have enhanced this well’s post-frac deliverability by 55% to 73%. After the optimization process is completed, the software provides the engineer with proposed hy-
Table 2 Software results for the well a116 Data source
Field result
Neural net
Optimized
Post-frac deliverability
918 ŽMCFD.
967 ŽMCFD.
1507 ŽMCFD.
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Fig. 9. A screen display of the software’s output.
draulic fracture parameters for the well. Fig. 9 is a screen display of the software output.
7. Application to other fields This method can be applied, not only to gas storage operation, but to other types of operations as well. This is true as long as production history and historical data on prior treatments are available. With some modifications, this method can also be applied to new fields where no hydraulic fractures were performed in the past. In such cases, it is necessary that reservoir data be available. If permeability profile for the wells in the field is not available, well logs can be used to generate them ŽMohaghegh et al., 1996a.. The reason why a specific number of wells is not suggested Žfor 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 simulation possible. The success of the simulation and fracture design process is directly related to the accuracy of such data. Acquisition of the above mentioned data can be very expensive, especially for older fields. The methodology introduced in this paper, uses available data such as well completion, production data, and past hydraulic fracture treatment data. The hybrid system developed in this study is able to forecast gas storage well deliverability with a high degree of accuracy. This system is also capable of assisting practicing engineers in the design of optimum hydraulic fractures. This software is currently being used for candidate well selection and hydraulic fracture design optimization in the Clinton sand. A hybrid system that is made up of two neural networks and a genetic algorithm routine is developed for design and optimization of hydraulic fracturing procedures in a gas storage field in Ohio. The major difference between this system with conventional two- or three-dimensional hydraulic fracture simulators is that the developed hybrid system provide a solution for hydraulic fracture treatment design and optimization in the absence of conventional reservoir data that are an absolute necessity when
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
using conventional Ž2D or 3D. simulators. The main component of the hybrid system has been successfully 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
171
storage wells to hydraulic fracturing with the aid of a neural network. SPE Computer Applications Journal, Apr., 54–57. Michalewicz, Z., 1992. Genetic AlgorithmsqData Structures Evolution Programs. Springer-Verlag, ISBN 3-540-55387-8, 1992. Mohaghegh, S., Ameri, S., Arefi, R., 1996a. Virtual measurement of heterogeneous formation permeability using geophysical well log responses. The Log Analyst 37 Ž2., 32–39. Mohaghegh, S., Aminian, K., Ameri, S., McVey, D.S., 1996b. Predicting well stimulation results in a gas storage field in the absence of reservoir data, using neural networks. SPE Reservoir Engineering Journal, Nov., 54–57.
Hydraulic fracture design and optimization of gas storage wells Shahab Mohaghegh a
a,)
, Bogdan Balanb b, Valeriu Platon c , Sam Ameri
a
Petroleum and Natural Gas and Engineering Department, West Virginia UniÕersity, P.O. Box 6070, Morgantown, WV 26506, USA b 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 fracture simulators. 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 cases where detail reservoir data are not available or prohibitively expensive to acquire. Through the use of two virtual intelligence techniques, namely neural networks and genetic algorithms, hydraulic fracture treatments are designed using only the available data. The unique design optimization method presented here is a logical continuation of the study that was presented in two previous papers wMcVey et al., 1996. Identification of parameters influencing the response of gas storage wells to hydraulic fracturing with the aid of a neural network. SPE Computer Applications Journal, Apr., 54–57; Mohaghegh et al., 1996b. Predicting well stimulation results in a gas storage field in the absence of reservoir data, using neural networks. SPE Reservoir Engineering Journal, Nov., 54–57.x. A quick review of these papers is included here. This method will use the available data on each well, which includes basic well information, production history and results of previous frac job treatments, and provides engineer with a detail optimum hydraulic fracture design unique to each well. The expected post-hydraulic fracture deliverability for the designed treatment is also provided to assist engineers in estimating incremental increase in recovery to be used in economic calculations. There are no simulated data throughout this study and all data used for 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 selecting candidate 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 gas storage field with very little reservoir data and provides a means for optimum design of hydraulic fractures for such wells. The background of this study is presented followed by a quick review of the main technology used to achieve the objective. The methodology that has been used will then be introduced in detail in order to make reproduction of the
0920-4105r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 0 - 4 1 0 5 Ž 9 9 . 0 0 0 1 4 - 5
162
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
process possible for interested readers. Results and discussion follow the procedure and a few notes on the application of this methodology to other fields Žwhere different sets of data may be available. are presented. The new methodology being introduced in this paper is a hybrid technique that tightly integrates model-building abilities of neural networks with intelligent and powerful search and optimization functionality of genetic algorithms. Available data Žprevious hydraulic fracture design details coupled with production data. are used to construct and train a neural model of the hydraulic fracturing procedure in a particular field. Upon successful completion of this step, a genetic algorithm is used to search through all possible combinations of the hydraulic fracture parameters in order to find the most promising combination of the parameters. In applying this methodology Žinstead of detail reservoir data., historical data on prior hydraulic fracture treatments are used to develop a neuro-model of the stimulation characteristics in a particular formation. Historical data of past hydraulic fracture treatments can usually be found in well files. The most challenging part of using such data is their conversion into electronic format. Some companies have invested substantial resources in converting their well files into electronic format. These companies are candidates for application of the methodology presented in this paper. An application to a gas storage field in Ohio is discussed. The new methodology presented here is not a substitution for conventional Žphysics-based. approaches. This methodology is a tool that can be employed when conventional methods can not be used due to lack of necessary data such as detail stress, thickness, porosity, and permeability profiles. This method also can be used in conjunction with conventional tools such as two- or three-dimensional hydraulic fracture simulators to enhance productivity.
2. Background In two previous papers ŽMcVey 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 in predicting post-stimulation well performance and selecting candidate wells for stimulation treatment. In those papers, it was mentioned that this approach could also be extended to optimize the stimulation design parameters. The optimization of hydraulic fracture 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 chromosome. 1 All the possible combinations of genes within this chromosome produce 10 21 distinct, possible, solutions. If one could examine 10 6 solutions per second, it would take 10 15 seconds Žabout 300 million years. to exhaustively search the model space. In the past, making intelligent guesses about the values of the parameters, and use of trial and error was used to solve problems like this. Holland Ž1975. proposed an optimization technique that exploited an analogy between function optimization and the biological process of evolutionary adaptation. Genetic algorithms maintain a population of individuals Žpotential solutions. and act in a way that favors the ‘‘creation’’ and ‘‘survival’’ of better individuals. This innovative technique solves complex problems by imitating Darwinian theories of evolution on a computer. In biological evolution, only the winners survive to continue the evolutionary process. Note that one does not need to know what aspect of the organism makes it a winner, nature just assumes that if it lives, it must be doing something right. Genetic algorithms apply the same evolutionary technique to a wide variety of real-world problems like scheduling, adaptive control, optimal control, database query optimization, gas pipeline operation, inverse modeling in geophysics, etc. By setting the parameters randomly throughout the search space, a population of chromosomes — each representing a potential hydraulic fracture design — is created. This is the first step in implemen-
1
A chromosome is the binary representation of all parameters concatenated to form one member of the genetic population.
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171 Table 1 List of the parameters used in the genetic algorithm for optimization Fracture parameters being optimized Maximum sand concentration Žlbrgal. Average injection rate ŽBPM. Sand laden fluid viscosity Žcp. Water amount Žbbl. Nitrogen amount Žbbl. Sand amount Žsacks. Sand mesh size Acid amount Žgal. Fluid type Acid type Iron control Bacteria control Paraffin dispersing agent Clay stabilizer Surfactant Methanol Contractor
tation of a genetic algorithm. From this population of solutions, the worst are discarded and the best solutions are then ‘‘bred’’ with each other by mixing the parameters Žgenes. from the most successful organ-
163
isms, thus creating a new population. During reproduction, the chromosomes undergo different genetic operation such as selection, cross-over, mutation and inversion ŽMichalewicz, 1992.. The selection operator is responsible for choosing two organisms to become parents. As in real life, this type of continuous adaptation creates a very robust individual. The whole process continues through many ‘‘generations’’, with the best genes being handed down to future generations. The result is typically a very good solution to the problem. By continually cycling these operators, a surprisingly powerful search engine is constructed, which inherently preserves the critical balance needed with any search: the balance between exploitation Žtaking advantage of information already obtained. and exploration Žsearching new areas.. Although simplistic from a biologist’s viewpoint, these algorithms are sufficiently complex to provide robust and powerful search mechanisms. Table 1 is the list of 17 parameters being optimized during this study. These parameters can be divided into two general categories. First are parameters that have distinct and discrete values, or members, such as contractor, acid type, and sand mesh size. Therefore, selecting one member for each pa-
Fig. 1. Field results and network predictions for 48 treatments in Clinton sand.
164
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
Fig. 2. Schematic diagram of the methodology developed in this study.
rameter in this category requires random selection. Parameters in the second category have continuous values such as average injection rate, water amount and sand concentration. Any value between some designated minimum and maximum can be chosen for these parameters. A potential solution to the hydraulic fracture optimization problem includes a combination of values of these 17 parameters. A gene represents each parameter and when combined together the 17 genes form a chromosome. Each chromosome is a potential solution. As mentioned earlier one of the keys to a successful genetic algorithm is having a way of ranking solutions. This is done using a ‘‘fitness function’’. 2 In this study, the neural network that has been developed, trained and successfully tested as the neural model of the hydraulic fracture treatment in this field ŽMohaghegh et al., 1996b. Žneural module
2
A fitness function in any problem is the model or the function that is being optimized.
a2 — as it will be explained later. is the fitness function. 4. Methodology A tool, which is able to predict post-hydraulic fracture deliverability of the gas storage wells in the Clinton sand with 95% accuracy was described in two previous papers ŽMcVey et al., 1996; Mohaghegh et al., 1996b.. The developed tool was trained on more that 570 different hydraulic fracture treatments. It was shown that this tool could predict post-hydraulic fracture deliverability even on new hydraulic fractures Ži.e., hydraulic fractures it had not been trained on.. Fig. 1 shows the neural network’s predictions vs. field results for three consecutive years: 1989, 1990 and 1991. The robustness of the neural model was established by successfully predicting the post-hydraulic fracture deliverability of the treatments for the years 1989 through 1991. This neuro-model was used as the fitness function for the genetic algorithm to predict the outcome of hydraulic fractures. This
S. Mohaghegh et al.r Journal of Petroleum Science and Engineering 23 (1999) 161–171
makes the ranking and selection process of the genetic algorithm possible. A two-stage process was developed to achieve optimized hydraulic fracture design of gas storage wells in the Clinton sand that is the main objective of this study. A detail, step by step procedure is presented in this section; Fig. 2 is a schematic diagram of the procedure. For the first stage, a new neural network Žneural module a1. is designed and trained specifically for this study. No information on the hydraulic fracture design parameters are presented to this neural network. The only data available to this neural net is basic well information and production history. This will be all the information that will be available in each well that is being considered for a hydraulic fracture treatment. This neural network is trained to use the data as input and estimate a post-hydraulic fracture deliverability as output. This process is a rapid screening of all the wells to ‘‘weed-out’’ the wells that should not be considered for further study. This module will identify and separate the so-called ‘‘dog wells’’ that would not be enhanced considerably even after a hydraulic fracture. The wells that have passed the rapid screening test will enter the second stage of the process that is the actual hydraulic fracture design stage. A second neural net Žneural module a2. has been trained for this stage with more than 570 different hydraulic fracture treatments that have been performed on gas storage wells in the Clinton sand. During the training process, the network has learned how the wells respond to hydraulic fractures by building an internal representation of the hydraulic fracturing process in the Clinton sand. This internal representation is in the form of connection-weights between neurons. This network is capable of providing post-hydraulic fracture deliverability with high accuracy using well information, historical data and hydraulic fracture design parameters as input. Fig. 3 shows how this neural network is being used in conjunction with the genetic algorithm. The input to neural module a2 can be divided to three categories: Ž1. basic well information, Ž2. production history and Ž3. hydraulic fracture parameters. The objective is to optimize the third Žlast. category. Each chromosome in the genetic population is an individual solution Žfrac job design. for a particular
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Fig. 3. Schematic diagram of neural module a2, the fitness function.
well. Therefore, for each well the first two parts of the input Žnamely basic well information and production history. remains constant while the third part enters the genetic algorithms. Fig. 1 illustrates the accuracy of this neural network. The output of the genetic algorithm is the optimized hydraulic fracture design for each well. The tool also will provide the engineer with expected post-hydraulic fracture deliverability once the suggested design is used for a hydraulic fracture treatment. This result may be saved and printed. The design parameters can then be given to any service company for implementation.
5. Detail procedure The well selection and hydraulic fracture design take place in two stages. 5.1. Stage one: rapid screening In this stage, a criterion is set for rapid screening of all wells in the database. A screen display of this part of the software is shown in Fig. 4. Neural module a1, that has been trained on basic well information and production history, is used to screen the wells and selects those that meet a certain post-hydraulic fracture deliverability criterion threshold, set by the design engineer. Those wells that meet or exceed the threshold will be identified and will go for further analysis and hydraulic fracture
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Fig. 4. A screen display of the first window of the software’s user interface.
design. A preliminary post-hydraulic fracture deliverability for each well will be calculated and displayed. The post-hydraulic fracture deliverability that is presented at this stage is expected as a result of a generic 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 this point. This is due to the fact that the optimization process has an average post-hydraulic fracture deliverability enhancement of 20% in this field. At this point, the design engineer is presented with a list of candidate wells that meet andror exceed the post-hydraulic fracture deliverability threshold set previously ŽFig. 4.. The engineer must select one well at a time and enter the second stage for optimization. 5.2. Stage two: optimization The following steps are taken in this stage. Step 1: One of the four fracturing fluids Žwater, gel, foam, foamrwater. is selected. Note that these
four procedures were chosen because they have been routinely performed in the aforementioned field in the past. In a previous paper ŽMohaghegh et al., 1996b., it was demonstrated that if a new hydraulic fracture procedure is used, Ža procedure that this software has not been trained for., the software will provide the user with a reasonable answer. This is due to the fact that virtual intelligence paradigms do not undergo complete breakdown, once they encounter new and unfamiliar environments and information. They ‘‘degrade gracefully’’. Actually it was shown that once the software has been exposed to the new procedure, it will learn the new procedure quickly and therefore its performance returns to its normal accuracy Žrefer to Fig. 6 of Mohaghegh et al., 1996b.. Step 2: One hundred random combinations of input variables Žhydraulic 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 fracture deliverability for this particular field is used to forecast post-frac deliverability for 100 cases generated in step 1 ŽFig. 3..
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Fig. 5. A screen display of optimization process.
Step 4: The outcome of neural module a2 will be ranked from 1 to 100, 1 being the highest post-hydraulic fracture deliverability. Step 5: The highest-ranking combination of parameters Ždesign. is compared with the last highestranking design and the better of the two is saved in the memory as the optimum design. Step 6: The top 25 designs of step 4 will be selected for the next step and the rest will be discarded. Step 7: Cross-over, mutation, and inversion operators are used on the top 25 designs of step 6 and a new 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 convergence criteria are suggested. The software provides the design engineer with information to make this decision. During the optimization process, the highest post-hydraulic fracture deliverability ever achieved is displayed along with number of genera-
tions that have passed without any enhancement in post-hydraulic fracture deliverability. One may decide that if, after so many generations no enhancement is taken place, it is time to stop the process. As a second convergence criteria, the engineer may look at the cumulative post-hydraulic fracture deliverability curve for each generation that is displayed on real time. The slope of this curve determines whether every new generation is an improvement over the last generation. A positive slope indicates overall improvement of one generation compared to the previous generation and suggests that the optimization should continue. A zero or negative slope, on the other hand, suggest no improvement has taken place.
6. Results and discussions In order to demonstrate the application of this method, it was decided to perform design optimization on wells that were treated during 1989, 1990
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Fig. 6. Post-hydraulic fracture deliverability enhancement due to optimization.
and 1991. Since the actual results of hydraulic fracture treatments on these wells were available, it would provide good comparisons. We used the software to: Ža. predict the hydraulic fracture treatment and compare it with the actual field results and, Žb.
see the enhancement that would have been achieved if this software were used to design the treatment. Neural module a2 in the software is responsible for prediction of output Žhydraulic fracture treatment results. from new sets of input data Žhydraulic frac-
Fig. 7. Post-hydraulic fracture deliverability enhancement due to optimization.
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Fig. 8. Post-hydraulic fracture deliverability enhancement due to optimization.
ture designs for particular wells.. It would be reasonable to expect that if this module predicts hydraulic fracture treatment results within a certain degree of accuracy for one set of the input values, it should predict the results of another set of input values within 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 frac designs. It is expected that circles and squares should be close to one another. Fracture treatment parameters that have been generated by the software itself using the combined neuro-genetic procedure resulted in the hydraulic fracture treatment results shown by triangles. Note that the same module in the software that has produced the triangles has produced the squares, and in both cases from a set of input data which is new to the module. From these figures, one can observe that by using this software to design a hydraulic fracture treatment for this field, one can enhance treatment results by an average of 20%. It should also be noted that these wells were chosen from among 100 candidate wells. If the software were available at the time of the selection process, one would expect some of the
restimulated wells to have been substituted with candidate wells with better potentials. Table 2 shows the result of this process on one particular well. Well a1166 was treated and its post-hydraulic fracture deliverability was determined to be 918 MCFD. The software predicted that this well’s post-hydraulic fracture deliverability would be 967 MCFD, which is within 5.5% of the actual value. Using the neuro-genetic optimization process introduced here, the software predicts a post-hydraulic fracture deliverability of 1507 MCFD. Using the 5.5% tolerance for the software’s accuracy for this well, this method could have enhanced this well’s post-frac deliverability by 55% to 73%. After the optimization process is completed, the software provides the engineer with proposed hy-
Table 2 Software results for the well a116 Data source
Field result
Neural net
Optimized
Post-frac deliverability
918 ŽMCFD.
967 ŽMCFD.
1507 ŽMCFD.
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Fig. 9. A screen display of the software’s output.
draulic fracture parameters for the well. Fig. 9 is a screen display of the software output.
7. Application to other fields This method can be applied, not only to gas storage operation, but to other types of operations as well. This is true as long as production history and historical data on prior treatments are available. With some modifications, this method can also be applied to new fields where no hydraulic fractures were performed in the past. In such cases, it is necessary that reservoir data be available. If permeability profile for the wells in the field is not available, well logs can be used to generate them ŽMohaghegh et al., 1996a.. The reason why a specific number of wells is not suggested Žfor 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 simulation possible. The success of the simulation and fracture design process is directly related to the accuracy of such data. Acquisition of the above mentioned data can be very expensive, especially for older fields. The methodology introduced in this paper, uses available data such as well completion, production data, and past hydraulic fracture treatment data. The hybrid system developed in this study is able to forecast gas storage well deliverability with a high degree of accuracy. This system is also capable of assisting practicing engineers in the design of optimum hydraulic fractures. This software is currently being used for candidate well selection and hydraulic fracture design optimization in the Clinton sand. A hybrid system that is made up of two neural networks and a genetic algorithm routine is developed for design and optimization of hydraulic fracturing procedures in a gas storage field in Ohio. The major difference between this system with conventional two- or three-dimensional hydraulic fracture simulators is that the developed hybrid system provide a solution for hydraulic fracture treatment design and optimization in the absence of conventional reservoir data that are an absolute necessity when
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using conventional Ž2D or 3D. simulators. The main component of the hybrid system has been successfully 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
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storage wells to hydraulic fracturing with the aid of a neural network. SPE Computer Applications Journal, Apr., 54–57. Michalewicz, Z., 1992. Genetic AlgorithmsqData Structures Evolution Programs. Springer-Verlag, ISBN 3-540-55387-8, 1992. Mohaghegh, S., Ameri, S., Arefi, R., 1996a. Virtual measurement of heterogeneous formation permeability using geophysical well log responses. The Log Analyst 37 Ž2., 32–39. Mohaghegh, S., Aminian, K., Ameri, S., McVey, D.S., 1996b. Predicting well stimulation results in a gas storage field in the absence of reservoir data, using neural networks. SPE Reservoir Engineering Journal, Nov., 54–57.