- Email: [email protected]
Genetic algorithms in oil industry: An overview
Journal of Petroleum Science and Engineering 47 (2005) 15 – 22 www.elsevier.com/locate/petrol
Genetic algorithms in oil industry: An overview Oswaldo Velez-Langs* Departamento de Informa´tica, Estadı´stica y Telema´tica, Escuela Superior de Ciencias Experimentales y Tecnologı´a, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain Facultad de Ingenierı´as, Corporacio´n Universitaria del Sinu´, Carrera 1w Calle 38, Monteria, Colombia Received 31 August 2004; accepted 29 November 2004
Abstract The study presented here is directed to accumulate the body of knowledge which is up to now built around the techniques of Evolutionary Computation in the Oil Industry, particularly in the Exploration and Production business. The models presented cover specific aspects of application in reservoir characterization; nevertheless applications in other aspects are shown. The results are directed to improve the satisfaction by the performance of the methods of simulation of those properties in the reservoir characterization that have impact in the petroleum production. Additionally a brief framework is presented for the conception of evolutionary engineered reservoir characterization systems. D 2005 Elsevier B.V. All rights reserved. Keywords: Evolutionary algorithms; Genetic algorithms; Reservoir characterization; Seismic inversion; Exploration; Production
1. Introduction The use of computer-aided techniques to assist in the reservoir characterisation process is becoming standard in the oil industry. As computers become faster and more computing power is made affordable, companies dedicate more resources to data analysis. The techniques aim at the incorporation into the reservoir models of all data available so that more * Departamento de Informa´tica, Estadı´stica y Telema´tica, Escuela Superior de Ciencias Experimentales y Tecnologı´a, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain. Fax: +34 91 488 7049. E-mail address: [email protected]. 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2004.11.006
realistic models can be generated for improved prediction capabilities. bIntelligent techniques such as neural computing, fuzzy reasoning, and evolutionary computing for data analysis and interpretation are an increasingly powerful tool for making breakthroughs in the science and engineering fields by transforming the data into information and information into knowledgeQ, as it is mentioned in Nikravesh and Aminzadeh (2001). The process makes use of measurements made on the field to restrict the range of values that the parameters might take. The measurements used are wide-ranging and include seismic data, data from geological analogues, core and log data from wells, well test data, and production data. The result of the process is a set of flow simulation models that, to a
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O. Velez-Langs / Journal of Petroleum Science and Engineering 47 (2005) 15–22
greater or lesser extent, agree with the measurements made upon the reservoir. There are very many papers in the literature that describe this process, including Oliver et al. (1996), Tan and Kalogerakis (1996), Wu et al. (1999) and Floris et al. (2001). To properly characterise the flow simulation model requires that every part of the reservoir be adequately described. Direct inversion of the complete model is not a practical proposition, so it is necessary to introduce a coarse grid of pilot points (or control points) and some interpolation method. There are numerous papers that discuss the choice of pilot points and interpolation methods (Bissell, 1994; Cuypers et al., 1998). Having selected these, some optimisation technique is needed to match the numerical results to the measurements. Most attempts to automate this process have used gradient-type methods. In Nikravesh et al. (2003) we have a fully devoted book in soft computing techniques for oil exploration main subjects of: geophysical analysis, computational geology, reservoir and production engineering, nevertheless one paper more adequate to this is found in McCormack et al. (1999). Our work intends to introduce in a comprehensive study, the body of knowledge up to now built around the techniques of Evolutionary Computation in the oil industry, particularly in the exploration and production business, doing special mention to the advantages that these offer to oil industry. Evolutionary systems have been studied for possible applications to optimisation problems. Evolutionary computation techniques such as Genetic Algorithms Data Management
(GAs), Evolutionary Strategies (ESs), Classifier Systems (CSs), and Evolutionary Programming (EP), draw their inspiration from nature. Particularly, Genetic Algorithms (GAs) were proposed by Holland (1975) as an abstraction of biological evolution drawing on ideas from natural evolution and genetics for the design and implementation of robust adaptive systems. Over the last 20 years, GAs have received much attention because of their potential as optimisation techniques for complex functions and an extensive number of applications (Goldberg, 1989; Michalewicz, 1992). The paper is organized in the following way: The second section shows aspects for to keep in mind of the advantage to use Evolutionary Algorithms in oil Industry problems. The third section illustrates a short framework for to mix Evolutionary Computation in a Reservoir Characterization Problem, the quarter section reflected works and applications and finally something final comments.
2. Why evolutionary algorithms in oil industry? There is an inherent complexity when one tries to carry out a project of simulation of a reservoir (Saleri, 1998), own need arises to handle the whole synergy (as is illustrated in Fig. 1) with the most adequate methods that permit it. We find in computational methods inspired in the same nature an important alternative. Genetic algorithm (GA) is one of the stochastic optimization methods which is simulating the process of natural evolution. GA follows the same principles Reservoir Field Development
Geology Electric Records
Core Obtention
Surface Operations
Monitoring
Geophysical Production Software
Environment
Geostatistical Hardware
Labor
Others
Fig. 1. Multidisciplinary aspects involved in the management and simulation of reservoirs from Saleri (1998).
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as those in nature (survival of the fittest, Charles Darwin). Although initially they were proposed as an academic investigation, today GAs turn out to be one of the most promising approaches for dealing with complex systems which at first nobody could imagine that from a relative modest technique. GA is applicable to multi-objectives optimization and can handle conflicts among objectives. Therefore, it is robust where multiple solutions exist. In addition, it is highly efficient and it is easy to use. GAs starts with an initial population of feasible solutions (individuals) to the problem being addressed. Individual solutions are then selected from the population according to a stochastic process that (in some sense) rewards to the individuals with better performance, and their genetic information is recombined and modified following probabilistic transition rules such as the genetic operators to form a new population. The process is repeated until a convergence is detected, or a specified maximum number of function evaluations or a generation is reached. The formulation of a GA for a specific problem requires the definition of three main issues: the design of the genome to contain the variables that define a possible solution and the generation of the phenotype (a realisation of the reservoir simulation model), the selection and breeding structures used to generate solutions, and the genetic operators such as crossover and mutation used to generate new solutions. This is the same approach for the direct application in Reservoir Characterization Problem. In biological terms, the genotype is the information contained in the genetic code (or genome), and the physical representation of this information is the phenotype. Likewise, in the language of genetic algorithms, the array of variables is the genotype and the numerical model is the phenotype. Hence, all the variables required to construct the appropriate numerical reservoir simulation model without ambiguity can be specified in a large one-dimensional array. This implies a one-to-one correspondence between genotype and phenotype. However is possible, and more practical, to establish a one–many correspondence that show the spatial relationship of the geostatistical components of this problem join with the properties of the field as porosity and permeability for example. The result is the modified GA for Reservoir characterization (Romero et al., 2000).
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The initialization process is delineated to continuation: ! The initial values of the geostatistical parameters are drawn randomly from their a priori probability distribution Functions. ! Sets of well data are generated which are consistent with both the measurements for the field properties at every well (for example permeability) and the estimated errors for each well measurement. ! The third step involves the use of a geostatistical method to generate complete petrophysical property fields for each set of well measurements. The selection process is based on the evaluation of the fitness of the individual models. The fitness of an individual corresponds to its objective function and this function can be defined, for example, as the weighted sum of squared errors related to the measurements. The elitism practice let that the better individual in the generation n can be cloned to the generation n+1. The crossover operator for the multidimensional chromosomes used the mask method. A mask is generated to define from which parent a particular gene (data point or well zone) is copied. The mask is defined by randomly choosing a row over the relevant simulation layer, and switching the array elements located thereafter. This process is repeated on each layer. Not one but various mutation operators could be designed in these cases. For the many real number chromosomes, mutation operators should include cases in which the mutation can be for a random change assuming a uniform probability density function and cases in which the mutation can be change by a small random quantity assuming a quadratic probability density function centred on the current value.
3. Inserting evolutionary components in reservoir characterization Upon developing a Evolutionary Computation (EC) System, a programmer writes code that creates and manipulates (in a form pre-specified) certain software components or populations, this code and its pre specification in the behaviour permit that these software components be found established in a concrete
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framework, the EC takes place precisely inside this framework and many times is not extensible out of this framework. Then we can begin to consider the effects that can be presented outside of this framework. Oil exploration and production is the process of discovering and developing new petroleum or natural gas reservoirs. Typically, the process starts with a thorough analysis of the geology in a potential region, particularly the probability of finding hydrocarbons (oil or gas), and the economic factors such as risk and investment needed. If it is decided to explore for resources in the region, a seismic exploration survey is conducted. In a survey, a controlled sound source is used to set off sound waves. These waves penetrate the earth, propagate, reflect, refract and then reach back to the surface of the earth where they are recorded by geophones or hydrophones. Reservoir characterization is a critical step in reservoir development and future production management. Knowing the details of a reservoir allows the simulation of different scenarios. The problem, however, is to define an accurate and suitable reservoir model including small-scale heterogeneity. Currently, the most abundant data about the reservoir, which is the seismic data, do not have enough resolution. The typical resolution of seismic data is on the order of 100 feet or more, which does not give enough detail of reservoir properties. In contrast, well log data, which are collected by inserting sensing devices into an exploratory well, give an excellent description of the well at scales ranging from centimetres to hundreds of meters. However, due to its high cost,
only a few well locations have log data. This scarce information is usually not sufficient to build a reservoir model that includes the small scale variations. In between wells, geological information needs to be estimated. A viable approach to construct a reservoir model is using both seismic and well log data. This approach first builds a framework using seismic scale and well log scale data, then fills in small details using statistical or soft computing methods. These methods are generally stochastic in nature, hence they generate many different realizations (reservoir models). This trait is actually an advantage, since the uncertainties of the different scenarios can be studied by generating a large number of equally possible reservoir models. Consequently, this approach of applying stochastic methods on seismic and well log data is widely used in reservoir characterization (Xie, 2001; Wong et al., 2002; Nikravesh et al., 2003). When to design a Reservoir Characterization Problem with incorporated EC characteristics, we should set aside the typical software process when doing a genetic algorithm. As was said previously a GA is a program that stores individuals represented by structures of data and manipulates these individuals to generate successive populations. This works in a centralized way and does not exist in the natural equivalent of this algorithm. However, the evolutive effects arise to Reservoir Characterization Problem. A small modification of the approach presented in Velez-Langs (2002) permits us to identify the existing relations among an adaptive (evolutionary) process
Table 1 Adaptive process dimensions and reservoir characterization components identification Adaptive dimensions
Reservoir characterization problem
Meaning of the adaptation (What is adapted?)
Beings (elements) that participate in the evolution process: geostatistical parameters and data, spatial relationship, field properties at every well Perception of the environment by elements and relations of these that assure a decentralized selection process: objective function as the weighted sum of squared errors, mask generated from a particular gene in a parent (data point or well zone) for the crossover, elitism criterion, mutation based in random change assuming a uniform probability density function Energy, aptitude or capacity of the elements to perform a task or to utilize certain resources: adequate aptitude to generate a simulation model to production data (history matching) for example Functionality of each element, global functionality: suite of solutions (corresponding to different realisations of the reservoir model) from which to select a representative group for further analysis
Adaptation process (How to adapt to the system?)
Adaptation content (What is the criterion?)
Objective (What is the reason of the adaptation?)
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and the Reservoir Characterization Problem components. Table 1 shows it more clearly.
4. Practical works and applications Most geoscience’s applications began in early 1990s. Gallagher and Sambridge (1994) presented an excellent overview on the use of GAs in seismology. Other applications include geochemical analysis, well logging and seismic interpretation. This section tries to illustrate diverse works that have used the Evolutionary Computation paradigm in Oil industry, we have tried to organize this summary under the aspects of Reservoir Characterization, Gas Storage, Seismic Inversion, Engine Oil Development and Oil Field Development. The organization is not unique and not flexible since there are works that mix diverse aspects of them established previously. 4.1. Reservoir characterization The work of Batyrshin et al. (2005) describes a methodology based on the use of hybrid methods, such as principal component and factor analysis, fuzzy classification and evolutionary optimizations for analysis of well logs and for qualitative pore structure classification in carbonate formations. The developed approach does not require any previous assumptions to construct a model from the measured data set. Obviously, as a pattern recognition technique, it needs a good data set, valid and representative of different features present in the reservoir under study. The constructed porosity classification models can be applied to make predictions for the wells from the oil reservoirs pertaining to micro-fractured carbonate formations. This approach can be extended to the rock type characterization in the absence of adequate geological information. Bush and Carter (1996) try to match the simulation model to the measured history of a reservoir by adjusting some of the model parameters, it happens that more than one optimum exists, more than one set of parameters which reproduce the measured history of the reservoir were found. The challenge is to identify all the optima that are using as few function evaluations as possible.
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Soleng (1999) presents a genetic algorithm that is applied to the problem of conditioning the petrophysical rock properties of a reservoir model on historic production data. He has applied a genetic algorithm to the difficult optimization problem where each evaluation of the objective function implies a flow simulation of the whole reservoir. Ten independent runs are used to give a prediction with an uncertainty estimate for the total future oil production using two different production strategies. The work of Romero et al. (2000) describes the implementation of a Genetic Algorithm (GA) to carry out hydrocarbon reservoir characterisation by conditioning the reservoir simulation model to production data (history matching) on a predefined geological and structural model. The proposed technique combines the advantages of the pilot point method for the description of petrophysical properties with the advantages of GAs for global optimisation. The modified GA uses a complex genome which is divided into seven separate chromosomes for different types of reservoir parameters. Chromosomes containing the pilot point information are three-dimensional real number structures which include information for the wells, while the chromosomes for all other parameters are one-dimensional arrays. Specially designed crossover and mutation operators have been created to work with the nonstandard genome structure. The main advantage of this work is that the method appears to be reasonably insensitive to the parameter settings used to control the GA, which makes it suitable as a general automatic reservoir characterisation algorithm. It also requires only a modest number of forward simulations, and can be readily implemented (and parallelised) for computer-aided history matching. In Rahman et al. (2001), an integrated novel model for hydraulic fracturing design optimization is presented, which recognizes complex interactions between a hydraulically coupled fracture geometry module, a hydrocarbon production module and an investment-return cash flow module. Free design variables are identified and various design constraints are formulated, which must be satisfied so that an optimum design obtained is executable in the field using the specified surface equipment (pump, tubing, etc.) and that treatment does not cause any undesirable formation damage by uncontrolled fracture growth and/or multiple secondary fracture initiation. The
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model is formulated within the framework of a multivariate and multiobjective optimization method, which is based on the combined features of Genetic Algorithm and Evolutionary Operation. A new approach for modelling the dynamic process of Fluid flow in porous media is presented in Yu and Lee (2002). They propose using a Genetic Algorithm (GA) as an inverse method to model fluid flow in a pore network Cellular Automaton (CA). This GA evolves the CA to produce specified flow dynamic responses. The method is applied to a rock sample data set. In Yu et al. (2003), a hybrid GP-fuzzy approach to model reservoir permeability is presented. This approach uses a two-step divide-and-conquer process for modelling. First, GP is applied to construct classifiers that identify permeability ranges. Within each range, ANFIS is employed to build a TakagiSugeno-Kang fuzzy inference system that gives permeability estimation. This method is applied to five well log data sets. The results show that this hybrid system gives more accurate permeability estimation than other previous works. Yang et al. (2003) present a paper with novel integrated models to analyze the production-injection operation systems (PIOS) for the reservoirs based on the concepts of systems engineering. More specifically, gas and/or water injection, reservoir and production performance, and the economic assessment are incorporated into these models. Four production operation methods are considered in the production models. The reservoir geological model is improved with time by the on-going monitoring results for better performance evaluation and prediction. The non-numerical parallel algorithms, including genetic algorithms and simulated annealing algorithms, are employed to optimize and control the nonlinear PIOS under different practical constraints throughout the life of a reservoir. 4.2. Gas storage The objective of the study of Mohaghegh (2003) provides a methodology, and builds a software tool based on this methodology, to address questions related to the stimulation/re-stimulation process in gas storage wells for to minimize costs. The ultimate output of the software tool is a list of the re-stimulation candidates for each year. The list will contain the selected candidates
and specifies whether that particular candidate should be re-fractured or chemically treated. In this study the author uses a series of artificial neural networks and genetic algorithm routines integrated with an extensive relational database–specifically developed for this study–to achieve the goals of the project. The Msc Thesis of Torres (2001), in Spanish, shows a general application model in gas reservoir simulation merging elements of the evolutionary computing and object-oriented paradigms. The model works in three ways: 1. Make an adaptive grid partition of the 3D structure in basis to a non-linear function. 2. Solve the non-linear algebraic equation systems in each block which are generated for the calculation of the gas properties, taking advantage of the objectoriented programming and genetic algorithms, this method is mainly advised when there are problems with typical methods like Newton method. 3. Find out an adaptive pressure distribution throughout the reservoir in basis to a double exponential function. Finally the model joins the three submodels to give solution to the non-linear equations system depicting the gas flow through the reservoir. 4.3. Seismic inversion Mansanne´ and Schoenauer (2000) try to cover an interesting challenge of the last 20 years in geophysics: the determination of the structure of the underground data from geophysical prospecting. The goal of the inverse problem in seismic reflection is to identify the velocity distribution in the underground from recorded reflection profiles of acoustic waves. The problem is turned into an optimization problem whose objective function is quite irregular. Indeed, it is highly nonlinear, exhibits several local minima and can be globally discontinuous. An efficient way to find a global optimum (or a good local optimum) is to use Genetic Algorithms. The work presented in this paper relies on the use of a hybrid GA based on a variable-length piecewise-constant representation built on Voronoi diagrams. In the Boschetti’s PhD thesis (1995) aspects of inversion of potential field data with GA are covered. It presented a GA that simultaneously generates a large number of solutions to various potential field inverse
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problems. It shows that in simple cases a satisfactory description of the ambiguity domain inherent in potential field problems can be efficiently obtained by a simple analysis of the ensemble of solutions. From this analysis information about the expected bounds of the unknown parameters as well as a measure of the reliability of the final solution can also be obtained. A new and interesting application field of EC is named Interactive Evolutionary Computation (IEC). Here, we have one method which provides the inclusion of qualitative geological expertise within a rigorous mathematical inversion scheme by simply asking an expert user to evaluate a sequence of forward geological models. This was presented by Wijns et al. (2003). The inverse modeling technique proposed in this way can help every time that a problem needs visual evaluation of the results or a priori expert knowledge. All that is required is a code that allows the user to forward a model process and view its result. 4.4. Engine oil development Yu and Rutherford (2001) demonstrate the generation of an engine test model using Genetic Programming. In particular, a two-phase modelling process is proposed to handle the high-dimensionality and sparseness natures of the engine test data. The resulting model gives high accuracy prediction on training data. 4.5. Oil field development The paper of Tu´pac et al. (2002) presents a Genetic Algorithm application for selecting the best alternative for oil field development under uncertainty. The alternatives in this study are related to the arrangement of wells in a known and delimited oil reservoir and serve as a basis for calculating the net present value, which is used to measure optimization: the optimal alternative is the one that maximizes the Net Present Value of the field. The results obtained have revealed that it is possible to discover the characteristics of the field when this method is used and that it achieves good results. 4.6. Production scheduling De Almeida et al. (2001) presents a review of the multiobjective fitness evaluation method called
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energy minimization, and presents an analysis of the method’s behavior when used in a genetic algorithm applied to production scheduling of a petroleum refinery. The experimental results are presented and analyzed, leading to an overall evaluation of the benefits provided by the model.
5. Final comments The work described here presents the state of the art in engineering applications from a point of view of the computational theory of the adaptation and the evolution for applications in Oil industry. It is vital to understand and to be able to delineate the specific aspects of the reservoir characterization domain and to observe like the EC paradigm presents techniques inherently distributed that are of private interest in the field mentioned. The use of this techniques offers a true benefit in exploration and production business. Our future work is to propose the construction of a Computational Intelligence Software tool (using especially GAs but not ruling out the possibility of using techniques of Fuzzy Systems of Neural Networks) focused in reservoir characterization field, adaptable to the needs and preferences of their users in relation to the domain characteristics. Through EC which works if possible in a distributed environment, this tool will be able to apply the developed EC methods to carry out the characterisation of a real reservoir for a major petroleum company. The development of this proposal intends to give solution to low performance in adaptability of the traditional developed systems at this time.
References Batyrshin, I., Sheremetov, L., Markov, M., Panova, A., 2005. Hybrid method for porosity classification in carbonate formations. J. Pet. Sci. Eng. 47, 36 – 50 (in this volume). Bissell, R., 1994. Calculating optimal parameters for history matching. Proc. Fourth European Conference on the Mathematics of Oil Recovery, Roros, Norway. Boschetti, F., 1995. Application of Genetic Algorithms to the Inversion of Geophysical Data. PhD thesis in Mathematical Geophysics. University of Western Australia, Perth. Bush, M.D., Carter, J.N., 1996. Application of a modified genetic algorithm to parameter estimation in the petroleum industry. In: Dagli, C., Akay, E., Philip-Chen, C.L., Fernandez, B., Ghosh, J.
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(Eds.), Intelligent Engineering Systems through Artificial Neural Networks, vol. 6. ASME Press, New York. Cuypers, M., Dubrule, O., Lamy, P., Bissell, R., 1998. Optimal choice of inversion parameters for history-matching with the pilot point method. Proc. Sixth European Conference on the Mathematics of Oil Recovery, Peebles, Scotland. De Almeida, M.R., Hamacher, S., Pacheco, M.A.C., Vellasco, M.B.R., 2001. The energy minimization method: a multiobjective fitness evaluation technique and its application to the production scheduling in a petroleum refinery. Proc. of the 2001 Congress on Evolutionary Computation, vol. 1, pp. 560 – 567. Seoul, Korea. Floris, F.J.T., Bush, M.D., Cuypers, M., Roggero, F., Syversveen, A.R., 2001. Methods for quantifying the uncertainty of production forecasts—a comparative study. J. Pet. Geosci. 7, 87 – 96. Gallagher, K., Sambridge, M., 1994. Genetic algorithms: a powerful tool for large-scale nonlinear optimization problems. Comput. Geosci. 20 (7–8), 1229 – 1236. Goldberg, D.E., 1989. Genetic Algorithms in Search, Optimization and Machine Learning. Addison-Wesley Publishing Company, NY. Holland, J.H., 1975. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. University of Michigan Press, Ann Arbor, MI. Mansanne´, F., Schoenauer, M., 2002. An automatic geophysical inversion procedure using a genetic algorithm. In: Wong, P., Aminzadeh, F., Nikravesh, M. (Eds.), Soft Computing for Reservoir Characterization and Modeling, Studies in Fuzziness and Soft Computing, vol. 80. Physica-Verlag, pp. 331 – 353. McCormack, M., Stoisits, R., MacAllister, D., Crawford, K., 1999. Applications of genetic algorithms in exploration and production. Lead. Edge 18 (6), 716 – 719. Michalewicz, Z., 1992. Genetic Algorithms+Data Structures=Evolution Programs. Springer Verlag, Berlin. Mohaghegh, S.D., 2003. Enhancing gas storage wells deliverability using intelligent systems. In: Nikravesh, M., Aminzadeh, F., Zadeh, L. (Eds.), Soft Computing and Intelligent Data Analysis in Oil Exploration. Elsevier Science, the Netherlands, pp. 445 – 467. Nikravesh, M., Aminzadeh, F., 2001. Past, present and future intelligent reservoir characterization trends. J. Pet. Sci. Eng. 31 (2–4), 67 – 79. Nikravesh, M., Aminzadeh, F., Zadeh, L., 2003. Soft Computing and Intelligent Data Analysis in Oil Exploration. Developments in Petroleum Science, vol. 51. Elsevier Science, the Netherlands. Oliver, D.S., He, N., Reynolds, A.C., 1996. Conditioning permeability fields to pressure data. Proc. Fifth European Conference on the Mathematics of Oil Recovery, Leoben, Austria, pp. 3 – 6. Rahman, M.M., Rahman, M.K., Rahman, S.S., 2001. An integrated model for multiobjective design optimization of hydraulic fracturing. J. Pet. Sci. Eng. 31 (1), 41 – 62.
Romero, C.E., Carter, J.N., Zimmerman, R.W., Gringarten, A.C., 2000. A modified genetic algorithm for reservoir characterization. Proc. of the 2000 SPE Seventh International Oil and Gas Conference and Exhibition, Beijing, China. Saleri, N.G., 1998. Re-engineering simulation: managing complexity and complexification in reservoir projects. Proc. of SPE Annual Technical Conference and Exhibition, Denver, Colorado. Soleng, H.H., 1999. Oil reservoir production forecasting with uncertainty estimation using genetic algorithms. Proc. of the Congress on Evolutionary Computation, vol. 2, pp. 1217 – 1223. Tan, T.B., Kalogerakis, N., 1996. Improved reservoir characterization using automatic matching procedures. J. Can. Pet. Technol. 32 (6), 26 – 33. Torres, J.L., 2001. Un Modelo Gene´tico-Objetual para la Simulacio´n de Yacimientos de Gas. Msc. thesis. Facultad de Minas, Universidad Nacional de Colombia, Medellin. Tu´pac, Y.J., Vellasco, M.M.B.R., Pacheco, M.A.C., 2002. Selection of alternatives for oil field development by genetic algorithms. Rev. Eng. Te´rm. Spec. Ed. 2, 51 – 54. Velez-Langs, O., 2002. Agents systems: a perspective from evolutionary computation. Proc. of 4th International Conference on Recent Advances in Soft Computing, Nottingham, United Kingdom. Wijns, C., Boschetti, F., Moresi, L., 2003. Inverse modelling in geology by interactive evolutionary computation. J. Struct. Geol. 25 (10), 162 – 1615. Wong, P.M., Aminzadeh, F., Nikravesh, M., 2002. Soft computing for reservoir characterization and modeling. Series Studies in Fuzziness and Soft Computing, vol. 80. Physical-Verlag. Wu, Z., Reynolds, A.C., Oliver, D.S., 1999. Conditioning geostatistical models to two-phase production data. SPE J. 4 (2), 142 – 155. Xie, D., 2001. Thin-bed Reservoir Characterization using Integrated 3-D Seismic and Well Log Data: a Case Study of the Central Boonsville Field, Fort Worth Basin, North-Central Texas, PhD thesis. Michigan Technological University, Houghton. Yang, D., Zhang, Q., Gu, Y., 2003. Integrated optimization and control of the production-injection operation systems for hydrocarbon reservoirs. J. Pet. Sci. Eng. 37 (1–2), 69 – 81. Yu, T., Lee, S., 2002. Evolving cellular automata to model fluid flow in porous media. Proc of the 2002 NASA/DoD Conference on Evolvable Hardware. IEEE Press, pp. 210 – 218. Yu, T., Rutherford, J., 2001. Modeling sparse engine test data using genetic programming. Proc. of The Seventh ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, San Francisco, California. Yu, T., Wilkinson, D., Xie, D., 2003. A hybrid GP-fuzzy approach for reservoir characterization. In: Riolo, R.L., Worzel, B. (Eds.), Genetic Programming Theory and Practice. Kluwer, pp. 271 – 290.
Genetic algorithms in oil industry: An overview Oswaldo Velez-Langs* Departamento de Informa´tica, Estadı´stica y Telema´tica, Escuela Superior de Ciencias Experimentales y Tecnologı´a, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain Facultad de Ingenierı´as, Corporacio´n Universitaria del Sinu´, Carrera 1w Calle 38, Monteria, Colombia Received 31 August 2004; accepted 29 November 2004
Abstract The study presented here is directed to accumulate the body of knowledge which is up to now built around the techniques of Evolutionary Computation in the Oil Industry, particularly in the Exploration and Production business. The models presented cover specific aspects of application in reservoir characterization; nevertheless applications in other aspects are shown. The results are directed to improve the satisfaction by the performance of the methods of simulation of those properties in the reservoir characterization that have impact in the petroleum production. Additionally a brief framework is presented for the conception of evolutionary engineered reservoir characterization systems. D 2005 Elsevier B.V. All rights reserved. Keywords: Evolutionary algorithms; Genetic algorithms; Reservoir characterization; Seismic inversion; Exploration; Production
1. Introduction The use of computer-aided techniques to assist in the reservoir characterisation process is becoming standard in the oil industry. As computers become faster and more computing power is made affordable, companies dedicate more resources to data analysis. The techniques aim at the incorporation into the reservoir models of all data available so that more * Departamento de Informa´tica, Estadı´stica y Telema´tica, Escuela Superior de Ciencias Experimentales y Tecnologı´a, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain. Fax: +34 91 488 7049. E-mail address: [email protected]. 0920-4105/$ - see front matter D 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.petrol.2004.11.006
realistic models can be generated for improved prediction capabilities. bIntelligent techniques such as neural computing, fuzzy reasoning, and evolutionary computing for data analysis and interpretation are an increasingly powerful tool for making breakthroughs in the science and engineering fields by transforming the data into information and information into knowledgeQ, as it is mentioned in Nikravesh and Aminzadeh (2001). The process makes use of measurements made on the field to restrict the range of values that the parameters might take. The measurements used are wide-ranging and include seismic data, data from geological analogues, core and log data from wells, well test data, and production data. The result of the process is a set of flow simulation models that, to a
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greater or lesser extent, agree with the measurements made upon the reservoir. There are very many papers in the literature that describe this process, including Oliver et al. (1996), Tan and Kalogerakis (1996), Wu et al. (1999) and Floris et al. (2001). To properly characterise the flow simulation model requires that every part of the reservoir be adequately described. Direct inversion of the complete model is not a practical proposition, so it is necessary to introduce a coarse grid of pilot points (or control points) and some interpolation method. There are numerous papers that discuss the choice of pilot points and interpolation methods (Bissell, 1994; Cuypers et al., 1998). Having selected these, some optimisation technique is needed to match the numerical results to the measurements. Most attempts to automate this process have used gradient-type methods. In Nikravesh et al. (2003) we have a fully devoted book in soft computing techniques for oil exploration main subjects of: geophysical analysis, computational geology, reservoir and production engineering, nevertheless one paper more adequate to this is found in McCormack et al. (1999). Our work intends to introduce in a comprehensive study, the body of knowledge up to now built around the techniques of Evolutionary Computation in the oil industry, particularly in the exploration and production business, doing special mention to the advantages that these offer to oil industry. Evolutionary systems have been studied for possible applications to optimisation problems. Evolutionary computation techniques such as Genetic Algorithms Data Management
(GAs), Evolutionary Strategies (ESs), Classifier Systems (CSs), and Evolutionary Programming (EP), draw their inspiration from nature. Particularly, Genetic Algorithms (GAs) were proposed by Holland (1975) as an abstraction of biological evolution drawing on ideas from natural evolution and genetics for the design and implementation of robust adaptive systems. Over the last 20 years, GAs have received much attention because of their potential as optimisation techniques for complex functions and an extensive number of applications (Goldberg, 1989; Michalewicz, 1992). The paper is organized in the following way: The second section shows aspects for to keep in mind of the advantage to use Evolutionary Algorithms in oil Industry problems. The third section illustrates a short framework for to mix Evolutionary Computation in a Reservoir Characterization Problem, the quarter section reflected works and applications and finally something final comments.
2. Why evolutionary algorithms in oil industry? There is an inherent complexity when one tries to carry out a project of simulation of a reservoir (Saleri, 1998), own need arises to handle the whole synergy (as is illustrated in Fig. 1) with the most adequate methods that permit it. We find in computational methods inspired in the same nature an important alternative. Genetic algorithm (GA) is one of the stochastic optimization methods which is simulating the process of natural evolution. GA follows the same principles Reservoir Field Development
Geology Electric Records
Core Obtention
Surface Operations
Monitoring
Geophysical Production Software
Environment
Geostatistical Hardware
Labor
Others
Fig. 1. Multidisciplinary aspects involved in the management and simulation of reservoirs from Saleri (1998).
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as those in nature (survival of the fittest, Charles Darwin). Although initially they were proposed as an academic investigation, today GAs turn out to be one of the most promising approaches for dealing with complex systems which at first nobody could imagine that from a relative modest technique. GA is applicable to multi-objectives optimization and can handle conflicts among objectives. Therefore, it is robust where multiple solutions exist. In addition, it is highly efficient and it is easy to use. GAs starts with an initial population of feasible solutions (individuals) to the problem being addressed. Individual solutions are then selected from the population according to a stochastic process that (in some sense) rewards to the individuals with better performance, and their genetic information is recombined and modified following probabilistic transition rules such as the genetic operators to form a new population. The process is repeated until a convergence is detected, or a specified maximum number of function evaluations or a generation is reached. The formulation of a GA for a specific problem requires the definition of three main issues: the design of the genome to contain the variables that define a possible solution and the generation of the phenotype (a realisation of the reservoir simulation model), the selection and breeding structures used to generate solutions, and the genetic operators such as crossover and mutation used to generate new solutions. This is the same approach for the direct application in Reservoir Characterization Problem. In biological terms, the genotype is the information contained in the genetic code (or genome), and the physical representation of this information is the phenotype. Likewise, in the language of genetic algorithms, the array of variables is the genotype and the numerical model is the phenotype. Hence, all the variables required to construct the appropriate numerical reservoir simulation model without ambiguity can be specified in a large one-dimensional array. This implies a one-to-one correspondence between genotype and phenotype. However is possible, and more practical, to establish a one–many correspondence that show the spatial relationship of the geostatistical components of this problem join with the properties of the field as porosity and permeability for example. The result is the modified GA for Reservoir characterization (Romero et al., 2000).
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The initialization process is delineated to continuation: ! The initial values of the geostatistical parameters are drawn randomly from their a priori probability distribution Functions. ! Sets of well data are generated which are consistent with both the measurements for the field properties at every well (for example permeability) and the estimated errors for each well measurement. ! The third step involves the use of a geostatistical method to generate complete petrophysical property fields for each set of well measurements. The selection process is based on the evaluation of the fitness of the individual models. The fitness of an individual corresponds to its objective function and this function can be defined, for example, as the weighted sum of squared errors related to the measurements. The elitism practice let that the better individual in the generation n can be cloned to the generation n+1. The crossover operator for the multidimensional chromosomes used the mask method. A mask is generated to define from which parent a particular gene (data point or well zone) is copied. The mask is defined by randomly choosing a row over the relevant simulation layer, and switching the array elements located thereafter. This process is repeated on each layer. Not one but various mutation operators could be designed in these cases. For the many real number chromosomes, mutation operators should include cases in which the mutation can be for a random change assuming a uniform probability density function and cases in which the mutation can be change by a small random quantity assuming a quadratic probability density function centred on the current value.
3. Inserting evolutionary components in reservoir characterization Upon developing a Evolutionary Computation (EC) System, a programmer writes code that creates and manipulates (in a form pre-specified) certain software components or populations, this code and its pre specification in the behaviour permit that these software components be found established in a concrete
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framework, the EC takes place precisely inside this framework and many times is not extensible out of this framework. Then we can begin to consider the effects that can be presented outside of this framework. Oil exploration and production is the process of discovering and developing new petroleum or natural gas reservoirs. Typically, the process starts with a thorough analysis of the geology in a potential region, particularly the probability of finding hydrocarbons (oil or gas), and the economic factors such as risk and investment needed. If it is decided to explore for resources in the region, a seismic exploration survey is conducted. In a survey, a controlled sound source is used to set off sound waves. These waves penetrate the earth, propagate, reflect, refract and then reach back to the surface of the earth where they are recorded by geophones or hydrophones. Reservoir characterization is a critical step in reservoir development and future production management. Knowing the details of a reservoir allows the simulation of different scenarios. The problem, however, is to define an accurate and suitable reservoir model including small-scale heterogeneity. Currently, the most abundant data about the reservoir, which is the seismic data, do not have enough resolution. The typical resolution of seismic data is on the order of 100 feet or more, which does not give enough detail of reservoir properties. In contrast, well log data, which are collected by inserting sensing devices into an exploratory well, give an excellent description of the well at scales ranging from centimetres to hundreds of meters. However, due to its high cost,
only a few well locations have log data. This scarce information is usually not sufficient to build a reservoir model that includes the small scale variations. In between wells, geological information needs to be estimated. A viable approach to construct a reservoir model is using both seismic and well log data. This approach first builds a framework using seismic scale and well log scale data, then fills in small details using statistical or soft computing methods. These methods are generally stochastic in nature, hence they generate many different realizations (reservoir models). This trait is actually an advantage, since the uncertainties of the different scenarios can be studied by generating a large number of equally possible reservoir models. Consequently, this approach of applying stochastic methods on seismic and well log data is widely used in reservoir characterization (Xie, 2001; Wong et al., 2002; Nikravesh et al., 2003). When to design a Reservoir Characterization Problem with incorporated EC characteristics, we should set aside the typical software process when doing a genetic algorithm. As was said previously a GA is a program that stores individuals represented by structures of data and manipulates these individuals to generate successive populations. This works in a centralized way and does not exist in the natural equivalent of this algorithm. However, the evolutive effects arise to Reservoir Characterization Problem. A small modification of the approach presented in Velez-Langs (2002) permits us to identify the existing relations among an adaptive (evolutionary) process
Table 1 Adaptive process dimensions and reservoir characterization components identification Adaptive dimensions
Reservoir characterization problem
Meaning of the adaptation (What is adapted?)
Beings (elements) that participate in the evolution process: geostatistical parameters and data, spatial relationship, field properties at every well Perception of the environment by elements and relations of these that assure a decentralized selection process: objective function as the weighted sum of squared errors, mask generated from a particular gene in a parent (data point or well zone) for the crossover, elitism criterion, mutation based in random change assuming a uniform probability density function Energy, aptitude or capacity of the elements to perform a task or to utilize certain resources: adequate aptitude to generate a simulation model to production data (history matching) for example Functionality of each element, global functionality: suite of solutions (corresponding to different realisations of the reservoir model) from which to select a representative group for further analysis
Adaptation process (How to adapt to the system?)
Adaptation content (What is the criterion?)
Objective (What is the reason of the adaptation?)
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and the Reservoir Characterization Problem components. Table 1 shows it more clearly.
4. Practical works and applications Most geoscience’s applications began in early 1990s. Gallagher and Sambridge (1994) presented an excellent overview on the use of GAs in seismology. Other applications include geochemical analysis, well logging and seismic interpretation. This section tries to illustrate diverse works that have used the Evolutionary Computation paradigm in Oil industry, we have tried to organize this summary under the aspects of Reservoir Characterization, Gas Storage, Seismic Inversion, Engine Oil Development and Oil Field Development. The organization is not unique and not flexible since there are works that mix diverse aspects of them established previously. 4.1. Reservoir characterization The work of Batyrshin et al. (2005) describes a methodology based on the use of hybrid methods, such as principal component and factor analysis, fuzzy classification and evolutionary optimizations for analysis of well logs and for qualitative pore structure classification in carbonate formations. The developed approach does not require any previous assumptions to construct a model from the measured data set. Obviously, as a pattern recognition technique, it needs a good data set, valid and representative of different features present in the reservoir under study. The constructed porosity classification models can be applied to make predictions for the wells from the oil reservoirs pertaining to micro-fractured carbonate formations. This approach can be extended to the rock type characterization in the absence of adequate geological information. Bush and Carter (1996) try to match the simulation model to the measured history of a reservoir by adjusting some of the model parameters, it happens that more than one optimum exists, more than one set of parameters which reproduce the measured history of the reservoir were found. The challenge is to identify all the optima that are using as few function evaluations as possible.
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Soleng (1999) presents a genetic algorithm that is applied to the problem of conditioning the petrophysical rock properties of a reservoir model on historic production data. He has applied a genetic algorithm to the difficult optimization problem where each evaluation of the objective function implies a flow simulation of the whole reservoir. Ten independent runs are used to give a prediction with an uncertainty estimate for the total future oil production using two different production strategies. The work of Romero et al. (2000) describes the implementation of a Genetic Algorithm (GA) to carry out hydrocarbon reservoir characterisation by conditioning the reservoir simulation model to production data (history matching) on a predefined geological and structural model. The proposed technique combines the advantages of the pilot point method for the description of petrophysical properties with the advantages of GAs for global optimisation. The modified GA uses a complex genome which is divided into seven separate chromosomes for different types of reservoir parameters. Chromosomes containing the pilot point information are three-dimensional real number structures which include information for the wells, while the chromosomes for all other parameters are one-dimensional arrays. Specially designed crossover and mutation operators have been created to work with the nonstandard genome structure. The main advantage of this work is that the method appears to be reasonably insensitive to the parameter settings used to control the GA, which makes it suitable as a general automatic reservoir characterisation algorithm. It also requires only a modest number of forward simulations, and can be readily implemented (and parallelised) for computer-aided history matching. In Rahman et al. (2001), an integrated novel model for hydraulic fracturing design optimization is presented, which recognizes complex interactions between a hydraulically coupled fracture geometry module, a hydrocarbon production module and an investment-return cash flow module. Free design variables are identified and various design constraints are formulated, which must be satisfied so that an optimum design obtained is executable in the field using the specified surface equipment (pump, tubing, etc.) and that treatment does not cause any undesirable formation damage by uncontrolled fracture growth and/or multiple secondary fracture initiation. The
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model is formulated within the framework of a multivariate and multiobjective optimization method, which is based on the combined features of Genetic Algorithm and Evolutionary Operation. A new approach for modelling the dynamic process of Fluid flow in porous media is presented in Yu and Lee (2002). They propose using a Genetic Algorithm (GA) as an inverse method to model fluid flow in a pore network Cellular Automaton (CA). This GA evolves the CA to produce specified flow dynamic responses. The method is applied to a rock sample data set. In Yu et al. (2003), a hybrid GP-fuzzy approach to model reservoir permeability is presented. This approach uses a two-step divide-and-conquer process for modelling. First, GP is applied to construct classifiers that identify permeability ranges. Within each range, ANFIS is employed to build a TakagiSugeno-Kang fuzzy inference system that gives permeability estimation. This method is applied to five well log data sets. The results show that this hybrid system gives more accurate permeability estimation than other previous works. Yang et al. (2003) present a paper with novel integrated models to analyze the production-injection operation systems (PIOS) for the reservoirs based on the concepts of systems engineering. More specifically, gas and/or water injection, reservoir and production performance, and the economic assessment are incorporated into these models. Four production operation methods are considered in the production models. The reservoir geological model is improved with time by the on-going monitoring results for better performance evaluation and prediction. The non-numerical parallel algorithms, including genetic algorithms and simulated annealing algorithms, are employed to optimize and control the nonlinear PIOS under different practical constraints throughout the life of a reservoir. 4.2. Gas storage The objective of the study of Mohaghegh (2003) provides a methodology, and builds a software tool based on this methodology, to address questions related to the stimulation/re-stimulation process in gas storage wells for to minimize costs. The ultimate output of the software tool is a list of the re-stimulation candidates for each year. The list will contain the selected candidates
and specifies whether that particular candidate should be re-fractured or chemically treated. In this study the author uses a series of artificial neural networks and genetic algorithm routines integrated with an extensive relational database–specifically developed for this study–to achieve the goals of the project. The Msc Thesis of Torres (2001), in Spanish, shows a general application model in gas reservoir simulation merging elements of the evolutionary computing and object-oriented paradigms. The model works in three ways: 1. Make an adaptive grid partition of the 3D structure in basis to a non-linear function. 2. Solve the non-linear algebraic equation systems in each block which are generated for the calculation of the gas properties, taking advantage of the objectoriented programming and genetic algorithms, this method is mainly advised when there are problems with typical methods like Newton method. 3. Find out an adaptive pressure distribution throughout the reservoir in basis to a double exponential function. Finally the model joins the three submodels to give solution to the non-linear equations system depicting the gas flow through the reservoir. 4.3. Seismic inversion Mansanne´ and Schoenauer (2000) try to cover an interesting challenge of the last 20 years in geophysics: the determination of the structure of the underground data from geophysical prospecting. The goal of the inverse problem in seismic reflection is to identify the velocity distribution in the underground from recorded reflection profiles of acoustic waves. The problem is turned into an optimization problem whose objective function is quite irregular. Indeed, it is highly nonlinear, exhibits several local minima and can be globally discontinuous. An efficient way to find a global optimum (or a good local optimum) is to use Genetic Algorithms. The work presented in this paper relies on the use of a hybrid GA based on a variable-length piecewise-constant representation built on Voronoi diagrams. In the Boschetti’s PhD thesis (1995) aspects of inversion of potential field data with GA are covered. It presented a GA that simultaneously generates a large number of solutions to various potential field inverse
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problems. It shows that in simple cases a satisfactory description of the ambiguity domain inherent in potential field problems can be efficiently obtained by a simple analysis of the ensemble of solutions. From this analysis information about the expected bounds of the unknown parameters as well as a measure of the reliability of the final solution can also be obtained. A new and interesting application field of EC is named Interactive Evolutionary Computation (IEC). Here, we have one method which provides the inclusion of qualitative geological expertise within a rigorous mathematical inversion scheme by simply asking an expert user to evaluate a sequence of forward geological models. This was presented by Wijns et al. (2003). The inverse modeling technique proposed in this way can help every time that a problem needs visual evaluation of the results or a priori expert knowledge. All that is required is a code that allows the user to forward a model process and view its result. 4.4. Engine oil development Yu and Rutherford (2001) demonstrate the generation of an engine test model using Genetic Programming. In particular, a two-phase modelling process is proposed to handle the high-dimensionality and sparseness natures of the engine test data. The resulting model gives high accuracy prediction on training data. 4.5. Oil field development The paper of Tu´pac et al. (2002) presents a Genetic Algorithm application for selecting the best alternative for oil field development under uncertainty. The alternatives in this study are related to the arrangement of wells in a known and delimited oil reservoir and serve as a basis for calculating the net present value, which is used to measure optimization: the optimal alternative is the one that maximizes the Net Present Value of the field. The results obtained have revealed that it is possible to discover the characteristics of the field when this method is used and that it achieves good results. 4.6. Production scheduling De Almeida et al. (2001) presents a review of the multiobjective fitness evaluation method called
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energy minimization, and presents an analysis of the method’s behavior when used in a genetic algorithm applied to production scheduling of a petroleum refinery. The experimental results are presented and analyzed, leading to an overall evaluation of the benefits provided by the model.
5. Final comments The work described here presents the state of the art in engineering applications from a point of view of the computational theory of the adaptation and the evolution for applications in Oil industry. It is vital to understand and to be able to delineate the specific aspects of the reservoir characterization domain and to observe like the EC paradigm presents techniques inherently distributed that are of private interest in the field mentioned. The use of this techniques offers a true benefit in exploration and production business. Our future work is to propose the construction of a Computational Intelligence Software tool (using especially GAs but not ruling out the possibility of using techniques of Fuzzy Systems of Neural Networks) focused in reservoir characterization field, adaptable to the needs and preferences of their users in relation to the domain characteristics. Through EC which works if possible in a distributed environment, this tool will be able to apply the developed EC methods to carry out the characterisation of a real reservoir for a major petroleum company. The development of this proposal intends to give solution to low performance in adaptability of the traditional developed systems at this time.
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