Baris Guyaguler

A Comparison Study on Experimental Design and Response Surface Methodologies

Experimental design method is an alternative to traditional sensitivity analysis. The basic idea behind this methodology is to vary multiple parameters at the same time so that maximum inference can be attained with minimum cost. Once the appropriate design is established and the corresponding experiments (simulations) are performed, the results can be investigated by fitting them to a response surface. This surface is usually an analytical or a simple numerical function which is cheap to sample. Therefore it can be used as a proxy to reservoir simulation to quantify the uncertainties. Designing an efficient sensitivity study poses two main issues: • Designing a parameter space sampling strategy and carrying out experiments. • Analyzing the results of the experiments. (Response surface generation)

Optimization of Well Placement

Optimal placement of oil, gas or water wells is a complex problem that depends on reservoir and fluid properties, well and surface equipment specifications, as well as economic parameters. An optimization approach that enables the evaluation of all these information is presented. A hybrid of the genetic algorithm (GA) forms the basis of the optimization technique. GA operators such as uniform, single-point, two-point crossover, uniform mutation, elitism, tournament and fitness scaling were used. An additional operator that employs kriging is proposed. The GA was hybridized with the polytope algorithm, which makes use of the trends in the search space. The hybrid algorithm was tested on a set of mathematical functions with different characteristics in order to determine the performance sensitivity to GA operators and hybridization. Simple test cases of oil production optimization on 16×16 simulation grids with known optimum well locations were carried out to verify the hybrid GA results. Next, runs were carried out for a 32X32 problem. The locations of a production and injection well were optimized in the case of three existing producers. Exhaustive runs were carried out for these cases to determine the effects of the operators, hybridization and the population size on the performance of the algorithm for well placement problems. Subsequently, the optimum configuration of two injection wells were determined with two existing producers in the field. It was observed that the hybrid algorithm is able to reduce the required number of simulations substantially over simple GA.

Automated Reservoir Model Selection in Well Test Interpretation

Technological achievements in the area of well testing, such as permanent downhole gauges, demand automated techniques to cope with the large amounts of data acquired. In such an application, the need to interpret large quantities of data with little human intervention suggests the desirability of automated model recognition. Also in some cases the characteristic behavior of the pressure or its derivative curves for specific models may be hidden behind noise or human bias may lead to the selection of an invalid or inappropriate model. This paper demonstrates an approach based on Genetic Algorithm (GA) that is able to select the most probable reservoir model among a set of candidate models, consistent with a given set of pressure transient data. The type of reservoir model to be used is defined as a variable and is estimated together with the other unknown model parameters (permeability, skin, etc.). Several reservoir models are used simultaneously in the regression process. GA populations consist of individuals that represent parameters for different models. As the GA iterates, individuals that belong to the most likely reservoir model dominate the population, while less likely models become extinct. Since different models may require different numbers of parameters, the solution vectors have varying lengths. The GA is able to cope with such solution vectors of differing size. Information exchange (GA crossover operator) is allowed only between parameters that are physically related. Alternatively, we illustrate the use of GA as a preprocessor for conventional gradient-based algorithms such as LevenbergMarquardt. When combined with the GA, the dependency of such conventional algorithms to the initial guess is reduced and the overall regression performance is improved. For automated interpretations where the model is already known this method allows to virtually eliminate the initial guess determination step. Tests on real and synthetic pressure transient data indicated that the proposed method was able to select the correct reservoir model. The method revealed hidden implications of the pressure transient that may otherwise have been overlooked due to noise. As a preprocessor for more conventional nonlinear regression approaches, applying GA to a number of noisy pressure transient tests demonstrated that the method is robust and efficient. Introduction The conventional approach for well test analysis involves an initial selection step, to determine the most appropriate analytical model for the reservoir under investigation. This determination is made by the engineer and is mainly based on the shape of the pressure derivative curve. The choice of the appropriate model is a step that requires well-test analysis expertise and is a step that can lead to large errors in the final result. In some cases the pressure data may have associated noise. This noise is amplified on the derivative curve, on which the engineer bases his/her selection. The manual step of model selection is a hindrance in achieving full automation of the interpretation, such as would be desirable with the massive data sets obtained from permanent gauges. Post attempts at automating model selection have met with only partial success1–7. Some of these techniques for model recognition were reviewed by Horne 8. Most of these techniques are based on rule-based systems or neural networks. In this study a simultaneous regression and preferential sampling approach is proposed. The process of well-test analysis is automated in this study. Human involvement occurs only at the initial selection step of the candidate models. Simultaneous regression with Genetic Algorithm (GA)9 is then carried out on these candidate models. Each population consists of subpopulations, one for each model. The GA operators, crossover and mutation 10 are applied to create new populations. The model with a better fit to the data eventually dominates the population while the subpopulations representing other models become extinct. Thus at the end of such a run, not only is the most probable model exposed, but also the reservoir and model parameters that result in the best least squares fit to this model are obtained. Even in cases where the uncertainty in the reservoir model 2 AUTOMATED RESERVOIR MODEL SELECTION IN WELL TEST INTERPRETATION SPE 71569 is reduced, the dependency of the nonlinear regression process to the initial guess is another obstacle to interpretation. Some parameters do not have simple heuristics to help make a reasonable initial guess and noise in the data may complicate visual determination (e.g., straight line analysis) of the initial guess parameters. Conventional regression techniques may fail to converge to the right solution and fall into suboptimal solutions if the initial estimate is not appropriate. In the case of automated analysis, the consequences of such suboptimal convergence can be disastrous. In the case of conventional manual well-test analysis, precious time can be wasted in the regression procedure. In order to reduce the dependency of the behaviour of the nonlinear regression to the initial guess, a GA algorithm can first be applied. The solution obtained from the GA regression can then be seeded as the initial guess of the LevenbergMarquardt11 algorithm. The engineer in this case needs only to specify the bounds of the parameters rather than a single deterministic initial guess. These bounds can even be the physical bounds of the reservoir model parameters. This approach virtually eliminates the need to spend time assessing consistent parameter values for an initial guess.

Evolutionary proxy tuning for expensive evaluation functions: a real-case application to petroleum reservoir optimization

Decisions have to be made at every level of petroleum reservoir development. For many cases, optimal decisions are dependent on many nonlinearly correlated parameters, which makes intuitive judgement difficult. In such cases automated optimization is an option. Decisions should be based on the most relevant and accurate tools available. For the well placement problem a numerical simulator that computes the movement and interaction of subsurface fluids is the most accurate tool available to engineers. However, numerical simulation is most often computationally expensive making direct optimization prohibitive in terms of CPU requirements. To overcome the computational infeasibility, one can try to utilize mathematical proxies (surrogates) to replace numerical simulators. Although these proxies are very cheap to compute, they often require an initial investment in computation for calibration purposes. The magnitude of this initial computational investment is unclear. Also the calibration points, that are used to calibrate the proxy, are chosen synchronously; that is, the choice of a particular point to be simulated is independent of the others even though in real life the choice of later experiments would be based on the experience of earlier observations. In this study, an approach is proposed which employs direct optimization and proxy approaches simultaneously. The Genetic Algorithm (GA) forms the basis of the approach. The proxy ought to evolve intelligently as the GA iterates. This work investigated the design of a composite and adaptive algorithm, and tested its effectiveness in a range of artificial test problems and real field cases. Kriging was considered as the proxy. The polytope method was also utilized to help with local search. The composite algorithm was applied to the highly non-linear problem of an offshore Gulf of Mexico hydrocarbon reservoir development and significant improvement in efficiency was observed.