Automated Reservoir Model Selection in Well-Test Interpretation
- Barys Güyagüler (Stanford U.) | Roland N. Horne (Stanford U.) | Eric Tauzin (Kappa Engineering)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Evaluation & Engineering
- Publication Date
- April 2003
- Document Type
- Journal Paper
- 100 - 107
- 2003. Society of Petroleum Engineers
- 5.5 Reservoir Simulation, 5.6.5 Tracers, 5.1 Reservoir Characterisation, 5.6.3 Deterministic Methods, 4.6 Natural Gas, 5.1.2 Faults and Fracture Characterisation, 5.6.3 Pressure Transient Testing, 5.6.11 Reservoir monitoring with permanent sensors, 7.6.6 Artificial Intelligence, 5.6.4 Drillstem/Well Testing
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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 a genetic algorithm (GA) that is able to select the most probable reservoir model from 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. Because 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 the GA as a preprocessor for conventional gradient-based algorithms such as Levenberg- Marquardt.1 When combined with the GA, the dependency of such conventional algorithms on the initial guess is reduced, and the overall regression performance is improved. For automated interpretations in which the model is already known, this method allows us to 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 because of noise. As a preprocessor for more conventional nonlinear regression approaches, applying the GA to a number of noisy pressure-transient tests demonstrated that the method is robust and efficient.
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 based mainly on the shape of the pressure-derivative curve. The choice of the appropriate model is a step that requires well-test-analysis expertise and 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 success.2-8 Some of these techniques for model recognition were reviewed by Horne.9 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 the GA10 is then carried out on these candidate models. Each population consists of subpopulations, one for each model. The GA operators, crossover and mutation,11 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 the reservoir and model parameters that result in the best least-squares fit to this model are also obtained.
Even in cases in which the uncertainty in the reservoir model 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 may 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. To reduce the dependency of the behavior 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 Levenberg-Marquardt1 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.
In this work, the ordinary GA was modified to handle simultaneous regression of several analytical reservoir models. The problem definition and configuration are summarized in Table 1.
Analytical reservoir models have varying numbers of parameters. For example, models that have a boundary have a distance to the boundary parameter. Dual-porosity models have storativity and transmissivity ratio parameters. Most models have permeability, skin factor, and a wellbore storage coefficient as common parameters. The differing number of parameters calls for variable length chromosomes within the GA.12 The range, precision, and length of binary representation of the parameters are given in Table 2. Model parameters and individual chromosome lengths are given in Table 3.
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