Recent work on deconvolution allows well test interpretation engineers to combine several shut-in periods into a single, much longer deconvolved response, allowing identification of boundaries overlooked in the analysis of these individual shut-ins.Initial algorithms by von Schroeter et al (2004) 1 require the individual shut-in responses to be consistent in terms of wellbore storage and skin. An alternate method by Levitan (2005) 2 allows inconsistent early time responses to be combined, but requires multiple deconvolutions and an iterative search of the reservoir initial pressure.The new suggested algorithms waive the von Schroeter et al limitation without the drawbacks of the Levitan method. These algorithms are illustrated with real data coming from permanent gauges. This paper also points out the remaining limitations of the deconvolution process. This paper was written as a technical communication. It was made a short as possible in order to complement past publications 1-2 on the subject. Readers are invited to use these publications for the details of the equations and a more exhaustive list of references.
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The simulated annealing solution technique haa been a powerful reservoir characterization tool in geostatistics. ThB paper proposes an algorithm that uses this method to constrain the permeabtity distribution of a given reservoir model to the well test data collected at several wells. The technique can be used for single or multiple well tests.In order to keep the execution time of this algorithm within an acceptable range, the perturbation on the pressure transient due to a local permeability heterogeneity is determined in the form of an. analytic influence function.The results given by this approximation are compared to the results given by a simulator, ,and its use in the simulated annealing algorithm is defined according to its reliability. The algorithm is tested on an example, showing that the use of the analytic influence function allows considerable reduction in the computing time without decreasing the robustness of the method.
Summary 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 simulated annealing solution technique haa been a powerful reservoir characterization tool in geostatistics. ThB paper proposes an algorithm that uses this method to constrain the permeabtity distribution of a given reservoir model to the well test data collected at several wells. The technique can be used for single or multiple well tests.In order to keep the execution time of this algorithm within an acceptable range, the perturbation on the pressure transient due to a local permeability heterogeneity is determined in the form of an. analytic influence function.The results given by this approximation are compared to the results given by a simulator, ,and its use in the simulated annealing algorithm is defined according to its reliability. The algorithm is tested on an example, showing that the use of the analytic influence function allows considerable reduction in the computing time without decreasing the robustness of the method.
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