Model Selection for Well Test and Production Data Analysis

Abstract

Summary. The estimation of reservoir properties from production or pressure data measured during production or well tests is an important process for reservoir characterization and performance prediction. A key step in that process is the selection of a reservoir model for use in the interpretation of the data. We develop a procedure for selecting the most appropriate model from a pool of candidates. A parameter estimation algorithm is used to evaluate parameters within candidate models. Statistical measures are then used to select the most appropriate model. We demonstrate our procedure for model selection with actual well test data and production data from the Devonian shale. We show how our methodology can be used to evaluate whether certain reservoir features can be identified from measured production or pressure data. We also present a test for evaluating whether independent estimates of reservoir properties are consistent with measured pressure and production data. Introduction Production or pressure data measured at wells during reservoir production or well tests are significant sources of information for estimating reservoir properties to predict future reservoir performance. Two key steps in the process for estimating reservoir properties from pressure/production data are selection of an appropriate reservoir model and estimation of parameters within that model. The latter step has received much attention in the literature. A number of automatic history-matching (or parameter-estimation) algorithms have been proposed for that purpose. Type curve and other graphic methods are also available for estimating parameters for selected reservoir models. Perhaps more difficult, but no less important, is the selection of the most appropriate reservoir model. Generally, this requires first selecting the appropriate set of material and energy balances for the physical processes involved, as well as the fluid properties and reservoir geometry. Then, the reservoir properties must be chosen. These properties may vary significantly with location in the reservoir. However, we cannot expect to estimate those properties accurately throughout the reservoir on the basis of the limited data usually available. Instead, we usually parameterize the unknown properties in a way that is consistent with geologic data and other data from the reservoir so that fewer unknown parameters need be established on the basis of the pressure/production data. A common method of parameterization is zonation, for which reservoir properties are assumed to be uniform throughout various regions of the reservoir. As we use "model" to refer to the set of equations that relate the reservoir parameters to the dependent, or simulated, quantities, different parameterizations correspond to different reservoir models. Here we consider situations for which the measured pressure/production data may be explained adequately with reservoir models containing relatively few unknown parameters. Specifically, we deal with reservoir models in which the unknown properties are assumed to be uniform; our method for model selection is not limited, however, to such situations. We do not deal specifically with selection of appropriate material and energy balances or fluid properties; these rather broad topics are addressed in a number of texts (e.g., see Refs. 1 through 3). We develop a systematic, quantitative method for choosing from among candidate reservoir models the most appropriate model for a given set of pressure/production data. We illustrate the importance of model selection for the accuracy of estimates of the reservoir properties. We also demonstrate how our method for model selection can be used to establish whether a given set of measured data is sufficient for identifying certain reservoir features. For example, it can be used to ascertain whether sufficient data have been measured to determine boundary effects, skin, or the presence of more than a single-porosity system. Thus, our method can be used to quantify the information about reservoir properties that is "contained" in the measured data. Model Selection A key difficulty in choosing the most appropriate reservoir model is that several different reservoir descriptions (or models) may apparently satisfy the available information about the reservoir. That is, the models may be consistent with available geological and petrophysical information and seem to provide more or less equivalent matches of the measured pressure/production data. The issue may be further complicated when type curve or other graphic methods are used to evaluate the parameters within a given model because different sets of parameters may provide matches of different precision corresponding to different regions of the data. That is, no "perfect" matches can be expected because of the finite accuracy of the measurements and simplified nature of the models, so the best compromise in matching the data is not at all apparent. This latter consideration can often be alleviated when parameter estimation methods are used. Proper formulation of the performance index can lead to a unique set of estimates that may be called best (in a certain sense discussed in more detail later) provided that the proper reservoir model is selected. Thus, we believe a method for selecting the most appropriate reservoir model for use in conjunction with parameter estimation methods is a particularly attractive method for analyzing reservoir production or well test data. We have developed a method to choose, on the basis of measured pressure/production data, the most appropriate reservoir model (or reservoir description) from among a set of candidate reservoir models. A pool of candidate models that are consistent with all available information about the reservoir is to be determined. We then use statistical measures to choose the most appropriate model from among these candidates. As discussed later, the pool of candidates may be formed as a hierarchy of models, as determined by the most complete model (in the sense of the greatest number of unknown parameters) that the engineer believes is necessary for describing the reservoir. The hierarchy is characterized by increasing numbers of unknown parameters. It is important that at least one model satisfactorily describes (or "explains") the data (it is sufficient that the most complete model does so). This can generally be established satisfactorily by examination of a plot of the differences between the observed data and the corresponding quantities simulated with parameters obtained from a history match of the data. SPEFE P. 215^

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