Summary
In this paper we present a method to integrate well test, production, shut-in pressure, log, core, and geological data to obtain a reservoir description for the Pagerungan field, offshore Indonesia. The method computes spatial distributions of permeability and porosity and generates a pressure response for comparison to field data. This technique produced a good match with well-test data from three wells and seven shut-in pressures. The permeability and porosity distributions also provide a reasonable explanation of the observed effects of a nearby aquifer on individual wells. As a final step, the method is compared to an alternate technique (object modeling) that models the reservoir as a two-dimensional channel.
Introduction
The Pagerungan field has been under commercial production since 1994. This field was chosen to test a method of integrating dynamic well data and reservoir description data because the reservoir has only produced single phase gas, one zone in the reservoir is responsible for most of the production, and good quality well-test, core, and log data are available for most wells.
The method that was used to perform the inversion of the spatial distribution of permeability and porosity uses a parameter estimation technique that calculates the gradients of the calculated reservoir pressure response with respect to the permeability and porosity in each of the cells of a reservoir simulation grid. The method is a derivative of the gradient simulator1 approach and is described in Appendices A and B. The objective is to find sets of distributions of permeability and porosity such that the calculated response of the reservoir closely matches the pressure measurements. In addition, the distributions of permeability and porosity must satisfy certain constraints given by the geological model and by other information known about the reservoir.
Statement of Theory and Definitions
The process of obtaining a reservoir description involves using a great amount of data from different sources. It is generally agreed that a reservoir description will be more complete and reliable when it is the outcome of a process that can use the maximum possible number of data from different sources. This is usually referred to in the literature as "data Integration."
Reservoir data can be classified as "static" or "dynamic" depending on their connection to the movement or flow of fluids in the reservoir. Data that have originated from geology, logs, core analysis, seismic and geostatistics can be generally classified as static; whereas the information originating from well testing and the production performance of the reservoir can be classified as dynamic.
So far, most of the success in data integration has been obtained with static information. Remarkably, it has not yet become common to completely or systematically integrate dynamic data with static data. A number of researchers,2–5 are studying this problem at present. This work represents one step in that direction.
Well Testing as a Tool for Reservoir Description.
Traditional well-test analysis provides good insight into the average properties of the reservoir in the vicinity of a well. Well testing can also identify the major features of relatively simple reservoirs, such as faults, fractures, double porosity, channels, pinchouts, etc. in the near well area. The difficulties with this approach begin when it is necessary to use the well-test data on a larger scale, such as in the context of obtaining a reservoir description. One of the main reasons for these difficulties is that traditional well-test analysis handles transient pressure data collected at a single well at a time, and is restricted to a small time range. As a result, traditional well-test analysis does not make use of "pressure" events separated in historical time. The use of several single and multiple well tests to describe reservoir heterogeneity has been reported in the literature,6 however, this approach is not applied commonly because of the extensive efforts needed to obtain a reservoir description.
The method presented in this paper uses a numerical model of the reservoir to overcome these shortcomings. It will be shown that pressure transients can be used effectively to infer reservoir properties at the scale of reservoir description. Well-test data, both complete tests and occasional spot pressure measurements, will be used to this effect. The well-test information allows us to infer properties close to the wells and, when combined with the shut-in pressures (spot pressure), boundary information and permeability-porosity correlations, provides the larger scale description.
General Description of the Method
The proposed method is similar to other parameter estimation methods and thus consists of the following major items: the mathematical model, the objective function and the minimization algorithm.
Mathematical Model.
Because of the complexity of the reservoir description, the reservoir response must be computed numerically. Therefore, the pressure response is found using a numerical simulator. The reservoir is discretized into blocks. The objective is to find a suitable permeability-porosity distribution so that values of these parameters can be assigned to each of the blocks.
Bilinear pressure diffusion and termination of bilinear flow in a vertically fractured well injecting at constant pressure
