Automated Parameter Estimation from Well Test Data Using the Signal Theory

Abstract

This paper presents a new methodology for the automated parameter estimation from well test data, based on type curve matching using the Signal Theory. This procedure solves the inverse problem faster than the conventional techniques, with the additional advantage that the results are not affected by noisy data. The new procedure has been proved with hundred of synthetic and field cases, and it can be used for the interpretation of all the different tests currently of common use in the field. In the present paper this technique is applied to three tests, all already published in the literature. The methodology derived in the study surpasses the currently available matching theory based on non linear regression, since it requires a smaller computing time and its assured convergence (selection) of the correct (best) model that describes the physical conditions of the formation on the vicinity of the well. On the other hand, the conventional regression methods require large computing times for the solution of the system of non linear equations; in addition, they are affected by the presence of noise in the recorded pressure response and usually present convergence problems when the initial solution for the unknown parameters is not close enough to the searched solution. The conventional type curve matching procedure inherently introduces interpretation subjectivity and the possibility of errors, because of the close similarity of the different pressure responses, and to its visual solution approach, which currently is not well understood; thus, it is not possible to develop fully efficient codes that could emulate this human function. Based on a comprehensive set of type curves, the technique proposed in this paper allows an automated match of the pressure response, without the need of the visual effort of the analyst. The Signal Theory has been modified for the automated interpretation of well test data. The new matching correlation derived in this work, based on rules of shift, multiply and sum, solves the matching of pressure data in an improved way. Introduction Reservoir Management is usually defined as an integrated continuous process, requiring a full cooperation and Teamwork between various disciplines to use the resources available to optimize the exploitation of the reservoir. Reservoir management requires economic evaluation and analyses of the asset and associated projects throughout the life of the reservoir, always observing the safety and environmental regulations. The petroleum engineer has had for a few decades numerical reservoir simulators, which must be properly adjusted to match the behavior of the integrated system (reservoir, production string and surface facilities). Observation of model performance under different producing conditions, aids in selecting an optimum set of producing conditions for the reservoir. Today we are now in a situation where the capability of the simulators to use reservoir data frequenty exceeds the availability of data. With regard to the estimation of the properties of the formation, there are several methods available; among them well test analysis has demonstrated to be an excellent source of characterization dynamic data, representing average values in the drainage region of the well. Other sources for the estimation of properties, like well logging and petrophysical laboratory studies, consider far smaller rock volumes. It has been common in the past that advances in a particular discipline are used (transferred) to other areas resulting in a faster overall development. Petroleum engineering has successfully used knowledge from other fields of study, such as heat conduction and geohydrology, borrowing solutions for some problems and applying them for related conditions, especially for well test analysis.