Automated History Matching Of Well Tests
Authors: Welty Douglas H. , Miller William C. 
Published: December 2007

This paper presents a nonlinear least-squares procedure for automatically history matching well procedure for automatically history matching well test data using a mathematical reservoir simulator. The procedure described here is especially dependable because it uses both the Taylor Series point and the steepest descent direction in a novel manner to define the search direction whenever the classical Gauss-Newton least squares procedure is inefficient.

Several interesting applications including (1) a drillstem test analysis, (2) an anisotropy detection in a tertiary oil recovery pilot, (3) a hydraulic fracturing interpretation and (4) a wildcat well evaluation demonstrate the procedure's utility and show how it can be a useful adjunct to other methods of analyzing well test data.

Introduction

Numerous automated history matching schemes have been discussed in the literature during the past several years. It is a popular topic because past several years. It is a popular topic because history matching is probably the single most difficult and time consuming phase of any field study. It is often an essential step in characterizing the reservoir and its performance, thus establishing a valid basis for projections into the future. Various efforts have been directed toward nonlinear regression procedures, linear or nonlinear programming techniques, inverse simulation techniques, and optimal control theory. Also, considerable research into better regression algorithms has been done.

Much of the literature deals with improved methods that are either suitable for very general use or are very specialized to minimize the required number of reservoir simulations. Our efforts to date represent what we feel is a good balance of these somewhat conflicting goals.

This paper addresses one facet of the history matching problem: well test analysis. However, the method described has much more general utility. Transient pressure tests are frequently conducted in wells and represent an invaluable source of data for formation evaluation. Such data can be analyzed using analytical techniques, using a reservoir simulator to history match the data, or both. Both methods have advantages and disadvantages; thus neither one is a panacea. Analytical techniques (manual methods) require only a desk calculator, whereas reservoir simulation usually requires a large computer system. Reservoir simulation affords the opportunity to reconcile all of the test data simultaneously, whereas manual methods frequently utilize only portions of the available data. Analytical techniques are somewhat limited due to assumptions incorporated in the analysis, but reservoir simulation can be used under the wide variety of heterogeneous conditions encountered in nature and with very unusual test configurations. Additionally, reservoir simulation permits the same tool to be used for analysis and prediction.

For many of our applications, the advantages of reservoir simulation outweighed the disadvantages. The key item missing was a practical method of rapidly and reliably adjusting key reservoir properties to obtain a satisfactory history properties to obtain a satisfactory history match. If the user had to intervene whenever the search ran into difficulty, many of the advantages of automation would be lost. Our solution was to couple a finite difference reservoir simulator to a proven nonlinear least-squares parameter estimation program. The result, called HITCH (HIstory maTCH), has been quite satisfactory with respect to versatility and cost effectiveness.

The Reservoir Simulators

The reservoir simulator used in the first three examples was a one component, single-phase, three-dimensional, finite difference simulator.