Estimation of the Location of the Boundary of a Petroleum Reservoir

Abstract

This paper considers the problem of estimating the shape of a petroleum reservoir on the basis of pressure data from wells within the boundaries of pressure data from wells within the boundaries of the reservoir. It is assumed that the reservoir properties, such as permeability and porosity, are properties, such as permeability and porosity, are known but that the location of the boundary is unknown. Thus, this paper addresses a new class of history-matching problems in which the boundary position is the reservoir property to be estimated. position is the reservoir property to be estimated. The problem is formulated as an optimal-control problem (the location of the boundary being the problem (the location of the boundary being the control variable). Two iterative methods are derived for the determination of the boundary location that minimizes a functional, depending on the deviation between observed and predicted pressures at the wells. The steepest-descent pressures at the wells. The steepest-descent algorithm is illustrated in two sample problems: 1. the estimation of the radius of a bounded circular reservoir with a centrally located well, and 2. the estimation of the shape of a two-dimensional, single-phase reservoir with a constant-pressure outer boundary.

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