Abstract
Numerical simulation models describing field behavior require reliable estimates for various reservoir parameters which cannot be measured directly. A trial-and-error procedure, linear and nonlinear regression analysis on a random search, and electric analogue computation are presently used in order to obtain these estimates. They suffer either from lengthy computation times or from the necessity to build a physical model for each reservoir. This paper describes a balanced error-weighted gradient method that systematically reduces the difference between observed and calculated reservoir performance data, thereby leading to a history performance data, thereby leading to a history match. The scheme resembles closely the mechanical balancing of an electric analyzer once one has determined quantitatively the interference relationships between the individual well regions. These relationships are found by changing the reservoir parameter of each region in turn by a constant value, while all other regional values remain at their base level. Then the interference relationships are ordered in matrix form. The diagonal elements of this matrix yield the gradients for the regional reservoir parameter values and thereby the direction of the change necessary to obtain a reduction in the matching error. The magnitude of change in each region is taken proportional to the regional error. Such a weighting proportional to the regional error. Such a weighting of the gradients enables one to cope with the interference. Particular car has to be exercised in defining what components constitute the influential reservoir parameters of a field. Case studies of oil and gas parameters of a field. Case studies of oil and gas fields yielded information for choosing these. Therefore, the proposed presentation will consist of a detailed description of the matching procedure and its application to several reservoirs, as well as general guidelines for field history matching.
Introduction
The partial differential equation
..(1) where k = permeability h = reservoir thickness = viscosity = porosity
c = compressibility p = pressure x = space coordinatesy t = time Q = injection, or production rate describes the pressure behavior in an oil or gas reservoir. Finite-difference techniques, variational, and finite-element methods can be used to obtain a numerical solution to Eq.1 as no analytical solutions are known for the conditions that adequately describe a reservoir. Only if a cell or element happens to contain a well is a rough estimate of the local k and value known.. Several times throughout the entire life of the reservoir the static reservoir pressure may be measured at the wells. However, k and are only point measurements when compared to the over-all reservoir size. Therefor, calculated and observed pressure behavior will rarely agree if those k and values are used in the computation of Eq. 1. Usually they must be adjusted to yield a match between the two pressure behaviors. Only then reliable predictions pressure behaviors. Only then reliable predictions can be made concerning the future reservoir behavior. In the past, the reservoir was more or less arbitrarily divided into a certain number of regions.
SPEJ
p. 295
