Ajuste automático de histórico em reservatórios de petróleo utilizando o método TSVD

Abstract

Reservoir simulation is an essential tool extensively used by reservoir engineers. It is mostly employed to predict reservoir behavior under different circumstances, thus supporting decisions that frequently involve large fnancial costs. In order to use this tool properly different petro-physical properties of the reservoir must be well known, such as permeability and porosity. Unfortunately, direct measures of these properties are viable only near the wells. A way of estimating these properties is through the so called History Matching process. History matching process consists on the inverse problem of estimating reservoir properties through matching simulated data to reservoir history, which are available in reservoirs that are operating for some time. In this work we present a study for the automatic history matching based in a two-phase (oil/water), two dimensional reservoir model. The rate of oil production and the pressure measured at the wells are taken as the history of the reservoir. In this work, we aim to estimate the permeability distribution of the reservoir. The history matching problem consists on minimizing an objective function that measures the mismatch between reservoir history and simulated data, which turns the problem into a nonlinear least square problem. In order to solve this problem the Gauss-Newton method was employed combined with the Truncated Singular Value Decomposition (TSVD) technique. The TSVD technique reduces considerably the number of parameters to estimate, reducing also the computational effort involved in solving the problem. In order to use the TSVD method in an effcient way it is necessary to have the derivative and the adjoint of the direct problem. The development of these tools was an important part of this work.