A Newton-Raphson Iterative Scheme for Integration of Multiphase Production Data into Reservoir Model
WU, ZHAN, Texas A&M U.
The purpose of this paper is to present a new iterative inversion algorithm for
integrating production data into geostatistical models. The significant feature of the
proposed algorithm is that the computation of the sensitivity matrix for production data
with respect to cell parameters can be avoided. This leads to dramatic reduction of
computational cost. Generally, the computational cost of the gradient simulation method,
adjoint method and Carter's method for generating sensitivity coefficient are dependent on
the number of grid block, observed data and wells, respectively. In this paper, instead of
generating the sensitivity matrix required for minimizing the least square objective
function, our approach relies on solving
the inversion
equations
which are derived based
on a necessary condition for a minimum. In comparison with other optimization methods, the
proposed iteration scheme converges fast since the inversion
equations
can be solved
through the Newton-Raphson method. At each iteration, the computational requirement of our
approach is to solve the finite difference
equations
and the linear adjoint
equations
once, the reservoir parameters can be updated. Moreover, based on the Bayes theorem,
geostatistical data can be honored simultaneously while the production data are
matched.The proposed method is demonstrated for the inversion of permeability and porosity
fields in a two-dimensional two-phase reservoir with nine production wells and four water
injectors. Two numerical examples show that our new approach converges quickly for
integrating the water oil ratio data into geostatistical models.
AAPG Search and Discovery Article #90911©2000 AAPG Pacific Section and Western Region Society of Petroleum Engineers, Long Beach, California