Method for quickly forming a stochastic model representative of the distribution of a physical quantity in a heterogeneous medium by suitable selection of geostatistical realizations

Abstract

A method having an application to production problems in reservoir engineering for quickly forming a stochastic model representative of the distribution of a physical quantity in a porous heterogeneous medium, which is calibrated in relation to dynamic data, by suitable selection of geostatistical realizations to be combined linearly. An iterative gradual deformation process is used, wherein an initial geostatistical realization (y) of the medium and a number (N−1)(N>1) of other realizations (z)i=1, . . . ,(N−1), which are independent of initial realization (y), are linearly combined at each iteration, by applying constraints to the linear combination coefficients of realizations (y) and (z)i=1, . . . ,(N−1), and an objective function (J) measuring the difference between a set of simulated data deduced from said combination by means of a simulator and said dynamic data is minimized. To quickly minimize the objective function, the Lagrange multiplier (λ), λ ∈ Rassociated with the constraint relating to the specified values of the coefficients of realizations (z)i=1, . . . ,(N−1) is calculated. The absolute value λof the icomponent of multiplier λ indicates the sensitivity of the objective function in relation to the igeostatistical realization (z).