History matching problem in reservoir engineering using the propagation–backpropagation method

Abstract

This paper describes the application of the adjoint method to the history matching problem in reservoir engineering. The history matching problem consists in adjusting a set of parameters, in this case the permeability distribution, in order to match the data obtained with the simulator to the actual production data in the reservoir. Several numerical experiments are presented which show that our method is able to reconstruct the unknown permeability distribution in a reliable and efficient way from synthetic data provided by an independent numerical forward modelling code. An efficient and flexible regularization scheme is introduced as well, which stabilizes the inversion and enables the reservoir engineer to incorporate certain types of prior information into the final result.

Level Set Methods for Structural Inversion and Image Reconstruction

“…For more details, see [44]. The above-described regularization schemes only operate on the updates (or forcing terms f in a time-dependent setting) but not on the level set function itself.…”

Reservoir characterization using stochastic initializations and the level set method

“…There are two (incompressible) fluids in the reservoir, water and oil. In our numerical simulator, we use tabulated values for the relative permeabilities K r w and K r o as shown in [27], which correspond to a Corey function with coefficients n w = 3 and n o = 2. The viscosity values for oil and water are µ o = 0.79 × 10 −3 Pa s and µ w = 0.82 × 10 −3 Pa s, and the porosity is taken to be constant φ = 0.213 in the reservoir.…”

“…The numerical physical time-step (which is unrelated to the time-step of the artificial shape evolution) used in the simulator is 0.1 days, and the reservoir is monitored over a period of 120 days. For more details regarding our reservoir simulation tools, we refer to [27,28].…”

Recent progress on reservoir history matching: a review

“…5 is modified by adding another term to penalize the roughness of the model (Tykhonov regularization) or to penalize deviations from the initial guess. Lee et al [97], Makhlouf et al [114], Cheng et al [32] and others used Tykhonov regularization in addition to the data mismatch in the objective function while González-Rodríguez et al [64] used a related method that restricted updates to a new parameter space defined by a weighted norm that measures the smoothness of a function.…”