Petroleum Engineering

Model Selection and Uniqueness Analysis for Reservoir History Matching

"History matching" (model calibration, parameter identification) is an established method for determination of representative reservoir properties such as permeability, porosity, relative permeability and fault transmissibility from a measured production history; however the uniqueness of selected model is always a challenge in a successful history matching.

Up to now, the uniqueness of history matching results in practice can be assessed only after individual and technical experience and/or by repeating history matching with different reservoir models (different sets of parameters as the starting guess).

The present study has used the stochastical theory of Kullback & Leibler (K-L) and its further development by Akaike (AIC) for the first time to solve the uniqueness problem in reservoir engineering. In addition —based on the AIC principle and the principle of parsimony — a penalty term for OF has been empirically formulated ,regarding geoscientific and technical considerations. Finally a new formulation (Penalized Objective Function, POF) has been developed for model selection in reservoir history matching and has been tested successfully in a North German gas field.