History Matching Field Scale Model Using LET Based Relative Permeability

Abstract

Summary This paper presents a novel approach for history matching (HM) field scale models using relative permeability. The approach uses an LET parametrization of the relative permeability where the L, E and T parameters adjusts the lower, middle, and upper part of the relative permeability curve, in the history matching. This ensures both flexibility in the HM workflow and physically meaningful shapes on the history matched relative permeability curves. The approach is demonstrated on the openly available Norne field model using the OPM Flow simulator. In reservoir simulation the relative permeability is used to compute the effective permeability in multi-phase flow. Having reliable relative permeability in the reservoir model is thus crucial to ensure useful results from the simulations, and this has been confirmed in both up-scaling and HM studies. Traditionally, the relative permeability is computed from laboratory experiments on cores and represented as tables in the simulator. Tabulated relative permeability is flexible and efficient, but it makes it cumbersome to adjust in history matching routines which often is needed since the core-scale experiments can not capture the full heterogeneity and variability of the relative permeability curves in the reservoir. We, therefore, instead of tables, use a LET formula in the history matching. Different values for the LET parameters are used for different inter-well flow regions to ensure sufficient flexibility in the HM and that well data from one region does not affect the history matching outside its region of influence. The flow regions are pre-computed based on simplified single-phase flow using the fluid-diagnostic tools available in the MRST toolbox. The LET parameterization is implemented in OPM Flow simulator. Initial investigations show that the simulation time is as good or better than the tabulated version due to less issues for the non-linear solver. This is expected as the LET curves are smooth, while kinks in the tabulated relative permeability is known to cause convergence issues for the non-linear solver. Moreover, the initial results from the Norne model are promising and demonstrate a significant potential for inclusion of LET based relative permeability in HM workflows. The compact LET parameterization allows for flexible and accurate control of the variability of prior model ensembles, and the smoothness of the curves promotes a robust and well-behaved assimilation process. Also, the representation supports comparisons of history matched relative permeability properties across the ensemble and between flow regions.