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.

Accurate modelling of flow in geothermal and hydrocarbon reservoirs is necessary for performance prediction. When fractures are naturally present as in many brittle reservoir rocks, they can control flow. In this case, a thorough knowledge of fracture location, orientation, density, abutting relationships and geologic attributes is crucial. In the subsurface, these parameters usually are associated with a high degree of uncertainty because their observability is limited. Fractures intersected by boreholes can be detected and characterized to some extent using established measurement techniques such as image logging, core analysis or spinner logs. Yet, the majority are not sampled, hampering modelling.

In this conceptual study, we focus on fracture aperture as the only unknown parameter, while assuming that location, orientation and length of all fractures are known a priori. While this assumption usually is not fulfilled, it allows us to study effects of fracture aperture on flow independently. We extract fracture patterns from mapped outcrops serving as reservoir analogues. The resulting detailed 2.5-dimensional models contains hundreds of natural fractures evolved over geologic time. We estimate fracture aperture from the in situ stress in the reservoir of interest using a modified version of the method of Barton & Bandis, acknowledging the limitations of this method by increasing the uncertainty in stress state, material properties of the rock, and other input quantities. These estimates are then used as prior for inverse modelling.

We apply an iterative Ensemble Kalman Filter, the Ensemble Smoother with Multiple Data Assimilation (ES-MDA), to reduce the uncertainty of fracture aperture and improve simulation results. Ensemble Kalman Filters are widely used for data assimilation or history matching in the context of sub-surface flows. Here, we use synthetic flow and transport data from a separate simulation with known fracture aperture as reference data in the ES-MDA framework.

The modified Barton-Bandis model provides prior realisations for an ensemble-based data assimilation framework at low computational cost. First results suggest that the realisations have some variety and reproduce physical relations such as the correlation of fracture aperture to fracture length and shear displacement to fracture orientation. Future work needs to validate the modified model with a mechanical simulator.

Preliminary results of our ES-MDA framework with plausible flow model parameterizations indicate that valuable information about the aperture distribution in the considered fracture geometry could be obtained. This amounts to one step forward towards a satisfying characterization of fracture parameters with dynamic data from a geological reservoir.