Anchoring methodologies for pore-scale network models: Application to relative permeability and capillary pressure prediction

The work described in this paper attempts to extend the predictive capability of pore-scale network models by using real experimental data as lithological "anchors". The development of such an anchored model capable of relative permeability and capillary pressure prediction would clearly be of great utility, providing a cheap and flexible tool for interpolating and extrapolating sparse and expensive laboratory data sets. Moreover, once the model had been anchored to reservoir rock samples, a wide range of sensitivities could be examined without recourse to additional experiments. In the context of gas reservoir engineering, a preliminary methodology — utilising mercury injection capillary pressure (MICP) data — has been developed that could permit both the matching of existing experimental gas/oil relative permeability curves and the quantitative prediction of additional data sets. Two approaches have been considered. The first involves matching capillary pressure data from MICP experiments to extract pore size distribution and pore volume scaling information. These parameters are then used to predict the relative permeability curves directly. A second approach is to simply match the gas-oil relative permeability curves using a highly constrained bond model. Capillary pressure prediction is then treated as an inverse problem. The constrained set of adjustable parameters in the macropore network model comprises: coordination number (z), pore size distribution exponent (n), pore volume exponent (ν) and pore conductivity exponent (λ) — i.e. only 4 simple parameters. Results demonstrate that this basic four-parameter model is sufficient to reproduce the vast majority of experimental drainage relative permeability curves examined. Only one network simulation per sample is required to match both the wetting and non-wetting curves and each parameter obtained from the matching process lies within a narrow range of possible values. These highly encouraging results suggest that further overparameterisation of the model is unnecessary in the context of drainage processes. However, we also show that anchoring network models to mercury intrusion data alone is insufficient for predicting relative permeabilities a priori — there is an interdependence of parameters and, consequently, an infinite set of parameter combinations will produce almost indistinguishable capillary pressure curves. Therefore, future analysis of MICP data should be performed in conjunction with the analysis of some other independent experiment — an experiment which gives one additional datum that forms the “missing