A STOCHASTIC PORE-SCALE NUMERICAL APPROACH TO PERMEABILITY AND TORTUOSITY PREDICTION IN CARBONATE SYSTEMS

Prediction of flow properties such as permeability and tortuosity are vital for groundwater and fossil fuel resources development. Flow properties of homogeneous rocks can be estimated from porosity using empirically derived deterministic equations. However, the use of porosity as a key factor in predicting flow properties of heterogeneous carbonate rocks can be misleading because a single porosity value has been shown to be associated with a range of permeability and tortuosity values.

This study aims to probe the use of pore size distribution as the key variable to predict the range of permeability and tortuosity values that could be associated to a given porosity value. The proposed approach consists of pore-scale numerical simulations of stochastically constructed 3D pore microstructures. Our hypothesis is that this approach can lead to the establishment of new correlations between the flow properties and pore size distribution of carbonate rocks, as well as new statistical methods to predict the flow properties of carbonate rocks.

To test this hypothesis, five synthetic pore size distribution curves mimicking pore size distributions obtainable from NMR T2 measurements were modelled. Pore size varied from 2 to 30 μm (spherical shape). Each of the synthetic curves was used to stochastically create multiple 3D pore microstructures of the same porosity and pore size distribution. MATLAB was used to stochastically generate the 3D pore microstructures while flow of water through the generated microstructures was simulated with STAR CCM+, a CFD software which solves Navier-Stoke equations using the finite element methodology. The resulting distribution of permeability and tortuosity were analysed for possible correlations with pore size distribution.

Our results confirmed that a single pore size distribution is not associated with a single but multiple permeability and tortuosity values. The range of permeability and tortuosity values obtained show unimodal distribution which based on Monte Carlo theory can be interpreted as the most probable flow property of a carbonate rock with a given pore size distribution. This contribution will discuss the potentiality of this new approach to develop a predictive understanding of the relationship between flow properties and pore size distribution of carbonate rocks.