A solid/fluid substitution scheme constrained by pore-scale numerical simulations

Abstract

Estimating the effects of pore filling material on the elastic moduli or velocities of porous and fractured rocks attracts widespread attention. This effect can be modelled by a recently proposed triple-porosity scheme, which quantifies this effect from parameters of the pressure dependency of the elastic properties of the dry rock. This scheme divides total porosity into three parts: compliant, intermediate and stiff. Each type of pores is assumed to be spheroidal and characterized by a single aspect ratio. However, the implementation of this model requires the asymptotic values of the elastic moduli at much higher pressures where only non-closable pores remain open. Those pressures are beyond the capacity of most rock physics laboratories and can even crush typical sandstone samples. Experimental data at such pressures are usually unavailable. To address this issue, we introduce pore-scale numerical simulations in conjunction with effective medium theories (EMT) to compute the asymptotic values directly from the microtomographic images. This workflow reduces the uncertainty of model predictions on the geometric information of stiff pores and strengthens the predictive power and usefulness of the model without any adjustable parameters. Applying this to a Bentheim sandstone fully filled with liquid and solid octadecane gives a reasonable match between model predictions and laboratory measurements. This success verifies the accuracy and applicability of the model and indicates its potential in further exploitation and characterization of heavy oil reservoirs and other similar reservoirs.