Multiple-Porosity and Multiple-Permeability Poroelasticity

Abstract

Since the advent of basic ideas in the theory of fluid seepage in fissured porous media, much effort has been placed in engineering and science departments of various disciplines in trying to foster the concept of dual-porosity continua. In keeping with these efforts, this dissertation aims to extend the existing theories of single and dual-porosity, fluid saturated, homogenous, isotropic and linearly elastic materials to account for higher levels of pore structure complexity, namely the multiple-porosity and multiple-permeability poroelasticity.

An illustrative and inductive methodology is taken in presenting the natural extensions from fundamental concepts associated with constitutive modeling of dual-porosity materials to this new case. However, deductive proof and reasoning is provided when derivation of terms and equations was required. In particular, a closure to the problem of material property coefficients of a multiple-porosity mixture, whose constituents follow Biot's formulations of stress-strain relation, is presented. Results are compared and validated with related documentations on the topic for dual-porosity mixtures, while possible variations are thoroughly discussed and rationalized.

A Complete and integrated analytical solution to a class of generalized plane-strain multiple-poroelastic problems featuring rectangular, cylindrical or spherical geometries is developed. Again, this solution is compared and validated with currently published solutions of its dual-porosity counterparts. Results indicate that the problem's time scales, and consequently, the associated coupled phenomenon - known as the Mandel-Cryer effect in poromechanics literature - would proliferate when the number of distinct porosity networks in the analytical model is increased.

Further along this dissertation, field applications of these solutions, according to a number of related petroleum-industry problems are presented. Variations of the multiple-porosity/multiple-permeability Cryer's and axisymmetric Mandel's problems are developed to account for additional boundary conditions due to an inner concentric cavity within their geometry. The former solution applies to investigation of sealing capacity and integrity of caprocks during CO2 geo-sequestration operations, while the latter is used to derive formulas for compaction (porosity reduction) and transient analysis of depleting multiple-porosity/multiple-permeability reservoirs.

Findings indicate that neglecting or over-simplifying the complex effect of distinguishable pore structures within the rock matrix, such as fractures and vugs, might produce errors which often tend to underestimate either flow or deformation aspects of its response to application of external stresses or pore pressure. In some other cases, however, the results suggest that proper and consistent selection of effective properties of lumped-porosity models can return practically accurate results.

This dissertation is the first comprehensive documentation on the theory of multiple-porosity and multiple-permeability poroelasticity. It certainly holds a number of simplifying assumptions which include but are not limited to the model's homogeneity and isotropy, linearity of constitutive relations, as well as constraints on the ongoing physical exchange phenomena within its porous structure. Relaxing any of these restrictive assumptions would indeed bring about an entirely new area of research and study on the topic.