Over the last century, the state of stress in the earth’s upper crust has undergone rapid changes because of human activities associated with fluid withdrawal and injection in subsurface formations. The stress dependency of multiphase flow mechanisms in earth materials is a substantial challenge to understand, quantify, and model for many applications in groundwater hydrology, applied geophysics, CO₂ subsurface storage, and the wider geoenergy field (e.g., geothermal energy, hydrogen storage, hydrocarbon recovery). Here, we conduct core-scale experiments using N₂/water phases to study primary drainage followed by spontaneous imbibition in a carbonate specimen under increasing isotropic effective stress and isothermal conditions. Using X-ray computed micro-tomography images of the unconfined specimen, we introduce a novel coupling approach to reconstruct pore-deformation and simulate multiphase flow inside the deformed pore-space followed by a semi-analytical calculation of spontaneous imbibition. We show that the irreducible water saturation increases while the normalized volume of spontaneously imbibed water into the specimen decreases (46–25%) in response to an increase in effective stress (0–30 MPa), leading to higher residual gas saturations. Furthermore, the imbibition rate decreases with effective stress, which is also predicted by a numerical model, due to a decrease in water relative permeability as the pore-space becomes more confined and tortuous. This fundamental study provides new insights into the physics of multiphase fluid transport, CO₂ storage capacity, and recovery of subsurface resources incorporating the impact of poromechanics.

Fluid injection and withdrawal in a porous medium create changes in pore pressure that alter effective stresses within the medium. This leads to pore volume changes, which can be described by the poroelastic theory. These changes in pore volume can influence fluid flow processes, such as capillary diffusion and imbibition, potentially altering multiphase flow characteristics in subsurface reservoirs with a focus on oil recovery in the naturally fractured carbonate reservoirs. In this study, a semi-analytical model is developed to analyze the impact of stress-dependent spontaneous imbibition. The model allows us to study the influence of stress-dependent effects on porosity, absolute permeability, relative permeability, and capillary pressure on the imbibition and oil recovery mechanisms of both intact rock and fracture in naturally fractured carbonate reservoirs. In order to capture the geomechanical interactions involved, pure compliance poroelastic definitions and nonlinear joint normal stiffness equations are used to assess the deformation of intact rock and fracture, respectively. The model shows that increasing effective confining stress shifts the imbibition capillary pressure curve upward, resulting in improved absorption of the wetting phase into the smaller pores and enhanced extraction of the nonwetting phase. Model calculations provide a rationale for how and why irreducible water saturation increases during compression of mixed-wet carbonates and decreases in the case of initially strong water-wet carbonates. It is also shown how higher relative permeability of the wetting phase leads to a greater diffusion of the wetting phase and improved oil recovery for the less deformed mixed-wet rock.

Three-dimensional (3-D) printing provides a fast, cost-effective way to produce and replicate complicated designs with minimal flaws and little material waste. Early use of 3-D printing for engineering applications in the petroleum industry has stimulated further adoption by geoscience researchers and educators. Recent progress in geoscience is signified by capabilities that translate digital rock models into 3-D printed rock proxies. With a variety of material and geometric scaling options, 3-D printing of nearidentical rock proxies provides a method to conduct repeatable laboratory experiments without destroying natural rock samples. Rock proxy experiments can potentially validate numerical simulations and complement existing laboratory measurements on changes of rock properties over geologic time scales. A review of published research from academic, government, and industry contributions indicates a growing community of rock proxy experimentalists. Three-dimensional printing techniques are being applied to fundamental research in the areas of multiphase fluid flow and reactive transport, geomechanics, physical properties, geomorphology, and paleontology. Further opportunities for geoscience research are discussed. Applications in education include teaching models of terrains, fossils, and crystals. The integration of digital data sets with 3-D printed geomorphologies supports communication for both societal and technical objectives. Broad benefits that could be realized from centralized 3-D printing facilities are also discussed.