In this review, various aspects of geological carbon sequestration are discussed in relation to the principles of two-phase flow in porous media. Literature reports on geological sequestration of CO₂ show that the aquifer storage capacity, sealing integrity of the caprock, and the in situ processes, for example, the displacement of brine by supercritical CO₂ (scCO₂), convection–diffusion–dissolution processes involving scCO₂ and brine, geochemical reactions, and mineral precipitation depend on the fluid–fluid–rock characteristics as well as the prevailing subsurface conditions. Considering the complexity of the interrelationships among various processes, experimental investigations and network of mathematical functions are required for the ideal choice of geological site with predictable fluid–fluid–rock behaviors that enhance effective monitoring. From a thorough appraisal of the existing publications, recommendations are made for improvement in the existing simulators to fully couple the entire processes involved in the sequestration operations and in situ mechanisms which include injection rate and pressure, brine displacement, simultaneous flow of free and buoyant phases of CO₂, various trapping mechanisms, convection–diffusion–dissolution processes, scCO₂–brine–rock reactions, precipitation of the rock minerals, and the consequences on the hydraulic and hydrogeological properties in the course of time as well as the quantity of injected CO₂. Suggestion is made for the inclusion of leakage parameters on site-specific basis to quantify the risks posed by the prevailing fluid–fluid–rock characteristics as well as their immediate and future tendencies. Calls are also made for thorough investigations of factors that cause nonuniqueness of the two-phase flow behavior with suggestions for the use of appropriate experimental techniques. The review comprehensively synthesizes the available knowledge in the geological carbon sequestration in a logical sequence.

This is an Open Access Article. It is published by Elsevier under the Creative Commons Attribution 3.0 Unported Licence (CC BY). Full details of this licence are available at: http://creativecommons.org/licenses/by/3.0/Causes and effects of non-uniqueness in capillary pressure and saturation (Pc–S) relationship in porous media are of considerable concern to researchers of two-phase flow. In particular, a significant amounts of discussion have been generated regarding a parameter termed as dynamic coefficient (τ) which has been proposed for inclusion in the functional dependence of Pc–S relationship to quantify dynamic Pc and its relation with time derivative of saturation. While the dependence of the coefficient on fluid and porous media properties is less controversial, its relation to domain scale appears to be dependent on artefacts of experiments, mathematical models and the intra-domain averaging techniques. In an attempt to establish the reality of the scale dependency of the τ–S relationships, we carry out a series of well-defined laboratory experiments to determine τ–S relationships using three different sizes of cylindrical porous domains of silica sand. In this paper, we present our findings on the scale dependence of τ and its relation to high viscosity ratio (μr) silicone oil–water system, where μr is defined as the viscosity of non-wetting phase over that of the wetting phase. An order of magnitude increase in the value of τ was observed across various μr and domain scales. Also, an order of magnitude increase in τ is observed when τ at the top and the bottom sections in a domain are compared. Viscosity ratio and domain scales are found to have similar effects on the trend in τ–S relationship. We carry out a dimensional analysis of τ which shows how different variables, e.g., dimensionless τ and dimensionless domain volume (scale), may be correlated and provides a means to determine the influences of relevant variables on τ. A scaling relationship for τ was derived from the dimensionless analysis which was then validated against independent literature data. This showed that the τ–S relationships obtained from the literature and the scaling relationship match reasonably well

Capillary pressure–saturation-relative permeability relationships (P_c–S_w–K_r) are functions of importance in modeling and simulations of the hydrodynamics of two-phase flow in porous media. These relationships are found to be affected by porous medium and fluid properties but the manner in which they are affected is a topic of intense discussion. For example, reported trends in fluid viscosity and boundary conditions effects have been found to be contrary to each other in different studies. In this work, we determine the dependency of dynamic K_r–S_w relationships (averaged data) on domain scale in addition to investigating the effects of fluid viscosity and boundary pressure using silicone oil (i.e. 200 and 1000 cSt) and water as the respective non-wetting and wetting fluids with a view to eliminating some of the uncertainties reported in the literature. Water relative permeability, K_rw, was found to increase with increasing wetting phase saturation but decreases with the increase in viscosity ratio. On the other hand, the oil relative permeability, K_rnw, was found to increase with the increasing non-wetting phase saturation in addition to the increase in viscosity ratio. Also, it was found that with the increasing boundary pressure K_rw decreases while K_rnw increases. The influence of scale on relative permeability was slightly indicated in the non-wetting phase with K_rnw decreasing as domain size increases. Effect of measurement location on dynamic relative permeability was explored which is rarely found in the literature. Comparison was also made between K_r–S_w relationships obtained under static and dynamic condition. Finally, mobility ratio (m) and dynamic coefficient (τ) were plotted as a function of water saturation (S_w), which showed that m decreases as τ increases at a given saturation, or vice versa.

A computationally efficient and simple alternative platform for the prediction of the domain scale dependence of the dynamic capillary pressure effects, defined in terms of a coefficient named as dynamic coefficient (τ), is developed using an artificial neural network (ANN). The input parameters consist of the phase saturation, media permeability, capillary entry pressure, viscosity ratio, density ratio, temperature, pore size distribution index, porosity and domain volume with corresponding output τ obtained at different domain scales. Different ANN configurations as well as linear and nonlinear multivariate regression models were tested using a number of performance criteria. Findings in this work showed that the ANN structures with double hidden layers perform better than those with a single hidden layer. In particular, the ANN configuration with 13 and 15 neurons in the first and second hidden layers, respectively, performed the best. Using this best-performing ANN, effects of increased domain size were predicted for three separate experimental results obtained from literature and our laboratory with different domain scales. Results showed increased magnitude of τ as the domain size increases for all the independent experimental data considered. This work shows the applicability and techniques of using ANNs in the prediction of scale dependence of two-phase flow parameters.

Numerical simulations for core‐scale capillary pressure (P^c)‐saturation (S) relationships have been conducted for a supercritical carbon dioxide‐water system at temperatures between 35°C and 65°C at a domain pressure of 15 MPa as typically expected during geological sequestration of CO₂. As the P^c‐S relationships depend on both S and time derivative of saturation ( ) yielding what is known as the “dynamic capillary pressure effect” or simply “dynamic effect,” this work specifically attempts to determine the significance of these effects for supercritical carbon dioxide‐water flow in terms of a coefficient, namely dynamic coefficient (τ). The coefficient establishes the speed at which capillary equilibrium for supercritical CO₂ (scCO₂)‐water flow is reached. The simulations in this work involved the solution of the extended version of Darcy's law which represents the momentum balance for individual fluid phases in the system, the continuity equation for fluid mass balance, as well as additional correlations for determining the capillary pressure as a function of saturation, and the physical properties of the fluids as a function of temperature. The simulations were carried out for three‐dimensional cylindrical porous domains measuring 10 cm in diameter and 12 cm in height. τ was determined by measuring the slope of a best‐fit straight line plotted between (1) the differences in dynamic and equilibrium capillary pressures against (2) the time derivative of saturation (dS/dt), both at the same saturation value. The results show rising trends for τ as the saturation values reduce, with noticeable impacts of temperature at 50% saturation of aqueous phase. This means that the time to attain capillary equilibrium for the CO₂‐water system increases as the saturation decreases. From a practical point of view, it implies that the time to reach capillary equilibrium during geological sequestration of CO₂ is an important factor and should be accounted for while simulating the flow processes, for example, to determine the CO₂ storage capacity of a geological aquifer. In this task, one would require both the fundamental understanding of the dynamic capillary pressure effects for scCO₂‐water flow as well as τ values. These issues are addressed in this article. © 2014 American Institute of Chemical Engineers AIChE J 60: 4266–4278, 2014