El-Amin, M.F. (King Abdullah University of Science and Technology) | Sun, Shuyu (King Abdullah University of Science and Technology) | Salama, Amgad (King Abdullah University of Science and Technology)
Geological storage of anthropogenic CO2 emissions in deep saline aquifers has recently received tremendous attention in the scientific literature. Injected CO2 plume buoyantly accumulates at the top part of the deep aquifer under a sealing cap rock, and some concern that the high-pressure CO2 could breach the seal rock. However, CO2 will diffuse into the brine underneath and generate a slightly denser fluid that may induce instability and convective mixing. Onset times of instability and convective mixing performance depend on the physical properties of the rock and fluids, such as permeability and density contrast. The novel idea is to adding nanoparticles to the injected CO2 to increase density contrast between the CO2-rich brine and the underlying resident brine and, consequently, decrease onset time of instability and increase convective mixing.
As far as it goes, only few works address the issues related to mathematical and numerical modeling aspects of the nanoparticles transport phenomena in CO2 storages. In the current work, we will present mathematical models to describe the nanoparticles transport carried by injected CO2 in porous media. Buoyancy and capillary forces as well as Brownian diffusion are important to be considered in the model. IMplicit Pressure Explicit Saturation-Concentration (IMPESC) scheme is used and a numerical simulator is developed to simulate the nanoparticles transport in CO2 storages.
In the current paper, a mathematical model to describe the nanoparticles transport carried by a two-phase flow in a porous medium is presented. Both capillary forces as well as Brownian diffusion are considered in the model. A numerical example of countercurrent water-oil imbibition is considered. We monitor the changing of the fluid and solid properties due to the addition of the nanoparticles using numerical experiments. Variation of water saturation, nanoparticles concentration and porosity ratio are investigated.
The problem of coupled structural deformation with two-phase flow in porous media is solved numerically using cellcentered finite difference (CCFD) method. In order to solve the system of governed partial differential equations, the implicit pressure explicit saturation (IMPES) scheme that governs flow equations is combined with the the implicit displacement scheme. The combined scheme may be called IMplicit Pressure-Displacement Explicit Saturation (IMPDES). The pressure distribution for each cell along the entire domain is given by the implicit difference equation. Also, the deformation equations are discretized implicitly. Using the obtained pressure, velocity is evaluated explicitly, while, using the upwind scheme, the saturation is obtained explicitly. Moreover, the stability analysis of the present scheme has been introduced and the stability condition is determined.
Coupling of solid deformation with fluid flow in porous media is one of the most challinging numerical issues in reservoir engineering applications such as CO2 sequestration and enhanced oil recovery. Several schemes; such as, fully implicit, IMplicit-EXplicit (IMEX), operator splitting, and IMplicit Pressure Explicit Saturation (IMPES); are widely used to solve the time-dependent partial differential equations that govern fluid flow in porous media. However, only few works address the issues related to mathematical and numerical modeling of the coupled flow-deformation problem. Furthermore, IMPES scheme is widely used for simulating the problem of two-phase flow in porous media. In spite of the fact that fully implicit method [1-5] is computationally expensive, it is unconditionally stable. The IMEX method [6-8] is more stable compares to the fully implicit method because it considers the linear terms implicitly and solves the other terms explicitly. The IMEX scheme is used to solve the ordinary differential equations resulting from the spatial discretization of the time-dependent partial differential equations. The operator splitting method [9-11] is used to simplify the original problem into a simpler form by the time-lag dimension. Furthermore, the iterative operator splitting [11, 12] has been considered as a part of the step of the iteration in the fully implicit method. The sequential method , on the other hand, is a modified version of the
IMPES method since the saturation is also evaluated implicitly. Comparing to the fully implicit method, the computational cost of the sequential method is less; therefore it is suitable for the large size models where stability becomes an important consideration.