Negara, Ardiansyah (Baker Hughes) | Salama, Amgad (King Abdullah University of Science and Technology) | Sun, Shuyu (King Abdullah University of Science and Technology) | Elgassier, Mokhtar (Baker Hughes) | Wu, Yu-Shu (Colorado School of Mines)
Shale gas resources have received great attention in the last decade due to the decline of the conventional gas resources. Unlike conventional gas reservoirs, the gas flow in shale formations involves complex processes with many mechanisms such as Knudsen diffusion, slip flow (Klinkenberg effect), gas adsorption and desorption, strong rock-fluid interaction, etc. Shale formations are characterized by the tiny porosity and extremely low-permeability such that the Darcy equation may no longer be valid. Therefore, the Darcy equation needs to be revised through the permeability factor by introducing the apparent permeability. With respect to the rock formations, several studies have shown the existence of anisotropy in shale reservoirs, which is an essential feature that has been established as a consequence of the different geological processes over long period of time. Anisotropy of hydraulic properties of subsurface rock formations plays a significant role in dictating the direction of fluid flow. The direction of fluid flow is not only dependent on the direction of pressure gradient, but it also depends on the principal directions of anisotropy. Therefore, it is very important to take into consideration anisotropy when modeling gas flow in shale reservoirs. In this work, the gas flow mechanisms as mentioned earlier together with anisotropy are incorporated into the dual-porosity dual-permeability model through the full-tensor apparent permeability. We employ the multipoint flux approximation (MPFA) method to handle the full-tensor apparent permeability. We combine MPFA method with the experimenting pressure field approach, i.e., a newly developed technique that enables us to solve the global problem by breaking it into a multitude of local problems. This approach generates a set of predefined pressure fields in the solution domain in such a way that the undetermined coefficients are calculated from these pressure fields. In other words, the matrix of coefficients is constructed automatically within the solver. We ran a numerical model with different scenarios of anisotropy orientations and compared the results with the isotropic model in order to show the differences between them. We investigated the effect of anisotropy in both the matrix and fracture systems. The numerical results show anisotropy plays a crucial role in dictating the pressure fields as well as the gas flow streamlines. Furthermore, the numerical results clearly show the effects of anisotropy on the production rate and cumulative production. Incorporating anisotropy together with gas flow mechanisms in shale formations into the reservoir model is essential particularly for predicting maximum gas production from shale reservoirs.
Negara, Ardiansyah (King Abdullah University of Science and Technology) | Salama, Amgad (King Abdullah University of Science and Technology) | Sun, Shuyu (King Abdullah University of Science and Technology)
Anisotropy of hydraulic properties of subsurface geologic formations is an essential feature that has been established as a consequence of the different geologic processes that they undergo during the longer geologic time scale. With respect to petroleum reservoirs, in many cases, anisotropy plays significant role in dictating the direction of flow that becomes no longer dependent only on the pressure gradient direction but also on the principal directions of anisotropy. Furthermore, in complex systems involving the flow of multiphase fluids in which the gravity and the capillarity play an important role, anisotropy can also have important influences.
Therefore, there has been great deal of motivation to consider anisotropy when solving the governing conservation laws numerically. Unfortunately, the two-point flux approximation of finite difference approach is not capable of handling full tensor permeability fields. Lately, however, it has been possible to adapt the multipoint flux approximation that can handle anisotropy to the framework of finite difference schemes. In multipoint flux approximation method, the stencil of approximation is more involved, i.e., it requires the involvement of 9-point stencil for the 2-D model and 27-point stencil for the 3-D model. This is apparently challenging and cumbersome when making the global system of equations.
In this work, we apply the equation-type approach, which is the experimenting pressure field approach that enables the solution of the global problem breaks into the solution of multitude of local problems that significantly reduce the complexity without affecting the accuracy of numerical solution. This approach also leads in reducing the computational cost during the simulation.
We have applied this technique to a variety of anisotropy scenarios of 3-D subsurface flow problems and the numerical results demonstrate that the experimenting pressure field technique fits very well with the multipoint flux approximation method. Furthermore, the numerical results explicitly emphasize that anisotropy could not be ignored for the proper model of subsurface flow.
Copyright 2013, Society of Petroleum Engineers This paper was prepared for presentation at the SPE Middle East Oil and Gas Show and Conference held in Manama, Bahrain, 10-13 March 2013. This paper was selected for presentation by an S PE program committee following review of information contained in an abstract submitted by the author(s). Contents of th e paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessar ily reflect any posit ion of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the written consent of the Society of Petroleum Engineers is prohi bited.
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.