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.
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.