Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs

Abstract

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.

Fluid flow through anisotropic and deformable double porosity media with ultra-low matrix permeability: A continuum framework

“…This result is consistent with the findings of k V /k H in [4,101] and R in [35]. If above layered system is rotated through an angle θ, we can approximate the new k # 2 as [26,62,88,89,97]…”

“…Due to this full tensor permeability k 2 , the direction of q 2 depends on both pressure gradient and the principal directions of anisotropy [89]. Finally, for c 1 and c 2 , we adopt prototype in [48,49,110] with minor modifications…”

“…Darcy's law is the most fundamental equation to describe fluid flow in conventional reservoirs or microcracks [89,101,124]. However, for unconventional and tight reservoirs with ultra-low matrix permeability (assuming isotropic), Darcy's law will overestimate the flow rate of liquid due to the interaction between fluid particles and the solid pore wall [38,108,118,119,123].…”

Acid Treatment as a Way to Reduce Shale Rock Mechanical Strength and to Create a Material Prone to the Formation of Permanent Well Barrier

“…Our observations in contrast to literature findings suggest that the etching reaction of carbonates with acid proceeds faster in A significantly higher etching rate was observed for the sample exposed in the parallel configuration, i.e., when the sample surface parallel to bedding was exposed to acid. Mass transport inside sedimentary rock matrices has been shown to be highly dependent on the direction in respect to rock bedding plane [29][30][31][32]. Typically, the diffusion rates in the direction perpendicular to the bedding plane are shown to be lower than that parallel to the bedding plane [30][31][32].…”

Flow and Transport in Tight and Shale Formations: A Review

“…Salama et al [145,146] also developed what they called the experimenting field algorithm in which the matrix of coefficients of a linear system is constructed automatically, rather than being inputted manually. This technique has been tested in various cases and shows to be very effective (Salama et al [147][148][149], Wu et al [150], Negara et al [151,152], and El-Amin et al [153]). Furthermore, Salama et al [154] and Salama [155] developed a technique that numerically solves the problem of flow towards a well in an efficient manner.…”