Flow of shale gas in tight rocks using a non-Linear transport model with pressure dependent model parameters (original) (raw)
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Transport In Porous Media, 2017
A nonlinear transport model for single-phase gas flow in tight porous media is developed. The model incorporates many important physical processes that occur in such porous systems: continuous flow, transition flow, slip flow, Knudsen diffusion, adsorption and desorption into and out of the rock material, and a correction for high flow rates. This produces a nonlinear advection-diffusion type of partial differential equation with pressure-dependent model parameters and associated compressibility coefficients, and highly nonlinear apparent convective flux (velocity) and apparent diffusivity. A key finding is that all model parameters should be kept pressure dependent for the best results. An application is to the determination of rock properties, such as porosity and permeability, by history matching of the simulation results to data from pressure-pulse decay tests in a rock core sample (Pong et al. in ASME Fluids Eng Div 197:51-56, 1994).
Some key technical issues in modelling of gas transport process in shales: a review
Geomechanics and Geophysics for Geo-Energy and Geo-Resources, 2016
As a result of small pore sizes and property heterogeneities at different scales, flow processes and the related physical mechanisms in shales can be dramatically different from those in conventional gas reservoirs. To accurately capture the ''unconventional'' flow and transport in shales requires reevaluation of dominant physics controlling flow in shales, as well as innovative hardware technologies to estimate critical material and flow properties. To do so, we need to quantify the current knowledge and identify technology gaps especially as related to the modeling fluid flow in shale gas reservoirs. While fluid flow in shale includes many important aspects, this paper focuses on fluid flow in complex heterogeneous shale matrix. It discusses the recent progress in the areas of multiscale fluid flow, fracturing fluid imbibition, and stressdependent shale matrix properties. Future research topics in the related areas are also suggested based on the identified technology gaps.
Comprehensive modeling of multiple transport mechanisms in shale gas reservoir production
Fuel, 2020
A boom in the production of shale gas has recently impacted the world's energy supply. The hydraulic fracturing technology has been widely used in the development of shale gas reservoirs. Models for accurate reservoir simulation are essential for their economic production. In this paper, a model for shale gas reservoir production is proposed to account for slip flow, Knudsen diffusion, surface diffusion, gas adsorption/desorption, stress dependence of a pore structure, a non-ideal gas effect, and a flow mechanism difference between organic and inorganic content in the shale matrix. This model is implemented in our in-house simulator with a coupled MINC-EDFM approach to study and predict shale gas production behavior. Comprehensive sensitivity studies are performed to analyze the importance of different parameters in shale gas production. These parameters are divided into two categories. The first category includes reservoir data, such as shale matrix porosity, a nanopore radius, an organic/inorganic volume ratio, hydraulic fracture half-length, and fracture spacing. The second category includes parameters relevant to flow mechanisms, such as a non-ideal gas effect, stress dependence, presence of an adsorbed layer as well as a selection of a flow mechanism model. It is found that parameters related to hydraulic fractures impact calculated gas production more than reservoir matrix data. Among the fracturing parameters, hydraulic fracture half-length has a stronger effect than fracture spacing, and among matrix properties, porosity has a larger impact than a nanopore radius or the assumed organic/inorganic content ratio. These results help to optimize a shale gas reservoir production design. In addition, in a synthetic case assuming a 1 nm pore radius, the presence of an adsorbed gas layer has a more tremendous effect compared to the non-ideal gas and stress dependence phenomena. Moreover, the developed simulator with the multiple transport mechanisms can be used to accurately predict shale gas reservoir production. The findings of this study help a better understanding of shale gas flow and can be used to enhance the production of shale gas reservoirs.
Modeling Gas Transport in Shale Reservoir – Conservation Laws Revisited
Transport of gas in a shale reservoir may be greatly different from that in a conventional reservoir. This is primarily due to shale's small pore size, extremely-low permeability and presence of adsorbed gas. It is also because the low permeability formation matrix is intervened with highly conductive hydraulic fractures. Although some of the involved mechanisms such as gas molecule slippage (Klingenberg effect) and non-Darcy flow (Forchheimer effect) have been extensively studied since early pioneering works decades ago, there is still a need for improved fundamental understanding and proper quantification. This paper clarifies some of the confusions floating around the topic of non-Darcy gas flow. A comprehensive model of gas transport in shale reservoirs, including contributions due to gas molecule slippage, inertial forces and gas desorption is constructed directly from the fundamental laws of mass, momentum and energy conservation. The model is then applied to simulate production from hydraulically fractured shale gas reservoirs.
Gas Flow Models of Shale: A Review
Energy & Fuels
Conventional flow models based on Darcy's flow physics fail to model shale gas production data accurately. The failure to match field data and laboratory-scale evidence of non-Darcy flow has led researchers to propose various gas-flow models for the shale reservoirs. There is extensive evidence that suggests the size of the pores in shale is microscopic in the range of a few to hundreds of nanometers (also known as nanopores). These small pores are mostly associated with the shale's organic matter portion, resulting in a dual pore system that adds to the gas flow complexity. Unlike Darcy's law, which assumes that a dominant viscous flux determines a rock's permeability, shale's permeability leads to other flow processes besides viscous flow such as gas slippage and Knudsen diffusion. This work reviews the dominant gas-flow processes in a single nanopore on the basis of theoretical models and molecular dynamics simulations, and lattice Boltzmann modeling. We extend the review to pore network models used to study the gas permeability of shale.
Modeling and simulation of gas flow behavior in shale reservoirs
Journal of Petroleum Exploration and Production Technology
Shale is a growing prospect in this world with decreasing conventional sources of fossil fuel. With the growth in demand for natural gas, there is impending need for the development of the robust model for the flow of shale gas (Behar and Vandenbroucke in Org Geochem, 11:15-24, 1987). So the major driving force behind the working on this major project is the unavailability of desired models that could lead to enhanced production of these wells and that too efficiently. This model mainly includes the movement of shale gas from tight reservoir through the conductive fractures to wellbore and production model of the decline in pressure inside the reservoir with respect to time. This result has been further compared with the help of MATLAB so as to obtain a complete pressure-derived model. The result shows the applicability of this in the real-life projects where it is difficult to model the fractures and obtain the flow rate with them in fractures and how to set the production facilities becomes a question.
Compressibility Coefficients in Nonlinear Transport Models in Unconventional Gas Reservoirs
Proceedings of AMMCS-CAIMS Congress 2015
Transport models for gas flow in unconventional hydrocarbon reservoirs possess several model parameters such as the density (r), the permeability (K), the Knudsen number (Kn), that are strongly dependent upon the pressure p. Each physical parameter, say g, in the system has an associated compressibility factor zg = zg (p) (which is the relative rate of change of the parameter with respect to changes in the pressure, [1]). Previous models have often assumed that zg = Const, such as Cui [9], and Civan [7]. Here, we investigate the effect of selected compressibility factors (real gas deviation factor (zZ), gas density (zr ), gas viscosity (zm ), permeability (zK), and the porosity (zf ) of the source rock) as functions of the pressure upon rock properties such as K and f.We also carry out a sensitivity analysis to estimate the importance of each model parameter. The results are compared to available data.
Numerical Simulation of Natural Gas Flow in Anisotropic Shale Reservoirs
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.
Transport in Porous Media, 2011
A theoretically improved model incorporating the relevant mechanisms of gas retention and transport in gas-bearing shale formations is presented for determination of intrinsic gas permeability and diffusivity. This is accomplished by considering the various flow regimes according to a unified Hagen-Poiseuille-type equation, fully compressible treatment of gas and shale properties, and numerical solution of the non-linear pressure equation. The present model can accommodate a wide range of fundamental flow mechanisms, such as continuum, slip, transition, and free molecular flow, depending on the prevailing flow conditions characterized by the Knudsen number. The model indicates that rigorous determination of shale-gas permeability and diffusivity requires the characterization of various important parameters included in the present phenomenological modeling approach, many of which are not considered in previous studies. It is demonstrated that the improved model matches a set of experimental data better than a previous attempt. It is concluded that the improved model provides a more accurate means of analysis and interpretation of the pressure-pulse decay tests than the previous models which inherently consider a Darcian flow and neglect the variation of parameters with pressure.
Modelling of gas flow in shale using a finite volume method
Applied Mathematical Modelling
Gas flow in shale is a very complex phenomenon, currently investigated using a variety of techniques including the analysis of transient experiments conducted on full core and crushed shale using a range of gases. A range of gas flow mechanisms may operate in shale including continuum flow, slippage, transitional flow and Knudsen diffusion. These processes, as well as gas sorption, need to be taken into account when interpreting experimental data and extrapolating the results to the subsurface. Several models have been published that attempt to account for these different processes. Unfortunately, these have a large number of unknown parameters and few studies have assessed the extent to which transient experiments may be used to invert for the key unknowns or the errors that are associated. Here we present a methodology in which various inversion techniques are applied to assess the viability of deriving key unknowns which control gas flow in shale from transient experiments with a range of noise. A finite volume method is developed for solving the model of Civan (2010, 2011a,b) of transient gas flow in shale. The model is applicable to non-linear diffusion problems, in which the permeability and fluid density both depend on the scalar variable, pressure. The governing equation incorporates the Knudsen number, allowing different flow mechanisms to be addressed, as well as the gas adsorption isotherm. The method is verified for unsteady-state problems for which analytical or numerical solutions are available. The method is then applied to a pressure-pulse decay test. An inverse numerical formulation is generated, using a minimisation iterative algorithm, to estimate some unknown physical parameters. Both numerically simulated noisy and experimental data are input into the formulation of the inverse problem. Error analysis is undertaken to investigate the accuracy of results. A good agreement between inverted and exact parameter values is obtained for several parameters. However, it was found that the strong correlation between intrinsic permeability and tortuosity meant that it was not possible to accurately invert simultaneously for these two parameters from the current pressure-pulse decay model.