Various flow regimes including Knudsen, transition, slip and viscous flows (Darcy's law), as applied to flow of natural gas through porous conventional rocks, tight formations and shale systems, are investigated. Data from the Mesaverde formation in the United States are used to demonstrate that the permeability correction factors range generally between 1 and 10. However, there are instances where the corrections can be between 10 and 100 for gas flow with high Knudsen number in the transition flow regime, and especially in the Knudsen's flow regime. The results are of practical interest as gas permeability in porous media can be more complex than that of liquid. The gas permeability is influenced by slippage of gas, which is a pressure-dependent parameter, commonly referred to as Klinkenberg's effect. This phenomenon plays a substantial role in gas flow through porous media, especially in unconventional reservoirs with low permeability, such as tight sands, coal seams, and shale formations. A higher-order permeability correlation for gas flow called Knudsen's permeability is studied. As opposed to Klinkenberg's correlation, which is a first-order equation, Knudsen's correlation is a second-order approximation. Even higher-order equations can be derived based on the concept used in developing this model. A plot of permeability correction factor versus Knudsen number gives a typecurve. This typecurve can be used to generalize the permeability correction in tight porous media. We conclude that Knudsen's permeability correlation is more accurate than Klinkenberg's model especially for extremely tight porous media with transition and free molecular flow regimes. The results from this study indicate that Klinkenberg's model and various extensions developed throughout the past years underestimate the permeability correction especially for the case of fluid flow with the high Knudsen number.

No abstract

Summary Core data from various North American basins with the support of limited amounts of data from other basins around the world have shown in the past that process speed or delivery speed (the ratio of permeability to porosity) provides a continuum between conventional, tight-, and shale-gas reservoirs (Aguilera 2010a). This work shows that the previous observation can be extended to tight-oil and shale-oil reservoirs. The link between the various hydrocarbon fluids is provided by the word “petroleum” in the “total petroleum system (TPS),” which encompasses liquid and gas hydrocarbons found in conventional, tight, and shale reservoirs. Results of the present study lead to distinctive flow units for each type of reservoir that can be linked empirically to gas and oil rates and, under favorable conditions, to production decline. To make the work tractable, the bulk of the data used in this paper has been extracted from published geologic and petroleum-engineering literature. The paper introduces an unrestricted/transient/interlinear transition flow period in a triple-porosity model for evaluating the rate performance of multistage-hydraulically-fractured (MSHF) tight-oil reservoirs. Under ideal conditions, this flow period is recognized by a straight line with a slope of –1.0 on log-log coordinates. However, the slope can change (e.g., to –0.75), depending on reservoir characteristics, as shown with production data from the Cardium and Shaunavon formations in Canada. This interlinear flow period has not been reported previously in the literature because the standard assumption for MSHF reservoirs has been that of a pseudosteady-state transition between the linear flow periods. It is concluded that there is a significant practical potential in the use of process speed as part of the flow-unit characterization of unconventional petroleum reservoirs. There is also potential for the evaluation of production-decline rates by the use of the triple-porosity model presented in this study.

Summary In this study, single-phase gas-flow simulation that considers slippage effects through a network of slots and microfractures is presented. The statistical parameters for network construction were extracted from petrographic work in tight porous media of the Nikanassin Group in the Western Canada Sedimentary Basin (WCSB). Furthermore, correlations between Klinkenberg slippage effect and absolute permeability have been developed as well as a new unified flow model in which Knudsen number acts implicitly as a flow-regime indicator. A detailed understanding of fluid flow at microscale levels in tight porous media is essential to establish and develop techniques for economic flow rate and recovery. Choosing an appropriate equation for flow through a single element of the network is crucial; this equation must include geometry and other structural features that affect the flow as well as all variation of fluid properties with pressure. Disregarding these details in a single element of porous media can easily lead to flow misinterpretation at the macroscopic scale. Because of the wide flow-path-size distribution in tight porous media, a variety of flow regimes can exist in the equivalent network. Two distinct flow regimes, viscous flow and free molecular flow, are in either side of this flow-regime spectrum. Because the nature of these two types of flow is categorically different, finding/adjusting a unified flow model is problematic. The complication stems from the fact that the viscosity concept misses its meaning as the flow regime changes from viscous to free molecular flow in which a diffusion-like mechanism dominates. For each specified flow regime, the appropriate equations for different geometries are studied. In addition, different unified flow models available in the literature are critically investigated. Simulation of gas flow through the constructed network at different mean flow pressures leads to investigating the functionality of the Klinkenberg factor with permeability of the porous media and pore-level structure.

Multiply-fractured horizontal wells are an efficient way to produce from tight gas, shale gas and tight oil formations. In this work, we present a linear composite model with a dual porosity inner zone to model production from a multiple fractured horizontal well. The composite solution uses linear dual porosity flow solution for the inner reservoir and a linear single porosity solution for the outer reservoir combined with continuity of pressure and flux at their interface. Solution to the problem was obtained in Laplace space. The solution that we have obtained is simple and fast, yet effective and can be applied to model production from fractured horizontal wells. For the cases of interest, we observe three linear flow periods in this model. The first linear flow is from the fractures into the wellbore, followed by linear flow in the matrix to the fractures and lastly linear flow in the outer single porosity reservoir to the inner reservoir. Each of these three linear flow periods is separated by a transition depending on the properties of the fracture, matrix and the outer reservoir. We use a numerical simulator to examine the validity of some of the assumptions made in the development of the work. While the model that we have made consists of only linear flow solutions, the numerical model accounts for two dimensional flows in all media. New solutions are presented in the form of type curves.