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.

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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.

Methods are presented for detecting and evaluating naturally fracturedreservoirs from porosity (sonic, neutron, and density)and resistivitylogs. It is shown that the porosity exponent of a naturally fracturedreservoir is smaller than the porosity exponent of the matrix. Charts havebeen generated for estimating the porosity exponent for these reservoirsas a function of total porosity, matrix porosity, and matrix-porosity exponent. Introduction The principles for the techniques presented here weredescribed previously using sonic and resistivity logs.The approach followed in this study was to use empiricalequations that had been derived for granular mediain the hope that they could be useful in the analysis offractured reservoirs. It was anticipated that thisapproach would result in a distinctive means of detectingand evaluating fractured media. The purpose of thispaper is to extend the method to other porosity logs, and to present ways to estimate fracture and totalporosity from logs. A theoretical model composed of cubes" indicated that the double-porosity exponent, m, shouldbe relatively small(ranging from about 1.1 to 1.3) fornaturally fractured systems. Towle was apparently thefirst investigator to indicate the similarity of a synthetic pore system (represented by cubes with spaces inbetween) to a fracture-type system. However, this modelconsidered only fractured porosity (matrix porosity waszero). This paper analyzes the behavior of the porosityexponent, m, in a naturally fractured reservoir by meansof a double-porosity model. It is found that the value ofm is certainly small and may range somewhere betweenabout 1.1 and the porosity exponent value of the matrix, depending on the degree of fracturing of the formation.Consequently, it appears that a comparison of thedouble-porosity exponent, m, (obtained from logs) with the matrix-porosity exponent, mb, (determined in thelaboratory) gives a reliable way to detect naturallyfractured systems. Values of water saturation are determined using aparameter, P, derived originally for the analysis ofintergranular media, and extended in this study to analyzefractured media. This parameter is a function of formation resistivity and porosity tool response. It has been foundempirically that P has a square-root-normal distributionfor zones 100-percent saturated with water. Hydrocarbonzones deviate from this distribution. By determining themean value of P at a water saturation of 100 percent, it ispossible to evaluate the resistivity index, I, for hydrocarbonzones and, hence, the values of water saturation. Log Properties for Detecting FracturesState of the Art Sonic amplitude logs have been used extensively inattempts to detect fractures. When the acoustic velocitygenerated by a logging tool is recorded, four wave typescan be identified: a compressional wave, a shear wave, a fluid or water wave, and a low-velocity wave.Generally, the compressional wave has been found to beattenuated more by vertical and high-angle fractures, while the shear wave seems to be more sensitive tohorizontal and low-angle fractures. However, experience has indicated that this measurement is not universally applicable because changes in amplitude as largeas those caused by fractures can be produced byvariations in lithology and tool centralization; and because, in practice, there might be solid contact across thefractures, so that the degree of acoustic discontinuity isdiminished. JPT P. 764^

Introduction Conventional reservoir engineering techniques and naturally fractured reservoirs do not mix well. The use of conventional techniques has led to underestimating or overestimating recoveries and reserves in many naturally fractured reservoirs worldwide. This paper is a follow-up to a previous article dealing with advances in the study of naturally fractured reservoirs(1). In that article I concentrated on types of fractures, how to intersect them, and on key items associated with data acquisition. In this paper I provide general information dealing with recovery estimates and reserves in naturally fractured reservoirs. The paper is intended for the general interest reader who is not a specialist in the field. Recovery Not all fractured reservoirs are the same. So talking about fractured reservoirs in general is not good enough. My recommendation is to initially classify the reservoir according to (1) geologic, (2) pore system, (3) hydrocarbon storage, and (4) matrix/fracture interaction points of view. Geologic Classification From a geologic point of view the fractures can be classified as being tectonic (fold and/or fault related), regional, contractional (diagenetic), and surface related(1–3). Historically most hydrocarbon production has been obtained from tectonic fractures, followed by regional fractures and followed by contractional fractures. In general, surface related fractures are not important from the point of view of hydrocarbon production. When classifying the fractures determine fracture dip and strike. Pore Classification It is possible to make preliminary estimates of productive characteristics of common reservoir porosity types following a classification proposed by Coalson et al(9). In this classification porosity classes are defined first by the geometry of the pores, and second by pore size. Included in. the geometry are the following pore categories: Intergranular, Intercrystalline, vuggy, and fracture. The combination of any of them can give origin to dual and even multiporosity behavior. Included in the pore size are megaporosity, macroporosity, mesoporosity, and microporosity. Table 1 shows typical petrophysical parameters for this classification adapted from a combination of Coalson et al. (9), and White(10). Included in this Table are the geometry, pore size, pore throat radius at 35% mercury saturation (Winland R35 values), permeability to air, immobile water saturation and typical capillary pressure curves coded A through D. These capillary pressures are shown on Figure 1. The aperture of the fractures and vugs deserve further discussion. From laboratory work and experience it has been found that nut shells and plastic materials can stop circulation losses in fractures with apertures as large as 5,000 microns. If in a given naturally fractured reservoir these materials cannot stop circulation losses the conclusion is reached that the apertures are bigger than 5,000 microns. In fact, secondary porosity apertures can actually reach cavern-size in some instances. Storage Classification From a storage point of view the fractures can be classified(3) as being of Type A, B or C. Many reservoirs that would otherwise be non-productive are commercial thanks to the presence of natural fractures,(8) In reservoirs of Type A the bulk of the hydrocarbon storage is in the matrix porosity and a small amount of storage is in the fractures.

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 (or delivery) speed provides a continuum between conventional, tight and shale gas reservoirs (Aguilera, 2010). This work extends the previous observation to tight oil and shale oil reservoirs. The link between the various fluids is provided by the word ‘petroleum’ in ‘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 have been extracted from published geologic and petroleum engineering literature. The paper introduces a new unrestricted transition flow period in tight reservoirs that is recognized by a straight line with a slope of -0.75 on log-log coordinates. This straight line occurs as a transition between 2 linear flow periods. Process speed is the ratio of permeability and porosity. The approximate boundary between viscous and diffusion dominated flow in gas reservoirs is estimated with Knudsen number which can be calculated from pore throat radius (a function of process speed). Viscous flow is present, for example, when the architecture of the rock is dominated by megaports, macroports, mesoports and sometimes microports (port = pore throat). Diffusion flow on the other hand is observed at the nanoport scale, which can occur in both tight and shale reservoirs. The process speed concept has been used successfully in conventional petroleum reservoirs for several decades and in tight and shale gas reservoirs during the past 3–4 years. The concept is extended in this paper to tight oil and shale oil reservoirs, and hence to the complete petroleum system, with the support of core and drill-cuttings data. The approach permits estimating volumes of petroleum-in-place, differentiating between viscous and diffusion dominated flow in gas reservoirs and the contribution of each flow mechanism with the use of a unified diffusion-viscous flow model. This is valuable, for example, in those cases where the formation to be developed is composed of alternating stacked layers of tight and shale reservoirs, or where there are lateral variations due to facies changes. It is concluded that there is significant practical potential in the use of process speed as part of the flow unit characterization and production performance prediction in unconventional petroleum reservoirs.