Improved Permeability Prediction Relations for Low Permeability Sands
01 Jan 2007-
TL;DR: In this article, the problem of estimating Klinkenbergcorrected permeability from single-point, steady-state measurements on samples from low permeability sands is addressed, and the original problem of predicting the corrected or "liquid equivalent" permeability has been under investigation since the early 1940s.
Abstract: This work addresses the problem of estimating Klinkenbergcorrected permeability from single-point, steady-state measurements on samples from low permeability sands. The "original" problem of predicting the corrected or "liquid equivalent" permeability (i.e., referred to as the Klinkenbergcorrected permeability) has been under investigation since the early 1940s — in particular, using the application of "gas
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TL;DR: In this paper, a unified Hagen-Poiseuille-type equation for gaseous flow regimes through tight porous media is described by rigorous application of a unified formulation.
Abstract: Gaseous flow regimes through tight porous media are described by rigorous application of a unified Hagen–Poiseuille-type equation. Proper implementation is accomplished based on the realization of the preferential flow paths in porous media as a bundle of tortuous capillary tubes. Improved formulations and methodology presented here are shown to provide accurate and meaningful correlations of data considering the effect of the characteristic parameters of porous media including intrinsic permeability, porosity, and tortuosity on the apparent gas permeability, rarefaction coefficient, and Klinkenberg gas slippage factor.
653 citations
Cites methods from "Improved Permeability Prediction Re..."
...Further, the approach taken by Florence et al. (2007) for correlation of the Klinkenberg gas slippage factor is not correct and consequently their correlation cannot represent the data over the full range of the gas molecular mass (commonly called weight)....
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...Florence et al. (2007) made an attempt at utilizing the Hagen–Poiseuille-type equation of Beskok and Karniadakis (1999) to derive a general expression for the apparent gas permeability of tight porous media and correlated some essential parameters by means of experimental data, including the…...
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01 Jan 2010
452 citations
TL;DR: In this article, a higher-order correlation for gas flow called Knudsen's permeability is studied, which is more accurate than Klinkenberg's model especially for extremely tight porous media with transition and free molecular flow regimes.
Abstract: 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.
318 citations
Cites methods or result from "Improved Permeability Prediction Re..."
...…constant close to unity Heid et al. (1950) bk = 11.419(k∞)−0.39 Jones and Owens (1979) bk = 12.639(k∞)−0.33 Sampath and Keighin (1982) bk = 13.851(k∞/φ)−0.53 Florence et al. (2007) bk = β (k∞/φ)−0.5 Gas β-Value Nitrogen 43.345 Air 44.106 Civan (2010) bk = 0.0094 (k∞/φ)−0.5 Correlation for…...
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...Civan (2010) and Florence et al. (2007) give the same results as they are very close in formulation....
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...…formulation can be related to Darcy’s equation as follows: q = fc qDarcy (12) where fc is a correction factor given by (Beskok and Karniadakis 1999; Florence et al. 2007): fc = [1 + α(kn) K n] [ 1 + 4K n 1 − b K n ] (13) We call this fc Knudsen’s correction factor as it was developed based on…...
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...Florence et al. (2007), using a different dataset, proposed the following Klikenberg’s permeability correlation for nitrogen: ka = 43....
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...where fc is a correction factor given by (Beskok and Karniadakis 1999; Florence et al. 2007): fc = [1 + α(kn) K n] [ 1 + 4K n 1 − b K n ] (13)...
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TL;DR: In this paper, the dusty-gas model for flow was used to model flow in shale gas systems, which couples diffusion to advective flow and showed that for very small average pore throat diameters, lighter gases preferentially produced at concentrations significantly higher than in situ conditions.
Abstract: Various attempts have been made to model flow in shale gas systems. However, there is currently little consensus regarding the impact of molecular and Knudsen diffusion on flow behavior over time in such systems. Direct measurement or model-based estimation of matrix permeability for these “ultra-tight” reservoirs has proven unreliable. The composition of gas produced from tight gas and shale gas reservoirs varies with time for a variety of reasons. The cause of flowing gas compositional change typically cited is selective desorption of gases from the surface of the kerogen in the case of shale. However, other drivers for gas fractionation are important when pore throat dimensions are small enough. Pore throat diameters on the order of molecular mean free path lengths will create non-Darcy flow conditions, where permeability becomes a strong function of pressure. At the low permeabilities found in shale gas systems, the dusty-gas model for flow should be used, which couples diffusion to advective flow. In this study we implement the dusty-gas model into a fluid flow modeling tool based on the TOUGH+ family of codes. We examine the effects of Knudsen diffusion on gas composition in ultra-tight rock. We show that for very small average pore throat diameters, lighter gases are preferentially produced at concentrations significantly higher than in situ conditions. Furthermore, we illustrate a methodology which uses measurements of gas composition to more uniquely determine the permeability of tight reservoirs. We also describe how gas composition measurement could be used to identify flow boundaries in these reservoir systems. We discuss how new measurement techniques and data collection practices should be implemented in order to take advantage of this method. Our contributions include a new, fit-for-purpose numerical model based on the TOUGH+ code capable of characterizing transport effects including permeability adjustment and diffusion in micro- and nano-scale porous media.
295 citations
TL;DR: It is found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales.
Abstract: Porous structures of shales are reconstructed using the markov chain monte carlo (MCMC) method based on scanning electron microscopy (SEM) images of shale samples from Sichuan Basin, China. Characterization analysis of the reconstructed shales is performed, including porosity, pore size distribution, specific surface area and pore connectivity. The lattice Boltzmann method (LBM) is adopted to simulate fluid flow and Knudsen diffusion within the reconstructed shales. Simulation results reveal that the tortuosity of the shales is much higher than that commonly employed in the Bruggeman equation, and such high tortuosity leads to extremely low intrinsic permeability. Correction of the intrinsic permeability is performed based on the dusty gas model (DGM) by considering the contribution of Knudsen diffusion to the total flow flux, resulting in apparent permeability. The correction factor over a range of Knudsen number and pressure is estimated and compared with empirical correlations in the literature. For the wide pressure range investigated, the correction factor is always greater than 1, indicating Knudsen diffusion always plays a role on shale gas transport mechanisms in the reconstructed shales. Specifically, we found that most of the values of correction factor fall in the slip and transition regime, with no Darcy flow regime observed.
282 citations
References
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TL;DR: In this paper, the authors present a simulation of the transition and free-molecular regime of pressure-driven liquid flow in a shear-driven and separated liquid flow model.
Abstract: Basic Concepts and Technologies * Governing Equations and Slip Models * Shear-Driven and Separated Micro Flows * Pressure-Driven Micro Flows: Slip Flow Regime * Pressure-Driven Flows: Transition and Free- Molecular Regimes * Thermal Effects in Micro Scales * Prototype Applications of Gas Micro Flows * Electrokinetically-Driven Liquid Micro Flows * Numerical Methods for Continuous Simulation * Numerical Methods for Atomistic Simulation
612 citations
TL;DR: This paper developed correlations for predicting a reservoir's in situ permeability from routine core-analysis data and found that the routine permeability values of tight gas sands are often more than 100 times greater than permeabilities under actual reservoir conditions because of the great relief of stress, absence of connate water, and increased gas slippage.
Abstract: To help moderate or reverse the persistent decline in US gas reserves, the industry is expanding its exploration and development efforts to include fields with permeabilities in the microdarcy range; however, the design of stimulation treatments to achieve commercial rates of production from such low-permeability rocks demands a more accurate means of determining their flow properties. Laboratory tests designed to develop correlations for predicting a reservoir's in situ permeability from routine core-analysis data have shown that the routine permeability values of tight gas sands are often more than 100 times greater than permeabilities under actual reservoir conditions because of the great relief of stress, absence of connate water, and increased gas slippage. The correlations developed can account for these three separate effects and produce a closer estimate of the reservoir's in situ effective gas permeability.
406 citations
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