Upscaling pore pressure-dependent gas permeability in shales

Journal of Petroleum Science and Engineering, 2019

Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyenproposed first to estimate bulk electrical conductivity, " , and permeability in sandstones from rock images-to scale up " and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions-determined from mercury intrusion capillary pressure (MICP) curves-and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the 2 two characteristic pore sizes, tortuosity, and porosity by assuming two different pore geometries: cylindrical and slit-shaped. Comparison of results obtained for eighteen tightgas sandstones indicates that the EMA estimates " and k more accurately when pores are assumed to be cylindrical. We also estimate k from the pore-throat size distributions and the measured electrical conductivity using the EMA and critical path analysis (CPA), another upscaling technique borrowed from statistical physics. Theoretically, the former is valid in relatively heterogeneous porous media with narrow pore-throat size distribution, while the latter is valid in heterogeneous media with broad pore-throat size distribution. Results show that the EMA estimates k more accurately than CPA and arrives within a factor of two of the measurements on average.

2018

Upscaling Klinkenberg-corrected gas permeability, k, in unconventional tight sandstones has numerous practical applications, particularly in gas exploration and production. In this study, we adapt the effective-medium approximation (EMA) model of Doyen – proposed first to estimate bulk electrical conductivity, σ", and permeability in sandstones from rock images – to scale up σ" and k in tight-gas sandstones from pore to core. For this purpose, we calculate two characteristic pore sizes: an effective hydraulic and an effective electrical pore size from pore-throat size distributions – determined from mercury intrusion capillary pressure (MICP) curves – and pore-throat connectivity. The latter is estimated from critical volume fraction (or percolation threshold) for macroscopic flow. Electrical conductivity and permeability are then scaled up from the

International Journal of Coal Geology, 2015

The pore network in shale reservoirs consists of pores associated with both organic matter and inorganic matrix. The range of pore sizes within the organic matter is usually an order of magnitude smaller than pore sizes within the inorganic matrix, causing a bimodal pore-size distribution for the total system revealed in nitrogen adsorption tests. We use a stochastic classification method based on a mixture of Gaussian assumption to separate two distributions of pores in organic matter and inorganic matrix. We construct an ensemble-based stochastic model conditioned to Total Organic Content (TOC) and the characteristics of pore-size distributions in organic and inorganic media. This treatment of different pore sizes in organic and inorganic enables us to assign sorption process only in organic matter. The model can be used to calculate the apparent gas permeability (AP) in shale from a combination of nitrogen-adsorption and SEM-image data. We validate the model with data from the literature, and use it to determine permeability and tortuosity from pulse-decay experimental data. The model results show that AP is more sensitive to the mean of pores within inorganic matrix than within organic matter. These results suggest pore sizes corresponding to each compartment; organic and inorganic should be considered to estimate permeability. The model results also confirm permeability enhancement owing to the sorption process in organic matter below critical sorption pressure.

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.

Journal of Fluid Mechanics, 2012

We study the gas flow processes in ultra-tight porous media in which the matrix pore network is composed of nanometre- to micrometre-size pores. We formulate a pressure-dependent permeability function, referred to as the apparent permeability function (APF), assuming that Knudsen diffusion and slip flow (the Klinkenberg effect) are the main contributors to the overall flow in porous media. The APF predicts that in nanometre-size pores, gas permeability values are as much as 10 times greater than results obtained by continuum hydrodynamics predictions, and with increasing pore size (i.e. of the order of the micrometre), gas permeability converges to continuum hydrodynamics values. In addition, the APF predicts that an increase in the fractal dimension of the pore surface leads to a decrease in Knudsen diffusion. Using the homogenization method, a rigorous analysis is performed to examine whether the APF is preserved throughout the process of upscaling from local scale to large scale....

EPJ Web of Conferences

The pore structure of a natural shale is obtained by three imaging means. Micro-tomography results are extended to provide the spatial arrangement of the minerals and pores present at a voxel size of 700 nm (the macroscopic scale). FIB/SEM provides a 3D representation of the porous clay matrix on the so-called mesoscopic scale (10-20 nm); a connected pore network, devoid of cracks, is obtained for two samples out of five, while the pore network is connected through cracks for two other samples out of five. Transmission Electron Microscopy (TEM) is used to visualize the pore space with a typical pixel size of less than 1 nm and a porosity ranging from 0.12 to 0.25. On this scale, in the absence of 3D images, the pore structure is reconstructed by using a classical technique, which is based on truncated Gaussian fields. Permeability calculations are performed with the Lattice Boltzmann Method on the nanoscale, on the mesoscale, and on the combination of the two. Upscaling is finally done (by a finite volume approach) on the bigger macroscopic scale. Calculations show that, in the absence of cracks, the contribution of the nanoscale pore structure on the overall permeability is similar to that of the mesoscale. Complementarily, the macroscopic permeability is measured on a centimetric sample with a neutral fluid (ethanol). The upscaled permeability on the macroscopic scale is in good agreement with the experimental results.

Scientific reports, 2015

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...

SPE Reservoir Evaluation & Engineering, 2019

Summary This work proposes an innovative laboratory method to measure shale gas permeability as a function of pore pressure, a key parameter for characterizing and modeling gas flow in a shale gas reservoir. The development is based on a solution to 1D gas flow under certain boundary and initial conditions. The details of the theoretical background, including formulations to estimate gas permeability and conceptual design of the test setup, are provided. The advantages of our approach, surpassing the currently available ones, include that it measures gas permeability (as a function of pressure) with a single test run and without any presumption regarding the form of parametric relationship between gas permeability and pore pressure. In addition, our approach allows for estimating both shale permeability and porosity at the same time from the related measurements. Numerical experiments are conducted to verify the feasibility of the proposed methodology.

2019

Fuel, 2016

Gas flow in shale is associated with both organic matter (OM) and inorganic matter (IOM) which contain nanopores ranging in size from a few to hundreds of nanometers. In addition to the noncontinuum effect which leads to an apparent permeability of gas higher than the intrinsic permeability, the surface diffusion of adsorbed gas in organic pores also can influence the apparent permeability through its own transport mechanism. In this study, a generalized lattice Boltzmann model (GLBM) is employed for gas flow through the reconstructed shale matrix consisting of OM and IOM. The Expectation-Maximization (EM) algorithm is used to assign the pore size distribution to each component, and the dusty gas model (DGM) and generalized Maxwell-Stefan model (GMS) are adopted to calculate the apparent permeability accounting for multiple transport mechanisms including viscous flow, Knudsen diffusion and surface diffusion. Effects of pore radius and pressure on permeability of both IOM and OM as well as effects of Langmuir parameters on OM are investigated. Moreover, the effect of total organic content and distribution on the apparent permeability of the reconstructed shale matrix is also studied. It is found that the distribution of OM and IOM has a negligible influence on apparent permeability, whereas the total organic content and the surface diffusion play a significant role in gas transport in shale matrix.

2016

One of the great challenges in modeling fluid flow in shale system is the existence of heterogeneities at different scales. Heterogeneity is not new to researchers studying reservoir characterization. However, in shale strata heterogeneities exist at different scales, i.e., from molecular scale to multiwell scale. While the goal is to predict gas and oil production in a section of reservoir (single well or multiple wells), we learned that processes at very small scale control the production at well scale. We have started a comprehensive research to integrate porosity and permeability, hence fluid flow at different scales. The research includes numerous mathematical and numerical models along bench experiments to validate our models (Figure 1). Molecular scale. At the molecular scale we study the interaction of fluid molecules (gas and liquid, hydrocarbons and aqueous) with pore inner walls [1]. The molecular scale research provides slip coefficients for further implementation in flu...

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.

Journal of Natural Gas Science and Engineering, 2015

Hydrocarbon production from liquid shale plays presents numerous challenges to modeling and understanding, specifically due to heterogeneity and low permeability. With the aid of the recent advances in high resolution characterization techniques, the current work proposes a partitioning scheme to divide porous media in shale into three different sub-media (porosity systems): inorganic matter and kerogen (in the shale matrix), along with fracture network (natural or hydraulic). A significant advantage of the presented model is its flexibility to incorporate different petrophysical and geological properties to each sub-media. Such capability extends the applicability of our approach to almost all carbon rich mudrocks with different levels of heterogeneity. Various production scenarios were then simulated to evaluate performance of the model. Although a very rich source of hydrocarbon, our results show that relatively high capillary pressure and very low rock permeability hinder oil production in organic-rich shale. Additionally, excessive pressure drop in the near fracture region and localized large gas to oil mobility ratio was observed to impact oil production rate.

A statistical technique for the pore-scale analyses of heterogeneity and representative elemental volume (REV) in unconventional shale rocks is hereby presented. First, core samples were obtained from shale formations. The images were scanned using microcomputed tomography (micro-CT) machine at 6.7 lm resolution with voxels of 990 9 990 9 1000. These were then processed, digitised, thresholded, segmented and features captured using numerical algorithms. This allows the segmentation of each sample into four distinct morphological entities consisting of pores, organic matter, shale grains and minerals. In order to analyse the degree of heterogeneity, Eagle Ford parallel sample was further cropped into 96 subsamples. Descriptive statistical approach was then used to evaluate the existence of heterogeneity within the subsamples. Furthermore, the Eagle Ford parallel and perpendicular samples were analysed for volumetric entities representative of the petrophysical variable, porosity, using corner point cropping technique. The results of porosity REV for Eagle ford parallel and perpendicular indicated sample representation at 300 lm voxel edge. Both pore volume distribution and descriptive statistical analyses suggested that a wide variation of heterogeneity exists at this scale of investigation. Furthermore, this experiment allows for adequate extraction of necessary information and structural parameters for pore-scale modelling and simulation. Additional studies focusing on re-evaluation at higher resolution are recommended.

Stratigraphy and Timescales, 2020

In recent years, unconventional hydrocarbon reservoirs (UHRs), specifically shale gas plays, have become a vast source of economically viable hydrocarbons, in response to better drilling and stimulation techniques. To further improve recovery, more detailed pore network modeling needs to be conducted by means of detailed pore network characterizations, based upon predefined pore size and pore type classification schemes. Through the quantification of the nano/microporous properties of the pore network, a better understanding on how hydrocarbon storage and migration phenomena operate within UHRs and how well they might respond to stimulation can be developed. Kasimovian-Gzhelian (Late Carboniferous) lacustrine sediments from the Upper Pastora Formation of the Ciñera-Matallana coalfield, NW Spain, were investigated to identify the potential for shale gas, by conducting a detailed pore network analysis using SEM-based porosity data, alongside traditional methods of formation evaluation. Here we show that the Upper Pastora Formation demonstrates shale gas potential and that the nanoporous network is a complex multifaceted and multi-scaled system composed of various pore types and sizes, each with specific dynamic properties and varying contributions toward total porosity. The present contribution provides a full pore network characterization and quantification, based on pore type and size, followed by a quantification of the porosity percentage held within each pore type and size. This work will provide an insight into the need for pore network characterizations alongside pore property quantifications with regard to computational fluid flow models and as such the need to carry out this work in conjunction with more traditional methods of shale gas exploration.