Continuum-Scale Gas Transport Modeling in Organic Nanoporous Media Based on Pore-Scale Density Distributions

This paper presents a continuum-scale diffusion-based model informed by pore-scale data for gas transport in organic nanoporous media. A mass transfer and adsorption model is developed by considering multiple transport and storage mechanisms, including bulk diffusion and Knudsen diffusion for free phase, surface diffusion for sorbed phase, and multilayer adsorption. The continuum-scale diffusion-based governing equation is developed solely based on free phase concentration for the overall mass conservation of free and sorbed phases, carrying a newly-defined effective diffusion coefficient and a capacity factor to account for multilayer adsorption. Diffusion of free and sorbed phases is coupled through the pore-scale simplified local density method based on the modified Peng-Robinson equation of state for confinement effects. The model is first utilized to analyze pore-scale adsorption data from the krypton (Kr) gas adsorption experiment on graphite. Then we implement the model to conduct sensitivity analysis for the effects of pore size on gas transport for Kr-graphite and methane-coal systems. The model is finally used to study Kr diffusion profiles through a coal matrix obtained through X-ray micro-CT imaging. The results show that the sorbed phase occupies most of the pore space in organic nanoporous media due to multilayer adsorption, and surface diffusion contributes significantly to the total mass flux. Therefore, neglecting the volume of sorbed phase and surface diffusion in organic nanoporous rocks may result in considerable errors. Furthermore, the results reveal that implementing a Langmuir-based model may be erroneous for an organic-rich reservoir with nanopores during the early depletion period when the reservoir pressure is high.

Permeability of Organic-Rich Shale

Summary Measured permeability of an organic-rich shale sample varies significantly with applied laboratory conditions, such as the confining pressure, temperature, and the measurement fluid type. This indicates that the measured quantity is influenced by several mechanisms that add complexity to the measurement. The complexity is mainly caused by stress dependence of the matrix permeability. Also, it is because organic-rich shale holds significant volumes of fluids in sorbed (adsorbed, dissolved) states; sorption can also influence the permeability through its own storage and transport mechanisms. The stress-dependence and sorption effects on permeability could develop under the reservoir conditions and influence the production, although we currently do not have a predictive permeability model that considers their coexistence. In this work, this is accomplished by considering that the shale matrix consists of multiple continua with organic and inorganic pores. Stress dependency of the permeability comes along with slit-shaped pores, whereas the sorption effects are associated with nanoscale organic capillaries. A simple conceptual flow model with an apparent shale permeability is developed that couples the molecular-transport effects of the sorbed phase with the stress dependence of the slit-shaped pores. The simulation results show the impact of the permeability model on the production. Sensitivity analysis on the new permeability model shows that the stress dependence of the overall transport is significant at high pore pressure, when the effective stress is relatively low. Diffusive molecular transport of the sorbed phase becomes important as the stress gets larger and, hence, the slit-shaped pores close. The constructed apparent-permeability vs. pore-pressure curves show the dominance of the molecular transport as an increase in permeability characterized by appearance of a minimum permeability value at the intermediate values of the pressure. One can use the new permeability model easily in history matching a well performance and optimizing its production.

Production-Data Analysis of Gas Reservoirs With Apparent-Permeability and Sorbed-Phase Effects: A Density-Based Approach

Summary Accounting for depletion-dependent permeability and sorbed-phase effects is an important step toward achieving reliable analysis of production performance in unconventional gas systems. This study demonstrates how to account for pressure-dependent apparent-permeability (e.g., gas-slippage) and desorption effects in gas-production analysis of boundary-dominated data with a density-based approach. In this work, apparent-permeability and desorption models are incorporated into the original density-based approach by modifying the definitions of depletion-driven variables that are the basis of the density-based type of analysis. The proposed modification of the original approach successfully enables associated analysis techniques to be applicable to natural-gas reservoirs with gas slippage and adsorbed gas. Results indicate that by modifying the definitions of the depletion-driven variables, the density approach can effectively and successfully capture the effects from gas slippage and desorption. Through a number of case studies, we show that gas-flow rate can be successfully predicted by rescaling liquid solution with the modified density-based variables. As an illustration, we show that resource calculations able to fully take into account these effects are possible when long-term production data are available. This work details the methodology required to do so, and illustrates its application to production-data prediction analysis for unconventional assets.

Laboratory Measurement of Sorption Isotherm Under Confining Stress With Pore-Volume Effects

Summary For unconventional gas resources such as coal and organic-rich shale, sorbed phase is an important component of storage and transport calculations. Routine measurements of sorption are, however, performed separately from the porosity and permeability measurements. In this work, a new gas-storage measurement technique is proposed that combines the porosity and sorption measurements. Because the measurement is performed by use of core plugs under confining stress, it allows investigating the storage capacity for varying effective stress and incorporating the storage data into a subsequent permeability measurement under the same conditions. During the construction of the sorption isotherm in the laboratory with the volumetric (gas expansion) method, at each pressure step, the sorbed gas taken up by the sample reduces the pore volume (PV) of the sample. As a result, the initially determined PV at low pressure must be corrected at the beginning and at the end of the pressure step. This correction can be performed relatively easily during the routine sorption measurements with the crushed samples; however, it is a challenging task with core plugs under confining stress because at each pressure step the PV could also change as a result of pore compressibility. Our approach is based on a new analytical model of total gas storability developed to interpret the measured multiple-step pressure data on a graphical domain in which the storage-parameter estimation can be performed fast and accurately with a straight line. The approach considers both the compressibility and the sorbed-phase effects on the porosity and the sorption parameters. Experimental storage data of shale and coal samples with varying total organic content (TOC) and maturity are used to demonstrate the applicability of the analytical method to the measurements. The results show that the sorption measurements can be performed with increased accuracy and relatively fast. The work is important for organic-rich sample characterization in the laboratory, and for gas-in-place and transport calculations.