Investigation of Gas Transport in Shale Reservoirs Using Multiscale Modeling and Principal Component Analysis
Authors: Chen Cheng 
Published: September 2015

Abstract
Upscaling of gas transport in shales is challenging because of the multiple scales of transport processes. Rock characterization using nanometer-scale digital rock technologies can capture fundamental geometrical and transport properties, but the obtained information is usually highly localized and contains significant uncertainties. An effective upscaling method is thus needed to propagate the pore-scale information across multiple spatial scales. A modified dual-porosity model was proposed to study multiscale gas transport in shales. The model consists of two domains, a kerogen domain, and an inorganic matrix. Within kerogen, gas transport is dominated by molecular diffusion and nonlinear adsorption and desorption. Within inorganic matrix, gas transport is dominated by convection and diffusion. A mass-exchange-rate coefficient is used to describe gas transport between kerogen and inorganic matrix. The modified dual-porosity model was used to perform history matching of a pressure-pulse-decay experiment in the laboratory. The four input parameters were absolute permeability and diffusivity within inorganic matrix, mass-exchange-rate coefficient between kerogen and inorganic matrix, and gas desorption-rate coefficient within kerogen; these parameters were solved using nonlinear optimization. The long tail of the pressure decline curve was well-captured by the model, implying it accounted for both fast- and slow-transport mechanisms. Permeability enhancement resulting from slip boundary and Knudsen diffusion was limited due to the relatively high pressure. Sensitivity analysis was conducted to study the impact of input variation on model output. There was a competing relationship between convection and diffusion within inorganic matrix; fast convection hindered diffusive transport, while with slow convection diffusive transport significantly affected pressure decline. Therefore, diffusive transport within inorganic matrix cannot be simply ignored. The effects of gas transport within kerogen and between kerogen and inorganic matrix depended significantly on the transport rate within inorganic matrix; when convection within inorganic matrix was slow, the transport processes within kerogen did not affect pressure decline in the short term; in contrast, when convection within inorganic matrix was fast, the transport processes within kerogen significantly affected the pressure decline in the short term. Thus, the impact of the transport processes within the slower domain depends primarily on the transport rate within the faster domain; this is referred to as hierarchical dependence. The principal component analysis (PCA) method was applied to study the continuous movement of the pressure decline curve resulting from input parameter variation; increased convective and diffusive transport rates within inorganic pores expedited pressure decline; conversely, increased mass-exchange-rate and desorption-rate coefficients slowed the pressure decline in the short term, but expedited pressure decline in the long term, when convection within inorganic matrix was fast. The modified dual-porosity model successfully captured the pressure decline curve measured in the laboratory. The interaction and interdependence between different transport processes were interpreted using the mechanisms of competing relationship and hierarchical dependence. PCA simultaneously processed hundreds of parameter realizations and the corresponding pressure decline curves; the ergodicity requirement was thus satisfied and the principal components of continuous curve movement can be extracted. The new modeling and analysis methods can advance the understanding of multiscale gas transport and consequently benefit storage evaluation and production prediction for shale gas recovery.