Gas flow through shale
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The growing demand for energy provides an incentive to pursue unconventional resources. Among these resources, tight gas and shale gas reservoirs have gained significant momentum because recent advances in technology allowed us to produce them at an economical rate. More importantly, they seem likely to contain a significant volume of hydrocarbon. There are, however, many questions concerning hydrocarbon production from these unconventional resources. For instance, in tight gas sandstone, we observe a significant variability in the producibilities of wells in the same field. The heterogeneity is even present in a single well with changes in depth. It is not clear what controls this heterogeneity. In shale gas, the pore connectivity inside the void space is not well explored and hence, a representative pore model is not available. Further, the effects of an adsorbed layer of gas and gas slippage on shale permeability are poorly understood. These effects play a crucial role in assigning a realistic permeability for shale in-situ from a laboratory measurement. In the laboratory, in contrast to in-situ, the core sample lacks the adsorbed layer because the permeability measurements are typically conducted at small pore pressures. Moreover, the gas slippages in laboratory and in-situ conditions are not identical. The present study seeks to investigate these discrepancies. Drainage and imbibition are sensitive to pore connectivity and unconventional gas transport is strongly affected by the connectivity. Hence, there is a strong interest in modeling mercury intrusion capillary pressure (MICP) test because it provides valuable information regarding the pore connectivity. In tight gas sandstone, the main objective of this research is to find a relationship between the estimated ultimate recovery (EUR) and the petrophysical properties measured by drainage/imbibition tests (mercury intrusion, withdrawal, and porous plate) and by resistivity analyses. As a measure of gas likely to be trapped in the matrix during production---and hence a proxy for EUR---we use the ratio of residual mercury saturation after mercury withdrawal (S[subscript gr]) to initial mercury saturation (S[subscript gi]), which is the saturation at the start of withdrawal. Crucially, a multiscale pore-level model is required to explain mercury intrusion capillary pressure measurements in these rocks. The multiscale model comprises a conventional network model and a tree-like pore structure (an acyclic network) that mimic the intergranular (macroporosity) and intragranular (microporosity) void spaces, respectively. Applying the multiscale model to porous plate data, we classify the pore spaces of rocks into macro-dominant, intermediate, and micro-dominant. These classes have progressively less drainage/imbibition hysteresis, which leads to the prediction that significantly more hydrocarbon is recoverable from microporosity than macroporosity. Available field data (production logs) corroborate the higher producibility of the microporosity. The recovery of hydrocarbon from micro-dominant pore structure is superior despite its inferior initial production (IP). Thus, a reservoir or a region in which the fraction of microporosity varies spatially may show only a weak correlation between IP and EUR. In shale gas, we analyze the pore structure of the matrix using mercury intrusion data to provide a more realistic model of pore connectivity. In the present study, we propose two pore models: dead-end pores and Nooks and Crannies. In the first model, the void space consists of many dead-end pores with circular pore throats. The second model supposes that the void space contains pore throats with large aspect ratios that are connected through the rock. We analyze both the scanning electron microscope (SEM) images of the shale and the effect of confining stress on the pore size distribution obtained from the mercury intrusion test to decide which pore model is representative of the in-situ condition. We conclude that the dead-end pores model is more representative. In addition, we study the effects of adsorbed layers of CH₄ and of gas slippage in pore walls on the flow behavior in individual conduits of simple geometry and in networks of such conduits. The network is based on the SEM image and drainage experiment in shale. To represent the effect of adsorbed gas, the effective size of each throat in the network depends on the pressure. The hydraulic conductance of each throat is determined based on the Knudsen number (Kn) criterion. The results indicate that laboratory measurements made with N₂ at ambient temperature and 5-MPa pressure, which is typical for the transient pulse decay method, overestimate the gas permeability in the early life of production by a factor of 4. This ratio increases if the measurement is run at ambient conditions because the low pressure enhances the slippage and reduces the thickness of the adsorbed layer. Moreover, the permeability increases nonlinearly as the in-situ pressure decreases during production. This effect contributes to mitigating the decline in production rates of shale gas wells. Laboratory data available in the literature for methane permeability at pressures below 7 MPa agree with model predictions of the effect of pressure.