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. We use the well-known pulse-decay experiment to estimate the main parameter of the APF, which is Darcy permeability. Our newly derived late-transient analytical solution and the late-transient numerical solution consistently match the pressure decay data and yield approximately the same estimated value for Darcy permeability at the typical core-sample initial pressure range and pressure difference. Other parameters of the APF may be determined from independent laboratory experiments; however, a pulse-decay experiment can be used to estimate the unknown parameters of the APF if multiple tests are performed and/or the parameters are strictly constrained by upper and lower bounds.
CO 2 storage compliance refers to the safe and consistent storage of a captured anthropogenic CO 2 slug in an underground geological structure. This paper investigates the storage compliance in coupled CO 2 enhanced oil recovery (EOR) and storage projects. Storage compliance requires an oilfi eld operator to maintain suffi cient CO 2 injection and storage capacities throughout an industrialscale CO 2 capture and EOR-storage operation. We investigate the uncertainty in two operational parameters that may raise a compliance consideration: annual captured CO 2 from the power plant and CO 2 injection loss in the oilfi eld. The objective is to maintain suffi cient CO 2 injection and storage capacities and maximize the economic benefi ts from the EOR-storage operation. We formulate and optimize the storage compliance problem using the method of optimization with Monte Carlo simulation. The results show that appropriate adjustment of the water-alternating-gas (WAG) ratio increases both the compliance and the economic benefi ts. Also, a CO 2 storage back-up in a saline aquifer allows the oilfi eld operator to implement more profi table EOR-storage designs. A risk-seeking operator may practice the saline aquifer back-up option to simultaneously maximize the benefi ts and mitigate the risk of storage capacity shortage. Finally, EOR-storage operation is less effi cient than aquifer storage in terms of storage effi ciency, and considerably more profi table in terms of tangible economic benefi ts.
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