Keywords: non–Darcy flow, Buckley–Leverett, Forchheimer, Barree–Conway, CO2, carbon dioxide, carbon sequestration, composite formation, aquifers, reservoirs, immiscible fluids, linear composite porous media, radial composite porous media, wellbore, numerical simulation, non–Darcy displacement, petroleum industry, oil industry, fluid displacement
Non–Darcy displacement in linear composite and radial aquifer during CO2 sequestration
This paper presents Buckley–Leverett type analytical solutions for non–Darcy displacement of two immiscible fluids in linear and radial composite porous media. High velocity or non–Darcy flow commonly occurs in the vicinity of the wellbore because of smaller flowing cross–sectional areas. However, the effect of such non–Darcy flow has been traditionally ignored. To examine the physical behaviour of multiphase immiscible fluids in non–Darcy displacement, an extended Buckley–Leverett type of solution is discussed. There exists a Buckley–Leverett type solution for describing non–Darcy displacement in a linear homogeneous reservoir. This work extends the solution to flow in linear and radial composite flow systems. We present several new Buckley–Leverett type analytical solutions for non–Darcy flow in more complicated flow geometries of linear and radial composite reservoirs, based on non–Darcy flow models of Forchheimer and Barree–Conway. As application examples, we use the analytical solutions to verify numerical simulation results as well as to discuss non–Darcy displacement behaviour. This theory of non–Darcy flow displacement is applied to evaluate the flow behaviour near wellbore areas during CO2 sequestration. The results show how non–Darcy displacement during CO2 injection in linear and radial composite systems is controlled not only by relative permeability, but also by non–Darcy coefficients, characteristic length, injection rates, as well as discontinuities in the saturation profile across the interfaces between adjacent composite flow domains. [Received: April 27, 2012; Accepted: April 29, 2013].