Mathematical Modeling of Extended Interface During Gravity Drainage With Application to CO2 Sequestration
Arfaei Malekzadeh, Farshad
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Removal of CO2 directly from anthropogenic sources (capture) and its disposal in geological formations can take place for medium-term time periods (storage), or it can be permanent (sequestration), with the CO2 eventually becoming dissolved in the aqueous phase. The latter is the main subject of this dissertation. Carbon dioxide sequestration covers a wide range of strategies and alternatives. The main objective of CO2 sequestration alternatives is secure disposal of carbon in large amounts and for a lengthy time scale (typically 1000 years). Injection of CO2 into subsurface formations is generally considered as the main option for CO2 sequestration. Geological sequestration through injection covers a broad variety of target formations: disposal in depleted oil and gas reservoirs, trapping in oil reservoirs, replacing CH4 in coal bed methane recovery processes, trapping in deep aquifers, and salt cavern placement are the major CCS alternatives in geologic formations. In this thesis, hydrogeologic interaction between the injectant (CO2) and the host fluid (saline water) during injection is the main subject of the project. Because of the density and viscosity contrast of displacing and displaced fluids, the pattern of saturation progression is complicated. A set of semi-analytical solutions is developed for quick estimation of the position of isosats (contours of saturation) during primary injection in homogenous cases with simple geometry. All of the mathematical solutions are developed based on two assumptions; incompressible fluids and rocks and vertical equilibrium (capillary-gravity condition) for geometries with large aspect ratio (L >> H). First, a series of analytical solutions for primary drainage for a set of linear relative permeability functions is developed. The first analytical solution is based on the assumption of locally linearized Leverett-J functions, and by using the method of characteristics, a formulation for the isosats’ geometry is obtained. A semi-analytical solution is then proposed for calculation of the position of isosats with linearized relative permeability functions and arbitrary capillary-saturation correlation. The analytical solution is extended to incorporate a specific form of nonlinearity of the relative permeability function. Nonlinear relative permeability functions are also incorporated in another semi-analytical solution, and the positions of the isosats for any arbitrary Leverett-J function and relative permeability functions are developed. Sequential gas-saline injection is also modeled in that chapter. For approximate verification of the analytical solutions, a FEM numerical model is developed and the results of the analytical solutions are compared with the numerical solutions. These new analytical solutions provide powerful tools for prediction of saturation distribution during injection in vertical and horizontal wells, as well as for carrying out stochastic assessments (Monte Carlo simulations) and parametric weight assessment. The domain of applications of the new solutions go far beyond the limited question of CO2 sequestration: they can be used for injection of any less viscous fluid into a reservoir, whether the fluid is lighter or denser than the host fluid (gas injection, water-alternating gas injection, water injection into viscous oil reservoirs, solvent injection).