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 Author Dutta, Sourav Title Mathematical Models and Numerical Methods for Porous Media Flows Arising in Chemical Enhanced Oil Recovery URL http://hdl.handle.net/1969.1/165997 Publication Date 2017 Date Accessioned 2018-02-05 21:20:03 Degree PhD Discipline/Department Mathematics Degree Level doctoral University/Publisher Texas A&M University Abstract We study multiphase, multicomponent flow of incompressible fluids through porous media. Such flows are of vital interest in various applied science and engineering disciplines like geomechanics, groundwater flow and soil-remediation, construction engineering, hydrogeology, biology and biophysics, manufacturing of polymer composites, reservoir engineering, etc. In particular, we study chemical Enhanced Oil Recovery (EOR) techniques like polymer and surfactant-polymer (SP) flooding in two space dimensions. We develop a mathematical model for incompressible, immiscible, multicomponent, two-phase porous media flow by introducing a new global pressure function in the context of SP flooding. This model consists of a system of flow equations that incorporates the effect of capillary pressure and also the effect of polymer and surfactant on viscosity, interfacial tension and relative permeabilities of the two phases. We propose a hybrid method to solve the coupled system of equations for global pressure, water saturation, polymer concentration and surfactant concentration in which the elliptic global pressure equation is solved using a discontinuous finite element method and the transport equations for water saturation and concentrations of the components are solved by a Modified Method Of Characteristics (MMOC) in the multicomponent setting. We also prove convergence of the hybrid method by assuming an optimal O(h) order estimate for the gradient of the pressure obtained using the discontinuous finite element method and using this estimate to analyze the convergence of the MMOC method for the transport system. The novelty in this proof is the convergence analysis of the MMOC procedure for a nonlinear system of transport equations as opposed to previous results which have only considered a single transport equation. For this purpose, we consider an analogous single-component system of transport equations and discuss the possibility of extending the analysis to multicomponent systems. We obtain error estimates for the transport variables and these estimates are validated numerically in two ways. Firstly, we compare them with numerical error estimates obtained using an exact solution. Secondly, we also compare these estimates with results obtained from realistic numerical simulations of flows arising in enhanced oil recovery processes. This mathematical model and hybrid numerical procedure have been successfully applied to solve a variety of configurations representing different chemical flooding processes arising in EOR. We perform numerical simulations to validate the method and to demonstrate its robustness and efficiency in capturing the details of the various underlying physical and numerical phenomena. We introduce a new technique to test for the influence of grid alignment on the numerical results and apply this technique on the hybrid method to show that the grid orientation effect is negligible. We perform simulations using different types of heterogeneous permeability field data which include piecewise… Subjects/Keywords Surfactant-polymer flooding; Multicomponent two-phase flow; Global pressure; Capillary pressure; Finite Element Method; Modified Method of Characteristics; Convergence analysis; Error estimates; Numerical simulations; Heterogeneous permeability Contributors Daripa, Prabir (advisor); Howard, Peter (committee member); King, Michael J (committee member); Kuchment, Peter (committee member); Lazarov, Raytcho (committee member) Language en Country of Publication us Record ID handle:1969.1/165997 Repository tamu Date Retrieved 2020-08-05 Date Indexed 2020-08-12 Grantor Texas A & M University Issued Date 2017-07-28 00:00:00

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…flooding, the use of surfactant further improves oil recovery by reducing the capillary pressure between the aqueous and the oil phases and by reducing the residual saturation limits of the rock matrix. ASP flooding 4 in which Alkali is also used in the…

…the evolution of the fluid phases and the dissolved components will be presented in the next chapter. Here we introduce one more fundamental rock-fluid characteristic associated with multiphase flows in porous media known as the capillary pressure. At…

…turn, determines the contact angle which is used to define capillary pressure pc at the pore-scale. Intuitively, capillary pressure can be understood as the excess pressure that the non-wetting phase should have to keep the interface steady between two…

…static fluids [14]. This notion allows us to define capillary pressure in terms of the macroscopic field variables by using a static force balance across the interface in the following way pc = pnw − pw , (1.2) where pnw and pw are…

…compressible two-phase flows under the assumption of no mass transfer between the phases and taking into account the effects of gravity, capillary pressure and heterogeneity [18, 19]. Some existence results for this new formulation have been presented…

…effect of capillary pressure is neglected. We direct the readers to Daripa et al. [27] and the papers cited therein. Error estimates and convergence analysis have been carried out previously for the MMOC [55], the MMOCAA [60]…

…various flooding schemes for multicomponent flows like SP flooding in heterogeneous permeability fields have been presented. This dissertation is laid out as follows. In chapter 2, the global pressure formulation of the governing equations for polymer…

…flooding and SP flooding are derived and presented along with the various constitutive relations. These include relevant models of capillary pressure and relative permeability and their dependence on the water saturation and the concentrations of the…