Full Record

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 |

Sample Search Hits | Sample Images | Cited Works

…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…