Upstream weighting and mixed finite elements in the simulation of miscible displacements
Vertex centred Discretization of Two-Phase Darcy flows on General Meshes
This paper concerns the discretization of multiphase Darcy flows, in the case of heterogeneous anisotropic porous media and general 3D meshes used in practice to represent reservoir and basin geometries. An unconditionally coercive and symmetric vertex centred approach is introduced in this paper. This scheme extends the Vertex Approximate Gradient scheme (VAG), already introduced for single phase diffusive problems in [9], to multiphase Darcy flows....
Vertical compaction in a faulted sedimentary basin
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy’s law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
Vertical compaction in a faulted sedimentary basin
In this paper, we consider a 2D mathematical modelling of the vertical compaction effect in a water saturated sedimentary basin. This model is described by the usual conservation laws, Darcy's law, the porosity as a function of the vertical component of the effective stress and the Kozeny-Carman tensor, taking into account fracturation effects. This model leads to study the time discretization of a nonlinear system of partial differential equations. The existence is obtained by a fixed-point argument....
Wall driven steady flow and heat transfer in a porous tube
Wax deposition in crude oils: a new approach
The complex phenomenon of solid wax deposition in wax saturated crude oils subject to thermal gradients has been treated in a number of papers under very specific assumptions (e.g. thermodynamical equilibrium between dissolved wax and the wax suspended in the oil as a crystallized phase). Here we want to consider a more general framework in which thermodynamical equilibrium may not exist, the whole system may form a gel-like structure in which the segregated solid wax has no diffusivity, the thermal...
Weak solutions for a well-posed Hele-Shaw problem
We analyze existence and uniqueness of weak solutions to the well-posed Hele-Shaw problem under general conditions on the fixed boundaries and non-homogeneous governing equation in the unknown domain and non-homogeneous dynamic condition on the free boundary. Our approach allows us also to minimize the restrictions on the boundary and initial data. We derive several estimates on the solutions in spaces, prove a comparison theorem, and show that the solution depends continuously on the initial...
Аналоговый метод решения краевых задач напорной фильтрации в неоднородном грунте
Асимптотические задачи, связанные с уравнением теплопроводности в перфорированных областях
Вариационные свойства некоторых обратных краевых задач фильтрации
Достаточные условия однолистности решения обратной задачи теории фильтрации при наклонном водоупоре
Задача о продвижении поверхности контактного разрыва при фильтрации несмешивающихся сжимаемых жидкостей (задача Веригина)
Исследование влияния неоднородности ядра каменно-земляной плотины на фильтрационные характеристики
Исследование задачи фильтрации в двухслойной прямоугольной перемычке
Исследование разностной схемы для нелинейний стационарной задачи теории фильтрации
Исследование распространения фильтрационных волн давления в пластах переменной толщины
К определению функций тока в неоднородных нефтяных пластах
Конечная скорость распространения возмущений в многомерных задачах двухфазной фильтрации
Корректные постановки начально-краевых задач для уравнений фильтрации жидкости с запаздыванием
Мгновенное возникновение особенностей у решения вырождающегося параболического уравнения.