Gas reservoirs with low permeability (k<0.1 mD) are among the unconventional reservoirs and are commonly termed as "Tight Gas Reservoirs". In conventional gas reservoirs that have high permeability, the flow of gas is basically controlled by the reservoir permeability and it is calculated using the Darcy equation. In these reservoirs, gas flow due to gas diffusion is ignored compared to Dar...

We analyze non-stationary, but stabilized flow towards a well in a reservoir with impermeable external boundaries (volumetric reservoir.) Two operating conditions: fixed production rate and given wellbore pressure are considered. Determination of conditions under which the Productivity Index (PI) is time invariant is the focus of our study. For the fixed production rate case the flow regime pro...

Sediment profiles in open channels are usually predicted by advection-diffusion models. Most basic forms consider the terminal settling velocity of a single particle in still clear water. Alternative forms account for hindered settling at higher concentrations. It is not known, however, how these modifications relate to mass and momentum conservation of each phase. For dilute flow, it is known ...

We present a numerical model for two-phase porous media ̄ow, where the phases are separated by a sharp interface. The model is based on a uni®ed pressure equation, and an advection equation for tracking a pseudo-concentration function. The zero-level set of this function de®nes the interface between the ̄uids. The ®nite element method is used for spatial discretization, with local grid re®nemen...

We consider a stationary two-phase Stefan problem with convection. The problem is governed by a coupled system involving a nonlinear Darcy law and the energy balance equation with second member in L 1. We prove existence of at least one weak solution of the problem, using the penalty method and the Schauder xed point principle.

Abstract. In this work we deal with the no-slip drift-flux model for gas-liquid flow dynamics. We focus on a situation where there is a free interface separating the gas-liquid mixture from a pure gas region which takes a positive pressure p∗. This situation is highly relevant for gas-liquid flow in the context of wellbore operations. Previous works have assumed that there is vacuum, i.e., the ...