Permeability identification of a weakly permeable partially saturated porous rock

The present paper deals with the determination of permeability in partially saturated conditions for weakly permeable porous continua such as argillites or deep clayey formations. The permeability can be deduced from measurements of transient weight loss of a sample submitted to a laboratory drying test: a decrease of relative humidity is imposed by saline solution in an hermetic chamber. Assumptions of constant gas pressure equal to atmospheric pressure and of negligible Fickean diffusive transport of vapour are adopted. The only transport phenomenon taken into account inside the sample is the Darcean advective transport of the water liquid. The forward problem is solved by following two modelling approaches: a linear one and a nonlinear one. The parameter identification procedure is based upon the solution of corresponding inverse problems. In the two cases, the Levenberg–Marquardt algorithm has been used for the minimization problem. In the linear approach, the solution of the forward problem is explicit. In the non linear approach, finite volume method for the spatial discretization combined with a Newton–Raphson algorithm has been used to solve the non linear forward problem. The identification method enables variations of permeability and capillary capacity to be estimated. Comparisons between linear and non linear approaches show that the first one is useful to give mean values and order of magnitude of permeability and capacity. A more complete information is deduced from the non linear approach as variations of equivalent capacity and permeability during a test are significant in most cases. The analysis of the obtained results shows that the basic modelling assumption of constant gas pressure inside the sample would not be relevant for lower range of relative humidities and liquid permeability than those investigated.     

Effect of Reactive Surface Areas Associated with Different Particle Shapes on Chemical-Dissolution Front Instability in Fluid-Saturated Porous Rocks

In this article, the effect of reactive surface areas associated with different particle shapes on the reactive infiltration instability in a fluid-saturated porous medium is investigated through analytically deriving the dimensionless pore-fluid pressure-gradient of a coupled system between porosity, pore-fluid flow and reactive chemical-species transport within two idealized porous media consisting of spherical and cubic grains respectively. Compared with the critical dimensionless pore-fluid pressure-gradient of the coupled system, the derived dimensionless pore-fluid pressure-gradient can be used to assess the instability of a chemical dissolution front within the fluid-saturated porous medium. The related theoretical analysis has demonstrated that (1) since the shape coefficient of spherical grains is greater than that of cubic grains, the chemical system consisting of spherical grains is more unstable than that consisting of cubic grains, and (2) the instability likelihood of a natural porous medium, which is comprised of irregular grains, is smaller than that of an idealized porous medium, which is comprised of regular spherical grains. To simulate the complicated morphological evolution of a chemical dissolution front in the case of the chemical dissolution system becoming supercritical, a numerical procedure is proposed for solving this kind of problem. The related numerical results have demonstrated that the reactive surface area associated with different particle shapes can have a significant influence on the morphological evolution of an unstable chemical-dissolution front within fluid-saturated porous rocks.     

Modeling of Heat and Mass Transfer in a Fractured Porous Medium

While fractured formations are possibly the most important contributors to the production of oil worldwide, modeling fractured formations with rigorous treatments has eluded reservoir engineers in the past. To date, one of the most commonly used fractured reservoir models remains the one that was suggested by Warren and Root nearly four decades ago. In this paper, a new model for fractures embedded in a porous medium is proposed. The model considers the Navier-Stokes equation in the fracture (channel flow) while using the Brinkman equation for the porous medium. Unlike the previous approach, the proposed model does not require the assumption of orthogonality of the fractures (sugar cube assumption) nor does it impose incorrect boundary conditions for the interface between the fracture and the porous medium. Also, the transfer coefficient between the fracture and matrix interface does not need to be specified, unlike the cases for which Darcy's law is used. In order to demonstrate the usefulness of the approach, a two-dimensional model of a fractured formation is developed and numerical simulation runs conducted.

The proposed model is derived through a series of finite element modeling runs for various cases using the Navier-Stokes equation in the channel while maintaining the Brinkman equation in the porous medium. Various cases studied include different fracture orientations, fracture frequencies, and thermal and solutal constraints. The usefulness of the proposed model in modeling complex formations is discussed. Finally, a series of numerical runs also provided validity of the proposed model for the cases in which thermal and solutal effects are important. Such a study of double diffusive phenomena, coupled with forced convection, in the context of fractured formations has not been reported before.     

The effects of micro-defects and crack on the mechanical properties of metal fiber sintered sheets

The effects of three types of defect (i.e., two micro defects—broken fibers and separation of fiber joints and one macro defect—crack) on the mechanical properties of porous metal fiber sintered sheets (MFSSs) are investigated by a combination of numerical simulation, analytical modeling, and experimental test. All simulations are based upon the previously developed micromechanics random beam model (Jin et al., 2013). Broken fibers are realized by removing cell edges (i.e., fibers between two joints) in an otherwise perfect model. Their induced decreases in the elastic moduli and strengths are found to be much lower than those of two dimensional (2D) foams and Kagome grids. For the defect in the form of separation of fiber joints, both analytical and numerical models are developed. The predicted linear decreases in the moduli and strengths (except for the compressive strength) with increasing number of separated fiber joints indicate that MFSSs be insensitive to the defect of joint separation. To explore the effect of crack, fracture toughness of MFSSs is measured and is found to be significantly higher than that of metal foams of the same relative density (i.e., volume fraction of the constituent solid material). The underlying ductile mechanism of MFSSs is further investigated by numerical simulations, showing that plastic deformation spreads all over the fibers in ligament rather than concentrates around crack tip. This study shows that MFSSs are superior in view of their resistance to the considered micro-defects and crack.