Improved permeability prediction for heterogeneous porous media by bundle-of-leaky-tubes with cross-flow model

An inherently limiting assumption of the Kozeny-Carman equation of permeability is not allowing interaction across the parallel flow through a bundle of tubes model. While this condition can be observed for flow through sufficiently high porosity homogeneous porous media, the Kozeny-Carman equation cannot represent the permeability of low porosity heterogeneous porous media. This paper presents a modeling of flow through a leaky-flow tube allowing interactions with flow occurring in other flow tubes in a bundle of tubes model of porous media. Then, the effect of such interactions is taken into account by incorporating the pore connectivity by means of the coordination number. The deviations of the real porous structure from the assumption of a bundle of tubes of uniform size are taken into account by the fractal representations. This leads to the modification of the Kozeny-Carman equation to a power-law equation of permeability whose parameters vary by well-described relationships

Performance comparison of the finite-difference, practical-finite-analytic, differential-quadrature, and differential-cubature methods for solving porous media immiscible fluids transport

Reviews and comparisons of the finite-difference, differential-quadrature, differential-cubature, finite-analytic, and practical-finite-analytic methods are presented. Numerical solution of immiscible fluids transport in porous media are illustrated. The cubature and practical finite-analytic methods are shown to have apparent advantages over the other methods because the numerical solution schemes are derived directly from the specific problems of interest

Application of differential quadrature to transport processes

AbstractThe methodology and numerical solution of problems concerning transport processes via the method of differential quadrature are presented. Application of the method is demonstrated by solving a simple one-dimensional, time-dependent (transient) diffusion process involving an irreversible reaction without any flux across the end boundary. In addition, the same technique is used (for the first time to the authors' knowledge) to solve a steady-state problem. For this purpose, a convection-diffusion problem involving an irreversible reaction is considered. The demonstration is carried out in two ways, (1) using the Bellman et al. technique which employs approximation formulas for higher order partial derivatives derived by iterating the linear quadrature approximation for the first order partial derivative, and (2) using individual quadratures to approximate the partial derivatives of first, as well as higher orders, as suggested by Mingle. Both approaches give the same results; however, the latter saves an appreciable amount of iterative computing effort despite the fact that it requires separate weighting coefficients for each individual quadrature. Since the technique of differential quadrature can produce solutions with sufficient accuracy even when using as few as three discrete points, both the programming task and computational effort are alleviated considerably. For these reasons the differential quadrature approach appears to be very practical in solving a variety of problems related to transport phenomena

Transient Wax Gel Formation Model for Shut-In Subsea Pipelines

Physics of wax gel formation during shut-in is analyzed and described over a crosssection of a typical subsea pipeline. Two regions are identified during this process: the liquid and gel regions. Phase transition is assumed to occur at the liquid-gel interface. Unsteady-state heat and mass transfer models are proposed for each region. Two diffusion streams are evaluated: the dissolved wax molecules moving from the pipe center toward the wall due to temperature gradient and subsequently concentration gradient and the wax molecules diffusing from the liquid-gel interface into the gel deposit. This model is essentially the modification of the model given by Bhat et al. [1] which considered transient heat transfer and neglected mass transfer of wax molecules through the gel deposit and the model by Singh et al

Effective permeability upscaling from heterogenous to homogenous porous media

An effective method to upscale permeability is presented to represent a heterogeneous reservoir with homogeneous permeability and porosity values. As a result, there is no need to deal with dual-porosity or dual-permeability models in reservoir simulations. Thus, the required CPU time for reservoir production and flow simulations is reduced significantly

TRANSIENT WAX GEL FORMATION MODEL FOR SHUT-IN SUBSEA PIPELINES

ABSTRACT Physics of wax gel formation during shut-in is analyzed and described over a cross-section of a typical subsea pipeline. Two regions are identified during this process: the liquid and gel regions. Phase transition is assumed to occur at the liquidgel interface. Unsteady-state heat and mass transfer models are proposed for each region. Two diffusion streams are evaluated: the dissolved wax molecules moving from the pipe center towards the wall due to temperature gradient and subsequently concentration gradient and the wax molecules diffusing from the liquid-gel interface into the gel deposit. This model is essentially the modification of the model given by Bhat et al [1] which considered transient heat transfer and neglected mass transfer of wax molecules through the gel deposit and the model by Singh et al This paper presents a transient-state formulation circumventing the limitations of these previous models and better represents the true cooling and gelation process occurring in a shut-in subsea pipeline filled with waxy crude