Faruk Civan

Differential quadrature for multi-dimensional problems

The technique of differential quadrature for the solution of partial differential equations, introduced by Bellman et al., is extended and generalized to encompass partial differential equations involving multiple space variables. Approximation formulae for a variety of first and second order partial derivatives and typical weighting coefficients are presented. Application of these formulae is demonstrated on the solution of the convection-diffusion equation for the two- and three-dimensional space dependent cases and for both the transient and steady-state dispersion of inert, neutrally buoyant pollutants from continuous sources into an unbounded atmosphere.

A Fully-Coupled Free and Adsorptive Phase Transport Model for Shale Gas Reservoirs Including Non-Darcy Flow Effects

Accurate modeling of gas through shale-gas reservoirs characterized by nano-meter pores where the effects of various non-Darcy flow regimes and the adsorbed-layer are important is presented and demonstrated by several examples. Quantification of gas transport may be accomplished using the transport equation that is valid for all flow regimes. This equation though needs further modification when transport is through a media where the gas is adsorbed onto the pore wall. In the presence of adsorption, there is a pore pressure dependent loss of porosity and cross-sectional area to free gas transport. The apparent gas permeability correction is accomplished for various flow regimes using the Knudsen number by consideration of the reduction of the cross-sectional area to free gas transport in the presence of adsorption. We show that transport in the adsorbed layer may contribute significantly in the total gas transport in these nanopores. An effective transport model is presented to account for the impact of adsorption through two mechanisms. First, we modify the transport equation to account for the pore-pressure dependent-reduction in the volume available to free gas transport; second, we model transport through the adsorbed layer using Fick’s law of diffusion. The coupled model is then compared to conventional transport models over a wide range of reservoir properties and conditions.

A comparative study of differential quadrature and cubature methods vis-à-vis some conventional techniques in context of convection-diffusion-reaction problems

Abstract This paper presents a comprehensive comparative study of the differential quadrature and cubature methods in relation to the conventional techniques of the finite difference and finite element methods. The basis of comparison is the numerical accuracy and the computational efficiency in terms of CPU time. This is done in context of linear and nonlinear convection-diffusion-reaction problems. In addition, this paper also provides a few innovations in the quadrature method. These include a modified quadrature formulation in which the Neumann boundary condition of the problem is directly incorporated into the weighting coefficient matrices and two other quadrature formulations in which the progressive solutions of the problem are carried out by a domain decomposition technique and by a Crank-Nicolson version of the quadrature method.

Convenient formulae for determination of relative permeability from unsteady-state fluid displacements in core plugs

Convenient interpretation formulae are presented and demonstrated for determination of relative permeability from unsteady-state, two-phase fluid displacements in laboratory core tests under constant rate or pressure conditions. These formulae allow the effective processing of the after-breakthrough immiscible fluid displacement data by considering constant fluid and core properties, negligible gravity effect, and sufficiently high flow rates to overcome the capillary end-effects. The fluid mobility and characteristic parameters of immiscible displacement processes are related by means of Darcys law and specially derived functions. Analyses of various experimental data demonstrate that the present analytic method uniquely and rapidly determines the relative permeability within the accuracies of the simplifying considerations, which may closely approximate the conditions of usual laboratory core tests.

Practical model for chemically induced formation damage

Abstract A phenomenological model to simulate formation damage by dissolution/precipitation, ion exchange, fines migration and clay swelling is presented. The model parameters are determined by an optimum history matching of the model predictions to laboratory core test data. The capability and validity of the model are demonstrated by comparing the model predictions with experimental data. This model can be used for diagnosis, evaluation, and simulation of reservoir formation damage during drilling, production, and chemical flooding processes.

Alteration of permeability by fine particle processes

Permeability reduction and skin effect caused by water sensitivity of clay particles in petroleum reservoirs is a primary source of decreasing well performance. Therefore, it is of paramount interest to the petroleum industry to understand the fundamental mechanisms leading to skin development and to find ways to alleviate this problem. Numerous studies have been reported in the literature addressing some aspect of permeability reduction phenomena. The applicability of these studies is limited to particular cases considered. What is needed is a fundamental approach to describe the particulate processes which will allow for later extension and modification as more data become available and our understanding of various processes advances. In this respect, Civan and Knapp (1987) took the approach of phenomenological modeling, in which all governing phenomena were described based on fundamental conservation laws and principles. They considered the combined effects of formation swelling and migration and retention of fine particles in porous media during flow for prediction of the permeability reduction. Specifically, their study was limited to the case of injection of a suspension of fine particles to porous media. This model was tested and confirmed using the data of Hart et al. (1960), who studied the effect of injecting brine containing dead bacteria into Berea cores. In this study, the model of Civan and Knapp (1987) is extended to include the swelling and capture of clay particles from the pore surface by fluid shear. The extended model considers two distinct sources of particles: those directly generated within the porous media and others previously deposited in porous media from the flowing suspension of particles as shown in Fig. 1. Addition of this feature enables the model to simulate a wide variety of realistic cases involving particulate processes in petroleum reservoirs. This model is verified using the data of Hart et al. (1960), Gruesbeck and Collins (1982), and Khilar and Fogler (1983). In each case, however, some of the information required for simulation is missing. Therefore, the missing data are approximated based on the description of the experimental system and common knowledge available in the literature. Various model parameters are determined using the statistical parameter identification method described by Kerig and Watson (1986). It is shown that the model can reproduce the fundamental characteristics of the experimental measurements within the uncertainties of the experimental data.

Porous-Media Momentum Equation for Highly Accelerated Flow

A new porous-media momentum (capillary-orifice model) equation has been developed to account for unsteady flow through porous media. The equation contains not only the familiar permeability and non-Darcy factor terms but also momentum flux and acceleration terms. An analysis of the order of magnitude of these terms indicates when they are important.

Microscopic Dynamics of Water and Hydrocarbon in Shale-Kerogen Pores of Potentially Mixed-Wettability

Distribution of alkanes and water in organic pores of shale, referred to as kerogen, is essential information required for estimation of shale-reservoir oil- and gas-in-place, adsorption of hydrocarbon, and fate of frac-water. A practical modeling approach is presented for proper description of the kerogen pore systems with different mixed wettability, surface roughness, tortuous paths, and material disorder. Three kerogen models, namely activated kerogen, kerogen free of active sites, and grapheme-slit pore, with proper surface-oxidized functional groups and high-temperature-and-pressure maturation, are constructed by simulation. Distribution of octane and water in the organic pores of these models is predicted by molecular dynamics simulation. Comparison of results reveals the importance of accurate characterization of kerogen pore systems by particular pore morphology, surface activation, and pore size. The improved kerogen models provided here are shown to determine the placement, distribution, and trapping of frac-water in shale depending on the maturity of the kerogen within organic-rich shales. Copyright 2013, Society of Petroleum Engineers.

Modeling Formation Damage by Asphaltene Deposition During Primary Oil Recovery

Asphaltene precipitation and deposition during primary oil recovery and resulting reservoir formation damage are described by a phenomenological mathematical model. This model is applied using experimental data from laboratory core flow tests. The effect of asphaltene deposition on porosity, permeability, and the productivity of vertical wells in asphaltenic-oil reservoirs are investigated by simulation.

Formation damage and filter cake buildup in laboratory core tests: Modeling and model-assisted analysis

A mathematical model for the analysis of formation damage in laboratory core tests is presented. The model considers filter cake buildup on sand face, invasion of external particles, release of formation fines, migration and retention of external particles and formation fines, interphase transfer of particles, and alteration of porosity and permeability. The effects of wettabilities of fine particles and pore surfaces, relative permeabilities and capillary pressure on formation damage in two-phase flow conditions are also included. Simulation results from the model are in good agreement with experimental results from core tests. This model can be used for the analysis of formation damage due to particulate processes in laboratory core tests.