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Motivated by the reservoir engineering concept of the productivity index of a producing oil well in an isolated reservoir, we analyze a time dependent functional, diffusive capacity, on the solutions to initial boundary value problems for a parabolic equation. Sufficient conditions providing for time independent diffusive capacity are given for different boundary conditions. The dependence of the constant diffusive capacity on the type of the boundary condition (Dirichlet, Neumann or third-type boundary condition) is investigated using a known variational principle and confirmed numerically for various geometrical settings. An important comparison between two principal constant values of a diffusive capacity is made, leading to the establishment of criteria when the so-called pseudo-steady-state and boundary-dominated productivity indices of a well significantly differ from each other. The third type boundary condition is shown to model the thin skin effect for the constant wellbore pressure production regime for a damaged well. The questions of stabilization and uniqueness of the time independent values of the diffusive capacity are addressed. The derived formulas are used in numerical study of evaluating the productivity index of a well in a general three-dimensional reservoir for a variety of well configurations.

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This thesis describes a new dynamic network model for imbibition which is based on a physically realistic description of the complex dynamics of corner film flow, swelling and snap-off. The model shows that film flow is a capillary driven non-linear diffusive process and that the competition between snapoff and frontal displacements is rate dependent and results in rate dependent relative permeabilities and residual saturations. In contrast to previously published models in which length scales for snap-off are either specified a priori or calculated assuming steady-state film flow and constant film conductivities, in the present model, snap-off arises as a natural consequence of the fully transient nature of film flow and swelling. The network model is used to analyse the complex interaction between displacement rate, contact angle, aspect ratio and pore and throat shape on relative permeability and residual saturation. Computed relative permeabilities and residual saturations are compared with laboratory measurements reported in the literature. It is concluded that the magnitude of the rate effect on imbibition relative permeabilities and residual saturations for a particular rock microstructure and wettability condition depends largely on the pore-throat aspect ratio. Higher aspect ratios result in stronger rate effects than do smaller aspect ratios.

The use of foam-forming surfactants offers promise to improve sweep efficiency and mobility control for enhanced oil recovery (EOR). This thesis provides an in depth understanding of transport of surfactant and foam through porous media using a combination of laboratory experiments and numerical simulations. In particular, there are several issues in foam EOR processes that are examined. These include screening of surfactant adsorption onto representative rock surfaces, modeling of foam flow through porous media, and studying the effects of surface wettability and porous media heterogeneity. Surfactant adsorption onto rock surfaces is a main cause of foam chromatographic retardation as well as increased process cost. Successful foam application requires low surfactant adsorption on reservoir rock. The focus of this thesis is natural carbonate rock surfaces, such as dolomite. Surfactant adsorption was found to be highly dependent on electrostatic interactions between surfactants and rock surface. For example, the nonionic surfactant Tergitol 15-S-30 exhibits low adsorption on dolomite under alkaline conditions. In contrast, high adsorption of cationic surfactants was observed on some natural carbonate surfaces. XPS analysis reveals silicon and aluminum impurities exist in natural carbonates, but not in synthetic calcite. The high adsorption is due to the strong electrostatic interactions between the cationic surfactants and negative binding sites in silica and/or clay. There are a number of commercial foam simulators, but an approach to estimate foam modeling parameters from laboratory experiments is needed to simulate foam transport. A one-dimensional foam simulator is developed to simulate foam flow. Chromatographic retardation of surfactants caused by adsorption and by partition between phases is investigated. The parameters in the foam model are estimated with an approach utilizing both steady-state and transient experiments. By superimposing contour plots of the transition foam quality and the foam apparent viscosity, one can estimate the reference mobility reduction factor (fmmob) and the critical water saturation (fmdry) using the STARS foam model. The parameter epdry, which regulates the abruptness of the foam dry-out effect, can be estimated by a transient foam experiment in which 100% gas displaces surfactant solution at 100% water saturation. Micromodel experiments allow for pore-level visualization of foam transport. We have developed model porous media systems using polydimethylsiloxane. We developed a simple method to tune and pattern the wettability of polydimethylsiloxane (PDMS) to generate porous media models with specific structure and wettability. The effect of wettability on flow patterns is observed in gas-liquid flow. The use of foam to divert flow from high permeable to low permeable regions is demonstrated in a heterogeneous porous micromodel. Compared with 100% gas injection, surfactant-stabilized foam effectively improves the sweep of the aqueous fluid in both high and low permeability regions of the micromodel. The best performance of foam on fluid diversion is observed in the lamella-separated foam regime, where the presence of foam can enhance gas saturation in the low permeable region up to 45.1% at the time of gas breakthrough. In conclusion, this thesis provides new findings in surfactant adsorption onto mineral surfaces, in the methodology of estimating foam parameters for reservoir simulation, and in micromodel observations of foam flow through porous media. These findings will be useful to design foam flooding in EOR processes.

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No description available.

No description available.

We investigate how the formation of heterogeneity and structures in flows through explicit porous microstructures depends upon the geometric and topological observables of the porous medium. Using direct numerical simulations of single-phase, isothermal, laminar fluid flow through realistic three-dimensional stochastically generated pore structures, hereafter referred to as pore spaces, the characteristics of the resulting steady state velocity fields are related to physical characteristics of the pore spaces. The results suggest that the spatially variable resistance offered by the geometry and topology of the pore space induces a highly heterogeneous fluid velocity field therein. Focus is placed on three different length scales: macroscopic (cm), mesoscopic (mm), and microscopic (microns). At the macroscopic length scale, volume averaging is used to relate porosity, mean hydraulic radius, and their product to the permeability of the pore space. At the mesoscopic scale, the effect of a medium's porosity on fluid particle trajectory attributes, such as passage time and tortuosity, is studied. At the final length scale, that of the microscopic in-pore fluid dynamics, finite time Lyapunov exponents are used to determine expanding, contracting, and hyperbolic regions in the flow field, which are then related to the local structure of the pore space. The results have implications to contaminant transport, mixing, and how chemical reactions are induced at the pore-scale. A description of the adopted numerical methods to simulate flow and generate the pore space are provided as well.