Yannis C. Yortsos

Percolation theory of vapor adsorption—desorption processes in porous materials

A percolation model for adsorption—desorption phenomena in porous solids is developed. The model relates the sorption isotherm characteristics and the hysteresis observed to the pore space geometry (size distribution) and topology (connectivity) and the physical parameters of the process. Kelvins equation is taken to represent the process at the local (pore) level, while the porous solid is represented by a network of pores. The statistics of the pores occupied by vapor during adsorption or desorption are determined from Kelvins equation and the network properties. In contrast to adsorption, desorption processes (both primary and secondary) are strongly dependent on accessibility properties of the network. Exact analytical expressions are derived for the accessibility functions when the porous medium is represented by a Bethe lattice. These results generalize previous work in ordinary percolation. Alternatively, an algorithm is developed for regular lattices, and numerical results from Monte Carlo simulations in square lattices are also presented. The model is shown to predict major characteristics of both primary and secondary sorption isotherms and suggests methods for thei rinterpretation. This study is motivated and extends previous work by G. Mason (Proc. R. Soc. London A 390, 47 (1983)).

Optimization of fluid front dynamics in porous media using rate control. I. Equal mobility fluids

In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. For a fixed arrangement of injection and production points (sources and sinks), such optimization is possible by controling the injection rate policy. Despite its practical relevance, however, this aspect has received scant attention in the literature. In this paper, we provide a fundamental approach based on optimal control theory, for the simplified case when the fluids are miscible, of equal viscosity, and in the absence of dispersion and gravity effects. Both homogeneous and heterogeneous porous media are considered. From a fluid dynamics viewpoint, this is a problem in the deformation of material lines in porous media, as a function of time-varying injection rates. It is shown that the optimal injection policy that maximizes the displacement efficiency, at the time of arrival of the injected fluid, is of the “bang–bang” type, in which th...

Nucleation and pore geometry effects in capillary desorption processes in porous media

A percolation model previously developed by the authors for adsorption-desorption phenomena in porous solids (J. Colloid Interface Sci. 124, 162 (1988)), is extended to include nucleation effects during desorption, and to general size distributions of pore bodies and pore throats. Conditions under which nucleation is likely to be important are delineated. For such cases, desorption is treated as a growth problem with continuous generation of source sites. Accessibility functions are derived for Bethe lattice representations of the porous medium. Similar calculations are presented for the case when pore bodies and pore throats take arbitrary size distributions. The latter find also applications to other related processes in porous media. In view of the theory presented, the interpretation of experimental sorption isotherms is further discussed. 38 refs., 11 figs.

The Effect of Heterogeneity on In-Situ Combustion: The Propagation of Combustion Fronts in Layered Porous Media

This report extend the approach to heterogeneous systems, by considering the simpler case of in-situ combustion in layered porous media (and particularly to a two-layer model). Analytical models were developed to delineate the combined elects of fluid flow, reaction and heat transfer on the dynamics of combustion fronts in layered porous media, using as parameters the thermal coupling between the layers, the heat transfer to the surroundings and the permeability contrast.

On the Brinkman correction in unidirectional Hele-Shaw flows

We study the Brinkman correction to Darcy’s equation for unidirectional flows in a Hele-Shaw cell. Three examples, describing gravity-driven flow with variable density, pressure-driven flow with variable viscosity, and pressure-driven flow in a cell with a specific variation in aperture are discussed. In general, the Brinkman correction involves nonlocal terms, and it is not simply equal to an effective viscous shear stress involving the gap-averaged velocity. The latter is applicable at long wavelengths, however, provided that the viscosity is augmented by a prefactor equal to 12/π2.

The Effect of Heterogeneity on In-Situ Combustion: Propagation of Combustion Fronts in Layered Porous Media

Large fractions of heavy oil reserves remain in shallow reservoirs, consisting of relatively thin sands separated by nearly impermeable shales. A potential recovery method for heavy oil is in-situ combustion. Compared to other methods, in situ combustion involves the added complexity of exothermic chemical reactions and temperature-dependent kinetics. Previous theoretical work by the authors have focused on the process in a single layer [7]. In this report we try to extend the approach to heterogeneous systems, by considering the simpler case of in-situ combustion in layered porous media (and particularly to a two-layer model). Analytical models are developed to delineate the combined effects of fluid flow, reaction and heat transfer on the dynamics of combustion fronts in layered porous media, using as parameters the thermal coupling between the layers, the heat transfer to the surroundings and the permeability contrast. We find that in layered systems, the thermal coupling between layers leads to coherent traveling fronts, propagating at the same velocity. This coupling retards greatly fronts in the more permeable layers and accelerates only slightly those in the less permeable ones, until a common front velocity is attained. As in the single-layer case, there exists a unique solution, under adiabatic conditions, and multiple steady-state solutions, under non-adiabatic conditions. The latter lead to ignition and extinction conditions. We show that the layer thickness and the permeability contrast between the layers play a crucial role. Importantly, for a sufficiently large permeability contrast, relatively small layer thickness and under non-adiabatic conditions, steady-state propagation in the two layers cannot be sustained, and the process becomes extinct, even though, under the same conditions, sustained propagation would have been predicted for the equivalent single-layer problem with the average injection velocity. Simple constraints are derived to delineate this case. The analysis is useful for the understanding of the viability of in situ combustion in heterogeneous porous media.

Evaporative Cleanup of Water Blocks in Gas Wells

Gas flow into a wellbore can result in the evaporative cleanup of water blocks. This cleanup occurs primarily because the expansion of gas results in additional water being evaporated in the near-wellbore region. A study showed that the removal of water by the expanding gas leaves behind a saturation profile that is qualitatively different for low- and high-permeability rocks. As a result, the increase in gas relative permeability or the well productivity with time can vary substantially depending on the rock permeability and the well drawdown. A model was developed to determine the effect of evaporative cleaning on well productivity.

Visualization of steam injection in fractured systems using micromodels

We present visualization studies of hot water and steam injection in micromodel geometries that mimic a matrix-fracture system. Emphasis is placed on the matrix-fracture interaction during steam injection. We visualize the movement of steam and determine the conditions under which matrix penetration by steam occurs. More generally, the effectiveness of steam injection in displacing oil from the matrix is assessed. Displacement of oil was observed to occur by three mechanisms : a thermally-induced solution gas-drive, capillary imbibition of condensed water and displacement by steam, when the latter penetrated the matrix. Vaporization of light components at elevated temperatures generated an efficient solution-gas drive in the matrix, without the need for steam penetration. This also led to the formation of stable foam-like lamellae, which improved oil production by blocking the movement of steam and water in the fracture. This mechanism was also found to apply during hot water injection. Condensed water imbibed the matrix according to rules that govern imbibition of a fracture-matrix system. Steam penetration of the matrix occured when the steam rate exceeded a critical value, determined from drainage considerations. The results should be useful in modeling of steam injection in naturally fractured reservoirs.

Front Controllability in Two-Phase Porous Media Flow

The propagation of the front (i.e. the interface) between two immiscible fluids flowing through a porous medium is governed by convection, i.e. by the fluid velocities at the front, which in turn are governed by the pressure gradient over the domain. We investigated a special case of immiscible two-phase flow that can be described as potential flow, in which case the front is sharp and can be traced with a simple Lagrangian formulation. We analyzed the controllability of the pressure field, the velocity field and the front position, for an input in the form of slowly time-varying boundary conditions. In the example considered in this paper of order one equivalent aspect ratio, controllability of the pressures and velocities at the front to any significant level of detail is only possible to a very limited extent.Moreover, the controllability reduces with increasing distance of the front from the wells. The same conclusion holds for the local controllability of the front position, i.e. of changes in the front position, because they are completely governed by the velocities. Aspect ratios much lower than one (for instance resulting from strongly anisotropic permeabilities) or geological heterogeneities (for instance in the form of high-permeable streaks) are an essential pre-requisite to be able to significantly influence subsurface fluid flow through manipulation of well rates.

Steady-State Propagation of In-situ Combustion Fronts with Sequential Reactions

Summary The sustained propagation of a combustion front is necessary for the improved recovery of oil during an in-situ combustion process. The front is a sharp moving boundary layer and involves the complexities of combustion reactions. In this work, combustion will be represented in tersm of two oxidation reactions: high-temperature oxidation, the fuel burning reaction, and low-temperature oxidation, generating the necessary fuel. Due to their distinct reaction kinetics, the fuel generating and burning reactions occur separately in the reservoir. Their interaction and overall influence on combustion are investigated using an analytical approach based on the assumption of large activation energies. We identify conditions under which the reaction regions travel at different velocities, and conditions under which coherence develops. In the latter case, the sensitivity of the resulting state to the effect of various parameters is analyzed. Coherent reaction regions propagate closely spaced, thus minimizing the influence of deleterious heat losses and maximizing the process performance. The work is essential to oil and in situ bitumen recovery and emphasizes the importance of local chemical processes during air injection.