Birol Dindoruk

Development of Miscibility in Four-Component CO2 Floods

A rigorous tie-line extension criterion for the minimum miscibility pressure (MMP) is derived for dispersion-free, 1D displacements in four-component systems in which CO 2 displaces oil containing dissolved methane. The key tie-lines required for application of the MMP criterion are obtained by a simple graphical construction. A simplified technique for construction of solutions is demonstrated for the CO 2 /methane/butane/decane system. The new technique makes solution of certain four-component problems not much more difficult than solution of a Buckley-Leverett displacement of oil by water

Theory of Multicontact Miscible Displacement with Nitrogen

Analytical solutions for displacement of mixtures of methane, butane and decane by nitrogen or nitrogen/methane mixtures are used to explain conflicting experimental observations concerning the sensitivity of minimum miscibility pressures to changes in the compositions of an initial oil or the injection gas. The solutions presented show why some investigators have reported weak dependence of the minimum miscibility pressure (MMP) on methane concentrations while others have reported significant sensitivity. The analysis of displacement composition routes indicates that either observation can be correct for some ranges of initial and injection fluid compositions, and shows that the sensitivity behavior depends on the relative positions in composition space of three key tie lines, the initial, injection, and crossover tie lines.

Liquid film flow in a fracture between two porous blocks

Liquid film flow in a fracture between two porous bodies is mainly driven by pressure. The pressure drop across such a small distance could be significant. The flow of a liquid film is governed by the pressure drop across the fracture space, and therefore, understanding of liquid film flow in a single liquid bridge along a solid wall between two porous bodies is needed. The shape of the liquid bridge between the porous blocks is an unknown. The first step is to determine the shape of the free surface. Due to the nature of the problem, a boundary integral technique is found to provide the solution to the whole problem. Solutions are reported for a range of capillary numbers observed in cracked porous media. Pressure drop is correlated using a dimensionless capillary number group. Using analogy from the Darcy flow in porous media, a correlation for the equivalent Darcy permeability is developed.

Analytical Solution for Four Component Gas Displacements with Volume Change on Mixing

Analytical solutions obtained by the method of charac teristics are reported for the material balance equations that describe one-dimensional flow of four-component mixtnres in which components change voinme as they transfer between phases. Volume change induces variations in local flow ve locity, but we show that the variations can be decoupled from composition variations. We report example solutione for dis placements of a methane(CH4)/butane(C4)/decane(Cie) mix ture by carbon dioxide (C02) or nitrogen (N2). They show that flow behavior is controlled by three key tie lines: the in jection tie line, the initial tie line, and a crossover tie line. We calculate the eigenvalues and eigenvectors for the eigen value problem in terms of ruled surfaces of tie lines and the tie-line envelopes. That representation shows when continu ous composition variations connect pairs of key tie lines and when self-sharpening shocks are required. We also prove for ne-component systems with volume change that if there is a self-sharpening wave between two tie lines, the tie line exten sions must intersect. Finally, we show that development of miscibility can be controlied by any of the three key tie lines.

Global Triangular Structure in Four-Component Conservation Laws

This paper demonstrates that the mathematical structure of one-dimensional flows in which four components partition between two phases is governed by the geometry of equilibrium tie lines. We define global triangular structure, and we prove that models of four-component flow exhibit global triangular structure if and only if tie lines meet at one edge of a quaternary phase diagram, or if tie lines lie in planes. For such systems, shock and rarefaction surfaces coincide, and the analysis of wave structures is straightforward. We show also that when equilibrium K-values are independent of composition, the requirements for triangular structure are satisfied, though exampies are given for other triangular systems with variable K-values. An example solution is given for a four-component system with constant K-values. We report a solution for five-component flow with constant K-values to demonstrate that the simplifications that arise from triangular structure can be used to advantage in the construction of solutions to multicomponent Riemann problems.

Effect of Fractional Flow Heterogeneity on Compositional and Immiscible Displacements

The scale of heterogeneities in reservoirs is often smaller than the grid size used in large scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small scale fractional flow must be upscaled to the grid size in flow simulations.

Solution and upscaling of compositional and immiscible displacements in composite media

The scale of heterogeneities in reservoirs is often smaller than the grid size used in large-scale reservoir simulations. Relative permeabilities have the foremost effect on fluid flow and small-scale fractional flow must be upscaled to the grid size in flow simulations. Thus, systems with fractional flow heterogeneities, i.e. relative permeability variations, have to be solved and effective relative permeability functions determined. In this paper, benchmark analytical solutions are developed for a system consisting of two media in series where each medium is characterized with a different set of relative permeabilities, residual saturations and porosities. The analytical solutions show a significant discontinuity in the saturation and concentration profiles at the interface of the two media. Numerical results using several weighting schemes are compared against the analytical solutions for two-phase immiscible and partially miscible systems. It is shown that single-point upstream weighting requires about 100 grid blocks to capture the discontinuity at the interface, whereas third-order TVD weighting requires much fewer. Lastly, the validity of the JBN method and harmonic averaging for determination of effective relative permeabilities and overall pressure drop is tested. Both the JBN method and harmonic averaging cannot reproduce the pressure drop across the composite media prior to water breakthrough.

Chapter 1 – Gas Flooding

One of the most accepted and widely used technologies for enhanced oil recovery is injection of gas or solvent that is miscible or near miscible with reservoir oil. Understanding gas flooding requires a good understanding of the interaction of phase behavior and flow in the reservoir, and how oil and gas develop miscibility.

Prediction and Experimental Measurements of Water-in-Oil Emulsion Viscosities During Alkaline/Surfactant Injections

Oil production is generally a complicated multiphase flow inside pipelines, with possible water-in-oil (W/O) emulsions present with other usual phases such as free water and free oil. The W/O emulsions formed can present significant hurdles in production facilities for pumping fluids and during pipeline transport. It is well known that high shear rates provided by pumps, chokes, or valves result in stable emulsion behavior for a field in primary production. Several field tests are under way to test the potential of surfactant flooding as a tertiary-recovery mechanism. The effect of addition of surfactants on the emulsion rheology of production fluids, as in alkaline/ surfactant/polymer (ASP) flooding, is not very well understood. This understanding of W/O-emulsion rheology in ASP-injection oil recovery is essential for design of pumps and pipelines as well as for handling flow-assurance issues. In this paper, we report results from experiments as well as modeling of W/O-emulsion rheology that can form during ASP injections. We focus here only on the alkaline/surfactant (AS) part of these injections in order to clearly understand the impact of surfactants, removing the uncertainities that come with large rheology changes with polymer addition. The effect of surfactants on the rheology of W/O emulsions was studied by making two different types of emulsions: (1) native-brine W/O emulsions without surfactants to provide a baseline and (2) brine W/O emulsions with surfactants used in ASP injections. This way, the impact of ASP injections on emulsion rheology can easily be quantified. A new correlation is developed, based on in-house historical experimental data, to describe rheology of emulsions without surfactants. This correlation should assist in managing the uncertainties that come from extrapolating emulsion rheology measured in the laboratory to actual field conditions. Further, to understand the effect of ASP injections, new experimental measurements were made by adding surfactants to brine solutions. The addition of surfactants resulted in different rheology as compared with emulsions formed by brine solutions. These differences have been attributed to the W/O interfacial tension (IFT), and IFT was added to modify the original correlation. To our knowledge, this is the first study that explicitly relates emulsion rheology with IFT.

Quantification of Displacement Mechanisms in Multicomponent Gasfloods

Local displacement efficiency in gasfloods depends strongly on the minimum miscibility pressure (MMP) or minimum miscibility enrichment (MME). The values for these design parameters depend in turn on the displacement mechanisms: vaporizing, condensing, or a combination of the two known as a condensing/vaporizing (CV) drive. Characterization of the displacement mechanism, however, is currently limited to these broad categories, with little reference to the degree to which a CV displacement is condensing or vaporizing. This “discrete” classification approach can result in significant confusion in the interpretation and comparison of various miscible gasfloods. The focus of this paper, therefore, is to present a method to quantify in a continuous way the fraction of a multicomponent gasflood that is vaporizing or condensing as the pressure or gas enrichment is increased. The approach relies on finding key tie lines for a dispersionfree 1D displacement using method of characteristic theory (MOC). We quantify the displacement mechanism for any number of oil or gas components by calculating the displacement path lengths along ruled surfaces bounded by these key tie lines. We show how to determine the displacement mechanism along each of these ruled surfaces by the calculation and comparison of the key tie-line lengths. Several multicomponent fluid characterizations are considered, including a 12-component enriched-gasflood and a 13-component CO2 flood. The results show that as the pressure or enrichment is increased, condensation occurs at the expense of vaporization. We also show by numerical simulations that the sensitivity of the local displacement efficiency to dispersion depends on the condensing fraction of the displacement. We show that the trends in displacement efficiency sensitivity to dispersion oppose previously published results, which showed that vaporizing displacements are more sensitive to dispersion than condensing ones. The differing trends are likely the result of improper and discrete determination of the displacement mechanism.