Showing papers in "Spe Journal in 2003"

The Mathematical Model of Nonequilibrium Effects in Water-Oil Displacement

Abstract: Forced oil-water displacement and spontaneous countercurrent imbibition are the crucial mechanisms of secondary oil recovery. Classical mathematical models of both these unsteady flows are based on the fundamental assumption of local phase equilibrium. Thus, the water and oil flows are assumed to be locally distributed over their flow paths similarly to steady flows. This assumption allows one to further assume that the relative phase permeabilities and the capillary pressure are universal functions of the local water saturation, which can be obtained from steady-state flow experiments. The last assumption leads to a mathematical model consisting of a closed system of equations for fluid flow properties (velocity, pressure) and water saturation. This model is currently used as a basis for numerical predictions of wateroil displacement. However, at the water front in the water-oil displacement, as well as in capillary imbibition, the characteristic times of both processes are, in general, comparable with the times of redistribution of flow paths between oil and water. Therefore, the nonequilibrium effects should be taken into account. We present here a refined and extended mathematical model for the nonequilibrium two-phase (e.g., water-oil) flows. The basic problem formulation, as well as the more specific equations, are given, and the results of comparison with an experiment are presented and discussed.

Wettability, Saturation, and Viscosity From NMR Measurements

Abstract: This paper discusses a new nuclear magnetic resonance (NMR) method that can provide wettability, saturation, and oil viscosity values in rocks partially saturated with oil and brine. The method takes advantage of two new technological advances in NMR well logging—the MRF* Magnetic Resonance Fluid Characterization Method and NMR “diffusion-editing” (DE) pulse sequences. We discuss the principles underlying the fluid characterization method and the pulse sequences. The fluid characterization method is used to provide robust inversions of DE data suites acquired on fully brine-saturated and partially saturated rock samples. The outputs of the inversion are separate diffusion-free brine and oil T2 distributions for the fluids measured in the rocks. NMR measurements on partially saturated rocks are sensitive to wettability because of surface relaxation of the wetting-phase fluid. The surface relaxation rate, however, must be significant compared to the bulk relaxation rate in order for wettability to noticeably affect the NMR response. We present results showing that the surface relaxation rate at lower wetting-phase saturations is enhanced compared to that measured at higher saturations. The consequence of wetting-phase saturation on NMR-based wettability determination is discussed. Wettability affects the relaxation rates of both the wetting and nonwetting phases in partially saturated rocks. Surface relaxation of the wetting phase in a rock results in shorter relaxation times than would otherwise be observed for the bulk fluid. The nonwetting-phase fluid molecules do not come into contact with the pore surfaces, and therefore their relaxation rate in the rock is the same as in the bulk fluid. We present accurate and robust computations of diffusion-free T2 relaxation time distributions for both the wetting and nonwetting phases in four rocks that include two sandstones and two dolomites. A DE data suite was acquired on each rock, measured in two different partial saturation states and also fully brinesaturated. Wettability is determined by comparing the oil and brine T2 relaxation-time distributions measured in the partially saturated rocks with the bulk oil T2 distribution and with the T2 distribution of the fully brine-saturated sample. The brine and oil T2 distributions are used to compute saturation and oil viscosity values. A general discussion elucidating the sensitivity range and T2 limits of diffusion-based NMR methods is given in the appendix. The appendix also derives and displays the gain in signal-to-noise ratio that is achieved by using DE data sequences for fluid characterization in place of Carr-Purcell-Meiboom-Gill (CPMG) data suites.

Fast and Robust Algorithm for Compositional Modeling: Part II - Two-Phase Flash Computations

Abstract: In Part I of our study, stability analysis testing in the reduced space was formulated, and its robustness and efficiency in comparison to the conventional approach was explored. In this paper, we present formulations including, first, direct solution of the nonlinear equations, and second, minimization of Gibbs free energy for twophase flash computations in the reduced space. We use various algorithms including the successive substitution (SS), Newton’s method, globally convergent modifications of Newton’s method (line searches and trust region), and the dominant eigenvalue method (DEM) for direct solution of the nonlinear equations defining two-phase flash and the minimization of Gibbs free energy. We also suggest a criterion based on the tangent-plane-distance (TPD) for the initialization from the equilibrium ratios. The proposed criterion has a significant effect on reducing the number of iterations. The results from various algorithms reveal that the direct solution of the nonlinear equations in the reduced space, combined with the use of the TPD criterion for initialization in the combined SS and Newton’s method, can make flash computations extremely efficient. The efficiency and robustness of flash computations in the critical region are especially remarkable.

Interpretation of the Unusual Fluid Distribution in the Yufutsu Gas-Condensate Field

Abstract: It is generally believed that at steady state, a heavy fluid mixture cannot float, without motion, at the top of a light fluid mixture in a cavity. The expectation is that because of pressure diffusion, segregation occurs with the light fluid at the top and the heavy fluid at the bottom. We present, for the first time, an extensive set of measurements in 5-km vertical wells in a large hydrocarbon formation of 1-km thickness with horizontal dimensions on the order of several kilometers that show a high-density fluid mixture at the top of a light-density fluid mixture at steady state. The data in the 5-km wells show liquid in the middle, and vapor at the top and bottom. In the hydrocarbon formation, there is a gradual decrease of density with depth. A theoretical model based on the thermodynamics of irreversible processes is used to provide an interpretation of the unusual density variation vs. depth both in the hydrocarbon formation and in the long wells, as well as the unusual species distribution in the hydrocarbon formation. The results reveal that thermal diffusion (caused by geothermal temperature gradient) causes the segregation of heavy components in the subsurface fluid mixture to the cold side in the Earth (that is, the top), overriding pressure and molecular diffusion (Fickian diffusion). As a consequence of the competition of these three diffusion effects, a heavy fluid mixture can float at the top with a light fluid mixture underneath. In the past, thermal diffusion has been thought of as a second-order effect. For the fluid mixture in our work, thermal diffusion is the main phenomenon affecting the spatial density and species distribution.

Laboratory Evaluation of In-Situ Gelled Acids for Carbonate Reservoirs

Abstract: Three different commercial formulations (A, B, and C) of in-situ gelled acids are compared in detail at temperatures up to 150°F and acid concentrations from 5 to 20 wt% HCl. In-situ gelled acids are said to work by a gelation mechanism that occurs at the rock surface as the acid is spent. These acids contain a polymer, a crosslinker, and a breaker, in addition to other additives. Detailed viscosity measurements of each in-situ gelled acid were made with live, partially neutralized, and spent acid. A new experimental procedure was developed to partially neutralize the in-situ gelled acid with calcium carbonate, and then the apparent viscosity was measured as a function of shear rate in the range 1 to 3,000 s. The pH values of these samples varied from 0 to 6. Relative reaction rates with reservoir rock of the three in-situ gelled acids were compared at 100°F. Coreflood experiments were conducted with small acid volumes, so that permeability could be measured before acid breakthrough occurred. In-situ gelled acids all retarded the reaction of acid with reservoir rock, primarily as a result of the polymer present in the acid formulae. From viscosity measurements, live in-situ gelled acids A and B behaved more like gelled acids. Their viscosity in live acid was significantly higher than that of Acid C. In spent acid, the viscosity of Acid C was higher than that of Acids A or B. Acid C was most effective at initial HCl concentrations of 5 and 10 wt% at 100 and 150°F. Acids A and B were effective only at an initial HCl concentration of 10 wt% and 100°F. Coreflood studies showed that the polymer and crosslinker component of in-situ gelled acids irreversibly reduced the permeability of carbonate reservoir rock. As with any spent acids, mixing spent in-situ gelled acids with seawater resulted in calcium sulfate precipitation for all three of the acid systems.

Modeling of a Deepwater Turbidite Reservoir Conditional to Seismic Data Using Principal Component Analysis and Multiple-Point Geostatistics

Abstract: Geological interpretation and seismic data analysis provide two complementary sources of information to model reservoir architecture. Seismic data affords the opportunity to identify geologic patterns and features at a resolution on the order of 10’s of feet, while well logs and conceptual geologic models provide information at a resolution on the order of one foot. Both the large-scale distribution of geologic features and their internal fine-scale architecture influence reservoir performance. Development and application of modeling techniques that incorporate both large-scale information derived from seismic and fine-scale information derived from well logs, cores, and analog studies represents a significant opportunity to improve reservoir performance predictions. In this paper we present a practical new geostatistical approach for solving this difficult data integration problem and apply it to an actual, prominent reservoir. Traditional geostatistics relies upon a variogram to describe geologic continuity. However, a variogram, which is a two-point measure of spatial variability, cannot describe realistic, curvilinear or geometrically complex patterns. Multiple-point geostatistics uses a training image instead of a variogram to account for geological information. The training image provides a conceptual description of the subsurface geological heterogeneity, containing possibly complex multiple-point patterns of geological heterogeneity. Multiple-point statistics simulation then consists of anchoring these patterns to well data and seismic-derived information. This work introduces a novel alternative approach to traditional Bayesian modeling to incorporate seismic. The focus in this paper lies in demonstrating the practicality, flexibility and CPU-advantage of this new approach by applying it to an actual deep-water turbidite reservoir. Based on well log interpretation and a global geological understanding of the reservoir architecture, a training image depicting sinuous sand bodies is generated using a non-conditional object-based simulation algorithm. Disconnected sand bodies are interpreted from seismic amplitude data using a principal component cluster analysis technique. In addition, a map of local sand probabilities obtained from a principal component proximity transform of the same seismic is generated. Multiple-point geostatistics then simulates multiple realizations of channel bodies constrained to the local sand probabilities, partially interpreted sand bodies and well-log data. The CPU-time is comparable to traditional geostatistical methods.

Application of a New Multicomponent Gas Adsorption Model to Coal Gas Adsorption Systems

Abstract: A new multicomponent adsorption model is proposed for application to coal gas adsorption systems. The model is derived by combining the vacancy solution and Dubinin-Polanyi theories. Applications of the new adsorption model include the modeling of multicomponent adsorption processes associated with primary and enhanced coalbed methane recovery (ECBM). In the new model, the adsorbed phase in the single-component (pure) adsorption system is treated as a binary mixture of a singlecomponent gas with a hypothetical “vacancy” species, which also occupies adsorption space. The adsorption system is modeled as equilibrium between the gaseous phase and the adsorbed-phase vacancy solution. The Dubinin-Astakhov (D-A) equation is used to generate activity coefficients, as a function of the degree of porefilling, for the pure component gas in the binary (adsorbate+vacancy) adsorbed-phase mixture. The Wilson equation is chosen to fit pure component (D-A-derived) activity coefficient curves by optimizing the binary interaction coefficients. These binary interaction coefficients are then used to predict multicomponent adsorption equilibrium, although only the case of binary adsorption is modeled here. The adsorbed phase mixture for binary gas adsorption is treated as a ternary mixture of the two pure component adsorbates and the hypothetical vacancy species. Binary gas adsorption equilibrium is described by equilibrium between the gaseous components and the components in the adsorbed phase solution. Adsorbed-phase activity coefficients are calculated from the Wilson equation, with the binary interaction coefficients obtained from pure component adsorption data. Thus, only pure component adsorption data are required to make binary and multicomponent adsorption predictions with the new model. Two binary (CH4+CO2) gas adsorption experimental data sets with coal as the adsorbent and one binary (CH4+C2H6) gas adsorption data set with activated carbon as the adsorbent are used to test the predictions of the new model. In most cases the new model is able to predict binary gas adsorption accurately. The poor fit of the Wilson equation to the D-A-derived activity coefficients for some pure component data suggests that some improvement in model predictions could be made with the choice of a different activity coefficient equation. A unique feature of the current model is the ability to predict multicomponent gas adsorption at different temperatures from the pure component adsorption data collected at a single temperature. The temperature independence of pure component “characteristic” curves, as demonstrated in Dubinin-Polanyi theory, allows pure component adsorption to be predicted for a range of temperatures. These pure component data can then be used in modeling binary or multicomponent adsorption data at various temperatures. This is demonstrated for one experimental binary gas adsorption data set.

Analytical Theory of Coalbed Methane Recovery by Gas Injection

Abstract: Injection of either carbon dioxide (CO2) or nitrogen (N2) enhances recovery of coalbed methane. In this paper, we provide new analytical solutions for the flow of ternary gas mixtures in coalbeds. The adsorption/desorption of gaseous components to/from the coalbed surface is approximated by an extended Langmuir isotherm, and the gas-phase behavior is predicted by the PengRobinson equation of state (EOS). Langmuir isotherm coefficients are used that represent a moist Fruitland coal sample from the San Juan basin (U.S.A.). In these calculations, mobile liquid is not considered. Given constant initial and injection compositions, a self-similar solution consisting of continuous waves and shocks is found. Mixtures of CH4, CO2, and N2 are used to represent coalbed and injection gases. We provide examples for systems where the initial gas is largely CH4, and binary mixtures of CO2 and N2 are injected. Injection of N2-CO2 mixtures rich in N2 leads to relatively fast initial recovery of CH4. Injection of mixtures rich in CO2 gives slower initial recovery, increases breakthrough time, and decreases the injectant needed to sweep out the coalbed. The solutions presented indicate that a coalbed can be used to separate N2 and CO2 chromatographically at the same time coalbed methane (CBM) is recovered.