Steady-state Flow Experiments Research Articles

Integrated Physical and Digital Chalk Relative Permeability Evaluation: A Case Study

The Valhall chalk field has produced more than 1 billion barrels of oil equivalents over the last 40 years, primarily from the homogeneous Tor Formation. The underlying Hod Formation is more heterogeneous and is less maturely developed. The extent of heterogeneity poses a challenge in the evaluation of multiphase fluid flow properties. The objective of the work was to use digital core analysis to generate early relative permeability data to leverage and compare with conventional physical steady-state relative permeability data. Accurate digital and physical description of capillary pressure and relative permeability in the high-porosity chalk is complicated by both low permeabilities and heterogeneity. The main challenge with chalk is that flow occurs in a nano-environment. Physically, the nano-environment translates to low permeability, difficult rock preparation, and extensive experimental time, especiallyfor steady-state flow experiments. Representative three-dimensional (3D) digital rocks were generated using a combination of X-ray computed tomography (CT) and focused ion beam-scanning electron microscopy (FIB-SEM) methods. The digital rocks were used to simulate two-phase flow and generate relative permeabilities and sensitivity to wettability. Physical steady-state and digital relative permeabilities on several core plugs and subsets are compared in this study, which discusses the advantages of performing both as part of the formation evaluation process. The physical and digital results compare reasonably well. The physical results provide a relative permeability anchor, and the digital results provide the leverage of early results, parametric sensitivities, and quality assurance. Hence, integration between digital and physical core analysis yields a robust understanding and input for uncertainty modeling.

Low pressure gas transfer in fibrous media with progressive infiltration: correlation between different transfer modes

Permeation of gases in fibrous preforms of C/C composites has been studied with various degrees of infiltration, between 60% and 12% pore volume fraction, both experimentally with steady-state flow vs. pressure drop experiments and numerically with X-ray computerized micro-tomography (μ-CT), image processing and image-based computations. An excellent agreement has been found for Darcian permeabilities and for Knudsen diffusivities, when taking the mean solid chord length as a characteristic length scale. The reported tendencies of the mass transfer coefficients vs. porosity are in agreement with fibrous filters literature values, that are available for pore volume fractions above 55%. Accordingly, this work proposes useful extensions of these known correlations towards lower values of porosity. Finally, the dimensionless friction factors related to Knudsen diffusion, binary diffusion and viscous flow have been found to be correlated between each other, regardless the flow direction or the type of fibrous media. They are easy-to-use tools for large-scale numerical simulations of mixed-mode gas flow, eg. in Chemical Vapor Infiltration (CVI) or filter clogging simulations.

Conformational and rheological properties of bacterial cellulose sulfate

In this study, a water-soluble bacterial cellulose sulfate (BCS) was prepared with sulfur trioxide pyridine complex (SO3· Py) in a lithium chloride (LiCl)/dimethylacetamide (DMAc) homogeneous solution system using bacterial cellulose (BC). The structural study showed that the value for the degrees of substitution of BCS was 1.23. After modification, the C-6 hydroxyl group of BC was completely substituted and the C-2 and C-3 hydroxyl groups were partially substituted. In an aqueous solution, the BCS existed as a linear polymer with irregular coil conformation, which was consistent with the findings observed using atomic force microscopy. The steady-state shear flow and dynamic viscoelasticity were systematically determined over a range of BCS concentrations (1 %–4 %, w/v) and temperature (5 °C–50 °C). Steady-state flow experiments revealed that BCS exhibited shear thinning behavior, which increased with an increase in concentration and a decrease in temperature. These observations were quantitatively demonstrated using the cross model. Moreover, based on the dynamical viscoelastic properties, we confirmed that BCS was a temperature-sensitive and weak elastic gel, which was somewhere between a dilute solution and an elastic gel. Therefore, considering the special synthetic strategy and rheological behavior, BCS might be used as a renewable material in the field of biological tissue engineering, especially in the manufacture of injectable hydrogels, cell scaffolds, and as a drug carrier.

Rheology of graphene oxide suspended in yield stress fluid

• Suspensions of graphene oxide (GO) in Carbopol are also elastic yield stress fluids. • Addition of GO nanosheets in Carbopol decreases viscosity and elasticity. • Oxidation level of GO affects the rheological behavior. • Higher level of interaction of the GO/water system oxidized for 96 h. This work investigates the rheology of graphene oxide (GO) suspension on a yield stress model fluid. The effects caused by the variation of the GO concentration in the suspension and by the amount of oxygenated groups pendant present on the nanosheets surface, on the rheology of the suspensions were evaluated. The dispersant used was an aqueous solution of Carbopol® Ultrez 10. This is a transparent, nontoxic elastic yield stress fluid. GO nanosheets were produced from synthesis of graphite oxide (GrO) by modified Hummers method, and the nanosheets were characterized by XRD, Raman, FTIR, TEM and AFM techniques. The rheological behavior of these suspensions was characterized by oscillatory and steady-state flow experiments. The GO structure characterization shows that oxygenated functional groups were incorporated in its graphite surface in different levels after using two distinct times of oxidation. GO oxidized for 96 h (GO 96 h) showed greater interplanar distance and also presented few layers when compared with GO oxidized for 2 h (GO 2 h). The GO exfoliation process directly into the aqueous dispersion of Carbopol® showed to be an effective method. As for the pure Carbopol solutions, the GO suspensions were well modeled by the Hershel-Bulkley equation. The increase of GO concentration in the suspensions impairs the level of fluid structure and leads to a decrease in viscosity, yield stress, and elasticity. When compared, the GO 96 h promoted a lower decrease in viscosity, yield stress and elasticity than the GO 2 h suspension. For the suspension with a higher concentration of GO 96 h, it was observed the appearance of hysteresis at low shear rates. These results show that small changes in the GO nanosheets surface can significantly influence the rheological responses of a non-Newtonian fluid.

Estimation of Foam–Flow Parameters for Local Equilibrium Methods by Use of Steady-State Flow Experiments and Optimization Algorithms

Summary Foam has been successfully used in the oil industry for conformance and mobility control in gas-injection processes. The efficiency of a foam-injection project must be assessed by means of numerical models. Although there are several foam-flow models in the literature, the prediction of foam behavior is an important issue that needs further investigation. In this paper, we estimate foam parameters and investigate foam behavior for a given range of water saturation by use of two local equilibrium foam models: the population balance assuming local equilibrium (LE) model and the University of Texas (UT) model. Our method uses an optimization algorithm to estimate foam-model parameters by matching the measured pressure gradient from steady-state foam-coreflood experiments. We calculate the effective foam viscosity and the water fractional flow by use of experimental data, and we then compare laboratory data against results obtained with the matched foam models to verify the foam parameters. Other variables, such as the foam texture and foam relative permeability, are used to further investigate the behavior of the foam during each experiment. We propose an improvement to the UT model that provides a better match in the high-quality regime by assuming resistance factor and critical water saturation as a linear function of the pressure gradient. Results show that the parameter-estimation method coupled with an optimization algorithm successfully matches the experimental data by use of both foam models. In the LE model, we observe different values of the foam effective viscosity for each pressure gradient caused by variations of foam texture and the shear-thinning viscosity effect. The UT model presents a constant effective viscosity for each pressure gradient; we propose the use of resistance factor and critical water saturation as a linear function of the pressure gradient to improve the match in the high-quality regime, when applicable.

Rheology and structural changes of plasticized zeins in the molten state

Zeins, storage proteins from maize, are suitable for making biobased thermoplastic materials. The rheological behavior of a commercial zein plasticized with 20 w% glycerol was studied in the molten state by steady-state flow experiments in extrusion conditions and oscillatory rheometry. For low residence times, a shear-thinning viscoelastic behavior was observed, with G″ exceeding G′. After 300 s at 130 °C, the complex viscosity |η ∗| = 7 × 103 ω −0.46 was found to be similar to that of thermoplastic polymer melts used in fused deposition modeling. However, the ratio between the exponents of the power laws describing G′(ω) and G″(ω) did not meet the typical value of 2 for entangled polymer melts. Moreover, for longer residence times, the viscosity increased and a gelation phenomenon was observed with a crossing over of G′(ω) and G″(ω). Gel times ranged from 6000 s at 120 °C to 1700 s at 150 °C. The evolution of the macromolecular structure assessed by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and high-performance size exclusion chromatography suggested that this gelation phenomenon involves various types of covalent and non-covalent cross-links. Disulfide bonds played a significant role in gelation kinetics despite a very low cysteine residue content in the protein primary structure (about 1 mol%). These results suggested that plasticized zeins initially behave like a low-viscosity non-entangled polymer melt, before cross-linking progressively led to a continuous network.

The role of interfacial tension in colloid retention and remobilization during two-phase flow in a polydimethylsiloxane micro-model

The work presented here consisted of steady-state and transient two-phase flow experiments on the role of interfacial tension in colloid transport. Experiments were performed in a polydimethylsiloxane (PDMS) micro-model containing a network of pores with a mean pore size of 30µm. The flow network covered an area of 1mm×10mm. Water and Fluorinert FC43 were used as the two immiscible liquids. Since PDMS is a hydrophobic material, Fluorinert was the wetting phase, and water was the non-wetting phase in this micro-model. The interfacial tension was changed by adding a Fluorinert-soluble surfactant into Fluorinert FC43 to change the interfacial tension from 55mN/m to 30mN/m. The colloids were fluorescent carboxylate-modified polystyrene microspheres and 300nm in diameter. We directly observed colloid movement using confocal microscopy. We also obtained colloid concentration breakthrough curves by measuring the fluorescent intensities in the outlet of the micro-model.The breakthrough curves showed that during steady-state unsaturated flow, fewer colloids were retained in the system when interfacial tension was lower. During transient flow, more colloids were remobilized by the moving Fluorinert-water interfaces (FWIs) and Fluorinert-water-solid contact lines (FWSCs) under high interfacial tension. Visualization results showed that, at low interfacial tension, the fluid-fluid interfaces were almost flat; thus, less interfacial area was available for colloid attachment.Generally, confocal images and measured breakthrough curves clearly demonstrate the effect of interfacial tension on colloid retention and remobilization.

ANALYSIS OF FRACTIONAL FLOW AND RELATIVE PERMEABILITY OF HEAVY OIL AND KEROSENE DURING RECOVERY IN PETROLEUM RESERVOIR

This paper evaluates and compares the effect of fractional flow and relative permeability of heavy oil and Kerosene during recovery in a petroleum reservoir. Water fingering is one of the challenging problems during oil recovery and another comprehensive problem is, to exactly evaluate the amount of recover oil from a petroleum reservoir. To address these problems, the fractional flow and relative permeability of heavy oil and Kerosene are analyzed. The fractional flow approach is originated in the petroleum engineering literature and employs the saturation of one of the phases and a pressure as the independent variables. The fractional flow approach treats the multi-phases flow problem as a total fluid of a single mixed fluid and then describes the individual phases as fractional of the total flow. Laboratory steady state flow experiments are performed in two different types of oils (Heavy oil and Kerosene), to empirically obtain relative permeability and fractional flow curves, which have great influence in recovery efficiency calculation. Therefore, the famous Buckley-Leverett displacement mechanism has been used to calculate the performance of waterflooding. With Buckley-Leverett method, oil recovery from waterflooding is calculated and required water injection volume to achieve that oils recovery are estimated for heavy oil, which the total amount of oil produced up to the breakthrough is A φ B ×RF = 15901.92 m3 (= 99864.05 barrels) and for Kerosene is A φ B ×RF = 24992.06 m3 (156950.16 barrels). Additionally, the front flow of heavy oil is approximately spread to 80 m, and the front flow of light oil is approximately spread to 300 m. As a result indicates that fractional flow theory predicates a stable frontal displacement of all mobility ratios contrary to observed experimental facts. Therefore, fractional flow theory is suitable for describing the performance of stable displacement of oils by water.

Experimental results for oscillatory water flow in 10-ppi metal foam at low-frequencies

This experimental study presents results and interpretation of oscillatory water flow in open-cell metal foam. The tested foam had 10 pores per inch and a porosity of 88%. At relatively low frequencies, three flow displacements were employed in the experiment. The influence of frequency and displacement on pressure loss and friction factor is discussed. A correlation of friction factor as a function of the kinetic Reynolds number was determined. Porous media parameters, permeability and drag coefficient, were also found for the same foam via steady-state flow experiments in the Darcy and Forchheimer regimes. The friction factor of oscillating flow was found to be higher than that of steady state. The findings of this study are considered important for oscillating heat transfer in metal foam.

Magnetorheological fluids based on a hyperbranched polycarbosilane matrix and iron microparticles

Magnetorheological fluids (MFs) based on hyperbranched polycarbosilanes as a carrier medium and micron-sized carbonyl iron particles as filler have been synthesized for the first time. Their magnetorheological (MR) behavior has been studied in steady-state flow regime and under dynamic torsion oscillations on a commercial rheometer. At zero magnetic field, in spite of a rather high molecular mass, the hyperbranched polymers as well as their magnetic compositions with up to 72 mass% of magnetic filler demonstrate Newtonian behavior, and their viscosity considerably increases with magnetic filler content. In magnetic fields MFs show a huge MR response. Namely, in steady-state flow experiments a five orders of magnitude increase in viscosity was observed accompanied by magnetic-field-induced well-pronounced non-Newtonian behavior and a non-zero yield stress. Dynamic experiments demonstrate the transition from liquid-like to solid-like behavior of MFs with a large increase in both the storage and loss moduli under application of a magnetic field. In magnetic fields, the rheological behavior of the obtained MF resembles that of soft MR elastomers being mainly determined by the magnetic particle network formed due to magnetic interactions. In particular, like MR elastomers the MFs exhibit the Payne effect, i.e. dependence of the dynamic modulus on the strain amplitude.

Merging parallel tempering with sequential geostatistical resampling for improved posterior exploration of high-dimensional subsurface categorical fields

The sequential geostatistical resampling (SGR) algorithm is a Markov chain Monte Carlo (MCMC) scheme for sampling from possibly non-Gaussian, complex spatially-distributed prior models such as geologic facies or categorical fields. In this work, we highlight the limits of standard SGR for posterior inference of high-dimensional categorical fields with realistically complex likelihood landscapes and benchmark a parallel tempering implementation (PT-SGR). Our proposed PT-SGR approach is demonstrated using synthetic (error corrupted) data from steady-state flow and transport experiments in categorical 7575- and 10,000-dimensional 2D conductivity fields. In both case studies, every SGR trial gets trapped in a local optima while PT-SGR maintains an higher diversity in the sampled model states. The advantage of PT-SGR is most apparent in an inverse transport problem where the posterior distribution is made bimodal by construction. PT-SGR then converges towards the appropriate data misfit much faster than SGR and partly recovers the two modes. In contrast, for the same computational resources SGR does not fit the data to the appropriate error level and hardly produces a locally optimal solution that looks visually similar to one of the two reference modes. Although PT-SGR clearly surpasses SGR in performance, our results also indicate that using a small number (16–24) of temperatures (and thus parallel cores) may not permit complete sampling of the posterior distribution by PT-SGR within a reasonable computational time (less than 1–2 weeks).

Experimental and numerical investigations of the non-linear rheological properties of viscoelastic surfactant solutions: application and failing of the one-mode Giesekus model

In a series of experiments, we investigated the non-linear rheological properties of aqueous solutions of entangled wormlike micelles (WLMs) in steady-state shear flow and in large amplitude oscillating shear (LAOS) experiments. On grounds of their monoexponential stress relaxation properties, we studied semi-dilute solutions of the cationic surfactants cetylpyridinium chloride (CPyCl) or cetyltrimethylammonium bromide (CTAB) after addition of different amounts of sodium salicylate. The rheological data of these networks of WLMs were systematically compared with the numerically calculated results of the one-mode Giesekus constitutive equation. It turned out that the viscous resistance and the first normal stress difference, measured in steady-state shear flow, start-up, and relaxation experiments, were accurately predicted by the one-mode Giesekus model. In rheological tests, where we applied large oscillating shear amplitudes (LAOS), the transient shear stress could also approximately be described by means of the Giesekus model. The non-linear oscillating first normal stress difference, however, showed large deviations in respect to the theoretical predictions. These discrepancies between different rheological experiments, which we observed in oscillating and stationary flow, pointed to the existence of flow instabilities, which occurred in the LAOS regime. These, more complicated rheological processes, were induced by shear-banding and/or the presence of flow-induced phase transitions, which can occur in oscillatory and stationary shear. The non-linear phenomena, discussed in this article, are of general importance, and they can be equally observed in entangled solutions of flexible macromolecules.

Steady-state two-phase relative permeability functions of porous media: A revisit

Steady-state two-phase flow experiments are performed on a sand column equipped with two differential pressure transducers and six ring electrodes to measure the pressure drop across each phase, and electrical resistance across five successive column segments, respectively. The electrical resistivity index measured across various segments of the soil column is converted to water saturation by using the Archie equation. The results are analyzed by considering the water saturation and oil/water relative permeability as power functions of water and oil capillary numbers which are employed as independent variables. Results from earlier visualization studies on a glass-etched pore network are also analyzed by a similar manner to quantify the dependence of oil and water relative permeability on capillary numbers, and correlate the estimated parameters of power functions with the viscosity ratio. The new explicit relationships of relative permeabilities and water saturation with oil and water capillary numbers set the bases for a new conceptualization of the two-phase flow at reservoir-scale where the mobility of the fluids is decoupled from saturation and become non-linear functions of the local flow rates. The variation of the relative permeability exponents with the pore system dimensionality agrees qualitatively with the scaling behavior predicted by the gradient percolation approach.

Conceptual Darcy-Scale Model of Oil Displacement with Macroemulsion

Experiments have shown that injection of oil-in-water macroemulsions can be used as an effective enhanced-oil recovery (EOR) method, with potential increase in the volume of oil recovered. As emulsion drops move through the pore space, they give rise to multiscale flow effects that are commonly associated with mobilization of residual oil and macroscale mobility control or conformance. Compared to water injection, emulsion flooding can improve the macroscopic reservoir sweep as well as reduce the residual oil saturation. Prediction of reservoir flooding scenarios requires a physically meaningful two-phase flow model that accounts for the presence of emulsion drops in the aqueous phase. Conceptually in this work, we describe emulsions as an aqueous phase containing a certain concentration of oil drops. The aqueous-phase dynamic properties depend on the emulsions and porous media characteristics. Here, we propose to represent emulsion injection effects in a simplified fashion through changes in the relative permeability curves of both the aqueous and oil phases. Steady-state two-phase flow experiments were conducted to evaluate these relative permeability curves with and without the presence of oil drops dispersed in the aqueous phase. The effect of the relative permeability curves on Darcy-scale or continuum oil displacement was evaluated by comparing numerical reservoir-scale predictions of oil recovery for water and emulsion flooding using the experimentally determined relative permeabilities.

Estimating hysteresis in the soil water retention curve from monolith experiments

Water movement in unsaturated soils is commonly affected by hysteresis, a phenomenon often ignored as to keep the mathematical description of water flow and solute transport simple. In this study, the importance of hysteresis was quantified at lysimeter scale on two Belgian soils, a loamy and a sandy loam soil. Undisturbed soil monoliths (79cm diameter by 105cm height) were collected in each soil and the flow studied for various boundary conditions. Each monolith was equipped with different measuring devices to monitor online soil water content, pressure head, and outlet water fluxes. Four unsaturated steady state flow experiments were conducted on each monolith. Hydraulic properties were obtained by inverting the governing flow equation of Richards, using a global multilevel coordinate search inversion algorithm. Measured soil water contents, pressure heads, and outlet water fluxes were used in the objective function. First soil hydraulic parameters in the retention and hydraulic conductivity functions were estimated neglecting hysteresis and compared with the functions obtained using approaches considering hysteresis in their analysis. Hysteresis was incorporated in the retention curve using the simple empirical model proposed by Scott et al. (1983) and using the universal conceptual model of Mualem (1977). Hysteresis in both soils was characterized by a relative large difference between the main drying and wetting soil water retention curves. However, results showed that the effect of hysteresis was different on various components of water flow in the two studied soils. The Scott's model considerably improved pressure head estimates in the loamy soil and Mualem's model somewhat improved the soil water content estimates in the sandy loam soil. Outlet water fluxes in both soils were less sensitive to hysteresis. In general, the simple hysteretic model of Scott was more successful in studying hysteresis in both studied soils.

Virus Transport during Infiltration of a Wetting Front into Initially Unsaturated Sand Columns

We investigated the effect of different flow conditions on the transport of bacteriophage phiX174 in Memphis aquifer sand. Virus transport associated with a wetting front moving into an initially unsaturated horizontal sand column was experimentally compared with that observed under steady-state saturated vertical flow. Results obtained by sectioning the sand columns showthattotal (retained and free) resident virus concentrations decreased approximately exponentially with the travel distance. The rate of decline was similar under both transient unsaturated flow and steady-state saturated flow conditions. Total resident virus concentrations near the inlet were an order of magnitude greater than the virus concentration of the influent solution in both experiments, indicating continuous virus sorption during flow through this zone. Virus retardation was quantified using the ratio of the centroids of the relative saturation and virus concentration versus relative distance functions. The mean retardation factors were 6.43 (coefficient of variation, CV = 14.4%) and 8.22 (CV = 8.22%) for the transient unsaturated and steady-state saturated flow experiments, respectively. Attest indicated no significant difference between these values at P < 0.05. Air-water and air-water-solid interfaces are thought to enhance virus inactivation and sorption to solid particles. The similar retardation factors obtained may be attributable to the reduced presence of these interfaces in the two flow systems investigated as compared to steady-state unsaturated flow experiments in which these interfaces occur throughout the entire column.

Interfacial Coupling in Vertical, Two-Phase Flow Through Porous Media

: Vertical, two-phase flow through natural porous media is affected by interfacial coupling. Such coupling may be of two types: viscous and capillary. In this study, macroscopic defining equations for the viscous and capillary coupling parameters have been constructed. Moreover, these defining equations, together with modified forms of Kalaydjian's transport equations, have been used to construct equations that can be used to analyze the effect of interfacial coupling on vertical, two-phase flow in natural porous media. These equations reveal that viscous coupling is dependent explicitly on mobility ratio, and that the effect of viscous coupling on vertical flow is bounded. Moreover, these equations show that capillary coupling depends explicitly on porosity. Furthermore, on the basis of the analysis carried out, it is argued that the effect of viscous coupling on vertical flow is small, and that the effect of capillary coupling on horizontal flow is an order of magnitude larger than that of viscous coupling. The data from two sets of gravity-driven, steady-state, cocurrent and countercurrent flow experiments were used to test the interfacial coupling theory. It was found that the experimentally determined and predicted values of the capillary coupling parameters were consistent for both the wetting and the nonwetting phase, provided proper account was taken of the contribution of the net buoyant force to the driving force for each phase. Because of a lack of sufficient experimental evidence, further experimental testing of the theory must be undertaken before it can be accepted with confidence. Even so, the new equations should be, because they show explicitly the role of mobility ratio and porosity, useful tools for improving our understanding of the effect of interfacial coupling on vertical, two-phase flow through natural porous media.

Multi-functional heat pulse probe measurements of coupled vadose zone flow and transport

Simultaneous measurement of coupled water, heat, and solute transport in unsaturated porous media is made possible with the multi-functional heat pulse probe (MFHPP). The probe combines a heat pulse technique for estimating soil heat properties, water flux, and water content with a Wenner array measurement of bulk soil electrical conductivity (EC bulk). To evaluate the MFHPP, we conducted controlled steady-state flow experiments in a sand column for a wide range of water saturations, flow velocities, and solute concentrations. Flow and transport processes were monitored continuously using the MFHPP. Experimental data were analyzed by inverse modeling of simultaneous water, heat, and solute transport using an adapted HYDRUS-2D model. Various optimization scenarios yielded simultaneous estimation of thermal, solute, and hydraulic parameters and variables, including thermal conductivity, volumetric water content, water flux, and thermal and solute dispersivities. We conclude that the MFHPP holds great promise as an excellent instrument for the continuous monitoring and characterization of the vadose zone.

Steam-Water and Air-Water Capillary Pressures: Measurement and Comparison

Abstract Direct comparisons between steam-water and air-water capillary pressures have been few because of the difficulty in experimental measurement. An experimental method was developed to measure both steam-water and air-water capillary pressures using an X-Ray CT technique. Spontaneous water imbibition and gravity drainage tests were conducted in ceramic core samples for steam-water and air-water systems, respectively. The results were compared, and it was found that the steamwater capillary pressures were less than the air-water capillary pressures. Introduction Steam-water flow is of importance during steam injection into heavy oil reservoirs and water injection into geothermal reservoirs in which steam is produced. In these reservoirs, steam-water capillary pressure plays an important role in controlling fluid distribution, transfer of liquid between fracture and matrix, and well productivity. The study of steam-water flow in porous media may also be useful for other single-component two-phase systems or even some multicomponent gas-liquid systems such as solution gas-oil and gas-condensate systems in which there is also significant mass transfer between the two phases as pressure changes. However, it is difficult to measure steam-water capillary pressure using routine techniques (for example, semipermeable porousplate and centrifuge methods) due to the phase transformation and the significant mass transfer between the two phases. In situ fluid saturation measurement techniques, such as X-Ray CT, γ-ray, and NMR techniques, may be useful to overcome the difficulties. Many papers(1–4) have been published in oil-gas and oil-water flow, but few in the measurement of both steam-water and airwater capillary pressures. A similar fluid flow to steam-water flow is gas-condensate flow. Although a lot of papers(5–8) have been published on the measurement of relative permeability for gas-condensate systems, reports on the direct measurement of gas-condensate capillary pressure have been few. On the other hand, there has been some argument regarding the differences between steam-water and air-water flow through porous media in recent years. If there are no differences between the two, we could represent steam-water flow by air-water flow in which capillary pressure can be measured easily. Sanchez and Schechter(9) reported that the differences between steam-water and nitrogen-water relative permeabilities were almost negligible in an unconsolidated core sample. However, Horne et al.(10) found significant differences in experiments using Berea sandstone with a much lower permeability than that of the core sample used by Sanchez and Schechter(9). Accordingly, there may also be significant differences between steam-water and nitrogen-water capillary pressures. Very few direct comparisons of steam-water and air-water capillary pressures are available due to the scarcity of methods available to measure them. Li and Horne(11) developed a technique based on the Kelvin equation to calculate steam-water capillary pressure using the data from steady-state steam-water flow experiments. This method is suitable for steam-water systems but not for air-water systems. Therefore, we developed another method that could measure both steam-water and air-water capillary pressures in order to identify the differences between the two in this study. We conducted spontaneous water imbibition and gravity drainage in ceramic core samples for steam-water and air-water systems. The core sample was positioned vertically.

The Mathematical Model of Nonequilibrium Effects in Water-Oil Displacement

Summary 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 water-oil 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.