Undersaturated Region Research Articles

Enhancing PVT property predictions for black oil reservoirs through the application of supervised machine learning techniques

The study presents an innovative approach utilizing machine learning (ML) techniques to forecast essential characteristics of black oil reservoirs, namely the oil formation volume factor (Bo) and the solution gas-oil ratio (Rs). A suite of four established ML algorithms-Random Forest, Linear Regression, Ada Boost, and Gradient Boost were extensively conditioned using a dataset that includes 297 individual data points and evaluation is done using test data and a blind test of models. The study showcases the practical efficacy of ML in accurately predicting Bo and Rs, even with a relatively modest dataset. The potential of ML models to save time and costs by reducing the dependence on laborious laboratory measurements is underscored, presenting a transformative shift in reservoir engineering practices. Furthermore, the current research extends its impact by comparing ML predictions with various empirical correlations and actual values, demonstrating that ML models, particularly Gradient Boost, consistently outperform traditional correlations and it can be used to predict values in the undersaturated region too. It is observed from the blind test results that for the prediction of Bo Gradient boost and random forest models (R2 0.97, RMSE 0.01) is a preferable choice and for the prediction of Rs the Gradient boost model (R2 0.97, RMSE 22) can be preferred. The adaptability of ML models to integrate new data over time is a significant feature, ensuring continuous improvement in accuracy. This study adds to the expanding reservoir engineering knowledge base, highlighting the practical use of machine learning for accurately predicting crucial reservoir properties. Its significance goes beyond theoretical progress, providing tangible tools for reservoir engineers and geologists to improve decision-making in the management of oil and gas reservoirs.

Investigating mass transfer around spatially-decoupled electrolytic bubbles

Electrolytic bubbles have a profound impact on mass transport in the vicinity of electrodes and greatly influence the electrolyzer efficiency and cell overpotential. However, experimental measurements of concentration fields around electrolytic bubbles with high spatio-temporal resolution is challenging. In this study, a succession of spatially-decoupled electrolytic bubbles growing in an initially quiescent electrolyte is simulated. The bubbles grow and depart from a hydrophobic cavity at the center of a ring microelectrode. The gas-liquid interface is modeled using a moving mesh topology. A geometric cutting protocol is developed to handle topology changes during bubble departure. The simulated bubbles show good agreement with the bubble growth dynamics observed in experiments. The bubbles in this spatially-decoupled system outgrow the region of electrolyte that is saturated with dissolved hydrogen. This leaves the apex of the bubble interface exposed to an undersaturated region of the electrolyte which leads to an outward flux of hydrogen gas. This is shown to limit the gas evolution efficiency of bubbles even though that they grow at a constant volumetric rate. By analyzing the distribution of the flux of dissolved hydrogen along the bubble interface along with the development of dissolve hydrogen concentration profiles around the bubble, we show that the magnitude of the outward diffusive flux at the apex of the bubble decreases with increasing electrolysis current.

The P-µ-T Cubic Equation of Viscosity for Reservoir Oils

Summary Oil recovery simulation sensitivity increases with heavier oils for the existing viscosity models, driving into higher levels of difficulty when fitting viscosity data for rising oil heaviness, particularly below the saturation pressure. Keeping in view the similarity of trends of viscosity and density with isothermal pressures for reservoir oils, the P-μ-T cubic viscosity model, which was developed for pure hydrocarbon components, was extended to reservoir oils. Two parameters in the P-μ-T cubic viscosity model for mixtures with pure and pseudocomponents are identified for adjusting the viscosity data fitting: Kc for controlling the viscosity gradient with pressure and the “ε” shifting trends for increasing viscosity direction. These two parameters are treated as the adjustable parameters required for fitting the viscosity data. A total of 129 reservoir oils from different sources are used to validate the reliability of the P-μ-T viscosity model. The default model (where ε and Kc are 1 and 45, respectively), extended to 71 light oils, resulted in 31% of average absolute relative deviation (AARD) in viscosity prediction. However, separate adjusted parameters are obtained per oil for more accurate viscosity data fitting. Application of the model in this work results in (post-fitting) AARD% of 2.86% average for 36 low-viscosity oil data, 5.68% for 9 high-viscosity oil data, 9% for five oil blends, and 4.11% for bitumen blends. The model gives an AARD of 3.06% in the undersaturated region and 3.79% in the saturated region for the oil considered. The model predicts better the viscosity above saturation pressure for low-viscosity oils and below saturation pressure for high-viscosity oils. A comparative analysis of the P-μ-T cubic viscosity model vs. other models demonstrates its ability to successfully capture viscosity trends of oil and blends in all viscosity ranges. For simplicity, the P-μ-T cubic viscosity model is proposed with only two optimizing parameters even though using a third parameter improves the matching in heavy oils.

Impregnation of preparative high‐performance solid phase extraction chromatography columns by organophosphorus acid compounds

The flexible and reversible preparation of columns for use in high-performance solid phase extraction chromatography by physisorption of organophosphorus acid extractants has been investigated in detail. Two extractants have been evaluated, bis (2-ethyl-1-hexyl) phosphoric acid (HDEHP) and 2-ethyl-1-hexyl (2-ethyl-1-hexyl) phosphonic acid (HEHEHP), but the developed procedure should be broadly applicable to other extractants. The liquid-liquid solubility of the extractants in feed solvents consisting of aqueous ethanol solutions of varying composition has been determined. The total amount of adsorbed extractant has been quantified by complete desorption and elution with ethanol followed by acid-base titrimetry. Column impregnation with feed solutions of varying concentration in the undersaturated region has been systematically evaluated, and the influence of a subsequent water wash step has been explored. It is shown that to achieve a robust and reproducible physisorption, the adsorbed amount of extractant should be determined after the wash step, and care must be taken when using indirect methods of measurement. Equilibrium Langmuir-type adsorption isotherms as a function of the extractant concentration in the feed solution have been determined. Adsorption of HEHEHP is higher than HDEHP for equal feed compositions, but the solubility of HEHEHP is lower, resulting in approximately identical maximum coverage levels. The ability of the resulting columns to separate rare earth elements have been verified for a mixture of eight metals using a combined isocratic and gradient elution of nitric acid.

Moving boundary approach to forecast tight oil production

AbstractA novel semianalytical production predictive tool for tight reservoirs based on the application of material balance on a transient linear flow system is developed in this paper. This method considers two important regions during transient production of oil reservoirs: the saturated region where gas evolves and flows with oil, and the undersaturated region where only oil flows. A zonal moving boundary approach is used to evolve the two regions as the reservoir pressure gradually decreases. A semianalytical method is used to calculate pressures in the various regions and volumetric expansions. For both black oil and volatile oil scenarios, calculations from this analytical framework are able to match reservoir pressures, oil and gas rates, and cumulative gas–oil ratios determined using a reservoir simulator. The model was also applied to wells in tight reservoirs around the United States such as the Bakken (ND) and the Eagle Ford (TX) with reasonable success.

Application of New Technology to a Mature Piroxicam Crystallization Process To Gain Process Understanding and Control, via Industrial–Academic Collaboration

The established industrial seeded-cooling crystallization of piroxicam was interrogated to gain an understanding of increased batch failures due to polymorph contamination at commercial manufacturing scale. Alternative analysis of plant seed material revealed the presence of the undesired polymorph on the surface of seed batches that had been used in the failed crystallizations, identifying the root cause of the polymorph contamination. Additionally, analysis of the crystallization process with online process analytical technologies identified that a number of the seeding points lay in the undersaturated region of the solubility space and that these seed charges were dissolving. A number of process changes were investigated at lab scale to increase process robustness and eliminate batch failure while maintaining the filed process conditions. Implementation of the selected changes at commercial manufacturing scale resulted in a dramatic shift in process performance.

Spatial patterns of phytoplankton composition and upper-ocean biogeochemistry do not follow carbonate chemistry gradients in north-west European Shelf seas

A key difficulty in ocean acidification research is to predict its impact after physiological, phenotypic, and genotypic adaptation has had time to take place. Observational datasets can be a useful tool in addressing this issue. During a cruise in June–July 2011, measurements of upper-ocean biogeochemical variables, climatically active gases and plankton community composition were collected from northwestern European seas. We used various multivariate statistical techniques to assess the relative influences of carbonate chemistry and other environmental factors on these response variables. We found that the spatial patterns in plankton communities were driven more by nutrient availability and physical variables than by carbonate chemistry. The best subset of variables able to account for phytoplankton community structure was the euphotic zone depth, silicic acid availability, mixed layer average irradiance, and nitrate concentration (59% of variance explained). The spatial variations in phytoplankton and coccolithophores species composition were both found to be more strongly associated with nutrients and physical variables than carbonate chemistry, with the latter only explaining 14 and 9% of the variance, respectively. The plankton community composition and contribution of calcifying organisms was not observed to change under lower calcite saturation state (Ω) conditions, although no regions of undersaturation (Ω < 1) were encountered during the cruise. Carbonate chemistry played a more prominent, but still secondary, role in determining dinoflagellate and diatom assemblage composition (20 and 13% of total variance explained, respectively). Nutrient and physical variables also explained more of the spatial variations of most climatically active gases and selected biogeochemical response variables, although some also appeared to be influenced by carbonate chemistry. This observational study has demonstrated that ocean acidification research needs to be set in context with other environmental forcing variables to fully appreciate the primary, or indeed secondary, role that increasing fugacity of carbon dioxide has on biological communities and associated biogeochemical rates.

Generation of 1:1 Carbamazepine:Nicotinamide cocrystals by spray drying

The present study investigates the potential of spray drying as a technique for generation of pharmaceutical cocrystals. Carbamazepine–Nicotinamide cocrystal (CNC) was chosen as model cocrystal system for this study. Firstly, CNC was generated using liquid assisted grinding and used for generation of phase solubility diagram (PSD) and ternary phase diagram (TPD). Both PSD and TPD were carefully evaluated for phase behavior of CNC when equilibrated with solvent. The undersaturated region with respect to CNC, as depicted by TPD, was selected as target region to initiate cocrystallization experiments. Various points in this region, representative of different compositions of Carbamazepine, Nicotinamide and CNC, were selected and spray drying was carried out. The spray dried product was characterized for solid state properties and was compared with CNC generated by liquid assisted grinding. Spray drying successfully generated CNC of similar quality as those generated by liquid assisted grinding. Moreover, there was no significant impact of process variables on formation of CNC. Spray drying, owing to its simplicity and industrial scalability, can be a promising method for large scale cocrystal generation.

Methanol, acetaldehyde, and acetone in the surface waters of the Atlantic Ocean

[1] Oceanic methanol, acetaldehyde, and acetone concentrations were measured during an Atlantic Meridional Transect (AMT) cruise from the UK to Chile (49°N to 39°S) in 2009. Methanol (48–361 nM) and acetone (2–24 nM) varied over the track with enrichment in the oligotrophic Northern Atlantic Gyre. Acetaldehyde showed less variability (3–9 nM) over the full extent of the transect. These oxygenated volatile organic compounds (OVOCs) were also measured subsurface, with methanol and acetaldehyde mostly showing homogeneity throughout the water column. Acetone displayed a reduction below the mixed layer. OVOC concentrations did not consistently correlate with primary production or chlorophyll-a levels in the surface Atlantic Ocean. However, we did find a novel and significant negative relationship between acetone concentration and bacterial leucine incorporation, suggesting that acetone might be removed by marine bacteria as a source of carbon. Microbial turnover of both acetone and acetaldehyde was confirmed. Modeled atmospheric data are used to estimate the likely air-side OVOC concentrations. The direction and magnitude of air-sea fluxes vary for all three OVOCs depending on location. We present evidence that the ocean may exhibit regions of acetaldehyde under-saturation. Extrapolation suggests that the Atlantic Ocean represents an overall source of these OVOCs to the atmosphere at 3, 3, and 1 Tg yr−1 for methanol, acetaldehyde, and acetone, respectively.

Fluctuation–dissipation theorem for supersaturated electrolyte solutions

Highly supersaturated electrolyte solutions are prepared and studied employing an Electrodynamic Levitator Trap (ELT) technique. The containerless suspension of pl-size solution microdroplets achieved by means of this technique eliminates dust, dirt, convection flows and container walls which normally cause heterogeneous nucleation. This allows very high supersaturations to be achieved and studied. The experimental results obtained for solvent activity versus solute concentration have been processed by applying the least-squares regression. This has allowed processing of the data with large error bars obtained for the very high supersaturations. Theoretical study is based on the development of the Cahn–Hilliard formalism for electrolyte solutions. In the approach suggested the metastable state for electrolyte solutions is described in terms of the local conserved order parameter ω( r,t) associated with fluctuations of the mean solute concentration n 0. Parameters of the corresponding Ginzburg–Landau free energy functional which defines the dynamics of metastable state relaxation are determined and expressed through the experimentally measured solvent activity. A correspondence of 96–99% between theory and experiment for the all solutions studied was achieved and reported earlier [Izmailov et al., Phys. Rev. 52E (1995) 3923]. The theoretical approach suggested in this study for thermodynamics of supersaturated electrolyte solutions is further developed in order to describe the transient and stationary limits of the metastable state relaxation. Knowledge of these limits has allowed derivation of the Fluctuation–Dissipation Theorem (FDT) for supersaturated electrolyte solutions by specifying a time-dependent product of macroscopic mobility (inverse viscosity) and microscopic diffusivity. It is understood from general relationships of non-equilibrium thermodynamics that this product has a maximum at saturation point and is equal to zero at spinodal point. Further analysis of the FDT has revealed that the product of macroscopic mobility and microscopic diffusivity for electrolyte solutions has another particularity: a local minimum in the deeply undersaturated region of solute concentrations. Numerical analysis of the FDT has been carried out for the supersaturated, binary, electrolyte symmetric solutions.

Numerical Analysis of the Vertical Motion of a Single Micron-Sized Particle in a Thermal Gradient Diffusion Chamber with Electrostatic Levitation

A model to describe the vertical motion of a single micron-sized insoluble particle electrically suspended in an upward thermal gradient diffusion chamber is developed. Motion of the particle is determined by five forces: gravitational, electrostatic, aerodynamic drag, thermophoretic, and diffusiophoretic. Condensation/evaporation effects are taken into account. The model predicts the behavior of an aerosol particle with specified characteristics in a diffusion chamber. The use of an aqueous salt solution as the lower pool establishes two regions in the chamber: an undersaturated region with respect to water vapor in the lower portion of the chamber and a supersaturated region in the upper portion. This unique saturation profile combined with certain operating conditions of the chamber leads to an oscillatory motion of the particle.

Diffusion and cluster formation in aqueous solutions of potassium aluminum sulfate

The property and structure of aqueous KAl(SO 4) 2 · 12H 2O solutions were investigated by the measurements of diffusion coefficients and concentration gradients developed in vertical columns of supersaturated solutions. The diffusion coefficients decreased linearly with increasing concentration up to the saturation point and decreased more rapidly with increasing concentration in the supersaturated region. This drastic decrease of diffusion coefficient at supersaturated concentrations was similar to that observed in other supersaturated aqueous solutions which was attributed to the formation of solute clusters in metastable solutions. A cluster diffusion model employing the solution viscosity and thermodynamic data can provide a good correlation between predicted and experimental diffusion coefficients in undersaturated solutions, but fails to provide a reasonable prediction of the much lower values of diffusion coefficients in supersaturated solutions. The average size of the diffusing entities estimated from the diffusion coefficient data showed a steady growth with increasing concentration in the undersaturated region and a faster growth with increasing concentration in the supersaturated region. The average cluster sizes in supersaturated solutions were estimated from the data of concentration gradients in vertical columns and solution thermodynamics using the concept of the number and weight average molecular weights. The estimated cluster size increased with increasing degree of supersaturation as well as solution “age”, and showed good agreement with those estimated from the diffusion coefficient data.

Relationship between diffusivity and viscosity for supersaturated electrolyte solutions

Highly supersaturated electrolyte solutions are prepared and studied employing an electrodynamic levitator trap (ELT) technique. Very high supersaturations were achieved and studied. The theoretical study is based on the development of the Cahn-Hilliard formalism for electrolyte solutions. A correspondence of 96–99% between theory and experiment for all the solutions studied was achieved and reported earlier [Izmailov, Myerson and Na, Phys. Rev. E 52 (1995) 3923]. The theoretical approach suggested in this study for thermodynamics of supersaturated electrolyte solutions is further developed in order to describe the transient and stationary limits of the metastable state relaxation. Knowledge of these limits has allowed derivation of the fluctuation-dissipation theorem (FDT) for supersaturated electrolyte solutions by specifying a time-dependent product of macroscopic mobility (inverse viscosity), describing momentum dissipation, and microscopic diffusivity, describing local fluctuations of solute concentration. It is understood from general relationships of non-equilibrium thermodynamics that this product has a maximum at saturation point and is equal to zero at spinodal point. Further analysis of the FDT has revealed that the product has another particularity: a local minimum in the deeply undersaturated region of solute concentrations. Numerical analysis of the FDT has been carried out for the supersaturated, binary, electrolyte symmetric solutions such as NaCl, NaBr, KCl, KRr and NH 4Cl.

Fabrication and basic characteristics of dry-etched micro inductors

Thin-film meander inductors having 10/sup -6/-m-range coil spacing were fabricated successfully by a dry-etching technique. The inductance measured with a microstrip line increased with coil spacing due to dielectric coupling between the meander lines. The maximum value of the applicable current density was examined, and it was clarified that magnetic thin films are required to provide high saturation magnetization in order to remain in the undersaturated region in case of high current density applications. It is concluded that these results provide a basis for developing thin-film micro inductors and transformers. >

Constant-composition study of the kinetics of the dissolution of strontium fluoride in aqueous solution

A highly reproducible constant-composition technique has been used to study the rates of dissolution of strontium fluoride crystals over a range of undersaturation. At 25 °C and at higher driving forces (relative undersaturation 0.06–0.25) the process appears to follow normal diffusion-controlled dissolution, while at very low undersaturation (0.008–0.015) a surface-controlled reaction predominates. The two regions of undersaturation show markedly different dependences upon the addition of organic phosphonate inhibitors, the action of which can be interpreted in terms of a Langmuir-type adsorption equation.

The kinetics of dissolution of calcium oxalate monohydrate; a constant composition study

The dissolution of calcium oxalate monohydrate, COM, has been studied by a constant composition technique as a function of concentration, temperature, fluid dynamics and in the presence of crystallization inhibitors. The method enables kinetic data to be obtained at very low undersaturation with a precision hitherto unobtainable. A striking change in the mechanism of dissolution is observed as the undersaturation is reduced. At high undersaturation the first-order dependence of the rate of dissolution on the undersaturation suggests the diffusion controlled process normally assumed for dissolution reactions. At very low undersaturations, however, the effective order of reaction appears to approach the value of 2, proposed for a surface controlled reaction. Moreover, the two regions of undersaturation show markedly different dependencies on changes in temperature, hydrodynamics and upon the addition of adsorbing molecules. The theory of Burton, Cabrera, and Frank, as applied to dissolution processes, predicts a change in reaction order from n = 1 to n = 2 as the undersaturation is decreased. This paper represents the first indication of such a change in reaction order for the dissolution of an electrolyte.

Two-rate IPR Testinga Practical Production Tool

Abstract The Inflow Performance Relationship (IPR) of W.E. Gilbert and J. V. Vogel is expanded to include both saturated and undersaturated reservoirs. The equations derived have the flexibility to vary the IPR curvature to account for differing fluid properties of crude oils. The effects of water production are included. A method is presented to define the IPR curve using data from two or three production tests. This permits the calculation of effective formation pressure for the well concerned. It eliminates the need for extended shut-in production periods to obtain reservoir pressure. The use of this technique in stratified reservoir is discussed, showing how it can detect high- or low-pressure water stringers and explain water/oil ratios which increase or decrease with varying production rates. Introduction In calculating the productivity of an oil well, we employ the concept that inflow into the well depends on the difference in pressure between the reservoir and the well bore. With ps (static reservoir pressure) fixed and Pwf(bottom-hole flowing pressure) variable, then ps – Pwf (drawdown) will determine q (the flow rate). Flow rate will increase with drawdown, with qmax (maximum flow rate) occurring at 100% drawdown or zero bottom-hole flowing pressure. There will be a locus connecting the points labelled ps and qmax on the vertical and horizontal axes, providing the relationship (Fig. 1) of flow rate versus pressure. We have developed a functional relationship relating flow rate to bottom-hole flowing pressure. The relationship has been made simple, involving only a straight line and I or a quadratic curve. However, it is more general than some earlier models, and does seem to provide a satisfactory fit for the situations we have encountered. Should our model not be sufficiently flexible for certain purposes, more complex formulas can be employed. Evinger and Muskat(1) (1942) introduced the concept of Productivity Factor, closely related to Productivity Index (PI), the rate at which flow increases with drawdown, and pointed out that it would not be constant for two-phase flow (fluid and gas). Gilbert(2) (1954) introduced the term Inflow Performance (Figure in full paper) Relationship (IPR) for the relationship between flow rate and bottom-hole flowing pressure. Vogel(3) (1968) provided an easily understood method for the application of IPR techniques for solution-gas drive reservoirs. Patton(4) (1980) employed a straight line for the locus when bottom-hole pressure exceeds bubble-point pressure, and a Vogel (quadratic) locus for bottom-hole pressure below bubble-point pressure. References are given at the end of this paper to others who contributed to the evolution of the present concepts. Downhole Flowing Pressure Exceeds Bubble Point If both Ps and Pwf are greater than Pb (the bubble-point pressure), we are dealing with flow in the undersaturated region where production is due mainly to fluid and rock compressibility. There, the rate of flow varies directly with drawdown. Accordingly, the PI is constant. The IPR will take the form shown in Figure 2. The equation can be determined from any two points on the line. One point can be provided by a shut-in pressure test, but that is not essential.

Convection in Fractured Reservoirs Numerical Calculation of Convection in a Vertical Fissure, Including the Effect of Matrix-Fissure Transfer

Abstract A fractured reservoir undergoing pressure depletion, evolution of gas at the top of the oil zone leads to an unstable density inversion in the fissures. The resulting convection brings heavy oil into contact with matrix blocks containing light oil, and results in the transfer of dissolved gas between matrix and fissure in the undersaturated region of the oil zone. To provide a better understanding of this process, numerical solutions were obtained to the differential equations that describe convection in a vertical fissure and include the matrix-fissure transfer. The numerical procedure is an extension of the method of characteristics for miscible displacement problems in two dimensions. The effect of gas evolution in the upper portion of the oil zone is also included in the numerical model. Calculations for a vertical fissure of rectangular shape, with an initial sinusoidal perturbation of an in verse density gradient, show an initial exponential growth of the perturbation that agrees well with that predicted from mathematical theory. Calculations predicted from mathematical theory. Calculations for a vertical fissure having a similar, but slightly tilted, rectangular shape and with an initial, correspondingly tilted, inverse density gradient, show that the effect of the matrix-fissure transfer parameters on the time for overturning can be parameters on the time for overturning can be correlated quite well by curves obtained from mathematical perturbation theory. The most realistic calculations were carried out for the same vertical fissure having a slightly tilted rectangular shape, with declining pressure at the apex and gas evolution included in the gassing zone. The relative saturation-pressure depression in the fissure below the gassing zone can be characterized as increasing as the square of the time, following an incubation period. For practical ranges of the matrix-fissure period. For practical ranges of the matrix-fissure transfer parameters investigated, it is concluded that saturation-pressure depression will be significant. A preliminary correlation for this Pb depression was obtained. The fissure thickness was found to affect the Pb depression significantly. Introduction Most fractured reservoirs of commercial interest are characterized by the existence of a system of high-conductivity fissures together with a large number of matrix blocks containing most of the oil. It has been recognized for some time that analysis of the behavior of a fractured reservoir must involve an understanding of the performance of single matrix blocks under the various environmental conditions that can exist in the fissures. However, it has only recently been recognized that a similar need exists for a better understanding of convective mixing taking place within the oil-filled portion of the fissure system. In a fractured reservoir undergoing pressure depletion, gas will be evolved at all points of the reservoir where the oil pressure has declined below the original saturation pressure. This depth interval is referred to as the gassing zone. Because of the high conductivity of the fracture, the gas in the fissures will segregate rapidly from the oil before reaching the producing wells and most, if not all, of it will join the expanding gas cap. At a sufficient depth, however, the oil pressure will still be higher than the saturation pressure, and the oil there remains in an undersaturated condition. In the gassing zone, gas evolves from the oil in both the fissures and the matrix. The oil left behind in the fissures within the gassing zone contains less dissolved gas and is heavier than the oil below it in the undersaturated zone. This density inversion can result in considerable convection within the highly conductive fissures. As a result of this convection, heavy oil containing less gas is transported downward through the fissures, placing it in contact with matrix blocks containing lighter oil with more dissolved gas. Transfer of dissolved gas from matrix to fissure takes place owing to molecular diffusion through the porous matrix rock; and even more transfer takes place owing to local convection within the matrix block induced by the density contrast between fissure and matrix oil. SPEJ p. 281

Convection in Fractured Reservoirs - The Effect of Matrix-Fissure Transfer on the Instability of a Density Inversion in a Vertical Fissure

Abstract In a fractured reservoir undergoing pressure depletion, evolution of gas at the top of the oil zone leads to an unstable density inversion in the fissures. The resulting convection brings heavy oil into contact with matrix blocks containing light oil, and results in the transfer of dissolved gas between matrix and fissure in the undersaturated region of the oil zone. To provide a better understanding of dis process, an earlier perturbation analysis of a density inversion in a vertical fissure has been extended to include the matrix-assure transfer. It was found that matrix-fissure transfer does not affect the stability or instability of a density inversion, nor does it affect the spacing of density angers or the size of convection cells. A quantitative expression for the rate of growth of unstable density fingers was derived. The effect of matrix-fissure transfer is always to reduce the rate of growth. For practical reservoir cases, while any density inversion should be highly unstable, matrix-fissure transfer can be expected to cause a significant reduction in the linger growth rate. Introduction Most fractured reservoirs of commercial interest are characterized by the existence of a system of high-conductivity fissures together with a large number of matrix blocks containing most of the oil. It has been recognized for some time that the analysis of the behavior of a fractured reservoir must involve an understanding of the performance of single matrix blocks under the various environmental conditions that can exist in the fissures. However, only recently has it been recognized that a similar need exists for a better understanding of the convective mixing that probably takes place within the oil-filled portion of the fissure system. In a fractured reservoir undergoing pressure depletion, gas will be evolved at all points of the reservoir where the oil pressure has declined below the original saturation pressure. This depth interval is referred to as the gassing zone. Because of the high conductivity of the fracture, the gas in the fissures will segregate rapidly from the oil before reaching the producing wells and most, if not all, of it will join the expanding gas cap. At a sufficient depth, however, the oil pressure will still be higher than the saturation pressure, and the oil there remains in an undersaturated condition. (See Fig. 1.) In the gassing zone, gas evolves from the oil in both the fissures and the matrix. The oil left behind in the fissures within the gassing zone contains less dissolved gas and is heavier than the oil below it in the undersaturated zone. SPEJ P. 269

Crystallization and Fractionation Trends in the System Andesite-H2O-CO2-O2 at Pressures to 10 Kb

Phase relations of a Mount Hood andesite, which has the composition of an average orogenic andesite, have been determined as a function of O 2 fugacity at 1 atm and of H 2 O fugacity to pressures of 10 kb, at O 2 fugacities of the quartz-fayalite-magnetite (QFM) buffer. All runs contained either a H 2 O or H 2 O–CO 2 fluid phase; melts in runs with a H 2 O–CO 2 fluid phase were H 2 O undersaturated. The H 2 O contents of the melts and H 2 O fugacities were calculated from NaAlSi 3 O 8 –H 2 O thermo-dynamic data on the assumption of ideal mixing in the system H 2 O–CO 2 . One-atmosphere runs show that melting relations of silicates are little affected by f o 2 but that both ilmenite- and magnetite-out temperatures are raised by higher f o 2 . Ilmenite precipitates at higher temperature than magnetite. In these runs and in all runs at high pressure with H 2 O and H 2 O–CO 2 fluid phases, oxides were not stable at temperatures of the silicate liquidus. Oxides might be stable on the silicate liquidus if f o 2 rose two or more log units above the Ni–NiO (NNO) buffer. However, calculations indicate that in natural magmas, those processes which might change f o 2 —crystal-liquid equilibria or exchange of H 2 , or H 2 and H 2 O with the wall rocks—cannot raise f o 2 by that magnitude. Because differentiation of basalt melts to andesite must involve iron-rich oxide phase subtraction, such fractionation models appear unreasonable. For the Mount Hood andesite composition, plagioclase is the liquidus phase under H 2 O–saturated conditions to 5 kb and under H 2 O–undersaturated conditions at 10 kb when the H 2 O content of the melt is less than 4.7 wt percent. For higher H 2 O contents, either orthopyroxene or, at H 2 O saturation at pressure greater than 8 kb, amphibole assumes the liquidus. In all cases, clinopyroxene crystallizes at lower temperature than orthopyroxene. Melting curves in the H 2 O–under-saturated region may be contoured either as percent H 2 O in melt or as P e H 2 O ; in either case, the topology of the various silicate melting curves is different from the case of H 2 O–saturated melting. Therefore, melting relations determined at H 2 O–saturated conditions cannot be used successfully to predict melting relations in the H 2 O–undersaturated region. Amphibole melting relations were studied isobarically at 5 kb as a function of temperature and fluid-phase composition. Amphibole has a maximum stability temperature of 940 ± 15°C for fluid compositions of 100 to 44 mole percent H 2 O; for fluids containing more CO 2 than 56 percent (or, equivalently, less than 4.4 wt percent H 2 O in melt), the melting temperature is lower. The same relations would be seen if CO 2 were not present and the melt were H 2 O undersaturated. These rather low melting temperatures, relative to other silicate phases, preclude andesite generation by basalt fractionation involving amphibole at pressures less than 10 kb.