Multiple-Mixing-Cell Method for Three-Hydrocarbon-Phase Displacements

SPE Journal ◽  
2015 ◽  
Vol 20 (06) ◽  
pp. 1339-1349 ◽  
Author(s):  
Liwei Li ◽  
Saeid Khorsandi ◽  
Russell T. Johns ◽  
Kaveh Ahmadi
Keyword(s):  
Relative Permeability ◽  
Cell Model ◽  
Phase Identification ◽  
Displacement Efficiency ◽  
Compositional Simulation ◽  
Fractional Flow ◽  
Two Phase ◽  
Cell Method ◽  
Multiple Mixing ◽  
Three Phase

Summary Low-temperature oil displacements by carbon dioxide involve complex phase behavior, in which three hydrocarbon phases can coexist. Reliable design of miscible gasflooding requires knowledge of the minimum miscibility pressure (MMP), which is the pressure required for 100% recovery in the absence of dispersion or as defined by slimtube experiments as the “knee” in the recovery curve with pressure in which displacement efficiency is greater than 90%. There are currently no analytical methods to estimate the MMP for multicomponent mixtures exhibiting three hydrocarbon phases. Also, the use of compositional simulators to estimate MMP is not always reliable. These challenges include robustness issues of three-phase equilibrium calculations, inaccurate three-phase relative permeability models, and phase identification and labeling problems that can cause significant discontinuities and failures in the simulation results. How miscibility is developed, or not developed, for a three-phase displacement is not well-known. We developed a new three-phase multiple-mixing-cell method that gives a relatively easy and robust way to determine the pressure for miscibility or, more importantly, the pressure for high-displacement efficiency. The procedure that moves fluid from cell to cell is robust because it is independent of phase labeling (i.e., vapor or liquid), has a robust way to provide good initial guesses for three-phase flash calculations, and is also not dependent on three-phase relative permeability (fractional flow). These three aspects give the mixing-cell approach significant advantages over the use of compositional simulation to estimate MMP or to understand miscibility development. One can integrate the approach with previously developed two-phase multiple-mixing-cell models because it uses the tie-line lengths from the boundaries of tie triangles to recognize when the MMP or pressure for high-displacement efficiency is obtained. Application of the mixing-cell algorithm shows that, unlike most two-phase displacements, the dispersion-free MMP may not exist for three-phase displacements, but rather a pressure is reached in which the dispersion-free displacement efficiency is maximized. The authors believe that this is the first paper to examine a multiple-mixing-cell model in which two- and three-hydrocarbon phases occur and to calculate the MMP and/or pressure required for high displacement efficiency for such systems.

Multiple-Mixing-Cell Method for MMP Calculations

SPE Journal ◽  
2011 ◽  
Vol 16 (04) ◽  
pp. 733-742 ◽  
Author(s):  
Kaveh Ahmadi ◽  
Russell T. Johns
Keyword(s):  
Analytical Methods ◽  
Oil And Gas ◽  
Equilibrium Phase ◽  
Variable Number ◽  
Simulation Methods ◽  
Displacement Efficiency ◽  
Fractional Flow ◽  
Cell Method ◽  
Multiple Mixing ◽  
Tie Lines

Summary The minimum miscibility pressure (MMP) is a key parameter governing the displacement efficiency of gasfloods. There are several methods to determine the MMP, but the most accurate methods are slim-tube experiments, analytical methods, and numerical-simulation/cell-to-cell methods. Slim-tube experiments are important to perform because they use actual crude oil, but they are costly and time consuming. Analytical methods that use the method of characteristics (MOC) are very fast and help to understand the structure of gasfloods. MOC, however, relies on finding the unique and correct set of key tie lines in the displacements, which can be difficult. Slim-tube simulation methods and their simplified cell-to-cell derivatives require tedious fluid and rock inputs, and their MMP estimates can be clouded by dispersion. This paper presents a simple and accurate multiple-mixing-cell method for MMP calculations that corrects for dispersion, and is faster and less cumbersome than 1D simulation methods. Unlike previous mixing-cell methods, our cell-to-cell mixing model uses a variable number of cells, and is independent of gas/oil ratio, volume of the cells, excess oil volumes, and the amount of gas injected. The new method only relies on robust P/T flash calculations using any cubic equation-of-state (EOS). The calculations begin with only two cells and perform additional cell-to-cell contacts between resulting equilibrium-phase compositions based on equilibrium gas moving ahead of the equilibrium liquid phase. We show for a variety of oil and gas compositions that all key tie lines can be found to the desired accuracy, and that they are nearly identical to those found using analytical MOC methods. Our approach, however, is more accurate and robust than those from MOC because we do not make approximations regarding shocks along nontie-line paths, and the unique set of key tie lines converges automatically. The MMP using our mixing-cell method can be calculated in minutes using an Excel spreadsheet and is estimated from a novel bisection method of the minimum tie-line lengths observed in the cells at four or five pressures. Our multiple-mixing-cell method can calculate either the MMP or the minimum miscibility for enrichment (MME) independent of the number of components in the gas or oil. Our approach further supports the notion that the MMP is independent of fractional flow because we obtain the same key tie lines independent of how much fluid is moved from one cell to another.

Coefficients of thermal expansion of unidirectional fiber-reinforced composites using unit-cell model

2018 ◽  
Vol 53 (11) ◽  
pp. 1425-1436
Author(s):  
PC Upadhyay ◽  
JP Dwivedi ◽  
VP Singh
Keyword(s):  
Thermal Expansion ◽  
Cell Model ◽  
Unit Cell ◽  
Fiber Reinforced Composites ◽  
Reinforced Composites ◽  
Unit Cell Model ◽  
Fiber Reinforced ◽  
Two Phase ◽  
Thermal Expansion Coefficients ◽  
Three Phase

Coefficients of thermal expansion of some uniaxially fiber-reinforced composites have been evaluated using three-phase unit-cell model. Results have been compared with the values predicted by two other models based on composite cylinders assembly (CCA), and also with some earlier reported experimental values. An extension of the two-phase unit-cell model has also been presented for the evaluation of thermal expansion coefficients of three-phase composites. The formulation has been used to evaluate the overall coefficients of thermal expansion of AS-graphite/epoxy system with a low modulus coating on the fibers. The results have been compared with the results obtained from the Sutcu's recursive concentric cylinders model for composites containing coated fibers. From the comparison of results of the unit-cell models (both, two-phase and three-phase) with the results obtained from some other models available in the literature, it is concluded that the overall thermal properties of fiber-reinforced composites evaluated by the unit-cell model can be used as effectively as by any other model.

Relative Permeability Characterization for Water-Alternating-Gas Injection in Oil Reservoirs

SPE Journal ◽  
2016 ◽  
Vol 21 (03) ◽  
pp. 0799-0808 ◽  
Author(s):  
H.. Shahverdi ◽  
M.. Sohrabi
Keyword(s):  
Relative Permeability ◽  
Gas Injection ◽  
Hysteresis Effect ◽  
Oil Reservoirs ◽  
Unsteady State ◽  
Two Phase ◽  
Water Alternating Gas ◽  
Three Phase ◽  
Phase Water ◽  
Wag Injection

Summary Large quantities of oil usually remain in oil reservoirs after conventional waterfloods. A significant part of this remaining oil can still be economically recovered by water-alternating-gas (WAG) injection. WAG injection involves drainage and imbibition processes taking place sequentially; therefore, the numerical simulation of the WAG process requires reliable knowledge of three-phase relative permeability (kr) accounting for cyclic-hysteresis effects. In this study, the results of a series of unsteady-state two-phase displacements and WAG coreflood experiments were used to investigate the behavior of three-phase kr and hysteresis effects in the WAG process. The experiments were performed on two different cores with different characteristics and wettability conditions. An in-house coreflood simulator was developed to obtain three-phase relative permeability values directly from unsteady-state WAG experiments by history matching the measured recovery and differential-pressure profiles. The results show that three-phase gas relative permeability is reduced in consecutive gas-injection cycles and consequently the gas mobility and injectivity drop significantly with successive gas injections during the WAG process, under different rock conditions. The trend of hysteresis in the relative permeabilty of gas (krg) partly contradicts the existing hysteresis models available in the literature. The three-phase water relative permeability (krw) of the water-wet (WW) core does not exhibit considerable hysteresis effect during different water injections, whereas the mixed-wet (MW) core shows slight cyclic hysteresis. This may indicate a slight increase of the water injectivity in the subsequent water injections in the WAG process under MW conditions. Insignificant hysteresis is observed in the oil relative permeability (kro) during different gas-injection cycles for both WW and MW rocks. However, a considerable cyclic-hysteresis effect in kro is observed during water-injection cycles of WAG, which is attributed to the reduction of the residual oil saturation (ROS) during successive water injections. The kro of the WW core exhibits much-more cyclic-hysteresis effect than that of the MW core. No models currently exist in reservoir simulators that can capture the observed cyclic-hysteresis effect in oil relative permeability for the WAG process. Investigation of relative permeability data obtained from these displacement tests at different rock conditions revealed that there is a significant discrepancy between two-phase and three-phase relative permeability of all fluids. This highlights that not only the three-phase relative permeability of the intermediate phase (oil), but also the three-phase kr of the wetting phase (water) and nonwetting phase (gas) are functions of two independent saturations.

An Experimental Investigation of Viscous-Oil Recovery Efficiency as a Function of Voidage-Replacement Ratio

SPE Journal ◽  
2016 ◽  
Vol 21 (04) ◽  
pp. 1236-1253 ◽  
Author(s):  
Tae Wook Kim ◽  
E.. Vittoratos ◽  
A. R. Kovscek
Keyword(s):  
Relative Permeability ◽  
Oil Recovery ◽  
Crude Oils ◽  
Replacement Ratio ◽  
Two Phase ◽  
Foamy Oil ◽  
Three Phase ◽  
Solution Gas Drive ◽  
Gas Drive ◽  
Solution Gas

Summary Recovery processes with a voidage-replacement ratio (VRR) (VRR = injected volume/produced volume) of unity rely solely on viscous forces to displace oil, whereas a VRR of zero relies on solution-gas drive. Activating a solution-gas-drive mechanism in combination with waterflooding with periods of VRR less than unity (VRR < 1) may be optimal for recovery. Laboratory evidence suggests that recovery for VRR < 1 is enhanced by emulsion flow and foamy (i.e., bubbly) crude oil at pressures under bubblepoint for some crude oils. This paper investigates the effect of VRR for two crude oils referred to as A1 (88 cp and 6.2 wt% asphaltene) and A2 (600 cp and 2.5 wt% asphaltene) in a sandpack system (18-in. length and 2-in. diameter). The crude oils are characterized with viscosity, asphaltene fraction, and acid/base numbers. A high-pressure experimental sandpack system (1 darcy and Swi = 0) was used to conduct experiments with VRRs of 1.0, 0.7, and 0 for both oils. During waterflood experiments, we controlled and monitored the rate of fluid injection and production to obtain well-characterized VRR. On the basis of the production ratio of fluids, the gas/oil and /water relative permeabilities were estimated under two-phase-flow conditions. For a VRR of zero, the gas relative permeability of both oils exhibited extremely low values (10−6−10−4) caused by internal gas drive. Waterfloods with VRR < 1 displayed encouraging recovery results. In particular, the final oil recovery with VRR = 0.7 [66.2% original oil in place (OOIP)] is more than 15% greater than that with VRR = 1 (55.6% OOIP) with A1 crude oil. Recovery for A2 with VRR = 0.7 (60.5% OOIP) was identical to the sum of oil recovery for solution-gas drive (19.1% OOIP) plus waterflooding (40.1% OOIP). An in-line viewing cell permitted inspection of produced fluid morphology. For A1 and VRR = 0.7, produced oil was emulsified, and gas was dispersed as bubbles, as expected for a foamy oil. For A2 and VRR < 1, foamy oil was not clearly observed in the viewing cell. In all cases, the water cut of VRR = 1 is clearly greater than that of VRR = 0.7. Finally, three-phase relative permeability was explored on the basis of the experimentally determined two-phase oil/water and liquid/gas relative permeability curves. Well-known algorithms for three-phase relative permeability, however, did not result in good history matches to the experimental data. Numerical simulations matched the experimental recovery vs. production time acceptably after modification of the measured krg and krow relationships. A concave shape for oil relative permeability that is suggestive of emulsified oil in situ was noted for both systems. The degree of agreement with experimental data is sensitive to the details of gas (gas/oil system) and oil (oil/water system) mobility.

A Semianalytical Approach for Analysis of Wells Exhibiting Multiphase Transient Linear Flow: Application to Field Data

SPE Journal ◽  
2020 ◽  
Vol 25 (06) ◽  
pp. 3265-3279
Author(s):  
Hamidreza Hamdi ◽  
Hamid Behmanesh ◽  
Christopher R. Clarkson
Keyword(s):  
Numerical Model ◽  
Relative Permeability ◽  
History Matching ◽  
Volatile Oil ◽  
Low Permeability ◽  
Two Phase ◽  
Linear Flow ◽  
Field Case ◽  
Three Phase ◽  
Relative Permeability Curves

Summary Rate-transient analysis (RTA) is a useful reservoir/hydraulic fracture characterization method that can be applied to multifractured horizontal wells (MFHWs) producing from low-permeability (tight) and shale reservoirs. In this paper, we applied a recently developed three-phase RTA technique to the analysis of production data from an MFHW completed in a low-permeability volatile oil reservoir in the Western Canadian Sedimentary Basin. This RTA technique is used to analyze the transient linear flow regime for wells operated under constant flowing bottomhole pressure (BHP) conditions. With this method, the slope of the square-root-of-time plot applied to any of the producing phases can be used to directly calculate the linear flow parameter xfk without defining pseudovariables. The method requires a set of input pressure/volume/temperature (PVT) data and an estimate of two-phase relative permeability curves. For the field case studied herein, the PVT model is constructed by tuning an equation of state (EOS) from a set of PVT experiments, while the relative permeability curves are estimated from numerical model history-matchingresults. The subject well, an MFHW completed in 15 stages, produces oil, water, and gas at a nearly constant (measured downhole) flowing BHP. This well is completed in a low-permeability,near-critical volatile oil system. For this field case, application of the recently proposed RTA method leads to an estimate of xfk that is in close agreement (within 7%) with the results of a numerical model history match performed in parallel. The RTA method also provides pressure–saturation (P–S) relationships for all three phases that are within 2% of those derived from the numerical model. The derived P–S relationships are central to the use of other RTA methods that require calculation of multiphase pseudovariables. The three-phase RTA technique developed herein is a simple-yet-rigorous and accurate alternative to numerical model history matching for estimating xfk when fluid properties and relative permeability data are available.

Three-Phase Relative Permeability Measurements by Unsteady-State Method

1966 ◽  
Vol 6 (03) ◽  
pp. 199-205 ◽  
Author(s):  
A.M. Sarem
Keyword(s):  
Relative Permeability ◽  
Two Phase Flow ◽  
Phase Flow ◽  
Unsteady State ◽  
Two Phase ◽  
Three Phase ◽  
Three Phase Flow ◽  
State Method ◽  
Permeability Data ◽  
Saturation History

Abstract For the performance prediction of multiphase oil recovery processes such as steam stimulation, there is an acute need for three-phase relative permeability data. No fast and simple experimental technique, such as the unsteady-state method proposed by Welge for two-phase flow, is available for the three-phase flow. In this paper, an unsteady-state method is presented for obtaining three-phase relative permeability data; this method is as fast and easy as Welge's method for two-phase flow. Analytical expressions are derived by extension of the Buckley-Leverett theory to three-phase flow to express the saturation at the outflow face for all three phases in terms of the known parameters. It is assumed that the fractional flow and relative permeability of each phase are a function of the saturation of that phase. Other simplifying assumptions made include the neglect of capillary and gravity effects. The effect of saturation history upon relative permeability is acknowledged and attainment of similar saturation history in laboratory and field is recommended. The required experimental work and computations are simple to perform. The test core is presaturated with oil and water, then subjected to gas drive. During the test, required data are the rates of oil, water, and gas production, together with pressure drop and temperature. The ordinary gas-oil unsteady-state relative permeability apparatus can be readily modified to measure the required data. The proposed technique was applied to samples of a Berea and a reservoir core. The effect of saturation history upon relative permeability was studied on one Berea core. It was found that increase in initial water saturation has a similar effect upon three-phase relative permeability as it does in two-phase flow. Introduction In the light of increasing demand for three-phase, relative permeability data for predicting the performance of thermal and other multiphase-flow recovery processes, a simple and accurate method of experimental determination of such data is extremely desirable. Leverett and Lewis1 described the simultaneous flow method of obtaining three-phase relative permeability data. However, Caudle et al.2 reported that this method is very time consuming and cumbersome. Corey3 proposed calculating the three-phase relative permeability from measured krg data. Corey's theory is based on simplified capillary pressure curves,4 assuming a straight line relationship between 1/Pc2 and saturation. Also, Corey's method assumes a preferentially water-wet system. The simplest and quickest method of obtaining three-phase relative permeability data is the unsteady-state method where, for instance, oil and water are displaced by gas. However, in such a test the correlation of average saturation with relative permeability does not give a valid relationship because the rates of oil, water and gas flow in the sample change continuously from the upstream to downstream end. This difficulty in calculating valid relationships was solved by Welge for two-phase flow by deriving an expression from Buckley and Leverett frontal advance equations.5,6 In this paper, relations are established to determine the outflow face saturation and relative permeability to all phases in a three-phase flow displacement experiment. Proposed Method The fundamentals established by Buckley and Leverett5 for two-phase flow were extended to three-phase flow and used as a basis for the derivation of saturation equations. This approach is comparable to Welge's6 use of Buckley and Leverett theory in arriving at expressions to determine the outflow face saturation of the displacing fluid in a two-phase flow system.

Hysteresis in Flow in Porous Media With Phase Transitions

1999 ◽  
Author(s):  
Pavel Bedrikovetsky ◽  
Dan Marchesin ◽  
Paulo Roberto Ballin
Keyword(s):  
Porous Media ◽  
Relative Permeability ◽  
Oil Recovery ◽  
Initial Boundary ◽  
Oil Reservoirs ◽  
Flow In Porous Media ◽  
Fractional Flow ◽  
Two Phase ◽  
Initial Boundary Problem ◽  
Gas Drive

Abstract Two-phase flow with hysteresis in porous media is described by the Buckley-Leverett model with three types of fractional flow functions: imbibition, drainage and scanning. The mathematical theory for the Riemann problem and for non-self-similar initial-boundary problem is developed. The structure of the solutions is presented and the physical interpretation of the phenomena is discussed. We obtain the analytical solution for the injection of water slug with gas drive into oil reservoirs. The solutions show that the effect of hysteresis is to decrease gas flux (in the case where the drainage relative permeability lies below the imbibition relative permeability). This effect increases oil recovery for Water-Alternate-Gas injection in oil reservoirs.

Experimental Study and History-Match of Near-Miscible WAG Coreflood Experiments on Mixed-Wet Carbonate Rocks

2021 ◽  
Author(s):  
Mohamed Mehdi El Faidouzi
Keyword(s):  
Relative Permeability ◽  
Carbonate Rocks ◽  
Hysteresis Model ◽  
Relative Permeabilities ◽  
Two Phase ◽  
Recovery Method ◽  
Phase Displacement ◽  
Three Phase ◽  
Displacement Experiments ◽  
Phase Water

Abstract Water-alternating-gas (WAG) injection, both miscible and immiscible, is a widely used enhanced oil recovery method with over 80 field cases. Despite its prevalence, the numerical modeling of the physical processes involved remains poorly understood, and existing models often lack predictability. Part of the complexity stems from the component exchange between gas and oil and the hysteretic relative permeability effects. Thus, improving the reliability of numerical models requires the calibration of the equation of state (EOS) against phase behavior data from swelling/extraction and slim-tube tests, and the calibration of the three-phase relative permeability model against WAG coreflood experiments. This paper presents the results and interpretation of a complete set of two-phase and thee-phase displacement experiments on mixed-wet carbonate rocks. The three-phase WAG experiments were conducted on the same composite core at near-miscible reservoir condition; experiments differ in the injection order and length of their injection cycles. First, the two-phase water/oil and gas/oil displacement experiments and first cycles of WAG were used to estimate the two-phase relative permeabilities. Then, a synchronized history-matching procedure over the full set of WAG experiments and cycles was carried out to tune Larsen ans Skauge WAG hysteresis model—namely the Land gas traping parameter, the gas reduction exponent, the residual oil reduction factor and three-phase water relative permeability. The second part of this paper deals with the multiphase upscaling of microscopic displacement properties from plug to coarse grid reservoir scale. The two-phase relative permeability curves and three-phase WAG parameters were upscaled using a sector model to preserve the displacement process and reservoir performance. The result of the coreflood calibration indicate that the two-phase displacement and first cycles of WAG yield a consistent set of two-phase relative permeabilities. Including the full set of WAG experiments allowed a robust calibration of the hysteresis model.

RIEMANN SOLUTIONS FOR VERTICAL FLOW OF THREE PHASES IN POROUS MEDIA: SIMPLE CASES

2013 ◽  
Vol 10 (02) ◽  
pp. 335-370 ◽  
Author(s):  
PANTERS RODRÍGUEZ-BERMÚDEZ ◽  
DAN MARCHESIN
Keyword(s):  
Conservation Laws ◽  
Spatial Dimension ◽  
Immiscible Fluids ◽  
Fractional Flow ◽  
Two Phase ◽  
Riemann Solutions ◽  
Two Fluids ◽  
Three Phase ◽  
Three Phase Flow ◽  
Curve Method

We study Riemann solutions for a system of two nonlinear conservation laws that models buoyancy-driven flow of three immiscible fluids in a porous medium, which do not exchange mass. We also assume that the fluids are incompressible and the flow occurs in the vertical spatial dimension. We consider the simplified case in which two of the three fluids have equal densities, obtaining the Riemann solutions by the wave curve method. As expected, the solutions contain waves traveling both upwards and downwards. The sequences of waves contain rarefactions, shocks (sometimes traveling with characteristic speed), and constant states. The shocks found in this work are proper or generalized Lax shock waves. The solutions we found are L1-continuous with respect to the initial data. Waves involving only two fluids often take part in three-phase flow Riemann solutions; this is the basis of a useful tool (the wedge construction) to obtain shocks separating states in distinct two-phase regimes having a common fluid. This tool is similar to fractional flow theory, or Oleinik's convex construction. In this investigation, the wave curve method from the theory of conservation laws is combined with numerical calculations.

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