A Robust Three-Phase Isenthalpic Flash Algorithm Based on Free-Water Assumption

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Ruixue Li ◽  
Huazhou Andy Li
Keyword(s):  
Energy Conservation ◽  
Oil Recovery ◽  
Pure Water ◽  
Free Water ◽  
Conservation Equation ◽  
Feasible Region ◽  
Feed Mixture ◽  
Two Phase ◽  
Energy Conservation Equation ◽  
Three Phase

Isenthalpic flash is a type of flash calculation conducted at a given pressure and enthalpy for a feed mixture. Multiphase isenthalpic flash calculations are often required in compositional simulations of steam-based enhanced oil recovery methods. Based on a free-water assumption that the aqueous phase is pure water, a robust and efficient algorithm is developed to perform isenthalpic three-phase flashes. Assuming that the feed is stable, we first determine the temperature by solving the energy conservation equation. Then, the stability test on the feed mixture is conducted at the calculated temperature and the given pressure. If the mixture is found unstable, two-phase and three-phase vapor–liquid–aqueous isenthalpic flash can be simultaneously initiated without resorting to stability tests. The outer loop is used to update the temperature by solving the energy conservation equation. The inner loop determines the phase fractions and compositions through a three-phase free-water isothermal flash. A two-phase isothermal flash will be initiated if an open feasible region in the phase fractions appears in any iteration during the three-phase flash or any of the ultimately calculated phase fractions from the three-phase flash do not belong to [0,1]. A number of example calculations for water/hydrocarbon mixtures are carried out, demonstrating that the proposed algorithm is accurate, efficient, and robust.

A Robust Three-Phase Isenthalpic Flash Algorithm Based on Free-Water Assumption

2017 ◽  
Author(s):  
Ruixue Li ◽  
Huazhou Andy Li
Keyword(s):  
Phase Equilibria ◽  
Free Water ◽  
Conservation Equation ◽  
Feed Mixture ◽  
Outer Loop ◽  
Two Phase ◽  
Hydrocarbon Mixtures ◽  
Energy Conservation Equation ◽  
Three Phase ◽  
Vapor Liquid

Multiphase isenthalpic flash calculations are often required in compositional simulations of steam-based enhanced oil recovery methods. These flash calculations are challenging in the narrow-boiling regions and in the determination of the correct number of existing phases. Based on the free-water assumption that the aqueous phase is pure water, a robust and efficient algorithm is proposed to perform isenthalpic three-phase flash calculations in this work. Multiphase equilibria can be considered by this algorithm, including single-phase equilibria, two-phase equilibria, and three-phase vapor-liquid-aqueous equilibria. Isenthalpic flash is a type of flash calculation conducted at given pressure and enthalpy for a feed mixture. In the proposed algorithm, assuming the feed is stable, the temperature is first determined by solving the energy conservation equation. Then the stability test on the feed mixture is conducted at the calculated temperature and the given pressure. If the mixture is found unstable, the two-phase and three-phase vapor-liquid-aqueous isenthalpic flash calculations can be simultaneously initiated without resorting to stability tests. To achieve simultaneous flashes, the outer loop is used to update the temperature by solving the energy conservation equation. The inner loop is used to obtain phase fractions and compositions by performing a three-phase free-water isothermal flash. Note that a two-phase isothermal flash will be initiated if an open feasible region in the phase fractions appears in any iteration during the three-phase isothermal flash or any of the ultimately calculated phase fractions from the three-phase flash do not belong to [0,1]. Negative flash is allowed in the three-phase free-water isothermal flash. A number of example calculations for water/hydrocarbon mixtures are carried out to test the robustness of the proposed algorithm. At low to medium pressures, a good agreement can be achieved between the results obtained by this algorithm and those obtained by the conventional algorithm. This algorithm performs well for the narrow-boiling regions, for example, the three-phase vapor-liquid-aqueous equilibrium region encountered for the water/hydrocarbon mixtures. During the iteration, the new algorithm can readily handle the appearance and disappearance of phases in the inner loop as temperature updates in the outer loop. The number of stability tests involved in the new algorithm is significantly reduced, helping to boost its computational efficiency.

Energy conservation, time-reversal invariance and reciprocity in ducts with flow

2001 ◽  
Vol 431 ◽  
pp. 223-237 ◽  
Author(s):  
WILLI MÖHRING
Keyword(s):  
Energy Conservation ◽  
Sound Wave ◽  
Conservation Equation ◽  
Smooth Transition ◽  
Rotational Flow ◽  
Flow Energy ◽  
Energy Conservation Equation ◽  
Reversal Invariance ◽  
Edge Conditions ◽  
Piecewise Continuous

A sound wave propagating in an inhomogeneous duct consisting of two semi-infinite uniform ducts with a smooth transition region in between and which carries a steady flow is considered. The duct walls may be rigid or compliant. For an irrotational sound wave it is shown that the three properties of the title are closely related, such that the validity of any two implies the validity of the third. Furthermore it is shown that the three properties are fulfilled for lossless locally reacting duct walls provided the impedance varies at most continuously. For piecewise-continuous wall properties edge conditions are essential. By an analytic continuation argument it is shown that reciprocity remains true for walls with loss. For rotational flow, energy conservation theorems have been derived only with the help of additional potential-like variables. The inter-relation between the three properties remains valid if one considers these additional variables to be known. If only the basic gasdynamic variables in both half-ducts are known, one cannot formulate an energy conservation equation; however, reciprocity is fulfilled.

Simulation of astrophysical flows in isentropic approximation

2018 ◽  
Vol 27 (10) ◽  
pp. 1844014
Author(s):  
S. G. Moiseenko ◽  
G. S. Bisnovatyi-Kogan
Keyword(s):  
Shock Wave ◽  
Kinetic Energy ◽  
Energy Conservation ◽  
Conservation Equation ◽  
Numerical Errors ◽  
Energy Conservation Equation ◽  
Different Types ◽  
Entropy Conservation ◽  
Isentropic Approximation ◽  
Astrophysical Flows

One of the difficulties of numerical simulations of cold supersonic astrophysical flows is a big difference in different types of energy. Gravitational and/or kinetic energy of the gas could be much larger than its internal energy. In such a case, it is possible to get large numerical errors in the simulations. To avoid this difficulty, conservation of entropy equation was used instead of energy conservation equation. The entropy conservation equation does not contain the gravitational and kinetic energy. The application of the isentropic set of equations is correct when the flow does not contain shocks or the amplitude of the shocks (shock wave Mach number) is not large. We estimate the violation of the energy conservation low when the “shock wave” is isentropic.

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.

Flow of High Prandtl Number Fluid under Varying Axial Magnetic Field

2012 ◽  
Vol 256-259 ◽  
pp. 2412-2415
Author(s):  
Ru Quan Liang ◽  
Shuo Yang ◽  
Jun Hong Ji ◽  
Ji Cheng He
Keyword(s):  
Magnetic Field ◽  
Stokes Equations ◽  
Axial Magnetic Field ◽  
Internal Flow ◽  
Conservation Equation ◽  
Staggered Grid ◽  
Zone Method ◽  
Two Phase ◽  
Energy Conservation Equation ◽  
Structure Of Flow

From engineering actual conditions of single crystal grown by floating zone method, Navier-Stokes equations coupled with the energy conservation equation were solved on a staggered grid based on the half floating area physical model. The two-phase surface was captured by using the mass conserving level set method. The internal flow structure of flow field of high Pr number liquid bridge was studied under uniform magnetic field environment in microgravity, which is important to optimize the process of the crystal growth.

Influence of Vertical Vibration on Surface Velocity of a Liquid Bridge

2014 ◽  
Vol 580-583 ◽  
pp. 2890-2893
Author(s):  
Ru Quan Liang ◽  
Zhi Hui Zhang ◽  
Tai Yin Gao ◽  
Fu Sheng Yan
Keyword(s):  
Liquid Bridge ◽  
Stokes Equations ◽  
Silicone Oil ◽  
Conservation Equation ◽  
Vertical Vibration ◽  
Surface Velocity ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Two Phase ◽  
Energy Conservation Equation

In this paper, the vertical vibration influence on the surface velocity of a 5cSt silicone oil liquid bridge has been investigated numerically. The Navier-Stokes equations coupled with the energy conservation equation are solved on a staggered grid, and the two-phase surface is captured by using the mass conserving level set method. The present results indicate that the axial and radial surface velocities of the liquid bridge are suppressed by the external vertical vibration.

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