Mathematical Analysis of Miscible Displacement in Porous Medium

1992 ◽  
Vol 23 (6) ◽  
pp. 1375-1392 ◽  
Author(s):  
Pierre Fabrie ◽  
Michel Langlais
Keyword(s):  
Porous Medium ◽  
Mathematical Analysis ◽  
Miscible Displacement

A Method for Predicting the Performance of Unstable Miscible Displacement in Heterogeneous Media

1963 ◽  
Vol 3 (02) ◽  
pp. 145-154 ◽  
Author(s):  
E.J. Koval
Keyword(s):  
Porous Medium ◽  
Heterogeneous Media ◽  
Research Effort ◽  
Heterogeneous Systems ◽  
Extended Period ◽  
Miscible Displacement ◽  
Longitudinal Dispersion ◽  
Miscible Displacements ◽  
Geometrical Effects ◽  
Displacement Processes

KOVAL, E.J., CALIFORNIA RESEARCH CORP., LA HABRA, CALIF. Abstract Practical miscible displacement processes will be characterized by fingering of the solvent into the oil. The fingering process is brought on by viscosity differences, and can be accentuated by channeling and longitudinal dispersion. The effects of these factors on the efficiency of unstable completely miscible displacements are combined in what is called the K-factor method. This method, analogous to the Buckley-Leverett method, predicts recovery and solvent cut as a function of pore volumes of solvent injected. Experimental data are included and show excellent agreement with theory for a wide variety of sandstone cores and viscosity ratios. Introduction Theoretical considerations, laboratory experiments, and pilot tests lead to the conclusion that miscible displacements in the field will be unstable. In an unstable miscible displacement, the solvent fingers through the oil. This fingering leads to early breakthrough of the solvent and an extended period during which both oil and solvent are produced.For such a system, there appear to be four principal factors which bring about or accentuate the effects of instability: longitudinal dispersion (including geometrical effects), channeling, viscosity differences and gravity differences. Other factors, such as diffusion and flooding rate, can also influence the effects of instability, but at the flooding rates considered in this report, circa 15 ft/D, they are unimportant. Longitudinal dispersion can be thought of as a spreading of the solvent front caused by the presence of microscopic inhomogeneities. Channeling of the solvent occurs when a porous medium has macroscopic inhomogeneities; i.e., gross permeability variations. Viscosity differences lead to fingering of the less viscous solvent. This difference in viscosity accelerates the growth of fingers along paths previously developed because of permeability variations. Gravity differences lead to overriding of the usually less dense solvent. Although gravity effects are generally small at a flooding rate of 15 ft/D, they would, nevertheless, unnecessarily complicate the interpretation of flooding experiments. For this reason, all the experiments reported herein were done with matched density fluids.Fingering and the resultant poor areal sweep were recognized early as the dominant influences on the efficiency and the economics of miscible displacement processes. Much research effort has been spent on ways to minimize fingering and increase areal sweep such as the use of graded viscosity slugs or water slugs. Some researchers attempted to work out ways to prevent fingering completely; i.e., to achieve a stable displacement through gravity or latitudinal dispersion stabilization. Others did not attempt to control fingering but obtained an economic process by merely recycling the solvent and sweeping pattern by pattern.During this period, all aspects of fingering came under close scrutiny. Some researchers reported on how fingering looks and how it is affected by viscosity ratio, geometry, and slug size. Peaceman and Rachford suggested a mathematical approach to the prediction of unstable miscible displacements in relatively homogeneous sand packs, but their work cannot be extended conveniently to heterogeneous systems. Hence for a heterogeneous system, no method is presently available for predicting solvent cut and recovery as functions of pore volumes of solvent injected.The purpose of this investigation was to attempt to fill in the gap in our knowledge concerning the prediction of performance of unstable miscible displacements. Necessarily, the system selected for study was a relatively simple one. The restrictions placed on the system were:The system was linear;The solvent was miscible in all proportions with the oil in place;The solvent was continuously injected into the porous medium;Gravitational effects were eliminated by matching densities andAll the flood rates were high and constant at 15 ft/D to avoid any small rate effect and to minimize any diffusion effects. To simplify and to indicate that both longitudinal dispersion and channeling arise from permeability variations, the effects which they cause or influence have been termed heterogeneity effects. SPEJ P. 145^

ASYMMETRY OF THE CONCENTRATION FRONT DURING MISCIBLE DISPLACEMENT IN POROUS MEDIA

1958 ◽  
Vol 36 (11) ◽  
pp. 1476-1482
Author(s):  
A. E. Scheidegger ◽  
V. C. Larson
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Boundary Conditions ◽  
Miscible Displacement ◽  
Analogue Computer ◽  
Constant Concentration ◽  
Electrical Analogue ◽  
Displacement Experiments ◽  
The Asymmetry ◽  
Diffusivity Equation

During many feasible experiments concerning miscible displacement in porous media, it has been noted that the concentration front is slightly asymmetric. It is possible that this is due to an asymmetry in the boundary conditions which is present in most practicable displacement experiments. The present paper endeavors to investigate the influence of asymmetric boundary conditions upon the shape of the concentration front: The diffusivity equation basic to the theory of miscible displacement has been solved for the case of injection of fluid of constant concentration at one end of a long, linear porous medium. The solution has been effected by an electrical analogue computer. Curves showing the asymmetry are given.

Oil Recovery by Hydrocarbon Slugs Driven by a Hot Water Bank

1971 ◽  
Vol 11 (04) ◽  
pp. 342-350 ◽  
Author(s):  
Abbas A. Alikhan ◽  
S.M. Farouq Ali
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Oil Recovery ◽  
Miscible Displacement ◽  
Light Hydrocarbon ◽  
Hot Water ◽  
Residual Oil ◽  
Oil Viscosity ◽  
Connate Water ◽  
Experimental Apparatus

Abstract An experimented study was conducted of the recovery of oil from as porous medium overlain and underlain by heat-conducting formations and containing a residual oil or connate water saturation by injection of a small slug of a light hydrocarbon followed by 1/2 PV of hot water driven by a conventional waterflood. The fluid production histories and the temperature distribution obtained showed that a light hydrocarbon sag injected ahead of a hot water slug leads to a considerable increase in oil recovery. The net oil recovery was found to depend on the original oil viscosity, hydrocarbon slug viscosity, and the injection rate. The process was more effective in a previously waterflooded core rather than in one containing connate water. The over-all ratio of the total hydrocarbon produced to the hydrocarbon injected ranged from 1.10 to 3.96, the variation corresponding to the viscosity of the hydrocarbon slug employed. Introduction Numerous methods have been proposed for recovering oil from previously waterflooded porous media. Some methods involve the application of heat in one form or another, while others utilize miscible displacement processes. The proposed method involves a combination of the two, employing a small hydrocarbon slug followed by a slug of hot water, which is driven by a conventional waterflood. An attempt was made to investigate the conditions (residual oil saturation, viscosity, etc.) under which such a method would yield a sizable oil recovery. Use of a solvent dug followed by at heat-carrying agent was earlier considered by Pirela and Farouq Ali. The process was designed to take advantage of the improved ternary-phase equilibrium behavior at elevated temperatures in the alcohol slug process. The experimental runs were conducted under isothermal conditions. In another study, Avendano found that injection of a light crude oil into a core containing a highly viscous oil prior to steam injection led to a large improvement in oil recovery. A number of investigators have studied the effect of water-driven hydrocarbon slugs on oil recovery from waterflooded porous media. Csaszar and Holm employed slugs of propane in waterflood cores containing oils with viscosities ranging from 3 to 9 cp. The volume of the oil recovered was 2 to 3 times the propane injected, the efficiency of the process depending on the amount of mobile oil process depending on the amount of mobile oil near the point of injection and the viscosity of the in-place oil. Wiesenthal used gasoline as an intermediate slug when waterflooding cores containing oils having viscosities of 1.28 to 324 cp. He found that the process was effective in waterflooded porous media, especially in the case of viscous oils. Fitzgerald conducted similar experiments using gasoline and arrived at more or less the same conclusions. The process under consideration involves a combination of miscible displacement and hot waterflooding, both of which have been amply discussed in the literature. A comprehensive survey of miscible displacement has been presented by Perkins and Johnston, while a description of hot Perkins and Johnston, while a description of hot waterflooding may be found elsewhere. In the following, only the most important features of the two processes operating in the combination process will be considered. EXPERIMENTAL APPARATUS AND PROCEDURE PROCEDURE APPARATUS The porous medium used in the present investigation consisted of a steel cube 4 ft in length with a rectangular cross-section and inside dimensions of 1.5 × 3.5 in., packed with 130-mesh glass beads. The resulting core had a porosity of 39.95 percent (PV = 1,690 cc) and permeability of 7 darcies. The core was provided with 15 connections on one side for thermocouples and 5 connections on the other side for transducers. SPEJ P. 342

scholarly journals Experimental investigation of dispersion phenomenon in a fractured porous medium

2015 ◽  
Vol 4 (1) ◽  
pp. 209
Author(s):  
Ali Sanati ◽  
Mohammad Yousefi Khoshdaregi
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Dispersion Coefficient ◽  
Flow Direction ◽  
Fractured Reservoirs ◽  
Miscible Displacement ◽  
Naturally Fractured Reservoirs ◽  
Volume Calculation ◽  
Fractured Porous Medium ◽  
Core Samples

Dispersion of fluids flowing through porous media is an important phenomenon in miscible displacement. Dispersion causes instability of miscible displacement flooding; therefore, to obtain and maintain the miscibility zone, the porous medium dispersivity should be considered in displacing fluid volume calculation. Many works have been carried out to investigate the dispersion phenomenon in porous media in terms of theory, laboratory experiments and modeling. What is still necessary is to study the effects of presence of fracture in a porous medium on dispersion coefficient or dispersivity. In this work dispersion phenomenon in a fractured porous medium has been investigated through a series of miscible displacement tests on homogeneous sandstone core samples. Tests were repeated on the same core samples with induced fracture in the flow direction. The effects of fracture on miscible displacement flooding have been studied by comparison of the results of dispersion tests in the absence and presence of fracture. In the presence of fracture, breakthrough time reduced and the tail of effluent S-shaped curve smeared. Moreover, the slope of S-shaped curve at 1 pore volume of injected fluid was lower than homogeneous case which means dispersion coefficient increased. The results presented in this work provide an insight to the understanding of dispersion phenomenon for modeling of miscible displacement process through naturally fractured reservoirs.

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