Variable density and viscosity, miscible displacements in capillary tubes

AbstractA computational investigation of variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells is presented. As a first step, two-dimensional base states are obtained by means of simulations of the Stokes equations, which are nonlinear due to the dependence of the viscosity on the local concentration. Here, the vertical position of the displacement front is seen to reach a quasisteady equilibrium value, reflecting a balance between viscous and gravitational forces. These base states allow for two instability modes: first, there is the familiar tip instability driven by the unfavourable viscosity contrast of the displacement, which is modulated by the presence of density variations in the gravitational field; second, a gravitational instability occurs at the unstably stratified horizontal interface along the side of the finger. Both of these instability modes are investigated by means of a linear stability analysis. The gravitational mode along the side of the finger is characterized by a wavelength of about one half to one full gap width. It becomes more unstable as the gravity parameter increases, even though the interface is shifted closer to the wall. The growth rate is largest far behind the finger tip, where the interface is both thicker, and located closer to the wall, than near the finger tip. The competing influences of interface thickness and wall proximity are clarified by means of a parametric stability analysis. The tip instability mode represents a gravity-modulated version of the neutrally buoyant mode. The analysis shows that in the presence of density stratification its growth rate increases, while the dominant wavelength decreases. This overall destabilizing effect of gravity is due to the additional terms appearing in the stability equations, which outweigh the stabilizing effects of gravity onto the base state.

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Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.64 ◽

2013 ◽

Vol 721 ◽

pp. 295-323 ◽

Cited By ~ 16

Author(s):

M. O. John ◽

R. M. Oliveira ◽

F. H. C. Heussler ◽

E. Meiburg

Keyword(s):

Oil Recovery ◽

Stokes Equations ◽

Three Dimensional ◽

Viscous Fingering ◽

Variable Density ◽

Taylor Instability ◽

Constant Density ◽

Streamwise Vorticity ◽

Miscible Displacements ◽

Rayleigh Taylor Instability

AbstractDirect numerical simulations of the variable density and viscosity Navier–Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh–Taylor instability. The dominant wavelength of the Rayleigh–Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh–Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration applications.

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Miscible displacements between silicone oils in capillary tubes

European Journal of Mechanics - B/Fluids ◽

10.1016/s0997-7546(03)00035-9 ◽

2003 ◽

Vol 22 (3) ◽

pp. 271-277 ◽

Cited By ~ 33

Author(s):

Jun Kuang ◽

Tony Maxworthy ◽

Philippe Petitjeans

Keyword(s):

Capillary Tubes ◽

Miscible Displacements ◽

Silicone Oils

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Miscible displacements in capillary tubes: Influence of Korteweg stresses and divergence effects

Physics of Fluids ◽

10.1063/1.1481507 ◽

2002 ◽

Vol 14 (7) ◽

pp. 2052 ◽

Cited By ~ 53

Author(s):

Ching-Yao Chen ◽

Eckart Meiburg

Keyword(s):

Capillary Tubes ◽

Miscible Displacements ◽

Korteweg Stresses

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The Use of Capillary Tube Networks in Reservoir Performance Studies: 1. Equal-Viscosity Miscible Displacements

Society of Petroleum Engineers Journal ◽

10.2118/3068-pa ◽

1971 ◽

Vol 11 (02) ◽

pp. 99-112 ◽

Cited By ~ 24

Author(s):

Ralph Simon ◽

F.J. Kelsey

Keyword(s):

Flow Behavior ◽

Three Dimensional ◽

Reservoir Rock ◽

Reservoir Engineering ◽

Interconnected Network ◽

Spot Pattern ◽

Capillary Tubes ◽

Sweep Efficiency ◽

Miscible Displacements ◽

Electrical Resistivities

Abstract This paper concerns the use of network principles to study displacement phenomena in porous media. The information presented is for equal-viscosity, equal-density miscible displacements. The paper explains the reasons for using an interconnected network of capillary tubes to model the interconnected network of pores in a reservoir rock. A method is presented for defining the heterogeneity of a presented for defining the heterogeneity of a network of tubes based on tube-size and tube-location distribution functions. A technique is described for constructing a network whose heterogeneity models the heterogeneity of pores in a reservoir rock. The use of networks to provide information which can be used in the solution of reservoir engineering problems is illustrated with example calculations of the effect of heterogeneity on fingering, breakthrough, and selective plugging in linear systems, and the effect of heterogeneity on areal sweep efficiency in a five-spot pattern. Introduction Oil in a reservoir is contained in an interconnected three-dimensional network of pores. Direct evidence of the nature of this network of pores comes from examination of petrographic thin sections and three dimensional Scanning Electron Microscope (SEM) pictures of the pores. The SEM pictures show that the pores in a reservoir rock are channels through which flow can occur. These channels have highly irregular configurations so irregular that it is not practical at this time to calculate flow behavior through individual channels or through the interconnected network of the channels. It is practical, however, to use a computer to calculate flow behavior in an interconnected network of capillary tubes and several investigators have studied the problem of using a network of tubes to model a network of pores. pores. Fatt pioneered the idea of using a network of cubes model for reservoir engineering studies. He demonstrated that capillary pressures, relative permeabilities, and electrical resistivities permeabilities, and electrical resistivities calculated for a network model have the same characteristics as those measured for real pores in reservoir rocks. From this, Fatt concluded that the network of tubes is a valid model of real porous media. Rose reinforced Fatt's conclusion and showed that computers can be used to study the displacement characteristics of networks and to obtain results "…which can be supposed to have a direct bearing on the mechanics of petroleum recovery…" This paper takes two steps beyond the work of Fatt and Rose. First, it describes a technique for constructing a network whose heterogeneity models the heterogeneity of natural pores. This is done by matching calculated equal-viscosity miscible displacement behavior in the network with measured behavior in a laboratory core. Second, it illustrates the use of the network model for calculating the effects of heterogeneity on fingering, breakthrough, and plugging in linear systems and areal sweep efficiency in a five-spot pattern. The networks used in the studies in this paper consist of several hundred interconnected capillary tubes of different sizes. Four different types of connections or configurations were investigated and are shown below. These configurations are discussed in detail later in the paper. SPEJ P. 99

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Miscible displacements in capillary tubes: Effect of a preexisting wall film

Physics of Fluids ◽

10.1063/1.1640373 ◽

2004 ◽

Vol 16 (3) ◽

pp. 602-609 ◽

Cited By ~ 3

Author(s):

Ching-Yao Chen ◽

Eckart Meiburg

Keyword(s):

Capillary Tubes ◽

Miscible Displacements ◽

Wall Film

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Miscible displacements in capillary tubes. Part 1. Experiments

Journal of Fluid Mechanics ◽

10.1017/s0022112096008233 ◽

1996 ◽

Vol 326 ◽

pp. 37-56 ◽

Cited By ~ 159

Author(s):

P. Petitjeans ◽

T. Maxworthy

Keyword(s):

Viscous Fluid ◽

Tube Wall ◽

Immiscible Fluids ◽

Local Concentration ◽

Water Mixture ◽

Capillary Tubes ◽

Miscible Displacements ◽

Average Value ◽

Glycerine Water ◽

Dilute Limit

Experiments have been performed, in capillary tubes, on the displacement of a viscous fluid (glycerine) by a less viscous one (a glycerine–water mixture) with which it is miscible in all proportions. A diagnostic measure of the amount of viscous fluid left behind on the tube wall has been found, for both vertical and horizontal tubes, as a function of the Péclet (Pe) and Atwood (At) numbers, as well as a parameter that is a measure of the relative importance of viscous and gravitational effects. The asymptotic value of this diagnostic quantity, for largePeand anAtof unity, has been found to agree with that found in immiscible displacements, while the agreement with the numerical results of Part 2 (Chen & Meiburg 1966), over the whole range ofAt, is very good. At values of the averagePegreater than 1000 a sharp interface existed so that it was possible to make direct comparisons between the present results and a prior experiment with immiscible fluids, in particular an effective surface tension at the diffusing interface could be evaluated. The effect of gravity on the amount of viscous fluid left on the tube wall has been investigated also, and compared with the results of Part 2. A subsidiary experiment has been performed to measure both the average value of the diffusion coefficient between pure glycerine and several glycerine–water mixtures, in order to be able to calculate a representative Péclet number for each experiment, and the local value as a function of the local concentration of glycerine, in the dilute limit.

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The Use of Capillary Tube Networks in Reservoir Performance Studies: II. Effect of Heterogeneity and Mobility on Miscible Displacement Efficiency

Society of Petroleum Engineers Journal ◽

10.2118/3482-pa ◽

1972 ◽

Vol 12 (04) ◽

pp. 345-351 ◽

Cited By ~ 16

Author(s):

Ralph Simon ◽

F.J. Kelsey

Keyword(s):

Porous Media ◽

Plug Flow ◽

Network Models ◽

Miscible Displacement ◽

Mobility Ratio ◽

Displacement Efficiency ◽

Tube Radius ◽

Capillary Tubes ◽

Miscible Displacements ◽

Equal Density

Abstract Part II of this series extends the network technique to all miscible displacement mobility ratios and introduces a heterogeneity factor called H. As a result, the network model can be used to study the general miscible displacement case, i.e., miscible displacements with all mobility ratios in linear or areal flow systems having a range of heterogeneities. Engineering charts are presented which show the relationship between recovery, mobility ratio, heterogeneity and pore volumes injected. Introduction Part I of this series dealt with equal viscosity, and equal-density miscible displacements. Part II extends the network technique to miscible displacements with all mobility ratios. Part II also introduces a heterogeneity factor, H, used in designing network models. The equal-density limitation is retained. Plug flow is assumed in the capillary tubes. The Plug flow is assumed in the capillary tubes. The original fluid and injected fluid are considered ideal so there are no heat or volumetric effects from mixing. Viscosity of the mixtures is discussed in the section on Calculations. Part II is divided into three main sections. The first discusses the calculation methods. The second shows comparisons of data calculated by the network technique and data measured for real porous media. These comparisons demonstrate that porous media. These comparisons demonstrate that network models can indeed be used to predict the performance of displacements in real porous media. performance of displacements in real porous media. The third section illustrates the application of network methods to reservoir engineering problems. The illustration is accomplished with a series of charts that relate oil recovery to heterogeneity, mobility ratio, and pore volumes injected for the special cases of a linear system (length/width = 3/1) and five-spots. CALCULATIONS Two primary steps are required to calculate the effect of heterogeneity and mobility on miscible displacement efficiency. The first is to design a network with the desired heterogeneity. The second is to calculate the displacement phenomena that occur as the injection fluid advances through the network. A network is designed by specifying the following:Type linear or areal flow models.Tube configuration diamond, hexagonal, etc. In this paper all networks are the diamond configurations shown in Fig. 1.Size number of tubes in the network.Heterogeneity by using the heterogeneity factor (see Fig 2a).Tube radius distribution function all tube radius distribution functions are the single modal type shown in Fig. 2a.Tube location distribution all location distributions are random. SPEJ P. 345

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