X x = Martinelli momentum transfer parameter [ ( d P / = mole fraction solute in liquid, dimensionless = mole fraction solute in gas, dimensionless d2) L / ( d p / d ) G] l ' ' , dimensionless y y* = composition of vapor in equilibrium with annular liquid; defined by Equation ( 6 ) , dimensionless p p Subscripts u = annular liquid film e = entrained liquid G = gas phase L = liquid phase LITERATURE CITED = fluid viscosity, lb. mass/(ft.) (hr.) = fluid density, lb. mass/cu.ft.
A theoretical study has been mode of longitudinal dispersion mechanisms during steady flow of o fluid through unconsolidated spherical beads. The mathematical model utilizes a step function input of thermal energy and presents the solution for the transient behavior of the system. The longitudinal dispersion of the step input is considered the result of eddy mixing of the fluid, molecular conduction within the fluid, and a finite time log for heat transfer to occur between fluid and particle. The latter mechanism is characterized by both a fluid film resistance and on intraparticle resistance. The exact solution, involving on infinite integral,
Flow characteristics of polymer solutions and crosslinked gels through porous media form the bases for several important enhanced oil recovery processes. When a polymer solution is injected into a reservoir for mobility control, flow distribution determines the flood efficiency. When CR(III) crosslinking is applied to xanthan for profile modification, flow distribution of the gel solution along with gelation kinetics dictates gel placement and its effectiveness in improving subsequent water flooding. Rheological characteristics of xanthan and xanthan/Cr(III) solutions are discussed in this paper. Flow rate ratios between capillary bundles of contrasting permeabilities were measured. Flow rate ratios of shear-thinning xanthan and xanthan/Cr(III) solutions were shown to be higher than those of water at low shear rates. Thus, biopolymer solutions are expected to preferentially enter high-permeability streaks in a reservoir formation. A theory to explain this selective emplacement characteristic has been formulated by combining a rheological model and Darcy's law. Introduction Polymer flooding and profile modification are enhanced oil recovery methods to improve sweep efficiency in oilfields where water flooding is no longer economical. These processes involve injection of a polymer solution into the reservoir to reduce the mobility ratio or to modify the subsequent water injection profiles. Two types of polymer systems have been used in low-temperature reservoirs: polyacrylamides and polysaccharides. Among them, xanthan biopolymer is a commercial polysaccharide widely applied for enhanced oil recovery. Xanthan flooding improves sweep efficiency mainly by increasing viscosity of the flooding fluid (from that of water), thus lowering the mobility ratio between the displacing and the displaced fluid (oil). Viscosity of xanthan solutions at the water-oil interface determines the flooding effectiveness. Literature data are abundant regarding the viscosity of xanthan solutions of practical concentrations (less than 1000 ppm) for mobility control in many brines and at various shear rates. The xanthan concentration in gel solutions for profile modification is normally higher than that in flooding solutions. Rheological properties of the concentrated xanthan and gel solutions have not been widely reported. This paper presents viscosity data regarding xanthan and xanthan/Cr(III) solutions for profile modification and their dependence on shear rate as correlated by power-law equations. Profile modification using xanthan/Cr(III) gels is intended to divert flow from high-permeability streaks to poorly swept zones. Gelation of a xanthan/Cr(III) solution occurs during and after emplacement. Emplacement of the gel solution along with gelation kinetics determines the location and the extent to which reservoir permeabilities are modified. After a gel composition is designed in the laboratory, injection rate and pressure are the only remaining control variables during the emplacement process. If the thief zone is mechanically isolated from other zones, selective emplacement is ensured at the wellbore. Often, however, such mechanical isolation is impractical. In such cases, emplacement location is affected by inherent rheological properties of the polymer solution. P. 411^
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