Displacement unsteady state

In Eqs. (4.153) and (4.154), we recognize the general case of an unsteady state diffusion displacement in a solid body. 

The work of Higbte21 in 1935 provided the foundation for the penemoton theory, which supposes that turbulence transports eddies from the bulk of the phase to the interface, where they remain fora short but constant time before being displaced back into the interior of the phase to be mixed with the bulk fluid. Solute is assumed to penetrate into a given eddy during its stay at the interface by a process of unsteady-state molecular diffusion, in accordance with Pick s Second Law and appropriate boundary conditions ... 

However, rheokinetic effects cause the develproducts accumulate on the walls and in the axial zone the flow is accelerated, i.e. the feed rate of the reactants increases. As a result, the Vf = U,. equilibrium is violated, the front line is distmted and its central part is displaced towards the ouq ut. Consequently, the temperatiure becomes lower, the rate of combustion dr<, and the feed—combustion equilibrium is violated still more. Also, the frcmt region is cooled down and is transferred out of the tube. Therefore, for a rheokinetic liquid (polymerizing medium with a sharp viscosity growth), a low-temperature condition for the process is the only steady-state solution. The polymerization front normal to the flow can exist only as an unsteady state and this solution is unstable. 

Relative permeabilities are measured in the laboratory by two general methods, steady state and unsteady state displacement experiments. Although steady state experiments allow data collection over the entire saturation range, the fact that fluid distribution in the steady state experiments may not be the representative of a displacement process, makes the unsteady state experiments more applicable to the reservoir case, (Heaviside and Black (1983)). 

Batycky, J.P., McCaffery, F.G., Hodgins, and P.K., Fisher, D.B. "Interpreting Relative Permeability and Wettability From Unsteady-State Displacement Measurements", SPE J. (June 1981) 296-308. 

Civan, F., and Donaldson, E.C. "Relative Permeability From Unsteady State Displacements An Analytical Interpretation", SPE 16200 presented at SPE Production Operations Symposium, Oklahoma City, OK (March 8-10, 1987). 

The effect of residual oil saturation on polymer retention and the polymer retention during the displacement of oil from porous media has not been reported. Although some phenomena [1-11] indicated that more polymer is retained in the first segment of a porous media, the literature lacks quantitative data on the distribution of retained polymer in porous media. The mechanism of polymer retention during unsteady-state flow [11] has not been adequately described. 

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