Steady-state cocurrent flow

A novel flow cell has been developed to observe on a microscopic level the steady state, cocurrent flow of two pre-equilibrated phases in a porous medium. It consists of a rectangular capillary tube packed with a bilayer of monodisperse glass beads 109 microns in diameter. The pore sizes in the model are of the order of magnitude of those in petroleum reservoirs. An enhanced videomicroscopy and digital imaging system is used to record and analyze the flow data. 

The results of the two-phase, steady state, cocurrent flow experiments are summarized in Table II. The various fluid systems from Table I are listed along with selected injection rates and corresponding capillary numbers. Each velocity shown is the sum of the superficial velocities for the two fluids or, equivalently, the ratio of the superficial velocity of either fluid to its fractional flow. The utility of this quantity is discussed later. The viscosities given and used in calculating Ca are those of the wetting phases in the various systems. Most of the data are for 1 1 injection ratios. The observed flow mechanisms are given in the last column of Table II. 

TABLE II. STEADY STATE COCURRENT FLOW OBSERVATIONS... 

The mechanisms of steady state, cocurrent, two-phase flow through a model porous medium have been established for the complete range of capillary numbers of interest in petroleum recovery. A fundamental understanding of the mobile ganglia behavior observed requires a knowledge of how phases break up during flow through porous media. Several mechanisms have been reported in the literature and two have been observed in this flow cell. 

For simplicity of discussion and notation, we will refer to one phase as being liquid and the other phase as being gas. The gas phase flows upward in the -f-z-direction. The liquid phase may flow upward (cocurrent) or downward. A steady-state but otherwise general component balance gives... 

Fig. 1.28. Integrated, autothermal methane reformer with cocurrent flow in the reaction zone and countercurrent heat recovery. Simulated steady-state temperature and conversion profiles.

Example 4.11 Energy dissipation in countercurrent and cocurrent heat exchangers The two most commonly used heat exchangers are countercurrent and cocurrent at steady-state flow conditions as shown in Figure 4.17. Estimate the energy dissipated from these heat exchangers if the surroundings are at 290 K. Consider the data below ... 

Consider a simple mixer for extraction. In minimal entropy production, size I. time t. and duty J are specified and the average driving force is also fixed. We can also define the flow rate Q and the input concentration of the solute, and at steady state, output concentration is determined. The only unknown variables are the solvent flow rate and composition, and one of them is a decision variable specifying the flow rate will determine the solvent composition. Cocurrent and countercurrent flow configurations of the extractor can now be compared with the... 

The second issue for cooled tubular reactors is how to introduce the coolant. One option is to provide a large flowrate of nearly constant temperature, as in a recirculation loop for a jacketed CSTR. Another option is to use a moderate coolant flowrate in countercurrent operation as in a regular heat exchanger. A third choice is to introduce the coolant cocurrently with the reacting fluids (Borio et al., 1989). This option has some definite benefits for control as shown by Bucala et al. (1992). One of the reasons cocurrent flow is advantageous is that it does not introduce thermal feedback through the coolant. It is always good to avoid positive feedback since it creates nonmonotonic exit temperature responses and the possibility for open-loop unstable steady states. 

For a cocurrent flow of gas and liquid at steady state, the governing liquid-phase differential equations for species A and C in dimensionless form are... 

The differences between the TBR and the MR originate from the differences in catalyst geometry, which affect catalyst load, internal and external mass transfer resistance, contact areas, as well as pressure drop. These effects have been analyzed by Edvinsson and Cybulski [ 14,26] via computer simulations based on relatively simple mathematical models of the MR and TBR. They considered catalytic consecutive hydrogenation reactions carried out in a plug-flow reactor with cocurrent downflow of both phases, operated isothermally in a pseudo-steady state all fluctuations were modeled by a corresponding time average ... 

In the Higgins contactor, the resin is moved hydraulically up through the contacting zone. The movement of resin is intermittent and opposite the direction of solution flow except for the brief period of resin advancement when both flows are cocurrent. This type of operation results in a close approach to steady-state operations within the contactor. 

The double pipe, cocurrent heat exchanger is used to cool a distillate product using cold water circulating through the jacket as illustrated in Fig. 2.3. The overall heat transfer coefficient is taken to be U and the mass flow of distillate and water is and Wq, respectively. Under turbulent flow conditions, the fluid temperatures are taken to be uniform across individual flow cross sections. Find the relationship to predict how steady-state temperature changes with axial position, and from this, deduce an expression to compute the average AT... 

Assuming ID isothermal flow, steady-state, constant cross-sectional area, negligible mass transfer between the gas and liquid phases, and constant properties in a cross section, Merchuk and Stein (1981) used a separated flow model of Wallis (1969) for vertical gas-Uquid cocurrent flows to determine gas holdup in gas-liquid bubble columns and airlift reactors ... 

The line is the balance line, or operating line, of the separation in a steady-state process with cocurrent flow. It is identical to the line given by Eq. (1-178). Points on the balance line represent any chosen cross section of the separation unit, with the corresponding concentration X and Y. P, characterizes the entry cross section into the unit and 2 the exit cross section. 

Suppose the two-phase cocurrent flow is not at steady state. Instead, one of the phases is introduced as a pulse or in an interrupted fashion so that we have pulses of the second phase moving in the positive z-direction as the first phase moves continuously. If this... 

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