Complete mixing, assumption

Container concentration versus flush volumes (complete mixing assumption)... 

The assumption of equiUbrium between soHd and bulk melt is frequently violated because of lack of complete mixing ia the melt. A steady-state fictitious stagnant-film treatment may be employed to arrive at an effective distribution coefficient,... 

In most cases, laminar gas flow is an unrealistic assumption. A more realistic alternative is to assume a complete mixing of air in the collection system. The collection efficiency in the case of turbulent flow tj j- is given by... 

Chapter 2 developed a methodology for treating multiple and complex reactions in batch reactors. The methodology is now applied to piston flow reactors. Chapter 3 also generalizes the design equations for piston flow beyond the simple case of constant density and constant velocity. The key assumption of piston flow remains intact there must be complete mixing in the direction perpendicular to flow and no mixing in the direction of flow. The fluid density and reactor cross section are allowed to vary. The pressure drop in the reactor is calculated. Transpiration is briefly considered. Scaleup and scaledown techniques for tubular reactors are developed in some detail. 

As shown in Fig. 3, CHEMGL considers 10 major well-mixed compartments air boundary layer, free troposphere, stratosphere, surface water, surface soil, vadose soil, sediment, ground water zone, plant foliage and plant route. In each compartment, several phases are included, for example, air, water and solids (organic matter, mineral matter). A volume fraction is used to express the ratio of the phase volume to the bulk compartment volume. Furthermore, each compartment is assumed to be a completely mixed box, which means all environmental properties and the chemical concentrations are uniform in a compartment. In addition, the environmental properties are assumed to not change with time. Other assumptions made in the model include continuous emissions to the compartments, equilibrium between different phases within each compartment and first-order irreversible loss rate within each compartment [38]. 

Show that the results may be interpreted on the assumptions that the solids are completely mixed, that the gas leaves in equilibrium with the solids and that the adsorption isotherm is linear over the range considered. If the flowrate of gas is 0.679 x 10-6 kmol/s and the mass of solids in the bed is 4.66 g, calculate the slope of the adsorption isotherm. What evidence do the results provide concerning the flow pattern of the gas ... 

At any height z above the bottom of the bed, the heat transfer rate between the particles and the fluid, on the assumption of complete mixing of the solids and piston flow of the gas, is given by ... 

Human exposure limits through air exposure are to be applied at a plant that manufactures Heptachlor, C10H5CI7. Heptachlor is a chemical that is currently restricted in use to termite control, because of exposure concerns. These limits are given in ppm(v), but the release to the air is determined in g/s. Applying the volume flow with the current ventilation system and the volume of the plant in a complete mix reactor assumption resulted in a vapor phase concentration of 0.1 M-g/m. What is the vapor phase concentration in ppm(v) ... 

Complete Mix Reactor - The complete mix reactor is also labeled a completely stirred tank reactor. It is a container that has an inhnite diffusion coefficient, such that any chemical that enters the reactor is immediately mixed in with the solvent. In Example 2.8, we used the complete mix reactor assumption to estimate the concentration of three atmospheric pollutants that resulted from an oil spill. We will use a complete mix reactor (in this chapter) to simulate the development of high salt content in dead-end lakes. A series of complete mix reactors may be placed in series to simulate the overall mixing of a one-dimensional system, such as a river. In fact, most computational transport models are a series of complete mix reactors. 

The Great Salt Lake can be considered as a complete mix reactor for this problem. This is a valid assumption because the time scale of the salinity changes that lead to a salty lake is on the order of tens of thousands of years. 

Nonreacting liquid Under the assumption of complete mixing for the liquid phase and at steady-state conditions, mass transfer from gas to the liquid phase is equal to the mass transfer at the liquid-solid interface ... 

Under the assumption of complete mixing in the radial direction, the material balance is... 

In general, the material balances and the corresponding solutions for trickle and bubble bed reactors are the same, under the assumption that the plug-flow condition holds for both phases. Of course, the appropriate correlations should be used for the estimation of mass transfer coefficients. However, in packed bubble bed reactors, the liquid-phase is frequently found in a complete mixed state, and thus some adjustments have to be made to the aforementioned models. Two special cases will be presented here. 

Continuous flow of both phases in upflow and complete mixing of phases For packed bubble columns (upflow of both gas and liquid phases), under the assumption of complete mixed flow, the backmixing model of Ramachandran and Chaudhari (1980) is applicable. The relevant equations are presented in Section 3.5.1 for the continuous flow of gas and slurry phases in complete mixed-flow conditions (slurry CSTR reactor). 

The data can be evaluated using any commonly available non-linear regression program or with a linear regression, in which k,a is the slope from the plot of the natural log of the concentration difference versus time. Linearity of the logarithmic values over one decade is required for the validity of the measurement. Of course the assumptions inherent in the model must apply to the experimental system, especially in respect to completely mixed gas as well as liquid phases and reactions are negligible. Two common problems are discussed below. Other common pitfalls and problems are summarized in Table 3-3. 

A question to be resolved in predicting efficiency concerns the liquid-flow pattern. It is usual practice to assume that the vapour is fully mixed, but there is a diversity of treatments of the liquid phase. The two limiting cases are completely-mixed-liquid and plug-flow-liquid. Achieved efficiencies on well designed trays usually fall between these cases. The assumption of a well-mixed tray liquid is only valid for the smallest trays (pilot scale). 

Hikita and Nakanishi (H13), 1959 Film flow over spheres (1.42-4.12 cm. diameter) singly and in vertical groups of up to 5, spaced at 5-mm. intervals. CO2 absorbed in water films with and without surfactant additives, Nr, = 1-200. With pure water results for multiple spheres agree with assumption of complete mixing between spheres deviations with surfactants. 

We take the heat transfer coefficient a to be independent of the jet velocity and of the residence time in the vessel. Physically, this assumption together with the assumption of complete mixing of the substance in the reaction vessel and of a constant mean temperature throughout the vessel corresponds to the idea that for heat transfer the governing factor is the thermal resistance from the internal wall of the vessel to the outside space in which the temperature is kept at T0. In other words, our assumption corresponds to the concept of a vessel which is thermally insulated from outside. 

The assumption of a completely mixed reactor was tested by conducting a Br tracer experiment. The procedure used to test the assumption of complete mixing has been described in detail elsewhere (Deitsch and Smith 1995). Based on the results described in the preceding reference, it was... 

For a system in which condenser holdup may not be neglected, the equations based on the assumption of complete mixing within the condenser are (Robinson, 1969) ... 

In his analysis of this system, Saeman (SI) made the following basic assumptions (a) The suspension is completely mixed, (b) The system is operating at steady state, (c) The numerical rate of withdrawing product plus fines equals the nucleation rate, (d) The weight rate of withdrawing product plus fines equals the crystallization rate, (e) The shape factor is constant (linear crystal size proportional to cube root of volumetric size). (f) The linear rate of crystal growth is constant and proportional to the supersaturation. 

The counter-current backmixing model of Fryer and Potter has been modified by assuming mixed flow in the emulsion phase. The terminal conversions obtained with the present model are compared with those of the original model and found to agree well except at very low values of bubble diameter. The assumption of complete mixing in the emulsion phase converts the original two-point boundary value problem into a simpler initial value problem, thereby considerably reducing the mathematical complexity. 

The assumption of complete mixing in the emulsion phase renders the concentration C constant in the bed, and Equations 6 and 7 can be rearranged aS... 

The behavioural features of the fluidized bed have been modeled based on a modified representation of the Fryer-Potter model. The restrictive assumption of plug flow of the emulsion gas has been removed, and model equations developed based on complete mixing of the emulsion gas. This simplification, in addition to bringing the model closer to reality, has led to the conversion of a boundary value problem (Fryer-Potter model) to a simpler initial value problem. Except at very low bubble diameters, the predictions of the two models (based on terminal conversion) agree closely with each other. On the other hand, agreement between the average concentration profiles in the bed predicted by the two models is less satisfactory. While therefore the modified model proposed in this work has the advantage of simplicity and is perhaps closer to reality, further experimental work on industrial size equipment is necessary for a firmer opinion on the latter (nature of gas flow in the emulsion phase). 

The determination of volumetric mass transfer coefficients, kLa, usually requires additional knowledge on the residence time distribution of the phases. Only in large diameter columns the assumption is justified that both phases are completely mixed. In tall and smaller diameter bubble columns the determination of kLa should be based on concentration profiles measured along the length of the column and evaluated with the axial dispersed plug flow model ( 5,. ... 

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