Fluid-density, variations

At constant pressure and granted ideal plug flow, the behavior of a tubular reactor at steady state is mathematically analogous to that of a batch reactor A volume element of the reaction mixture has no means of knowing whether it is suspended tea bag-style in a batch reactor or rides elevator-style through a tubular reactor being exposed to the same conditions it behaves in the same way in both cases. As in a batch reactor, what is measured directly are concentrations—here in the effluent—and a finite-difference approximation is needed to obtain the rate from experiments with different reactor space times and otherwise identical conditions. For a reaction without fluid-density variation ... 

For reactions with fluid-density variations, especially gas-phase reactions with change in mole number, the basic material balance... 

Since conversion across the reactor is minimal, no correction for possible fluid-density variation with conversion need be applied. 

For tubular reactors and reactions with no fluid-density variation, the reactor space time, t = VIV, takes the place of the actual time, t. 

For a continuous stirred-tank reactor at steady state and a reaction with no fluid-density variation, the evaluation can be based on a plot of concentrations instead of rates. Replacement of -rA by appCA in eqn 3.3 for A yields... 

Example 3.2. Decomposition of a herbicide in a CSTR Accelerated life tests of an experimental herbicide in oleic solution in a 500-ml CSTR at 125° C give the results shown in the first three columns of Table 3.4. The analytical method is said to have a possible error of 0.005 M however, the feed concentration CA° is not affected because a stock solution of exactly known composition was used. The flow rate is accurate to 0.02 mL s . Fluid-density variation is negligible. 

In a continuous stirrer-tank reactor at steady state, a first order-first order reversible reaction with no fluid-density variation describes a straight line with slope k and intercept 1 in a plot of l/x versus t (see Figure 5.3). Again, it makes no difference whether x is calculated from the concentration of A or P or any physical... 

For the simple network 5.26 and a reaction with no fluid-density variation, the magnitude of the effect is easily calculated The cumulative selectivity of conversion to P (moles of A converted to P per mole of A consumed, see definition 1.11) in batch and continuous stirred-tank reactors as a function of fractional conversion,/A, is... 

Table 5.4. Cumulative selectivity of conversion to higher-order product in first- and second-order parallel steps with no fluid-density variation in batch and CSTR, (calculated for apCa°/ aq = ) ...

Derivation. For liquid-phase batch, where —rF = — dCF/dr, eqn 10.9 is obtained by integration of eqn 10.8 over time for a continuous stirred tank, eqn 10.10 is obtained from eqn 10.8 and the material balance for the functional groups, —rF = (CF° — Cf)/t. Equations 10.9 and 10.10 assume the reverse reaction to be negligible or suppressed, the rate coefficient to be independent of conversion, and no significant fluid-density variation to occur upon reaction. 

The chemist or engineer designing his experiments to establish quantitative kinetics of gas-phase reactions will do his best to look for constant-volume equipment. However, occasionally he may have to work with data obtained at constant pressure. The complication here is that a change in mole number affects the reaction volume and, thereby, the concentrations of the participants, distorting their histories from which reaction orders and rate coefficients are deduced Fluid-density variation disguises kinetics and must be corrected for. 

Spatial fluid density variations are frequently inherited from the filling history of the reservoir. The initial fluids expelled from a source rock are relatively dense liquids. As a source rock becomes more thermally mature, it expels progressively lighter fluids and eventually gases. When such fluids fill a reservoir, and fill and spill from compartment to compartment within a reservoir, each part of the reservoir can end up with different proportions of fluids of different maturity and density. Field observations show that the segment of the reservoir closest to the source kitchen has often received the latest, lowest density charge. Those areas farthest away from the source kitchen may contain earlier denser fluids that have filled and spilled to their current location. 

Buoyancy forces due to fluid density variations are accounted for by the linear Bousinesq approximation. 

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