Initiator mass balance

The SimuSolv program (Program B) which was written to simulate the reaction finishing process with extra initiator addition is similar to Program A and uses the monomer and initiators mass balance equations with optimized values of the kinetic parameters. The semibatch step had been experimentally optimized for obtaining... 

The presence of a liquid layer on the surface of the filter cake will cause solute to diffuse from the top layer of cake into the liquid. Also if disturbed the layer of liquid will mix with the surface layer of filter cake. This effect can be incorporated into the digital simulation by assuming a given initial depth of liquid as an additional segment of the bed which mixes at time t=0 with the top cake segment. The initial concentrations in the liquid layer and top cake segment are then found by an initial mass balance. 

First, we read in the dataset of complexation reactions and specify that the initial mass balance calculations should include the sorbed as well as aqueous species. We disable the ferric-ferrous redox couple (since we are not interested in ferrous iron), and specify that the system contains 1 g of sorbing mineral. 

Percentage conversion calculated as mmol of aldehyde/mmol of olefin present initially mass balance 97-99% (exception styrene, 93%). Loss of olefin occurred during charging and depressurization of the autoclave. 

We are separating 1000 kmol/h of a feed containing propane, n-butane, and n-pentane. The feed pressure is 4.0 atm This feed is 22.4 mol% propane, 44.7 mol% n-butane, and the remainder n-pentane. In the overall process we plan to recover 99.6% of the propane in the propane product, 99% of the n-butane in the n-butane product, and 99.7% of the n-pentane in the n-pentane product. In column 1 recover 99.5% of the n-butane in the bottoms product. For purposes of your initial mass balances, assume 1) There is no n-pentane in the propane product stream, and 2) There is no propane in the n-pentane product stream Check these guesses after you have run the simulations. Both columns operate at 4.0 atm Operate each column at 1.15 L/D minimum Use the optimum feed stage for each column. 

Besides equilibrium constant equations, two other types of equations are used in the systematic approach to solving equilibrium problems. The first of these is a mass balance equation, which is simply a statement of the conservation of matter. In a solution of a monoprotic weak acid, for example, the combined concentrations of the conjugate weak acid, HA, and the conjugate weak base, A , must equal the weak acid s initial concentration, Cha- ... 

It is often experimentally convenient to use an analytical method that provides an instrumental signal that is proportional to concentration, rather than providing an absolute concentration, and such methods readily yield the ratio clc°. Solution absorbance, fluorescence intensity, and conductance are examples of this type of instrument response. The requirements are that the reactants and products both give a signal that is directly proportional to their concentrations and that there be an experimentally usable change in the observed property as the reactants are transformed into the products. We take absorption spectroscopy as an example, so that Beer s law is the functional relationship between absorbance and concentration. Let A be the reactant and Z the product. We then require that Ea ez, where e signifies a molar absorptivity. As initial conditions (t = 0) we set Ca = ca and cz = 0. The mass balance relationship Eq. (2-47) relates Ca and cz, where c is the product concentration at infinity time, that is, when the reaction is essentially complete. 

In the SMB operation, the countercurrent motion of fluid and solid is simulated with a discrete jump of injection and collection points in the same direction of the fluid phase. The SMB system is then a set of identical fixed-bed columns, connected in series. The transient SMB model equations are summarized below, with initial and boundary conditions, and the necessary mass balances at the nodes between each column. 

Here, m(tp) is the mass of the system contents at final time t and m(t ) is the mass at initial time t . As before, both component and overall mass balances may be written in integral form. 

The mechanism involved the overall conversion of [5] to [P], The reverse reaction is insignificant because only the initial velocity in one of the forward direction is concerned. The mass balance equation expressing the distribution of the total enzyme is ... 

Kevan and colleagues69 studied the products of the radiolysis of solid diaryl sulfones at room temperature, such as p,p -ditolyl, diphenyl sulfone and dibenzothiophene-S,S-dioxide. The products found for the first two were S02 and the diaryl hydrocarbon. For p,p -ditolyl sulfone the S02 yield is linear with dose upto about 13 Mrad, above which it falls off considerably from linearity. The initial yields give G(S02) = 0.05, which is equal within experimental error to the yield of p,p -bitolyl. The only another organic product observed had a smaller yield by a factor of 7, and could not be identified. The authors pointed out that no polymeric product was found in contrast to what is known on benzene radiolysis. The mass balance suggests that a simple decomposition as shown by equation 50 is the net consequence of radiolysis. 

This mass balance equation shows that material that is initially at radial position rin will move to radial position r for some downstream location, >0. A worked example of radial velocities and curved streamlines is given in Chapter 13, Example 13.10. 

In the above reactions, I signifies an initiator molecule, Rq the chain-initiating species, M a monomer molecule, R, a radical of chain length n, Pn a polymer molecule of chain length n, and f the initiator efficiency. The usual approximations for long chains and radical quasi-steady state (rate of initiation equals rate of termination) (2-6) are applied. Also applied is the assumption that the initiation step is much faster than initiator decomposition. ,1) With these assumptions, the monomer mass balance for a batch reactor is given by the following differential equation. 

The experiments were carried out with two initiators. According to published data (B.), at the base temperature, Tb, the fast initiator, II, has a half-life of 3.5 minutes, and the slow initiator, 12, has a half-life of 95 minutes. A minor modification of the monomer mass balance (Equation 7) is required for the case of two initiators. 

Thus, the initial value of the initiator concentrations, [Il]° and [I2]°, are calculated with Equation 15, for given values of the initial loading, feed rates, temperature, and time for the main semi-batch step, and [M]° is fixed according to experimental data from the base case semi-batch step. The nonlinear differential equation for [M] in terms of [II] and [I2] is given by Equation 16. Equation 10, with a redefinition of terms, is the differential equation mass balance for [II] and [12]. In the finishing step, only one of the initiators would be added for residual monomer reduction. Thus, Qm = 0,... 

The system of differential mass balance equations (2)- (5) should be solved, provided that the "in" time functions were known, with the initial conditions ... 

The earher the information on resource efficiency is used in synthesis design, the more efficient process development wiU be. Therefore, appropriate metrics are initially applied to a choice of literature protocols and prehminary experimental data. As knowledge about the process increases, for example, during scale up, it is successively fed into the mass balance. In addition, environmental impacts associated with the mass balance can be evaluated. 

INITIAL specifies the start of the INITIAL region specify the initial concentrations DYNAMIC specifies the start of the DYNAMIC region represent the model equations is a check on the total mass balance... 

Liquid flows continuously into an initially empty tank, containing a full-depth heating coil. As the tank fills, an increasing proportion of the coil is covered by liquid. Once the tank is full, the liquid starts to overflow, but heating is maintained. A total mass balance is required to model the changing liquid volume and this is combined with a dynamic heat balance equation. 

The heating period begins with FLAG set initially to zero. When Xy > 1 then FLAG becomes 1, and the distillation period begins at statement 10. At each time interval the subroutine TCALC is used to make the iterative bubble point calculation. The component mass balance determines the removal of volatiles in the vapour, where the total molar flow rate, V, is determined from the energy balance. 

This section describes the continuous flux melting model used in Bourdon et al. (2003) and has many similarities with the model of Thomas et al. (2002). A significant difference is that the model described here keeps track of the composition of the slab as it dehydrates. This model is based on mass balance equations for both the mantle wedge and the slab. We assume secular equilibrium in the U-series decay chain initially ... 

The other state variables are the fugacity of dissolved methane in the bulk of the liquid water phase (fb) and the zero, first and second moment of the particle size distribution (p0, Pi, l )- The initial value for the fugacity, fb° is equal to the three phase equilibrium fugacity feq. The initial number of particles, p , or nuclei initially formed was calculated from a mass balance of the amount of gas consumed at the turbidity point. The explanation of the other variables and parameters as well as the initial conditions are described in detail in the reference. The equations are given to illustrate the nature of this parameter estimation problem with five ODEs, one kinetic parameter (K ) and only one measured state variable. 

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