Material balance component balances

The information flow diagram for a non-isothermal, continuous-flow reactor (in Fig. 1.18, shown previously in Section 1.2.5) illustrates the close interlinking and highly interactive nature of the total material balance, component material balance, energy balance, rate equation, Arrhenius equation and flow effects F. This close interrelationship often brings about highly complex dynamic behaviour in chemical reactors. 

Formulation of the mathematical model here adopts the usual assumptions of equimolar overflow, constant relative volatility, total condenser, and partial reboiler. Binary variables denote the existence of trays in the column, and their sum is the number of trays N. Continuous variables represent the liquid flow rates Li and compositions xj, vapor flow rates Vi and compositions yi, the reflux Ri and vapor boilup VBi, and the column diameter Di. The equations governing the model include material and component balances around each tray, thermodynamic relations between vapor and liquid phase compositions, and the column diameter calculation based on vapor flow rate. Additional logical constraints ensure that reflux and vapor boilup enter only on one tray and that the trays are arranged sequentially (so trays cannot be skipped). Also included are the product specifications. Under the assumptions made in this example, neither the temperature nor the pressure is an explicit variable, although they could easily be included if energy balances are required. A minimum and maximum number of trays can also be imposed on the problem. 

With the foregoing assumptions, the process steps of interest may be described starting with two material balances, a balance for the light component and a total balance The balances are taken on the first and i-th cells and are written for a differential time dt. 

Errors in the MESH equations of Sec. 4.1.2 should be small, including the stage energy total material and component balances and summation equation should be small. The physical solution criteria above should take precedence over any mathematical criteria, such as having Newton-Raphson functions approach zero (Sec. 4.2.6). 

To complete the material balance, components in streams 215 and 325 are provided in kg/h as... 

In general, a polymerization process model consists of material balances (component rate equations), energy balances, and additional set of equations to calculate polymer properties (e.g., molecular weight moment equations). The kinetic equations for a typical linear addition polymerization process include initiation or catalytic site activation, chain propagation, chain termination, and chain transfer reactions. The typical reactions that occur in a homogeneous free radical polymerization of vinyl monomers and coordination polymerization of olefins are illustrated in Table 2. 

Since all stages in the model have a general designation, the equations are written for any stage (j = 1, 2,. .N). The equations required to completely define a stage include material balance, energy balance, and phase equilibrium equations. The component material balance around stage j is written in terms of total flows and mole fractions ... 

In this method, the component material balance, enthalpy balance, and phase equilibrium equations are written for component i on stage j at unsteady state ... 

Equation (17.1) is a total material balance. Another balance can be written by equating input to output for component A. Since the number of moles of this component in a stream is the product of the flow rate and the mole fraction of A in the stream, the input of component A to the section under study, for a two-component system, is moles per hour, the output is... 

If the material and component balances are to be carried out using a computer, preparing the program and simulation at this stage may prove very beneficial Once the program is ready, data can be quickly processed and inconsistencies easily detected before or during the test, before it is too late. 

Mass transfer is a main concern in chemical and bioprocess engineering since most industrial processes uses mass transfer operations not only to mix components but also to separate them The design of these operations is a core part of a chemical and bioprocess engineer curriculum and is based on knowing material balances, energy balances, equilibrium, and mass transfer. 

The solution methodology involves a numerical integration using the method of Sundaram and Evans [1]. The overall material and component balances are given by... 

The influence of the liquid flow rate variation on die mass transfer efficiency is described [149] for a distillation unit with an enridunent zone above the feed section and a striping zone below it. The unequally distributed liquid over the three column cross-sections is tricMing downward countercurrently to the uniformly entering vapour flow, which is ideally mixed by the column internals at the feed section. On the trasis of the material and component balances, different conc trations for die liquid and vapour flow leaving die enrichment zone result. For the simulation it is assumed [149] that all parallel sections have same number of theoretical stages. 

Consider the single-stage phase split shown in Fig. 3.1a. Overall material balances and component material balances can be written as... 

In addition to being able to predict the energy costs of the heat exchanger network and utilities directly from the material and energy balance, it would be useful to be able to calculate the capital cost, if this is possible. The principal components that contribute to the capital cost of the heat exchanger network are... 

Let us take each of these components in turn and explore whether they can be accounted for from the material and energy balance without having to perform heat exchanger network design. 

The amounts of each phase and their compositions are calculated by resolving the equations of phase equilibrium and material balance for each component. For this, the partial fugacities of each constituent are determined ... 

Design Procedure. The packed height of the tower required to reduce the concentration of the solute in the gas stream from to acceptable residual level ofjy 2 may be calculated by combining point values of the mass transfer rate and a differential material balance for the absorbed component. Referring to a sHce dh of the absorber (Fig. 5),... 

Total material, condensable component, and energy balances can be written for the entire column ... 

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