Material balances components

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

The constant-molar-overflow assumption represents several prior assumptions. The most important one is equal molar heats of vaporization for the two components. The other assumptions are adiabatic operation (no heat leaks) and no heat of mixing or sensible heat effects. These assumptions are most closely approximated for close-boiling isomers. The result of these assumptions on the calculation method can be illustrated with Fig. 13-28, vdiich shows two material-balance envelopes cutting through the top section (above the top feed stream or sidestream) of the column. If L + i is assumed to be identical to L 1 in rate, then 9 and the component material balance... 

For each stage J, the following 2C -1- 3 component material-balance (M), phase-equilibrium (E), mole-fraction-summation (S), and energy-balance (H) equations apply, where C is the number of chemical species ... 

By combining Eq. (13-73) with Eq. (13-74), Lj is ehminated to give the following working equations for component material balances ... 

Spreadsheet Structure There are three principal sections to the spreadsheet. The first has tables of as-reported and normalized composition measurements. The second section has tables for overall and component flows. These are used to check the overall and component material balance constraints. The third has adjusted stream and component flows. Space is provided for recording the basis of the adjustments. The structure changes as the breadth and depth of the analysis increases. 

Step 6 Write the Component Material Balances. The Phase II auditing steps define the pollutants and wastes that are among the team s focus. Its objective has always been to identify specific wastes or pollutants that the enterprise can reduce these are the components the team needs to assess in the material balances. It is important to note that once the material balance for each unit operation has been completed for raw-material inputs and waste outputs, it is necessary to repeat the procedure for each contaminant of concern. 

Step 7 Write an Overall Material Balance. Remember that the P2 audit focuses on a unit process, but that there are individual unit operations that make up this process. The team will need to develop a series of material balances for each unit operation, and an overall material balance about the entire unit process, to bring closure to a solution of parameters of interest. The individual or component material balances developed may be summed to give a balance for the whole process, production area, or factory. 

The total number of moles n, and composition x, in the distillate receiver can now be obtained from the material and component material balances ... 

As has been mentioned earlier, the CID generates a number Ni , of composition intervals. Within each interval, it is thermodynamically as well as technically feasible to transfer a certain mass of the key pollutant from a waste stream to a lean stream. Furthermore, it is feasible to pass mass from a waste stream in an interval to any lean stream in a lower interval. Hence, for the J th composition interval, one can write the following component material balance for the key pollutant ... 

Component material balance for chloroethanol around the reactor... 

Select an iterative value of Cp which satisfies Eq. (11.15). Therefore, one can calculate the reject concentration by rearranging the component material balance on the solute (Eq. 11.21), i.e.. 

As indicated previously, Eq. (4.5.1) may be applied to die total mass of each stream (referred to as an overall or total material balance) or to die individual eomponents of the streams (referred to as a componential or component material balance). Often the primary task in preparing [Pg.120]

The third term on the left side of the equation has significance in reactive systems only. It is used with a positive sign when material is produced as a net result of all chemical reactions a negative sign must precede this term if material is consumed by chemical reactions. The former situation corresponds to a source and the latter to a sink for the material under consideration. Since the total mass of reactants always equals the total mass of products in a chemical reaction, it is clear that the reaction (source/sink) term (R should appear explicitly in the equation for component material balances only. The overall material balance, which is equivalent to the algebraic sum of all of the component balance equations, will not contain any (R term. 

Perform an overall material balance and the necessary component material balances so as to provide the maximum number of independent equations. In the event the balance is written in differential form, appropriate integration must be carried out over time, and the set of equations solved for the unknowns. 

The component material balances for an ideal CSTR are the following set of algebraic equations ... 

Phase Balances for Components. Material balances can be written for each phase. For the general case of unsteady operation and variable physical properties, the liquid-phase balance is... 

A dynamic model should be consistent with the steady-state model. Thus, Eqs (1) and (4) should be extended to dynamic form. For the better convergence and computational efficiency, some assumption can be introduced the total amounts of mass and enthalpy at each plate are maintained constant. Then, the internal flow can be determined by total mass balance and total energy balance and the number of differential equations is reduced. Therefore, the dynamic model can be established by replacing component material balance in Eq. (1) with the following equation. 

For any given stage, n, the component material balance equations for each phase are thus defined by... 

This combined equation represents a differential total material balance of a component, whether present as HA or the reaction product A-, within the reacting phase. The reader is referred to Olander s original paper for a more complete rationale for generating these differential component material balances for systems of reacting species near equilibrium. By using Olander s technique, the system of four differential equations with reaction terms can be simplified significantly to two differential equations with no reaction terms. 

Mooney et al. [70] investigated the effect of pH on the solubility and dissolution of ionizable drugs based on a film model with total component material balances for reactive species, proposed by Olander. McNamara and Amidon [71] developed a convective diffusion model that included the effects of ionization at the solid-liquid surface and irreversible reaction of the dissolved species in the hydrodynamic boundary layer. Jinno et al. [72], and Kasim et al. [73] investigated the combined effects of pH and surfactants on the dissolution of the ionizable, poorly water-soluble BCS Class II weak acid NSAIDs piroxicam and ketoprofen, respectively. 

The principle of the component material balance can also be extended to the atomic level and can also be applied to particular elements. 

This situation is one involving both a total and a component material balance, combined with a kinetic equation for the rate of decomposition of the waste component. Neglecting density effects, the total material balance equation is... 

For a batch system, with no inflow and no outflow, the total mass of the system remains constant. The solution to this problem thus involves a liquid-phase component material balance for the soluble material, combined with an expression for the rate of mass transfer of the solid into the hquid. 

For reactions involving heat effects, the total and component material balance equations must be coupled with a reactor energy balance equation. Neglecting work done by the system on the surroundings, the energy balance is expressed by where each term has units of kj/s. For steady-state operation the accumulation... 

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. 

The component material balance, when coupled with the heat balance equation and temperature dependence of the kinetic rate coefficient, via the Arrhenius relation, provide the dynamic model for the system. Batch reactor simulation examples are provided by BATCHD, COMPREAC, BATCOM, CASTOR, HYDROL and RELUY. 

The information flow diagram (Fig. 3.27) for this system shows the two component material balance relations to be linked by the equilibrium and transfer rate relationships. 

The sign of the transfer term will depend on the direction of mass transfer. Assuming solute transfer again to proceed in the direction from volume VL to volume VG, the component material balance equations become for volume VL... 

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