Material balancing procedures

The occurrence of a chemical reaction in a process brings several complications into the material balance procedures described in the previous sections. TTie stoichiometric equation of the reaction imposes constraints on the relative amounts of reactants and products in the input and output streams (if A B, for example, you cannot start with 1 mol of pure A and end with 2 mol of B). In addition, a material balance on a reactive substance does not have the simple form input = output, but must include a generation and/or consumption term. 

In using the materials balance model, the flows and compositions of each material were identified and, the balances over each individual process in the NGL plant were conducted. The mass conservation law implies that the mass of an input to several processes should be equivalent to the mass of the output of that process (Himmelblau, 1967) [2]. The material balance procedure used in the case study was based on the discussions in (E.Mortis et.al, 2011) [4]. 

A third approach is suggested by Hugo s formulation of material balances at the limit of bulk diffusion control, described in Section 11.3. Hugo found expressions for the fluxes by combining the stoichiometric conditions and the Stefan-Maxvell relations, and this led to no inconsistencies since there are only n - 1 independent Stefan-Maxwell relations for the n fluxes. An analogous procedure can be followed when the diffusion is of intermediate type, using the dusty gas model equations in the form (5.10) and (5.11). Equations (5.11), which have the following scalar form ... 

In section 11.4 Che steady state material balance equations were cast in dimensionless form, therary itancifying a set of independent dimensionless groups which determine ice steady state behavior of the pellet. The same procedure can be applied to the dynamical equations and we will illustrate it by considering the case t f the reaction A - nB at the limit of bulk diffusion control and high permeability, as described by equations (12.29)-(12.31). 

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),... 

Simplified Design Procedure for Linear Equilibrium and Operating Lines. A straight operating line occurs when the concentrations are low such that and remain essentially constant. (The material balance is obtained from equation 35.) In cases where the... 

The conservation of mass law finds a major application during the performance of pollution-prevention assessments. As described earlier, a pollution-prevention assessment is a systematic, planned procedure with the objective of identifying methods to reduce or ehminate waste. The assessment process should characterize the selected waste streams and processes (Ref. 11)—a necessaiy ingredient if a material balance is to be performed. Some of the data required for the material balance calciilation may be collected during the first review of site-specific data however, in some instances, the information may not be collected until an actual site walk-through is performed. 

A VCM (vinyl chloride monomer) production unit uses three vertically mounted agitated reactors for the polymerization of vinyl chloride. Crude material balances infer about 8 to 10% monomer losses. Describe how you would go about assessing whether these losses are due to leaks such as fugitive air emissions. Be specific in recommending procedures and instruments. 

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. 

It may have been possible to implement very obvious waste-reduction measures already, before embarking on obtaining a material balance (even as early as at the end of Phase I). You should now consider the material balance information in conjunction with visual observations made during the data-collection period, to pinpoint areas or operations where simple adjustments in procedure could greatly improve the efficiency of the process by reducing unnecessary losses. 

Chapter 1 provides a summary of important equations for estimating the terminal temperatures in a heat exchanger. Here we formalize a short estimating procedure for a countercurrent flow situation. Assume that a specifier of a heat exchanger has defined a preliminary sizing of the unit. The system requires heat and material balances. 

We are now in a position to incorporate material balance into the synthesis procedure with the objective of allocating the pinch point as well as evaluating excess capacity of process MS As and load to be removed by external MSAs. These aspects ate assessed through the mass-exchange cascade diagram. 

In summary, the procedure to be adopted in material balance calculations involving reactive systems is as follows ... 

Simple material-balance problems involving only a few streams and with a few unknowns can usually be solved by simple direct methods. The relationship between the unknown quantities and the information given can usually be clearly seen. For more complex problems, and for problems with several processing steps, a more formal algebraic approach can be used. The procedure is involved, and often tedious if the calculations have to be done manually, but should result in a solution to even the most intractable problems, providing sufficient information is known. 

The procedure is based on the theory of recycle processes published by Nagiev (1964). The concept of split-fractions is used to set up the set of simultaneous equations that define the material balance for the process. This method has also been used by Rosen (1962) and is described in detail in the book by Henley and Rosen (1969). 

This procedure for deriving the set of material balance equations is quite general. For a process with n units there will be a set of n equations for each component. 

The split-fraction coefficients can be estimated by considering the function of the process unit, and by making use of any constraints on the stream flows and compositions that arise from considerations of product quality, safety, phase equilibria, other thermodynamic relationships and general process and mechanical design considerations. The procedure is similar to the techniques used for the manual calculation of material balances discussed in Section 4.3. 

The duplex range of stainless steels can be readily cast, wrought and machined. Problems can occur in welding, due to the need to keep the correct balance of ferrite and austenite in the weld area, but this can be overcome using the correct welding materials and procedures. 

Repeat the calculation until a satisfactory material balance is obtained. The usual procedure is to adjust the feed temperature up and down till a satisfactory balance is obtained. 

With the exception of this method, all the methods described solve the stage equations for the steady-state design conditions. In an operating column other conditions will exist at start-up, and the column will approach the design steady-state conditions after a period of time. The stage material balance equations can be written in a finite difference form, and procedures for the solution of these equations will model the unsteady-state behaviour of the column. 

A well-known class of techniques for reducing the number of iterates is the use of tearing (L4). We shall illustrate this procedure by way of an example taken from Carnahan and Christensen (C3). Let us consider the two-loop network shown in Fig. 5 and assume that formulation A is used. To abbreviate the notation let us denote the material balance around vertex i [Eq. (35)] by fi = 0 and the model of the element [Eq. (36)] by fu — 0. Then assuming all external flows and one vertex pressure, p, say, are specified, we have a set of 12 equations that must be solved simultaneously. But if we now assume a value for ql2, the remaining equations may be solved sequentially one at a time to yield the variables in the following... 

Consider the segment of tubular reactor shown in Figure 8.3. Since the fluid composition varies with longitudinal position, we must write our material balance for a reactant species over a different element of reactor (dVR). Moreover, since plug flow reactors are operated at steady state except during start-up and shut-down procedures, the relations of major interest are those in which the accumulation term is missing from equation 8.0.1. Thus... 

In the beginning there is a general loop to decide if more lot sizing procedures should be applied to the existing quant network to meet the constraint of the minimum batch sizes of products. Then the quant network is examined, free usable stocks and free quantities of quants are made available. The material balances of any quant are calculated and decisions are taken whether quants require further explosions of their BOM. Structures for a fast cycle checking, sorting of existing quants and quant links and forecast intervals are built up. A recalculation of the due dates for all quants - also the ones of orders - can be done if specified by the user. 

The basis for the analysis using the SCM is illustrated in Figure 9.3. The gas film, outer product (ash) layer, and unreacted core of B are three distinct regions. We derive the continuity equation for A by means of a material balance across a thin spherical shell in the ash layer at radial position r and with a thickness dr. The procedure is the same as that leading up to equation 9.1-5, except that there is no reaction term involving (- rA), since no reaction occurs in the ash layer. The result corresponding to equation 9.1-5 is... 

The material and energy balances of a tubular vessel are based on the conservation law, Eq 2.42, applied to a differential ring between r and r+dr and z and z+dz. A material balance is derived, for example, in problem P5.08.01, and is quoted in Table 2.6 along with the heat balance. The result is a pair of second order partial differential equations, usually nonlinear, that must be solved numerically. Table 2.6 indicates one possible procedure, but computer software is plentiful. 

Method (b). Numerical integration of the four equations, (3) to (6) is accomplished with ODE, either Constantinides or POLYMATH. Alternately, the material balances (11 and (2) and only the two differential equations (3) and (4) can be solved together. This procedure is better carried out with POLYMATH ODE. 

Materials foam cup, thermometer, stirring rod, ice, water, balance Procedure... 

The compositions of the various streams may be calculated in terms of three unknowns x[ and 2, the ratios of solute to solvent in the first and second washing thickeners respectively, and qP, the amount of insoluble solid B in the underflow streams. An overall material balance is made and then a balance is made on the agitator and its thickener combined, the first washing thickener and the second washing thickener. The procedure is as follows. 

Ridelhoover and Seagrave [57] studied the behaviour of these same reactions in a semi-batch reactor. Here, feed is pumped into the reactor while chemical reaction is occurring. After the reactor is filled, the reaction mixture is assumed to remain at constant volume for a period of time the reactor is then emptied to a specified level and the cycle of operation is repeated. In some respects, this can be regarded as providing mixing effects similcir to those obtained with a recycle reactor. Circumstances could be chosen so that the operational procedure could be characterised by two independent parameters the rate coefficients were specified separately. It was found that, with certain combinations of operational variables, it was possible to obtain yields of B higher than those expected from the ideal reactor types. It was necessary to use numerical procedures to solve the equations derived from material balances. 

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