Mass balance problem

V. CAUSES OF AND APPROACHES TO SOLVING MASS BALANCE PROBLEMS... 

V. Causes of and Approaches to Solving Mass Balance Problems. 186... 

Figure 1 Distillation process mass balance problem...

These two examples have illustrated some of the key steps in solving mass balance problems. In particular, the number of mass balance equations that are available for ensuring you have zero degrees of freedom and the use of the system box to limit yourself to the streams that are of interest. These steps are also key points for the analysis of energy balances in processes, the topic of Section 1.3 in this chapter. 

The mass-balance problem can be solved graphically. The median connecting the vertex C with the AB edge corresponds to the transformation of an equimolar AB mixture into C. Extending this line with an equal segment gives the position of the pole n of coordinates (0,1) and (1,0). From this point, stoichiometric lines can be drawn for any initial composition of the reaction mixtures. When the reaction preserves the number of moles (v, = 0) the stoichiometric lines are parallel. 

Figure 13.8 also shows that the area under the curve is greater for the experimental data than that predicted by the model. This indicates a mass balance problem with the experimental procedure. This mass balance problem is also addressed... 

Be able to solve mass balance problems involving a single chemical reacdon (Sec. 

The heat and mass balance problem/exercise is addressed by considering the rotary cement kiln a combustion system surrounded by a control volume across... 

In many unsteady-state mass balance problems, itiis convenient to take as the system the fluid in some container. Thus, as the mass of fluid increases or decreases, the volume of the system changes. 

The mass balance problem can be solved readily for organic carbon. The filtrates of each fraction filtered sequentially are missing organic matter of a size larger than the membrane cutoff. By measuring either the retentate or filtrate TOC in mg/L, the mass of TOC in each successive filtrate fraction can be determined if it is assumed that (I) the TOC of molecular size less than the membrane cutoff passes in proportion to the volume (2) the membrane behaves ideally as a molecular sieve at each cutoff and (3) the volume is known. Given these conditions, a system of equations (Table V) for either retentate or filtrate fractions can be... 

In this section, we have intentionally omitted mass balance problems. As you will see in Chaps. 7 and 8, this topic is treated in detail and with an emphasis on being quantitative. 

Where possible, a single electrolyte compartment in an undivided cell geometry is favored as it considerably simplifies the constmction, electrolyte flow circuit and maintenance needs, while avoiding the potential drop and mass balance problems which can be associated with a microporous separator or ion-exchange membrane. 

Now let us pose the same mass balance problem in a third fashion (Fig. 2.4). Here, we have eight unknowns and seven relations. Thus, the degree of freedom is 1, so strictly speaking, the problem is not solvable. However, actually, it can be solved for an assumed value of F or Fjj or F r, which will be called the basis and we will notice a simple linear relation between the solution and the chosen basis. This linear relation makes the solution quite useful. 

In the previous section, we have seen that, for a single reaetion, the rates of reaction for different components can all be expressed in terms of the rate of reaction of one component (together with the stoichiometric numbers), or the conversion of one of the reactants, or the yield of one of the produets (of course, together with the stoichiometric numbers). These information and relations for the single reaction are adequate for the solution of any mass balance problem with a single reaction and can be easily extended to multiple reaction systems, as will be shown later. However, in this section, we will try to make the calculations even more systematic. This will require, first, that we introduce the sign convention for the stoichiometric numbers, as we... 

In order to carry out the necessary heat balance, we must first compute the input and output streams and their composition. This means that we should formulate and solve the mass balance problem first. 

Thus, the mass balance problem is solvable. Note that can be easily computed from n f and the given conversion ... 

Irrespective of how we have obtained the spanning tree G°, we choose a reference node in the mass balance problem, it will be clearly the environment node, thus C is the matrix in (3.1.6). We now can classify the nodes (units) n N = N - o according to their distance from Mq. Thus N is partitioned... 

Limitations in this model affect the ability to close mass balances, to represent separate biological processes, and to achieve robust model calibration for some parameters. Mass balance problems arise from failure to account for mass in the sediment due to the fundamental imprecision of BOD as a state variable. Further, we suppose to estimate a contribution for all of modeling processes in calculated values. This model turns out to be easy to use and presents interesting perspectives of combination with a simplified hydraulic model to obtain a practical tool. 

The overall mass-balance problem can be considered in a slightly different way by assessing volumes of acid required to account for the observed abundance of secondary porosity present in an entire sequence. By assuming a value for the generating capacity for the production of organic acids from... 

We consider a simple mass balance problem to demonstrate the use of MATLAB to solve a system of linear equations. For the separation system of Figure 1.9, we know the inlet mass flow rate (in kilograms per hour) and the mass fractions of each species in the inlet (stream 1) and each outlet (streams 2, 4, and 5). We wish to compute the mass flow rates of each outlet stream. 

---