Continuous processes mass balance problem

The chemical engineer almost never has kinetics for the process she or he is working on. The problem of solving the batch or continuous reactor mass-balance equations with known kinetics is much simpler than the problems encountered in practice. We seldom know reaction rates in useful situations, and even if these data were available, they frequently would not be particularly useful. 

The following exercises are the continuation of the exercises given in Sect. 4.2.2. They address balancing problems with kinetic processes of the heat and mass transfer. 

Unlike water and solid waste, no comprehensive study has been published on air pollution from textile operations. Textile mills produce atmospheric emissions from all manner of processes, and these have been identified as the second greatest problem for the textile industry [8], There has been much speculation about air pollutants from textiles but, in general, air emissions data for textile manufacturing operations are not readily available [9-11]. Most published data are mass balance not direct measurements [12, 13], Direct reading tubes and gas chromatog-raphy/mass spectrometry (GC/MS) have been used more recently to get more reliable data [14, 15]. Hopefully, in the future air emissions data will continue to be collected from textile operations, and better definitions of industry norms can be expected. Considerable effort is now underway in that regard [14, 16]. 

To understand the processing and dispensing behavior of adhesives we often need to construct flow models of the process. While all models are approximations, they still have to satisfy continuity of mass and the balance of momentum and thermal energy. The constitutive equation, plus the appropriate initial and/or boundary conditions of the problem at hand, provide closure to these balance laws. While any realistic solution to a particular processing problem will generally involve numerical computations, several generic problems of interest may be amenable to analytical development. For instance, when a pressure-sensitive adhesive is pressed down unto a surface, we have an example of squeeze flow. Similarly, if a paste is spread onto a surface via a knife, we have an example of wedge flow. These two flows will be discussed for the PLF. 

The analysis of polymer processing is reduced to the balance equations, mass or continuity, energy, momentum and species and to some constitutive equations such as viscosity models, thermal conductivity models, etc. Our main interest is to solve this coupled nonlinear system of equations as accurately as possible with the least amount of computational effort. In order to do this, we simplify the geometry, we apply boundary and initial conditions, we make some physical simplifications and finally we chose an appropriate constitutive equations for the problem. At the end, we will arrive at a mathematical formulation for the problem represented by a certain function, say / (x, T, p, u,...), valid for a domain V. Due to the fact that it is impossible to obtain an exact solution over the entire domain, we must introduce discretization, for example, a grid. The grid is just a domain partition, such as points for finite difference methods, or elements for finite elements. Independent of whether the domain is divided into elements or points, the solution of the problem is always reduced to a discreet solution of the problem variables at the points or nodal pointsinxxnodes. The choice of grid, i.e., type of element, number of points or nodes, directly affects the solution of the problem. 

The ethanol (EtOH) balance directly relates F and P W is not involved, as there is no ethanol in the W stream. A material or component that goes directly from one stream into another without changing in any respect or having like material added to it or lost from it is called a tie component (element). If a tie component exists in a problem, in effect you can write a material balance that involves only two streams. To detect a tie component, ask yourself the question What component or element passes from one stream to another unchanged with constant mass The answer is the tie component. Frequently, several components pass through a process with continuity so that more than one stream can be connected drectly to its respective companion stream. Sometimes a minor constituent passes through with continuity, but if the... 

In this chapter we continue the quantitative development of thermodynamics by deriving the energy balance, the second of the three balance equations that will be used in the thermodynamic description of physical, chemical, and (later) biochemical processes. The mass and energy balance equations (and the third balance equation, to be developed in the following chapter), together with experimental data and information about the process, will then be used to relate the change in a system s properties to a change in its thermodynamic state. In this context, physics, fluid mechanics, thermodynamics, and other physical sciences are all similar, in that the tools of each are the same a set of balance equations, a collection of experimental observ ations (equation-of-state data in thermodynamics, viscosity data in fluid mechanics, etc.), and the initial and boundary conditions for each problem. The real distinction between these different subject areas is the class of problems, and in some cases the portion of a particular problem, that each deals with. 

---