Independent Variables in Steady-Flow Processes

Many kinds of material and chemical processes are carried out under steady flow conditions, and in analyzing such situations, just as in analyzing any situation, we must ensure that we have enough data to perform a proper analysis. This requires us to determine the number of independent variables required to dose the problem. The presentation here builds on material presented in 3.1,3.6,9.1, and 10.3.1. 

The differential forms of the stuff equations were given in 3.6. For a system of C components, the material balances take the form 

In these equations, index a runs over all inlets to the system while p runs over all outlets. The energy balance (12.3.2) is a special form of (3.6.3) assuming negligible mass for the boundary and negligible kinetic and potential energy changes across the system. Note we have C material balances (12.3.1) but only one energy balance (12.3.2). 

In the chemical processing industries, steady-flow systems are common, so the accumulation terms on the left sides of (12.3.1) and (12.3.2) are normally zero, and the rate forms of the balance equations can be used. Then the material and energy balances can be expressed as 

These constitute (C + 1) equations that can be solved for (C + 1) unknowns. In particular situations we may have additional equations available as a result of other constraints that apply, such as phase equilibrium. 

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When we apply thermodynamics to industrial and research problems, we should draw fundamental ideas from Parts 1 and 11, devise an appropriate solution strategy, as in Chapter 10, and combine those with a computational technique, as in Chapter 11. Such a procedme provides values for measurables that can be used to interpret novel phenomena, to design new processes, and to improve existing processes. The procedure is illustrated in this chapter for several well-developed situations. They include conventional phase-equilibrium calculations for vapor-liquid, liquid-liquid, and solid-solid equilibria ( 12.1) solubility calculations for gases in liquids, solids in liquids, and solutes in near-critical solvents ( 12.2) independent variables in steady-flow processes ( 12.3) heat effects for flash separators, absorbers, and chemical rectors ( 12.4) and effects of changes of state on selected properties ( 12.5). 

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