Spreadsheets energy balance calculations

Energy balance calculations are best solved using spreadsheets or by writing a short computer program. A suitable program is listed in Table 3.2 and its use described below. The use of a spreadsheet is illustrated in Example 3.14b. 

Set up a spreadsheet to perform material and energy balance calculations for single-unit and multiple-unit processes. 

The solution strategy will be to calculate H T) and tiiiT) by integrating the heat capacity formulas of Table B.2 from the reference temperature (500°C) to the unknown T at the gas outlet, look up 3 and Ha in the steam tables, substitute for H through 4 in the energy balance, and solve the resulting equation for T using a spreadsheet. 

A spreadsheet that performs the required material and energy balances and vapor-liquid equilibrium calculations on this process unit is shown on the next page. In the test case, a 40 mole benzene-60 mole% toluene mixture is fed to the evaporator at 120°C and a pressure high enough to assure that the feed stream remains in the liquid state. The unit operates at 7 = lOO C and P = 800 mm Hg. 

Process simulation software can also be used to help build simple energy balances in spreadsheet models, for example, by entering stream data to calculate mixture heat capacities, to calculate stream enthalpies, or to estimate heats of reaction. 

Another term used when discussing iteration methods is the tear stream. This is the stream that is guessed (or set to zero) when stepping through the process the first time. In Figure 7.16, if you compute in the order mixer, reactor, separator, then stream 6 is the stream you must assume and check - it is the tear stream. If you compute in the order reactor, separator, mixer, then stream 2 is the tear stream. You apply the Wegstein iteration method to the tear stream. Of course, if the calculations are simple, as would be the case if all physical properties are specified and there are no energy balances, then you can use a spreadsheet. It may be so fast that you do not care whether 10, 100, or 1000 iterations are needed. 

This full plant model captures some system thermal-hydraulic behavior that is not included in the heat balance spreadsheet programs. For example, the heat balance programs do not solve the momentum and energy equations to define the local working gas temperature and pressure. As shown in Figure 12-3, the gas temperature leaving the reactor (1150 K) is the same as that entering the turbine. In reality, and as modeled in TRACE, the gas temperature will be a function of the local pressure and velocity. Therefore, the TRACE results and heat balance spreadsheet calculations will never exactly match. 

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