# Making a System Balance (Part 2)

March 6, 2013
 KEYWORDS Excel workbook / material balance Email / Print / Reprints / More / Text Size+

Last month’s article showed how to make a system balance when the material and heat balances were coupled. Our example was the use of oxygen enrichment on natural gas combustion for heating aluminum.[1] We used Excel’s Goal Seek tool twice to obtain system-balance closure. The details are in Excel workbook SysBalCalc.xlsx, which can be downloaded from www.industrialheating.com. The workbook has a template for calculating over 20 stream properties for the system for each change in %O2. This month, we extend the technique to calculate the energy saved by preheating the combustion air.[2-4]

The air preheat system-balance calculation is more complex than for oxygen enrichment because of the presence of a recycling stream and the added recuperator heat exchanger. Goal Seek isn’t able to solve the equation sets for this example. Instead, we’ll need to use Excel’s Solver tool.

## Calculational Strategy

The first task is to calculate the heat loss from the heat exchanger for the basis case, which we assume is directly proportional to the cooled stack gas temperature. We do this by calculating the heat effect of dropping the temperature of stream 4 from 800°C to 700°C. Table 1 of worksheet AirPreHeat of downloadable workbook at www.industrialheating.com/SysBalCalc2 has the details of this calculation. The heat effect is -60,156 kJ/minute, which means that the heat loss must be 60,156 kJ/minute to close the heat balance.

An operator can raise the combustion-air temperature (stream 1") by increasing the flow of stream 1 from zero (basis case) while decreasing the flow of stream 1'. He must also lower the NG flow rate (stream 2) and the hot combustion airflow (stream 1") to maintain 118% stoichiometric condition. The heat-exchanger heat loss will decrease while the hot combustion gas temperature (stream 3) will increase. Only three of these dependent variables need be solved for because the others are related by simple cell formulae. The user enters a combustion air temperature >25°C and uses the worksheet template to find: the flow rate of NG; the burner hot gas temperature; and the cooled stack gas temperature. All other process variables will adjust based on cell formulae.

Excel’s Solver tool can solve multiple non-linear equation sets, so it’s perfect for this example. If you haven’t used Solver before, make sure it’s installed, and consult your Excel guidebook for advice on how to use it. We have three heat-balance equation sets to solve: overall system, burner and heat exchanger. The Solver scenario is saved in worksheet AirPreHeat. Just change the air-preheat temperature to some value >25°C, open Solver and click on the Solve button. This procedure could be automated for operator convenience.

## Results

Table 1 shows the results of calculations made at the basis case and four different air-preheat temperatures. For air preheated to 300°C (572°F), the NG flow decreased by 27% over the basis case. The actual airflow rate increases because it enters hotter, but the STP flow decreases as expected. We can now compare the energy savings obtained from air preheat versus oxygen enrichment. For example, decreasing NG flow by 14% requires an air-preheat temperature of 150°C, or air enriched to 30% O2. IH

References

1. Arthur Morris, “Making a System Balance, Part 1”, Industrial Heating, February 2013.

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