Figure 1. Basis case flowsheet for one minute of operation of a continuous aluminum heating process. Gas stream flows are at 1 atm pressure. Flow of streams 2, 3, 4 and 5 were obtained from a material balance and the heat loss from a heat balance.

Previous columns in this series have illustrated the use of Excel for making material- and energy-balance calculations on industrial heating processes. If you’re lucky, you can get enough plant data to keep the material and heat balances separate. But once you extrapolate your balances to situations where you don’t have plant data, the material- and heat-balance equations often become coupled. In that case, both must be made together, which complicates the arithmetic. The combination of a material and heat balance is called a system balance. The purpose of a system balance is to explore what happens to the system when you change one of the process variables. Here we show how to use Excel’s Goal Seek tool to make a system balance on an aluminum heating process. In part 2, we’ll show how to use Excel’s Solver tool.

Figure 1 shows a flowsheet for a steady-state aluminum heating process. As discussed in previous columns, the basis-case stream values were calculated by separate material and heat balances.^[1,2] This article explains how to use the downloadable Excel worksheet SysBalCalc.xlsx to calculate the effect of changing any one of 20 different process variables.

Developing the System-Balance Template

A system balance for this example requires solving two equation sets – one for the material balance and one for the heat balance. The material-balance equation set contains 13 different instream variables plus five natural gas (NG) composition variables. The overall process heat-balance equation set contains two heat-loss values and seven other heat-balance equations that connect with the outstream properties. For this example, plant data for the basis case NG flow was 32 actual m³/min (29.32 m³/min at STP). All of the oxidant flow-stream properties were defined except the flow, which is calculated by material-balance relationships written as cell formulae. Additional cell formulae calculate the properties of all other gas streams.

Using the System-Balance Template

When a process variable is changed, the process heat part of the system balance no longer closes. Making a system balance requires changing one of the material-balance variables until the heat balance does close. In this example, the NG flow was selected as the most important variable to use for closing the balance. This can be done by trial-and-improvement, but it’s better to use Excel’s Goal Seek tool.^[3] Suppose the combustion air is enriched to 25% O₂, and we wish to find the required NG flow. We employ Goal Seek to search for an NG flow that brings the total process heat to zero. The result is 29.4 m³/min NG flow, which is 8% less than without oxygen enrichment. The combustion airflow decreases by 23%, while the stack gas flow decreases 21%.

This closes the system balance, but not the burner heat balance because the hot gas temperature is no longer 1800°C (3272˚F). We again use Goal Seek to search for the hot combustion-gas temperature (stream #3 in the flowsheet) that brings the burner heat effect to zero. The result is 2039°C (3702˚F), or about 240°C higher than for the basis case. The revised system balance is now complete.

Clearly, oxygen enrichment significantly lowers the fuel consumption and stack gas flow. Previous IH columns on energy management have suggested other ways to lower fuel consumption, such as heating the combustion air, lowering the % excess air and lowering the stack gas temperature. The effect of these and other variables can be explored with the workbook. Visit www.industrialheating.com/sysbalcalc and try it! IH

References

1. Art Morris, “Making a Material Balance,”Industrial Heating, November 2012

2. Art Morris, “Making a Heat Balance,” Industrial Heating, December 2012

3. Wikipedia contributors, “Goal seeking”, Wikipedia, the Free Encyclopedia, November 2012. http://en.wikipedia.org/wiki/Goal_seeking