A material balance evaluates the stream composition and flow into and out of a system. Making one is not easy because of the presence of several chemical species, chemical reactions and the need to convert measured flow values into moles to simplify the balance arithmetic.

Here we show the use of Excel in preparing a material balance for a simple example – steady-state heating of aluminum ingots in a natural-gas-fired furnace. The specific objective is to calculate the unknown stream compositions and flows and convert the results to a form suitable for making a heat balance. The details are in the downloadable Excel workbook MatBalCalc.xls. We’ll also use three workbooks from earlier columns: VolCalc.xls, StoichCalc.xls and HeatCalc.xls.

Figure 1 shows the example flowsheet. The ingots move counter-currently to the flow of gas. The heating furnace is really a heat exchanger, where hot combustion gas transfers heat to the charge. The fuel is 95% CH4, 3% C2H6 and 2% N2, which is burned with dry air (21% O2). The pressure is 1 atm, and the listed instream flows are actual (not STP). An unknown amount of air leaks into the charging door (stream 5). The stack gas is analyzed on-line for percent O2.

## The Material Balance

Material entering a process is consumed, used productively, and is either lost or leaves the system as waste. A material balance can pinpoint changes that have the greatest potential to decrease waste production and, if done properly, allow a what-if calculation to show the effects of a process change on other process variables. Making one involves several steps.

First, write the chemical reactions that occur. Both reactions proceed to completion with excess air and show that 3 moles of product are formed for every mole of CH4 burned (but no change in volume) and 5 moles for every mole of C2H6 (with ½ mole increase in volume).

2O2 + CH4 → CO2 + 2H2O       

3½O2 + C2H6 → 2CO2 + 3H2O    

Next, create a ledger that lists all of the known stream flows and compositions. Enter a “?” where the stream flow or composition is unknown. Table 1 shows such a ledger, with one additional value calculated from workbook StoichCalc.xls. It shows that the volume ratio of air/NG is 11.27 at 18% excess air, so the airflow is 11.27 × 32 = 360.6 m3.

Material-balance calculations are easier using molar flows, so next we use workbook VolCalc.xls to calculate the natural gas (NG) flow as 1,308 g-mole/min, and airflow is 14,739 g-mole/min (2.884 lb-mole NG/min and 32.50 lb-mole air/min). For one g-mole of natural gas burned, workbook HeatCalc.xls shows that the CO2 and H2O production is 1.01 and 1.99 g-mole respectively, and it requires 2.005 g-mole O2 for stoichiometric combustion. These are multiplied by 1,308 to obtain values commensurate with the actual instream flows. The leak airflow is calculated from the increase in stack gas flow required to bring its composition to 3.3% O2. Table 2 (online only) summarizes the calculated flow for each substance. We see that about 2% of the air entering the furnace comes from the air leak.

Worksheet MatBalCalc.xls has a step-by-step explanation for each stream calculation, and it has a material-balance ledger in composition units. The results are presented in the correct form for making a heat balance, which we’ll cover next month. IH

Tables and workbook at www.industrialheating.com/MatBalCalc

References available online