Question

Table 2a contains representative facility energy use and production data for the commercial bakery example that we’ve discussed in the lectures.

Table 2a: Energy and production data for a commercial bakery
Production of baked bread (kg/year)	500,000
Production of frozen dough (kg/year)	400,000
Natural gas used to generate steam (TJ/yr)	0.97
Natural gas used directly in baking ovens (TJ/yr)	2.31
Electricity use (MWh/yr)	461

Table 2b contains data specific to baked bread and frozen dough production at this commercial bakery, which one might obtain through measurements taken at each process.

Table 2b: Process energy requirements for each product line
Product	Process	Natural use for steam (MJ/kg)	Direct natural gas use (MJ/kg)	Electricity use (kWh/kg)
Baked bread	Mix	-	-	0.02
	Ferment	0.84	-	-
	Shape	-	-	0.06
	Proof	0.46	-	-
	Bake	0.39	3.58	0.05
	Cool	-	-	0.08
	Slice	-	-	0.04
	Package	-	-	0.08
Frozen dough	Mix	-	-	0.07
	Form and chill	0.32	-	-
	Bake	-	1.30	0.01
	Cool	-	-	0.52
	Finish	-	-	0.07
	Package	-	-	0.07

Your job is to determine the energy inputs attributable to baked bread and frozen dough. You’ll do this by using the information in Tables 4a and 4b to assign the facility’s inputs of natural gas (for steam), natural gas (direct use), and electricity to the baked bread and frozen dough production lines. In other words, you’ll divide the facility into its sub-processes to avoid arbitrary allocation of facility energy inputs between its two co-products. This problem is similar to the bakery example we discussed in the class about avoiding allocation by breaking the process into detailed sub-processes.

1. How much of the facility’s annual natural gas use for steam is attributable to just the baked bread? Use units of TJ/year in your answer. (10 points)
2. How much of the facility’s annual direct natural gas use is attributable to just the baked bread? Use units of TJ/year in your answer. (10 points)
3. How much of the facility’s annual electricity use is attributable to just the baked bread? Use units of MWh/year in your answer. (10 points)

in the question when it says to use tables 4a and 4b it is supposed to say 2a and 2b

Answer 1

Answer (a):

Total Usage of Natural Gas for Stream attributable to baked breads = (0.84+0.46+0.39) MegaJoules/KG i.e. 1.69MJ/Kg

Total Annual Production of Baked Breads in a year = 5,00,000 kg

Hence, Total Usage of Natural Gas for Stream attributable to Baked Breads in a Year = 5,00,000 Kg x 1.69MJ/Kg i.e. 8,45,000 MJ/Year

1 TJ = 10,00,000 MJ

Hence, Total Usage of Natural Gas for Stream in TJ/Year = 8,45,000/10,00,000 = 0.845 TJ/Year

Answer (b):

Total Usage of Natural Gas in baking Ovens attributable to baked breads = 3.58 MJ/Kg

Total Annual Production of Baked Breads in a year = 5,00,000 kg

Hence, Total Usage of Natural Gas in baking Ovens attributable to baked breads in a Year = 5,00,000 Kg x 3.58 MJ/Kg i.e. 17,90,000 MJ/Year

1 TJ = 10,00,000 MJ

Hence, Total Usage of Natural Gas in baking Ovens attributable to baked breads in TJ/Year = 17,90,000/10,00,000 = 1.79 TJ/Year

Answer (c):

Total Electricity Usage attributable to baked breads = (0.02+0.06+0.05+0.08+0.04+0.08) kWh/Kg = 0.33 kWh/Kg

Total Annual Production of Baked Breads in a year = 5,00,000 kg

Hence, Total Electricity Usage attributable to baked breads in a Year = 5,00,000 Kg x 0.33 kWh/Kg i.e. 1,65,000 kWh/Year

1 mWh = 1,000 kWh

Hence, Total Electricity Usage attributable to baked breads in mWh/Year = 1,65,000/1,000 = 165 mWh/Year