If the unit operation, whatever its nature is seen as a whole it may be represented diagrammatically as a box, as shown in Figure. 4. 1. The mass and energy going into the box must balance with the mass and energy coming out.
The law of conservation of mass leads to what is called a mass or a material balance.
Mass In = Mass Out + Mass Stored
Raw Materials = Products + Wastes + Stored Materials.
ΣmR = ΣmP + Σ mW + ΣmS
(where Σ (sigma) denotes the sum of all terms).
ΣmR = ΣmR1 + Σ mR2 + ΣmR3 = Total Raw Materials
ΣmP = ΣmP1 + Σ mP2 + ΣmP3 = Total Products.
ΣmW= ΣmW1 + Σ mW2 + ΣmW3 = Total Waste Products
ΣmS= ΣmS1 + Σ mS2 + ΣmS3 = Total Stored Products.
If there are no chemical changes occurring in the plant, the law of conservation of mass will apply also to each component, so that for component A:
mAin entering materials = mA in the exit materials + mA stored in plant.
For example, in a plant that is producing sugar, if the total quantity of sugar going into the plant is not equalled by the total of the purified sugar and the sugar in the waste liquors, then there is something wrong. Sugar is either being burned (chemicallychanged) or accumulating in the plant or else it is going unnoticed down the drain somewhere. In this case:
MA = (mAP + mAW + mAU)
where mAUis the unknown loss and needs to be identified. So the material balance is now:
Raw Materials = Products + Waste Products + Stored Products + Losses
where Losses are the unidentified materials.
Just as mass is conserved, so is energy conserved in food-processing operations. The energy coming into a unit operation can be balanced with the energy coming out and the energy stored.
Energy In = Energy Out + Energy Stored
ΣER = ΣEP + ΣEW + ΣEL + ΣES
where
ΣER = ER1 + ER2 + ER3 + ……. = Total Energy Entering
ΣEp = EP1 + EP2 + EP3 + ……. = Total Energy Leaving with Products
ΣEW = EW1 + EW2 + EW3 + … = Total Energy Leaving with Waste Materials
ΣEL = EL1 + EL2 + EL3 + ……. = Total Energy Lost to Surroundings Σ
ES = ES1 + ES2 + ES3 + ……. = Total Energy Stored
Energy balances are often complicated because forms of energy can be interconverted, for example mechanical energy to heat energy, but overall the quantities must balance.
The Sankey diagram is very useful tool to represent an entire input and output energy flow in any energy equipment or system such as boiler generation,firedheaters, furnaces after carrying out energy balance calculation. Thisdiagram represents visually various outputs and losses so that energy managers canfocusonfinding improvements in a prioritized manner.
Example: The Figure 4.2 shows a Sankey diagram for a reheating furnace. From the Figure 4.2, it is clear that exhaust flue gas losses are a key area for priority attention.
Since the furnaces operate at high temperatures, the exhaust gasesleave at high temperatures resulting in poor efficiency. Hence a heat recovery device such as air preheater has to be necessarily part of the system. The lower the exhaust temperature, higher is the furnace efficiency.