CONSERVATION: MASS, MOMENTUM, AND ENERGY BALANCES - Biomass as a Sustainable Energy Source for the Future - page 83

Solution
A schematic of the heat exchanger with system boundaries is shown in Figure 3.3.
Assumptions:

1. Both control volumes indicated in Figure 3.3 are at steady state.

2. Heat transfer to the environment of the condenser is neglected, and no (shaft)
work is done by the condenser system.

3. KE and PE changes of the flows can be neglected.

a. Mass balances can be set up based on the fact that the condensing vapor
stream does not mix with the cooling water. Thus,

φ m , 1 = φ m , 2 and φ m , 3 = φ m , 4

Now, the ratio of mass flow rates can be derived from a steady-state
energy balance around the heat exchanger:

+

φ m , 1 h 1 + v 1 φ m , 3 h 3 + v 3

0= Q cv − W cv +

2 +gz 1 2 +gz 3

− φ m , 2 h 2 + v 2 − φ m , 4 h 4 + v 4

2 +gz 2 2 +gz 4

2 1

Condensate
1 bar, 45°C

Pyrolysis vapor
1 bar

Cooling water
20°C

Cooling water
35°C

3

4

1

2

Condensate
1 bar, 45°C

Pyrolysis vapor
1 bar

FIGURE 3.3 Schematic of the condenser; top: control volume for (a); bottom: control
volume for (b).