2. New shortcut model for refrigeration cycle

shown in Figure 1(b), ethylene and propylene are used in the lower and upper cycles,

In this example, the total shaft work requirement will be calculated using rigorous simulation and compared with the shaft work predicted using Carnot model (η = 0.6). Aspen HYSYS is applied for simulation of the cycles with physical properties calculated by choosing Soave-Redlich-Kwong as the fluid package. In the simulation, the partition temperature Tpart between the two cycles is optimized to minimize the total shaft work of the cascaded cycle. Tpart is allowed to change between the lowest temperature that the upper cycle can operate at, which is the normal boiling point for the refrigerant of the upper cycle, and the maximum temperature at which the lower cycle can reject the heat. At each partition temperature, the total shaft work of the cascaded cycles is calculated by adding the shaft work consumption of the upper cycle and the lower cycle. Then, the optimal partition temperature is identified by optimizing

Figure 3. Calculation the optimal partition temperature of ethylene-propylene cascade cycle (Tevap = �82�C, Tcond = 40�C

respectively.

6 Refrigeration

and Qevap = 523 kW).

the shaft work as shown in Figure 3.

This section presents the approach that is used in building a new refrigeration model for predicting the coefficient of performance of a refrigeration cycle [3]. The first step starts with generating performance data using a rigorous simulation package, Aspen HYSYS, where it is assumed that the detailed thermodynamic and unit operation models provide a relatively realistic representation of the refrigeration cycle. Inputs to the simulation software include the refrigerant evaporating temperature, process cooling duty and refrigerant condensing temperature. Rigorous simulations of refrigeration cycles are carried out with the following assumptions: (1) Soave-Redlich-Kwong equation of state is used to calculate thermodynamic and physical properties, (2) a centrifugal compressor that has an adiabatic efficiency of 75% compresses the refrigerant, (3) let-down valves are adiabatic, (4) there is negligible pressure drop in heat exchangers and pipe work and there are no heat gains or losses, (5) the refrigerant leaves the condenser as a saturated liquid and leaves the evaporator as a saturated vapor, (6) the temperature difference between the process source stream temperature and the evaporating temperature is 5C, and (7) the condensing temperature is variable, to account for heat rejection to ambient media or other heat sinks. The simulation outputs include the compressor power demand and the refrigerant condenser duty. The simulation is repeated for an appropriate range of operating conditions (evaporation and condensing temperatures). The inputs and outputs are then used to correlate the actual COP with the ideal COP. A simple linear relationship between COPid and COPact is obtained, as shown in equations below, for a simple refrigeration cycle using ethylene or propylene as a refrigerant [3].

For ethylene,

$$\text{COP}\_{\text{act}} = 0.741 \text{COP}\_{\text{id}} - 0.81 \tag{4}$$

For propylene,

$$\text{COP}\_{\text{act}} = 0.758 \text{COP}\_{\text{id}} - 0.747 \tag{5}$$

For ethylene-propylene cascade cycle,

$$\text{COP}\_{\text{act}} = 0.596 \text{COP}\_{\text{id}} - 0.213 \tag{6}$$

The potential benefit of the linear model is that it is the fast and easy evaluating refrigeration power demand, as will be illustrated in the following example.
