In a plant, mushrooms are produced as a substitute for meat products from food waste. The reaction takes place in a so-called air-lift reactor whose inflow consists of 3% ethanol, 15% waste and the rest water (mass-%).

Before the reactor, the inflow is sterilized at 100 ^oC, which is done by first raising the temperature from 20 ^oC to 100 ^oC in a heat exchanger 1, see Fig 1. Then follows a holding tank where the sterilization itself happens. After the sterilization, the stream is cooled to the reaction temperature of 30 ^oC with a cooling water stream which maintains the temperature T_{cooling (In)} and which is heated to the temperature T_cooling(out). The heating medium in heat exchanger 1 is saturated water vapor 5 bar.

The company wants to improve energy efficiency and improve the economics of the process. One of the proposals is shown in Fig 2. The proposal is to preheat material stream 1 before heat exchanger 1 with the hot stream off the sterilization. In addition to reducing heating costs, cooling water consumption is also reduced. The change means that a new heat exchanger (NH) must be purchased and new pipe systems, valves, etc. must be installed. The old heat exchanger 2 is discarded. The company's requirements for payback time of this type of investment are given in the table below.

The question is to assess using the pay-off method whether the process change is a profitable investment.

Data

Heat exchanger purchase price (USD) = 1.66C, where log (C) = K₁ + K₂ log(A) + K₃ (log A)²

A = heat exchanger area (m²) K₁ = 4.1884 K₂ = -0.2503 K₃ = 0.1974

The total cost of the investment (= basic investment) is obtained by multiplying the heat exchanger's purchase price with factor 4.

Dollar exchange rate: SEK 9 C_p (ethanol) = 2.4 kJ/kg K C_p (water) = 4.2 kJ/kg K C_p (biomass) = 2.2 kJ/kg ⁰C Steam cost: SEK 300/MWh Cost of cooling water: SEK 5/m³

The heat exchanger's U-value and cooling water temperatures are given by the following table.

Stream 1 (kg/s)	U (W/m2 oC)	Tcooling(in) (oC)	Tcooling(out) (oC)	Payback period (years)
4	1100	10	37	5

Fig 1. Current process

Flow	Temp
1	20
2	100
3	100
4	30
Steam	Saturated water vapor 5 bar
Condensate	Saturated water, 5 bar

Fig 2. Improved process

Flow	Temp
1	20
2	100
3	100
4	30
5	-
Steam		Saturated water vapor 5 bar
Condensate		Saturated water, 5 bar

Note: T = 90 C temperature of flow 5

added heat steom 5 bor cooled heot condensate, 5bor to reactor