# Increased Energy Efficiency of a Backward-Feed Multiple-Effect Evaporator Compared with a Forward-Feed Multiple-Effect Evaporator in the Cogeneration System of a Sugar Factory

## Abstract

**:**

## 1. Introduction

## 2. Forward-Feed Multiple-Effect Evaporator

_{0}, which is extracted from an extraction-condensing steam turbine. Although extracted steam is usually superheated, it is assumed that the steam has been de-superheated, and is saturated at the inlet of the evaporator. In each effect, steam or vapor condensation at pressure p

_{i}causes the evaporation of water in sugar juice at a lower pressure p

_{i}

_{+1}. Vapor leaving E1 is sent to the pan stage (P), the secondary juice heater (H2), and the second effect (E2), Vapor leaving E2 is sent to the primary heater (H1) and the third effect (E3). All vapor leaving E3 is sent to the final effect (E4). Syrup leaving E4 is pumped to a syrup tank before being sent to P.

_{i}to produce vapor and condensate at a lower pressure p

_{i+}

_{1}. Condensate from F2 and E4 is sent to a storage tank.

_{h}

_{,2}= T

_{amb}) to the saturation temperature (T

_{h}

_{,0}= 103 °C) corresponding to 112.7 kPa. Juice pressure is then decreased to the atmospheric pressure (101.3 kPa) after passing through FC. The model of the juice heaters is identical with the previous model presented by Chantasiriwan [9], and is represented by the following equations:

_{h}

_{,i}given by Hugot [14]:

_{in}) is a little above the atmospheric pressure (p

_{out}). The juice is allowed to flash in FC, resulting in a reduced mass flow rate (m

_{f}

_{,0}) that is determined from

_{0}) is related to the juice concentration at the inlet to the primary juice heater (x

_{in}) as follows:

_{out}to p

_{1}by a pump. It is assumed that pumping does not increase juice temperature. Therefore, juice temperature is T

_{out}at the inlet to E1. It should be noted that T

_{out}is lower than the saturation temperature (T

_{1}) in E1. Therefore, part of the heating surface area in E1 is used for juice heating, which increases juice temperature to the saturation temperature before water evaporation can occur.

_{f}

_{,i}) is the product of the average specific heat capacity of sugar juice and juice temperature in effect i, which is assumed to be saturation temperature. Saturated juice temperature is larger than the temperature of saturated liquid water at the same pressure due to the concentration of dissolved solids in juice and the hydrostatic pressure. It is expressed as

_{x}

_{,0}in Equation (9) accounts for the mass flow rate of steam required to raise juice temperature from T

_{out}to T

_{f}

_{,1}

^{(in}

^{)}. It is determined from

_{1}) is larger than the juice pressure (p

_{2}) in E2. Consequently, flash evaporation causes juice to be at the saturation temperature upon entering each of these effects. It also results in the reduced mass flow rate of juice in E2, which is

_{2}, which goes to E3. Its mass flow rate (m

_{e}

_{,1}) is

_{e}

_{,2}) of saturated vapor at pressure p

_{3}that goes to E4,

_{x}

_{,0}. It is determined by using the same model of juice heaters in Equations (3) and (4):

_{i}of Robert evaporator is given by Wright [15]:

_{1}) is normally required to equal or exceed the minimum value in order to create a sufficient temperature difference that provides a driving force in the crystallization process. It is assumed in this paper that this value is 150 kPa.

## 3. Backward-Feed Multiple-Effect Evaporator

_{0}for E1 and extracted steam at a specified pressure (p

_{a}) for P. This means that the backward-feed multiple-effect evaporator requires extracted steam at two pressures. By contrast, the forward-feed multiple-effect evaporator requires extracted steam at only one pressure.

_{x}

_{,i}. The juice temperature entering E4 is assumed to be the ambient temperature,

_{1}is sent to S1, which reduces its pressure to p

_{2}, and produces saturated vapor at the same pressure that is supplied to E3. Saturated juice leaving S1 and S2 are sent, respectively, to S2 and S3, which reduce juice pressure to p

_{3}and p

_{4}before the resulting concentrated juice or syrup is sent to a syrup tank. Saturated vapor leaving S2 at pressure p

_{3}is supplied to E4, whereas saturated vapor leaving S3 pressure p

_{4}is unused.

_{x}

_{,i}) required to raise juice temperature from a sub-cooled value to the saturation temperature in effect i is determined from

_{i}must be replaced by x

_{i-}

_{1}in Equation (25) because x

_{i-}

_{1}is the juice concentration at the outlet of effect i in the backward-feed multiple-effect evaporator. The surface area in effect i that is required to raise juice temperature from T

_{x}

_{,i}to T

_{f}

_{,i}

^{(in}

^{)}is determined by using the same model of juice heaters in Equations (3) and (4),

_{f}

_{,0}to

_{0}to

_{a}) from the turbine because there is no vapor bleeding from the evaporator. The model of the pan stage of the backward-feed multiple-effect evaporator is the same as that of the forward-feed multiple-effect evaporator. Therefore,

## 4. Cogeneration Systems

_{s}, pressure p

_{s}, and temperature T

_{s}is expanded in extraction-condensing steam turbines (T). Steam extracted at mass flow rate m

_{v,}

_{0}and pressure p

_{0}is supplied to the first effect of multiple-effect evaporator (MEE) of the FF system. The mass flow rate of remaining steam (m

_{c}) that is sent to condenser (C) is m

_{s}−m

_{v}

_{,0}. The BF system requires extracted steam at two pressures. Extracted steam at mass flow rate m

_{v}

_{,0}and pressure p

_{0}is sent to the first effect of multiple-effect evaporator. Extracted steam at mass flow rate m

_{a}and pressure p

_{a}is sent to the pan stage. Therefore, the mass flow rate of the remaining steam (m

_{c}) that is sent to the condenser in the BF system is m

_{s}− m

_{v,}

_{0}− m

_{a}.

_{fuel}), the inlet steam conditions (p

_{s}and T

_{s}), and the condensing pressure (p

_{c}) are the same in both systems, the energy efficiency parameter that may be used to compare both systems is power output. The power output of the FF system is

_{t}is isentropic efficiency of steam turbine, h

_{s}is specific enthalpy of steam at turbine inlet, h

_{0s}is specific enthalpy of the extracted steam at pressure p

_{0}and the same entropy as the inlet steam, h

_{cs}is specific enthalpy of the condensed steam at pressure p

_{c}and the same entropy as the inlet steam. The power output of the BF system is

_{as}is specific enthalpy of the extracted steam at pressure p

_{a}and the same entropy as the inlet steam. Since m

_{fue}

_{l}is known, m

_{s}can be determined from boiler efficiency, which is defined as

_{fw}is specific enthalpy of feed water, and HHV is the higher heating value of fuel.

## 5. Results and Discussion

_{in}= 15%, x

_{out}= 70%, p

_{4}= 16 kPa, and T

_{amb}= 30 °C. The total evaporator surface area and the total juice heater surface area of the forward-feed multiple-effect evaporator are, respectively, 13,000 m

^{2}and 2500 m

^{2}. In order to compare the performance of both systems, both evaporators should have the same total heating surface areas. Therefore, the total evaporator surface area of the backward-feed multiple-effect evaporator is 15,500 m

^{2}. This requirement is based on the assumption that the investment cost of an evaporator depends mostly on its total heating surface area. The optimum distribution of total heating surface area that maximizes the mass flow rate of processed juice at a given exhaust steam pressure is to be determined for each evaporator.

_{f}

_{,max}) in the forward-feed multiple-effect evaporator corresponding to the extracted steam pressure (p

_{0}) of 200 kPa. Since the mass flow rate of processed juice (m

_{f}

_{,in}) is a convex function of evaporator surface areas in the forward-feed multiple-effect evaporator, a line-search method can be used to find the optimum values of third-effect surface area (A

_{3}) and second-effect surface area (A

_{2}) that maximize the inlet juice mass flow rate (m

_{f,in}) as shown in Figure 4a,b. Figure 4c shows that m

_{f}

_{,in}increases monotonically with decreasing first-effect surface area (A

_{1}). However, vapor bled from the first effect must be supplied to the pan stage at a specified pressure (p

_{1}). This constraint limits the maximum mass flow rate of processed juice (m

_{f}

_{,max}) to 153.36 kg/s if p

_{1}is 150 kPa, as shown in Figure 4c. Figure 5 shows the determination of m

_{f}

_{,max}in the backward-feed multiple-effect evaporator corresponding to the extracted steam pressure (p

_{0}) of 200 kPa. A line-search method can also be used to find the optimum values of A

_{3}, A

_{2}, and A

_{1}that maximize the inlet juice mass flow rate as shown in Figure 5a–c. It should be noted that there is no constraint in this case. It can be seen from Figure 5c that m

_{f}

_{,max}is 158.05 kg/s. Figure 6 shows variations of m

_{f}

_{,max}and m

_{v}

_{,0}with p

_{0}for the forward-feed multiple-effect evaporator that have the optimum distribution of heating surface areas and variations of m

_{f}

_{,max}, m

_{v}

_{,0}, and m

_{a}with p

_{0}for backward-feed multiple-effect evaporator that have the optimum distribution of heating surface areas. It can be seen that all mass flow rates decrease monotonically with p

_{0}for both evaporators. Furthermore, m

_{f}

_{,max}appears to be more sensitive to p

_{0}in the forward-feed multiple-effect evaporator than the backward-feed multiple-effect evaporator.

## 6. Conclusions

^{2}of evaporator surface area and 2500 m

^{2}of juice heater surface area is capable of processing 125 kg/s of inlet juice flow rate using extracted steam at the pressure of 185.5 kPa and the mass flow rate of 43.45 kg/s. The cogeneration system that uses the forward-feed multiple-effect evaporator produces 36.14 MW of power output. The backward-feed multiple-effect evaporator that has 15,500 m

^{2}of evaporator surface area is capable of processing 125 kg/s of inlet juice flow rate using extracted steam at the pressure of 151.3 kPa and the mass flow rate of 30.62 kg/s. The cogeneration system that uses the backward-feed multiple-effect evaporator is also required to supply extracted steam at the pressure of 150 kPa and the mass flow rate of 10.63 kg/s for the pan stage. It produces 37.31 MW of power output. Therefore, the backward-feed multiple-effect evaporator is responsible for 3.2% more energy efficiency in this cogeneration system compared with the cogeneration system that uses the forward-feed multiple-effect evaporator.

## Funding

## Conflicts of Interest

## Abbreviations

Nomenclature | |

A | heat transfer surface of evaporator, m^{2} |

A_{h} | heat transfer surface of juice heater, m^{2} |

c_{p} | specific heat capacity, kJ/kg.K |

H | juice level in evaporator, m |

HHV | juice level in evaporator, kJ/kg |

h | specific enthalpy, kJ/kg |

m | mass flow rate, kg/s |

P | power output, kW |

p | pressure, kPa |

T | temperature, °C |

U | heat transfer coefficient of evaporator, kW/m^{2}.K |

U_{h} | heat transfer coefficient of juice heater, kW/m^{2}.K |

x | concentration of sugar juice, % |

Greek Symbols | |

ε | heat loss coefficient in evaporator |

η_{b} | boiler efficiency |

η_{t} | turbine efficiency |

ρ | density, kg/m^{3} |

Subscripts | |

a | vapor to pan stage |

b | vapor to juice heater |

c | vapor from flash tank, condenser |

e | flash evaporation |

f | sugar juice |

fw | feed water |

h | juice heater |

i | effect number |

l | saturated liquid |

s | Steam |

v | saturated vapor |

vl | vapor-to-liquid |

x | juice heating inside evaporator vessels |

Superscripts | |

in | inlet of an effect |

out | outlet of an effect |

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**Figure 3.**Cogeneration systems that use (

**a)**the forward-feed multiple-effect evaporator (FF system) and (

**b**) the backward-feed multiple-effect evaporator (BF system).

**Figure 4.**Procedure for finding the optimum surface area distribution in the forward-feed multiple-effect evaporator: (

**a**) finding the optimum third-effect surface area (A

_{3}), (

**b**) finding the optimum second-effect surface area (A

_{2}), and (

**c**) finding the first-effect surface area (A

_{1}) corresponding to the first-effect pressure (p

_{1}) of 150 kPa.

**Figure 5.**Procedure for finding the optimum surface area distribution in the backward-feed multiple-effect evaporator: (

**a**) finding the optimum third-effect surface area (A

_{3}), (

**b**) finding the optimum second-effect surface area (A

_{2}), and (

**c**) finding the optimum first-effect surface area (A

_{1}).

**Figure 6.**Variations of steam and juice mass flow rates with extracted steam pressure for (

**a**) the forward-feed multiple-effect evaporator and (

**b**) the backward-feed multiple-effect evaporator that have optimum distributions of heating surface areas.

**Figure 7.**Variations of power outputs of the FF and BF systems with the maximum sugar juice flow rate.

**Table 1.**Simulation results at optimum operating conditions for the FF and BF systems that process 125 kg/s of inlet sugar juice.

FF System | BF System | |
---|---|---|

A_{1} (m^{2}) | 7166 | 4884 |

A_{2} (m^{2}) | 1909 | 3597 |

A_{3} (m^{2}) | 1581 | 3455 |

A_{4} (m^{2}) | 2244 | 3564 |

A_{h}_{,1} (m^{2}) | 405 | - |

A_{h}_{,2} (m^{2}) | 2094 | - |

p_{0} (kPa) | 185.5 | 151.3 |

p_{1} (kPa) | 150.0 | 79.7 |

p_{2} (kPa) | 91.2 | 50.0 |

p_{3} (kPa) | 52.7 | 29.9 |

p_{4} (kPa) | 16.0 | 16.0 |

m_{v}_{,0} (kg/s) | 43.45 | 30.62 |

m_{a} (kg/s) | 13.16 ^{1} | 10.63 ^{2} |

P (MW) | 36.14 | 37.31 |

^{1}Vapor bled from the first effect at 150 kPa.

^{2}Extracted steam from turbine at 150 kPa.

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**MDPI and ACS Style**

Chantasiriwan, S. Increased Energy Efficiency of a Backward-Feed Multiple-Effect Evaporator Compared with a Forward-Feed Multiple-Effect Evaporator in the Cogeneration System of a Sugar Factory. *Processes* **2020**, *8*, 342.
https://doi.org/10.3390/pr8030342

**AMA Style**

Chantasiriwan S. Increased Energy Efficiency of a Backward-Feed Multiple-Effect Evaporator Compared with a Forward-Feed Multiple-Effect Evaporator in the Cogeneration System of a Sugar Factory. *Processes*. 2020; 8(3):342.
https://doi.org/10.3390/pr8030342

**Chicago/Turabian Style**

Chantasiriwan, Somchart. 2020. "Increased Energy Efficiency of a Backward-Feed Multiple-Effect Evaporator Compared with a Forward-Feed Multiple-Effect Evaporator in the Cogeneration System of a Sugar Factory" *Processes* 8, no. 3: 342.
https://doi.org/10.3390/pr8030342