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Energy Integration of Multiple Effect Evaporators with Background Process and Appropriate Temperature Selection Prashant Sharan, and Santanu Bandyopadhyay Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.5b03516 • Publication Date (Web): 25 Jan 2016 Downloaded from http://pubs.acs.org on February 1, 2016

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Industrial & Engineering Chemistry Research

Energy Integration of Multiple Effect Evaporators with Background Process and Appropriate Temperature Selection

Prashant Sharan

and

Santanu Bandyopadhyay*

Department of Energy Science and Engineering, Indian Institute of Technology Bombay, Powai, Mumbai 400 076, India.

Corresponding author: Tel:+91-22-25767894; Fax:+91-22-25726875 E-mail: [email protected]

ACS Paragon Plus Environment


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Abstract

Multiple effect evaporators (MEE) are energy intensive equipments. Often the focus is on minimizing the energy consumption of MEE as a standalone system, rather than that of the entire plant. In this paper, process integration techniques are applied to integrate various stages of a MEE with the background process. To identify various energy conservation opportunities, MEE is represented as a Grand Composite Curve (GCC) and integrated with the GCC of the background process. Change in utility consumption in the first effect, due to energy shift (in the GCC) between various effects, is determined in this paper. It is proved that for the minimum energy requirement all effects should be pinched. Using these mathematical results, a methodology for optimally integrating MEE with background process is developed. Furthermore, additional energy may be conserved by appropriately selecting effect temperatures. A methodology for appropriate selection of effect temperatures is also proposed in this paper. Applicability of the proposed methodologies is demonstrated through a case study. It is observed that 9.8% energy can be conserved by properly integrating MEE with the background and an additional 25.87% of energy can be conserved by selecting optimal effect temperatures.

Keyword: MEE; process integration; GCC; pinch analysis; energy conservation.


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Nomenclature A

change in hot stream value (kW)

c

liquor concentration (%)

CU

cold utility (kW)

f

vapor fraction

E

amount by which each effect is shifted away from pinch (kW)

F

feed flow rate (kg/s)

h

enthalpy (kJ/kg)

H

vapor enthalpy (kJ/kg)

HU

hot utility (kW)

K

total number of effect

l

liquor flow rate (kg/s)

mCp

heat capacity flow rate (kW/K)

S

utility requirement for first effect (kW)

T

temperature (oC)

V

vapor flow rate (kg/s)

W

total amount of water to be evaporated (kg/s)

Y

effect temperature (oC)

Z

change in energy required (kW)

Greek Letter ∆

change

λ

latent heat of vaporization (kJ/kg)

Subscript atm

atmospheric

B/G

background

cond

condensate

i

effect number

in

inlet

min

minimum

n

effect under consideration

out

outlet

sat

saturation



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Abbreviations BPR

Boiling point rise (°C)

GCC Grand composite curve GOR Gain over ratio MEE Multiple effect evaporator MPTA Modified problem table algorithm PTA

Problem table algorithm

RHS

Right hand side

TVC

Thermo-vapor compression


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1.

Introduction

Multiple effect evaporators (MEE) are used for evaporating the solvent and to increase concentration of the solute. In MEE, evaporation takes place in stages. Though MEE is an energy integrated system, as the vapor generated from a stage acts as a heat source for the other stage, it is energy intensive. MEE consumes 25-30 % of total energy consumed in pulp and paper industry1, and evaporates nearly 65-80% of water2. In desalination industry, energy cost for MEE varies between 20-30% of the total cost of water.3 Therefore, it is important to reduce energy requirement in MEE through energy integration. Various techniques, such as thermo-vapor compressor,4,5 liquor integration,6–8 condensate flashing,9 product flashing,1 vapor bleeding,1,10 etc., are proposed for reducing energy consumption of standalone MEE. In thermo-vapor compressor (TVC), a low-pressure vapor is mixed with a high-pressure motive steam to produce medium pressure steam for providing heat to MEE. Amer11 showed that if TVC system is properly integrated with MEE then gain over ratio (GOR) for 4 and 18 effects evaporator can go up to 8 and 18.5 respectively. GOR is defined as the ratio of mass of vapor generated to the mass of steam supplied. Optimal placement of TVC in MEE plays a dominating role on the GOR.12,13 Kouhikamali et al.13 showed that GOR for MEE is maximum when TVC is palced at stage operating with medium pressure. Liquor integration is also used for increasing the energy efficiency of MEE. Kaya and Sarac6 showed that GOR can be increased from 2.57 to 2.92 with feed pre-heating. Placing the feed pre-heater after first effect substantially improves the GOR of desalination system.7 Jyoti and Khanam8 reduced the steam consumption by 37.8% by liquor pre-heating. Other than TVC and liquor integration, feed and condensate flashing can also be applied for energy conservation in MEE. Vapor after losing its latent heat comes out as a condensate. As the pressure and temperature of condensate are higher than the subsequent stages, it can be flashed to lower pressure and the vapor generated can act as a heat source for lower stages. Khanam and Mohnaty1 introduced the concept of primary and secondary flash tanks and applied them for reducing the energy consumption of MEE. Economic analysis needs to be carried out for optimizing the number of flash tanks.8Instead of modeling various energy conservation techniques listed above separately, pinch analysis can be used for thermal integration of MEE and to identify various energy conservation opportunities.



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Pinch analysis serves as an excellent tool for energy integration of the overall system. One of the important tools of pinch analysis is grand composite curve (GCC), which is a plot between feasible heat transfer and shifted temperature. Problem table algorithm (PTA), proposed by Linnhoff and Flower14, or modified problem table algorithm (MPTA), proposed by Bandyopadhyay and Sahu15, may be used to generate the GCC. Sreepathi and Rangaiah16 wrote a review paper on heat recovery through pinch analysis. Li and Chang17 developed a pinch based method for reducing the energy consumption for heat exchanger network. In a recent handbook,18 the concept of pinch analysis and various applications are discussed. Pinch analysis is also used for energy conservation in MEE.19–24 Périn-Levasseur et al.20 applied pinch analysis for integration of MEE and studied the effect of change in operating pressure, minimum temperature driving force and heat pumps integration on utility requirement for the system. Cortés et al.21 used process simulation and integration for reducing energy consumption of sugar industry. Piacentino and Cardona22 applied pinch analysis to improve the thermal efficiency of the system and suggested to split MEE into above and below pinch and operate them separately. They also suggested that parallel feed MEE should be used to reduce exergy losses. These methodologies focus on reducing energy requirement of a standalone MEE. Additional energy may be conserved by integrating MEE with background process. Hillenbrand and Westerberg25 developed a method for integrating MEE with background process. Heat path diagram, to calculate the sensible heat transfer taking place in each effect, was applied to calculate the overall steam requirement. Smith and Jones26 described optimal design of integrated evaporation system by considering effect of minimum temperature driving force on the overall capital energy trade-offs. Singh et al.27 suggested that the MEE should be placed either entirely above or below the background pinch. Therefore, the benefits of integrating with local heat sources (also known as pockets) in GCC are not identified. Urbaniec et al.28 used process integration technique to integrate process streams, heat exchanger network and evaporators. They analyzed different possible flow sequence of MEE, for minimizing the energy consumption. Westphalen and Maciel29 calculated the possible energy integration with the background process with given evaporator temperatures and accordingly calculated the maximum vapor bleeding for each effect. Higa et al.10 studied the impact of the number of effects and vapor extraction on the total steam consumption of the system. Mesfun and Toffolo30 integrated MEE, background process, and heat and power


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cycle. These studies primarily focused on interaction of MEE with background process to achieve energy conservation. Effects of different design parameters on the overall energy consumption are not studied explicitly.

Operating temperature of different effects of MEE plays an important role on the energy requirement of the overall system. Various methods were proposed to determine appropriate temperatures for a standalone MEE. These methods include equal area of the evaporators,31,32 equal pressure drop between stages,9 equal temperature driving force between stages,33 etc. Piacentino and Cardona34 calculated exergy destruction for obtaining the temperature driving force between the effects. Background process plays an important role for selection of the optimum effect temperatures. Hillenbrand and Westerberg25 proposed an iterative method to selected the effect temperature by reducing the steam consumption while integrating with the background process. This method iterates for each effect temperature separately, making it complex to understand and inefficient to implement. Mesfun and Toffolo30 used genetic algorithm for calculating the optimal effect temperature, while integrating MEE with background process. Being a search based technique, this method fails to provide physical understanding to the designers.

Objective of this paper is to develop a methodology for optimal energy integration of MEE with background process and to identify appropriate effect temperatures to minimize the energy requirement of the overall system. The proposed methodology incorporates physical understanding of the overall heat integration problem with efficient iterative method, making it easy to implement. Applicability of the proposed methodologies is demonstrated through illustrative examples.

2.

Integration with background process

MEE may be represented as a number of streams exchanging thermal energy among them for achieving the required evaporation. Identification of these streams is important for generation of GCC. Once the GCC is identified, thermal integration of MEE with the background process may be achieved.



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2.1. Stream identification Schematic of nth effect of a MEE is shown in Figure 1. Liquor, from the n-1th stage, with mass flow rate, ln-1, temperature, Yn-1, and enthalpy, hn-1 after undergoing liquor integration enters the nth effect, with mass flow rate, ln-1, temperature, Tin,n, and enthalpy, hin,n. The vapor, from the previous stage, with mass flow rate, Vn-1, temperature, Yn-1 and enthalpy, Hn-1 enters the nth effect. Vapor condenses by losing its latent heat and leaves the evaporator at saturation temperature, Ysat,n-1 and enthalpy, hcond,n-1. Heat transferred from the condensing vapor to the liquor produces vapor with mass flow rate, Vn, at temperature, Yn and enthalpy, Hn. Concentrated liquor with mass flow rate, ln, at temperature, Yn, and enthalpy, hn, is passed to the next effect. Process stream for MEE can be defined as follows.

Energy requirement As energy is required in every effect for evaporation of water, it is represented as a cold stream. The temperature difference of 1oC is assumed between inlet (Yn) and outlet (Yn+1) stream. The heat capacity (mCp) of the stream is determined from the energy required to evaporate the water from the liquor.

mCp = Vn H n + ln hn − ln −1hin,n

( n = 1, 2,3,...K )

(1)

where, K is total number of effects.

Hot stream Vapor generated from an effect acts as a heat source for the next effect. This vapor loses its heat in three steps: sensible heat during de-superheating, latent heat through condensation, and sensible heat up to its desired temperature. Vapor coming out from any effect is in superheated state due to presence of solute in the liquor that causes rise in boiling point (BPR). The inlet temperature is Yn-1 and outlet temperature is given by saturation temperature at which the effect was operated (Ysat,n-1). The heat capacity is calculated as:

mCp =

(

Vn −1 H n−1,Yn−1 − H n −1,Ysat ,n−1 Yn −1 − Ysat , n −1

)

( n = 2,3,......., K + 1)

(2)

Once the steam gets de-superheated, it loses its latent heat (λn-1) by condensation. With an assumption of 1oC temperature difference, heat capacity is expressed as:

mCp = Vn −1λn −1 ( n = 2,3,....., K + 1)


(3)

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The condensate is cooled to atmospheric temperature (Tatm) before discharging it into the atmosphere and its heat capacity is given as:

mCp = Vn −1Cpcond

( n = 2,3,......, K + 1)

(4)

Liquor In MEE, liquor can be of three types: feed, inter-stage liquor, and product. Liquor entering any evaporator stage (either as feed or as inter-stage liquor) is at a temperature different from the effect temperature and may be thermally integrated. Similarly, the final product temperature might be different from last effect temperature and it can be integrated.

If the feed or inter-stage liquor is a cold stream, it can be heated up to its respective effect temperature (Yn). In case of hot stream, the liquor is cooled up to effect temperature (Yn+1) + ∆THE. An additional ∆THE is to account for direct heat transfer25. The concentrated liquor coming out form MEE might be at different temperature from that of product. Therefore, the product integration needs to be carried out. The heat capacities for liquor integration can be expressed as:

mCp =

ln −1 ( hin ,n − hn −1 ) Tin ,n − Yn −1

( n = 1to K + 1)

(5)

where, Tin,n is the temperature up to which liquor from n-1th is heat integrated. It may be noted that for a MEE with K number of effects, there are 5K+1 streams.

2.2. Grand Composite Curve As discussed earlier, additional energy integration can be achieved apart from internal integration of MEE, by integrating MEE with background process. Whatever streams are available for heat transfer, apart from MEE streams can be considered as background stream. Stream data for the background process can be identified from process flow sheet. Once the stream data for MEE as well as for the background process are identified, PTA14 or MPTA15 can be used for generating the GCC and calculating the utility requirement. A typical GCC for MEE with four effects is shown in Figure 2. Each evaporator effect is represented by two horizontal lines and a sloped line. Top horizontal line represents energy required for vaporization while the bottom line shows condensation. As these two processes are taking place at constant temperature, they are represented as horizontal line. These two horizontal



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lines are separated by a distance given as sum of minimum temperature driving force (∆Tmin) and BPR. This distance increases as one moves from first to last effect. This is because of increase in BPR. The temperature of liquor and condensate stream changes while undergoing heat transfer and are represented in the form of a sloped line in the GCC (see Figure 2). The condensate stream always has negative slope, as it loses heat. Feed pre-heating requires external heat, so it has positive slope as shown in Figure 2.

2.3. Mathematical Results From the schematic of MEE shown in Figure 1, the mass balance of liquor (ln-1) can be written as:

ln−1 = Vn + ln

(6)

Let the feed flow rate of liquor be F. Liquor achieves its desired concentration by removing W amount of solvent (water) present in the feed. For calculating the total amount of vaporization taking place, a vapor fraction (f) for each stage is introduced. V fn = n W

(7)

Overall mass balance for vapor production can be expressed as: n= K

∑ fn =1

(8)

n =1

The mass of liquor (ln) is given as: n

ln = F − ∑ f jW

(9)

j =1

Energy balance for nth effect is given as:

Vn −1 H n −1 + ln −1hin ,n = Vn H n + ln hn + Vn −1hcond ,n −1 ( n = 2,3,...., K )

(10)

Now substituting the value of ln from Eq(9), Eq(10) may be rewritten as: F ( hn − hin ,n ) = f n −1W ( H n −1 − hcond , n −1 + hn − hin , n ) − f nW ( H n − hn )

(11)

 j =n  −  ∑ f j − 2  W ( hin ,n − hn )  j =3 

Writing down the energy balance for first effect, the hot utility requirement for the first effect (S) is expressed as: S = f1W ( H1 − h1 ) + F ( h1 − hin ,1 )


(12)

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where, hin,1 is the enthalpy at which liquor is entering effect 1. It may be noted that the temperature and pressure of the vapor and liquor coming out from an effect are assumed to be in equilibrium with each other and with the effect. Pressure drop inside each effect, pumping work, and thermal loss from the evaporator are neglected while deriving above equation. It may also be noted that the energy balance in Eq(11) is without considering internal integration like liquor integration and condensate cooling. However, GCC of the overall MEE includes internal integration. Assuming ∆En-1 amount of energy shift is introduced between nth and n-1th effect (as shown in Figure 2). ∆En-1 can be condensate cooling, liquor integration or shifting of effects to integrate MEE with the background. Therefore, the modified energy balance can be expressed as: F ( hn − hin ,n ) + ∆En −1 = f nnew −1 W ( H n −1 − hcond n −1 + hn − hin , n ) −

(

i =n

)

new f nnew −1 W ( H n − hn ) − ∑ f n − 2 W ( hin , n − hn ) i =3

(13)

Where ∆En-1 is given as:

∆En −1 = En − En −1

(14)

En is amount by which a particular effect is shifted away from pinch (see Figure 2). If the

shift is taking place away from Y-axis then it considered to be positive and negative otherwise. fnew represents the new vapor fraction because of the shift ∆En-1 and is given as:

f new = f + ∆f

(15)

Where, ∆f is small change in vapor fraction because of energy shift. After some algebraic manipulations, Eq(13) may be simplified to:

∆En−1 = ∆f n−1W ( H n −1 − hcond n −1 + hn − hin ,n ) − ∆f nW ( H n − hn ) W

(

i=n

− ∑ ∆f i − 2 i =3

)(h

in , n

(16)

− hn ) W

As the magnitude of difference in liquor enthalpy is much smaller in comparison to latent heat of vaporization for vapor, the first term on right hand side (RHS) of Eq(16) can be approximated as: ∆f n −1W ( H n −1 − hcond , n −1 + hn − hin ,n ) ≈ ∆f n −1W ( λn −1 + hn − hin ,n ) ≈ ∆f n −1W λn −1

(17)

Similarly, liquor enthalpy can be approximated to condensate enthalpy and hence, the second term on RHS of Eq(16) may be simplified as:



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∆f nW ( H n − hn ) ≈ ∆f nW λn

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(18)

Change in liquor enthalpy can be neglected in comparison to first two RHS terms of Eq(16) and the overall equation can be modified as:

∆En−1 ≈ ∆f n −1W λn −1 − ∆f nW λn

(19)

Summing up the expanded version of Eq(19) for n = 2 to n = K, leads to:  ∆E1 ∆E1 + ∆E2 ∆E + ∆E2 + ............ + ∆EK −1  + + ............. + 1  ≈ λ3 λK  λ2  λ λ λ  − ( ∆f 2 + ∆f 3 + ......... + ∆f K ) W + ∆f1W  1 + 1 ....... + 1  λK   λ2 λ2

(20)

For ∆En-1 energy shift is taking place between n-1 and nth effect, Eq(20) suggests that:

 ∆En −1 ∆En −1 λ λ ∆E  λ  + + ............. + n −1  ≈ ∆f1W + ∆f1W  1 + 1 ....... + 1   λn +1 λK  λK   λ2 λ2  λn

(21)

The latent heat of vaporization can also be assumed to be constant, i.e.,

λ1 ≈ λ 2 ≈ ........ ≈ λ n ≈ ...λ K ≈ λ

(22)

Eq(21) can be further simplified to represent the change in mass flow rate for any effect ‘i’ because of energy shift between n-1th and nth effect:

( K - ( i -1) - ( n - i ) ) ∆E

n -1

λiW

∆f i ≈

j = i -1

- ∑ ∆f j j =1

K - ( i -1)

(n = i +1

to n = K )

1

From conservation of mass, the net change in mass flow rate of the system is zero. The change in mass flow rate for Kth effect can be calculated as: j = K −1

∆f K = − ∑ ∆f j

(23)

j =1

Due to ∆En-1 energy shift taking place, the vapor fraction for first stage is modified by ∆f1 and the utility requirement for effect 1 is changed to:

∆S n = ∆f1W ( H1 − h1 )

(24)

Eq(25) can be further simplified as:

∆S n ≈

( K − ( n − 1) ) ∆E

n −1

K λ1

( H1 − h1 ) ≈

( K − ( n − 1) ) ∆E K

n −1

This proves the following theorem.


(25)

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Theorem 1: When ∆En-1 amount of energy shift is taking place between nth and n-1th effect in GCC of a K-effect MEE, the change in utility requirement for the first effect (∆Sn) is approximately given by:  K − ( n − 1)  ∆S n ≈   ∆E n −1 K  

(26)

Integration of MEE with the background process reduces the net energy requirement for the system.10,25,29 Energy saving is the maximum when energy integration is performed for the last effect and the minimum for the first effect.10 Therefore, the operating effect (n) plays a vital role on net energy saving. Energy saving due to change in operating effect (n) can be calculated using Theorem 1. When MEE is integrated with the background process Theorem 1 can be used for maximizing the energy integration. It may be noted that enthalpy related assumptions are relaxed while generating GCC of the overall systems.

Based on Theorem 1, following corollary can be proved.

Corollary 1: If the effects are shifted away from pinch by En, the net change in utility K

requirement for the first effect of a K-effect MEE is ∑

n =1

En . K

Proof. Net change in utility requirement for effect 1 because of shifting between the effects is

given as: K

∆ S = ∑ ∆S n = n=2

K −1 K −2 1 ∆E1 + ∆E2 + ....... ∆EK −1 K K K

K −1 K −2 1 ( E2 − E1 ) + ( E3 − E2 ) + ....... ( EK − EK −1 ) = K K K K −1  E + E3 + ..... + EK  − E1 +  2  K K  

(27)

∆S =

(28)

It might happen that effect 1 is not pinched, as a result external utility might be required by other effects (as shown in Figure 2). Net hot utility required by the other effects, is the amount by which effect 1 is shifted away from pinch (E1). Net change in utility requirement for MEE is sum of net change in utility requirement for effect 1 (∆S) and E1 given as:



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∆HU =

E1 + E2 + E3 + ....... + EK K

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(29)

Corollary 1 explains the change in utility requirement for MEE due to energy shift taking place between the effects.

Let us assume that all effects of MEE are pinched and the hot utility requirement be HU (see Figure 3a). If a shift is introduced in GCC by shifting some of the effects away from the yaxis, En is positive (see Figure 3b). From Corollary 1, the new hot utility requirement is calculated to be:

HU new = HU +

E2 + E3 3

(30)

Increased utility requirement resulted due to shifting of effects away from the y-axis. This proves the following theorem.

Theorem 2: For the minimum energy consumption, all effects should be pinched.

It should be noted that the vapor fraction should be varied such that all the effects are pinched and the minimum energy is required for the MEE.

2.4. Integration Methodology Applying various mathematical results, reported in the previous sub-section, a detailed methodology to integrate MEE with background process is developed. Figure 4 represents the integration flowchart. The steps for integration of MEE with background process are as follows:

•

Step 1: Specify the input parameters like number of effects (K), effect temperatures (Y), feed temperature (Tfeed), feed concentration (cfeed), product concentration (cproduct), feed flow rate (F), minimum temperature driving force (∆Tmin), and stream data for background process.

•

Step 2: Assuming initial vapor fraction for each effect (fninitial) to be (1/K). Determine mass flow rate, liquor concentration, and enthalpy values for every effect.


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•

Step 3: Generate the process stream data for MEE. With known background and MEE process stream data, MPTA is used for energy targeting and generation of the GCC. Distance of GCC from y-axis for each effect is determined to be En. Note that En may be calculated directly from the GCC data. Net shift between each effect (∆En) is calculated using Eq(14).

•

Step 4: Determine change in vapor fraction for each stage (∆fn) using Eq(23). If ∆fn less than the desired accuracy, the procedure is terminated. Otherwise, new vapor fraction (fnnew) is calculated by summing fninitial and change in vapor fraction (∆fn) and procedure from Step 2 is repeated (with fninitial is replaced by fnnew).

It may be noted that it is not compulsory to assume initial vapor fraction for each effect to be equal in step 2. Any positive vapor fraction with overall summation being unity may be sufficient to initiate the proposed solution procedure.

2.5. Illustrative Example To demonstrate the proposed methodology for given effect temperature a case study of manufacturing of corn glucose is considered.35 The flow sheet for the process is shown in Figure 5. Input data for the MEE and background process stream data are listed in Tables 1 and 2. Correlations for liquor and vapor enthalpies as well as for BPR are shown in Table 3.

Using the solute balance, the total amount of water (W) to be evaporated is 0.589 kg/s. Assuming equal vapor fraction (finitial) i.e., (1/3) the mass flow rate of vapor, V1, V2 and V3 is calculated to be 0.196 kg/s from each effect. Liquor mass flow rates, l1, l2 and l3 are calculated to be 0.974 kg/s, 0.778 kg/s and 0.581kg/s, respectively. Similarly, liquor concentration, C1, C2 and C3 are 48.96%, 61.31% and 82 %, respectively. Using correlations listed in Table 3, BPR as well as liquor and vapor enthalpies can be calculated. Once the mass flow rate and enthalpy values are known, the process streams data for the MEE can be generated. With known process stream and background process data, MPTA is used to generate the GCC as shown in Figure 6. It can be observed that all effects are not pinched, E1 =-118.8 kW, E2=-17.4 kW and E3 =0. As stated in Theorem 2 all effect should be pinched for minimum energy consumption. As ∆E1=101.4 and ∆E2=17.4, the change in vapor fraction for three stages are ∆f1=0.056, ∆f2=-0.022 and ∆f3=-0.034. New vapor fraction are calculated to be f1new= 0.39, f2new=0.312 and f3new=0.298. GCC is generated again using new vapor fractions



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(not shown for brevity) and the procedure is repeated until convergence. For a given tolerance of 10-05, calculations converges after three iterations (at the end of third iteration, changes in vapor fractions are calculated to be ∆f1 = 7.06x10-06, ∆f2 = 2.5x10-06and ∆f3 = 9.56x10-06). The final hot utility requirement is 830.12 kW. Final design parameters are listed in Table 4 and the GCC for the integrated system is shown in Figure 7.

It may be noted that the hot utility requirement for the standalone MEE and the independent background process are 448 kW and 472.3 kW, respectively. Therefore, by integrating the MEE with the background process, as demonstrated above, 9.8% energy can be conserved. Using the methodology suggested by Higa et al.,10 the hot utility requirement for the integrated system calculated to be 866.77 kW which is 4.4% higher than the proposed methodology. Similarly, methodology proposed by Hillenbrand and Westerberg25 results in the utility requirement of 872.4 kW, which is 5.1% higher than the proposed methodology.

3.

Selection of Effect Temperatures

MEE is an energy intensive process. Significant energy can be conserved by appropriately selecting effect temperatures.36 However, using mathematically rigorous results, an algebraic methodology is proposed in this paper.

3.1.

Mathematical Results for Temperature Selection

In this sub-section, different mathematical expression for appropriate temperature selection is derived. In previous section, it is shown that the maximum energy integration can be achieved by adjusting vapor fractions to pinch all the stages. Effects of changing temperatures of non-pinch effects are discussed first.

Figure 8 shows simplistic representation of a MEE. Feed at given temperature enters the evaporator, whereas product and vapor condensates leave the evaporators at desired temperatures. To achieve the desired product concentration and cooling the condensate at atmospheric temperature, hot and cold utilities are required. Overall energy balance can be written as:


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Fh feed + HU − Whatm − ( F − W ) hproduct − CU = 0

(31)

HU − CU = Whatm + ( F − W ) hproduct − Fh feed = constant

(32)

It may be concluded that the net difference between hot and cold utility is constant. Without loss of generality, let nth effect controls the pinch. Therefore, n-1 effects are above pinch in GCC and K-n effects are below the pinch. Apart from nth effect, all other effect temperatures are changed in such a way that nth is still controlling the pinch. Let the new vapor and liquor enthalpy coming out from each stage be Hnew and hnew. For effects that are above pinch, change in energy requirement for each effect (Zi) is given as:

Z i = ( H inew − H i ) Vi + ( hinew − hi ) li − ( hinew −1 − hi −1 ) li −1

(33)

i =n

Z = ∑ Zi = ( H1new − H1 ) V1 + ( H 2new − H 2 )V2 ...... + ( H nnew −1 − H n −1 ) Vn −1 i =1

(34)

Similarly, change in hot stream (Ai) for every effect is given as: Ai = ( H inew − H i )Vi

(35)

Net change in hot stream for above pinch effect is: i =n

A = ∑ An = ( H1new − H1 )V1 + ( H 2new − H 2 )V2 ....... + ( H nnew −1 − H n −1 )Vn −1

(36)

Z − A=0

(37)

i =1

Eq (38) suggests that the hot utility remains constant. From Eq (33) it can be concluded that the cold utility requirement also remains constant. This proves the following lemma.

Lemma 1: Overall hot utility requirement for MEE remains constant if the temperatures of non-pinched effects are varied, for given vapor fraction at each stage.

If the mass flow rate of liquor and vapor for the effects above pinch point is changed without affecting the mass flow rate of below pinch effect. Then the GCC for below pinch does not change and the cold utility requirement is constant. So the hot utility also remains constant from Eq(33). Similarly, if the mass flow rate for effects below pinch is changed, the hot



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utility remains constant and so is the cold utility. This discussion leads to the following corollary.

Corollary 2: If the mass flow rates for the effects either above or below pinch are changed then the utility requirement for the system is constant, as long as total evaporation is constant.

Lemma 1 suggests that effect controlling pinch dictates the utility requirement of MEE. On the other hand, Theorem 2 suggests that for the minimum energy consumption all effects must be pinched. Therefore, to minimize the energy consumption of MEE, each effect temperature should be optimally selected and pinched. This method may be adopted for optimal selection of effect temperatures.

In the previous section, MEE and background process are integrated and represented as a single GCC. Energy integration between the MEE and the background process can also be achieved by integrating two different GCCs.37 One of the GCC may be reflected about the temperature axis and the other one kept as it is.10,29 By horizontally shifting one towards the other, till they touch each other, maximum energy integration may be achieved.37 This representation is followed in this section. Figure 9 shows the background GCC, reflected about the temperature axis and the GCC of the MEE kept as it is. Horizontal distance at every effect indicates the possibility of energy integration. Using Corollary 1 the net hot utility requirement for the overall system is: HU system = HU B / G + HU MEE −

E1 + E2 + ... + En K

(38)

From Eq(39) it can be concluded that higher the energy integration (i.e., E1+E2+...+En), lower is the utility required by the system. Therefore, the effect temperatures should be selected in such a way that the last term of Eq(39) is maximized. This proves the following theorem:

Theorem 3: The effect temperatures should be selected in such a way that the total energy recovery from the background GCC with respect to the GCC of the MEE (i.e., E1+E2+...+En) is the maximum.


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It should be noted that liquor flashing is neglected in this case. For designing of MEE as standalone system or for integration of MEE with background process with very low utility requirement, liquor flashing can play a dominating role. In such cases, the horizontal shifting at ever effect is modified by the difference between the two GCCs and the energy required for liquor flashing. This typically forces to select temperatures as low as possible. However, for brevity, details are not discussed here. Theorem 3 holds for integration of MEE with background with significant utility requirements. Selection of appropriate temperature for each effect is discussed below.

3.2.

Appropriate Temperature Selection Methodology

The steps for appropriate temperature selection for MEE to appropriately integrate with background process are as follows:

•

Step 1: Determine the GCC of the background process. From the GCC, identify the points at which the maximum energy from the background can be recovered. It should be noted that temperature selected are shifted temperatures.

•

Step 2: For above pinch integration, the shifted effect saturation temperature must be greater than the shifted background pinch temperature and is given as:

Tpinch B / G ≤ Yn - BPRn -1 − •

∆Tmin 2

(39)

Step 3: Similarly, for below pinch integration, the shifted effect temperature must be less than shifted background pinch temperature.

Tpinch B / G ≥ Yn + 1 + •

∆Tmin 2

(40)

Step 4: For feasible heat transfer to take place between two effects, the minimum operating temperature of nth effect should be higher than the maximum operating temperature of n+1th effect, and is given as:

Yn - BPRn -

∆Tmin ∆T -1 ≥ Yn +1 + min + 1 2 2


(41)


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While selecting the effect temperature, Eq(40)-Eq(42) should be satisfied. On the other hand, for effect temperature between Eq(40) and Eq(41), no energy integration with background process is possible. Based on these inequalities and Theorem 3, appropriate temperatures for each stage may be selected. Applicability of the proposed methodology is demonstrated next.

3.3.

Illustrative Example

The GCC for the background process is shown in Figure 10. From the GCC the points of maximum energy integration are identified. The maximum operating temperature is 117.4 oC (limited by steam supply temperature) and hence, the maximum energy integration temperature is 80 oC as the GCC has highest value (see Figure 10). The minimum operating temperature is assumed to be 55 oC for this example. It may be noted that it is not possible to select three operating temperatures between 80 oC and 55 oC, because of ∆Tmin and BPR (as suggested in Eq(42)). Therefore, the second effect is selected corresponding to the maximum energy integration. Eq(41) suggest that Y2 should be lower than 73 oC and hence, Y2 is selected as 73 oC (as GCC is monotonically decreasing). It may further be noted from Figure 10 that the GCC is monotonically increasing above 80 oC, and hence, Y1 is 117.4 oC to maximize energy integration. Using Eq(42), Y3 determined to be 57 oC.

Once the appropriate effect temperatures are selected, methodology proposed in the previous section is used for integrating MEE with the background process. The final design parameters are listed in Table 5 and the heat exchanger network is shown in Figure 11. This network has 22 heat exchangers with a hot utility requirement of 615.3 kW. It can be observed that by optimally selecting effect temperatures, 25.87% additional energy can be saved.

In Figure 11, and exchangers 9, 15 and 21 have heat duty less than 5 kW. For practical purpose, these exchangers are removed and the new network is shown in Figure 12. The new utility requirement comes out to be 619.4 kW. It may be noted that Exchanger 15 is not removed even though its duty is less than 5 kW as otherwise a separate heating exchanger would have required with same duty.

4.

Conclusion


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MEE is one of the most important components for many process industries. This is an energy integrated but energy intensive process. It is important to integrate MEE with background process to achieve significant energy conservation. In this paper two methodologies are proposed to integrate MEE with the background process. In the first methodology, integration of MEE with given effect temperatures with background process is proposed. Determination of optimal effect temperatures for maximum energy recovery is described in the second methodology. Applicability of the proposed methodologies is demonstrated through an illustrative example of corn glucose process. It is observed that energy integration of MEE with background process can conserve 9.8% of energy. An additional 25.87% energy can be conserved by selecting optimal effect temperatures. Optimal selection of effect temperatures improves GOR from 1.54 to 2.04.

The proposed methodologies are based on mathematical results. Theorem 1 quantifies the actual energy saving because of energy integration of MEE with background process. On the other hand, a process integration principle to minimize energy consumption for MEE is developed in Theorem 2. An optimal selection of effect temperatures is proposed in Theorem 3. These mathematical results are applicable beyond the scope of the present study. These results can be extended for integrating MEE with other energy conserving devices such as TVC, solar thermal collectors, etc. Future research work is directed towards demonstrating the applicability of these theorems to various other problems involving MEE. The future research is also directed towards minimization of the overall cost of the system.



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List of Table Captions

Table 1: Input data for the MEE Table 2: Background process Table 3: Correlations Table 4: Final design parameter for integrated system with given temperature. Table 5: Final design parameter for integrated system with optimal temperature.



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Table 1: Input data for the MEE Feed rate (kg/s) Feed concentration (%) o

Feed temperature ( C)

1.17

Number of effects

3

40.75

Liquor flow pattern

Forward feed

92

o

o

∆Tmin( C)

10 o

Steam temperature ( C)

127.4

First effect temperature Y1( C)

112.07

Final desired concentration (%)

82

Second effect temperature Y2(oC)

95.24

Product temperature (oC)

75.77

Third effect temperature Y3(oC)

75.77

Condensate temperature(oC)

30

Table 2: Background process Stream

Tin(oC)

Tout(oC)

Flow (kg/s)

mCp (kW/K)

H1

85

84

0.16

385.03

H2

85

60

0.16

0.70

H3

85

55

1.21

4.10

C1

30

155

1.43

5.06

C2

52

70

1.21

4.07

C3

69

92

1.17

3.97

Table 3: Correlations BPR of sugar containing solutions, Latent

BPRn = 0.33exp(4cn )

38

heat

of

vaporisation of steam,39

λn = 80.345Ysat ,n -

21035.87 + 2049.123 Ysat ,n - 4213.519ln (Ysat ,n Ysat ,n

+0.09182Ysat2 ,n -1.04 ×10-04 Ysat3 ,n + 8597.953 Enthalpy

of

saturated

H n = 4.154 Ysat , n + 2.0125 × 10-04 + 1.62 (Yn - Ysat ,n ) +

and superheated steam,39

2.0285 × 10 -04 (Yn2 - Ysat2 ,n ) - 0.3747 × 10 -07 (Yn3 - Ysat3 ,n ) + λn

Specific heat of corn

Cpn = 4.187(1 − cn (0.57 − 0.0018(Ysat , n − 20)))

glucose syrup,

38


.

)

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Table 4: Final design parameter for integrated system with given temperature. Parameters

Value

l1

0.941 kg/s

l2

0.76 kg/s

l3

0.582 kg/s

c1

50.66 %

c2

62.9 %

c3

82 %

HU

830.12 kW

CU

737.97 kW

Table 5: Final design parameter for integrated system with optimal temperature. Parameters

Value

l1

1.023 kg/s

l2

0.8 kg/s

l3

0.582 kg/s

c1

46.6 %

c2

59.6 %

c3

82 %

HU

615.3 kW

CU

523.1 kW



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List of Figure Captions

Figure 1: Schematic of nth effect evaporator of a MEE. Figure 2: Typical GCC for four effect evaporator Figure 3: Proof for Theorem 2 Figure 4: Flowchart for integration of MEE with background process. Figure 5: Process sheet data for manufacturing of corn glucose33 Figure 6: GCC for MEE and background process Figure 7: GCC with all effect pinched with background process. Figure 8: Schematic for MEE Figure 9: GCC for reflected background process and MEE Figure 10: GCC for background process Figure 11: Network for integrated MEE system Figure 12: Evolved network for integrated MEE system


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Liquor from n-1th effect

Vapour Generated

ln-1,Yn-1,hn-1

ln-1,Tin,n,hin,n

nth Effect

Vn,Yn,Hn

Vapour from n-1th effect

Vn-1,Yn-1,Hn-1

Condensate Vn-1,Ysat,n-1,hcond,n-1

Concentrated Liquor

ln,Yn,hn

Figure 1: Schematic of nth effect evaporator of a MEE.

Feed pre-heating Effect 1

E1

Energy required for evaporation

∆E1 Effect 2

E2

Condensation

∆Tmin+BPR

Effect 3

E4 Effect 4 Condensate cooling Heat (kW)

Figure 2: Typical GCC for four effect evaporator



HU

200

HU+(E2+E3)/3

180

Temperature (oC)

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Page 30 of 36

160

140

E2

120

100

80

E3

60

40

B

20

0 0

100 0

200 0

Heat (kW)

Figure 3: Proof for Theorem 2


3000

400 0

500 0

6000

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Start

Input Parameters: Number of effects (K), effect temperature (Yn), type of feed, feed temperature (Tfeed), feed and product concentration, mass flow rate of feed (F), minimum temperature driving force (∆Tmin) and background process stream data.

Assume equal evaporation between the stages,

f1initial=f2initial..........=fninitial..........=fKinitial=(1/K)

Calculate initial liquor concentration (cninitial) and mass flow rates Calculate liquor and vapour enthalpy Define MEE process stream, draw its GCC using MPTA and calculate utility requirement Calculate shifting for each stage (En)

fn

new

=fn

initial

Calculate net shift between each effect (∆En) using Eq(14) Calculate change in vapour fraction (∆fn) using Eq(23) Calculate new vapour fraction fnnew fnnew=fninitial + ∆fn NO

If |∆fn|< desired accuracy YES Display final design parameter

Stop

Figure 4: Flowchart for integration of MEE with background process.



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Vapour to Vent H2 F: 0.16 T:85 T:60

H1 C1 F:1.43 T:30 c:36

converter

y Flash y Vessel y y Carbon

F:1.43 T:155 c:36

Slurry feed tank

Filter Press-1 F:1.22

Carbon tank 1 H.P. Steam

Condensate to boiler C2

Spent Carbon+4% Syrup F:0.05 H3

Heat Exchanger 2

T:70 carbon

T:52

Heat exchanger 1 Cooling water

C3 L.P. Steam F:1.17 T:69 Spent Carbon+4% Syrup F:0.05

Vapour

Heat Exchanger 3

Filter Press-2

L.P. Steam

Condenser F=1.17 T:92 c:40.75

c:40.75

Ion Exchange F:1.22 unit T:55

L.P. Steam Carbon Tank 2

T:85

MEE

Product F:0.58 T:75.77 c:82

Figure 5: Process sheet data for manufacturing of corn glucose35

Figure 6: GCC for MEE and background process


Page 33 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


HU=830.11 kW

All Effects Pinched

CU=727.8 kW

Figure 7: GCC with all effect pinched with background process.

Steam (HU) Feed (hfeed)

Cooling (CU)

MEE

Product (hproduct) Condensate (hatm)

Figure 8: Schematic for MEE



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

HUB/G Background GCC

HUMEE

E1 MEE E2 En

Figure 9: GCC for reflected background process and MEE

Figure 10: GCC for background process


Page 34 of 36

Page 35 of 36

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48


19

10 H.P. Steam 251.5 kW

9

o

o

105.3 C

o

7

5

4 o

20

o

64.8 C

o

30 C

22

C1

18

59.4 C

o

155 C

70 C o

13

o

92 C 3

11

o

C3 o

6

322.2 kW

11

o

117.4 C

85 C l1 (117.4 C) 1 o 5 115.3 C

69.4 C 0

60 C

H1

o

16

o

V2 (73 C) 377.1 kW

nd

41.5 kW

0

73 C

Heat Exchanger duty

4=187.1 kW 6=12.5 kW

7=8.6kW

8=18.9 kW

9=1.1 kW

10=8.6 kW

11=20.8 kW

12=10.9 kW

13=43.1 kW

14==30.2 kW 16=6.2 kW

17=6.5 kW

18==59 kW

19=6.6 kW

20=26.5 kW

21=3.1 kW

22=41.5 kW

69.4 C

15

69.4 C

o

0

14

9

2 effect

5=8 kW

H3

H2

17 84 C

3=70.5 kW

o

55 C

o

12

1 2 o 107.2 C 105.3 C

2=54.24 kW

CU 28.5 kW

18

13

o

o

1=7.6 kW

20

o

79.9 C

o

o

19

69.4 C

117.4 C L.P. Steam 363.8 kW

100.3 C

114.3 C

3

o

V1 (117.4 C)

48.2 C

65.2 C

o

o

o

69.4 C

8

7

o

o

69.4 C

o

st

1 effect

o C2 52 C

69 C 2

322.3 kW

14

o

59.4 C

74.2 C

4

15=3.4 kW

o

38.2 C

21

17

o

66.5 C

68.1 C

o

43.9 C

16

8

487.9 kW

110.8 kW

o

l2 (73 C) 10 o

o

69.4 C

83 C

0

484.5 kW

48.2 C rd

3 effect o

57 C 5.7 kW

490.2 kW o

Product

57 C 6 o

o

75.8 C

67 C

12

o

59.4 C

15

Figure 11: Network for integrated MEE system ACS Paragon Plus Environment

21

22

CU

o

V3 (57 C) o

l3 (57 C)

495kW


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48

Page 36 of 36

19 H.P. Steam 255.7 kW

10

o

o

104.6 C

o

7

5

4 o

o

38.2 C 20

17

o

65.8 C

67.4 C

o

43.4 C

16

8

o

64.1 C

o

30 C

22

C1

18

58.9 C

o

155 C

70 C o

13

o

92 C 3

11

o

C3 o

6

o

322.2 kW o

117.4 C

o

100.3 C

11

69.4 C

12

0

60 C

H1

o

16

o

V2 (73 C) 377.1 kW

7=8.6kW

8=18.9 kW

10=8.6 kW

11=20.8 kW

12=10.9 kW

13=43.1 kW

14==30.2 kW

15=3.4 kW

16=6.2 kW

17=6.5 kW

18==59 kW

19=6.6 kW

20=26.5 kW

22=41.5 kW

0

69.4 C

15

69.4 C

o

73 C

Heat Exchanger duty

6=12.5 kW

0

14

nd

2 effect

5=8 kW

H3

H2

17

41.5 kW

2=54.24 kW

o

55 C

o

84 C

4=187.1 kW

CU 29.6 kW

18

13

o

o

85 C l1 (117.4 C) 1 o 5 115.3 C

1 2 o 107.2 C 105.3 C

1=7.6 kW

20

o

79.9 C

o

3=70.5 kW

19

69.4 C

117.4 C L.P. Steam 363.8 kW

48.9 C

65.9 C

o

114.3 C

3

o

V1 (117.4 C)

69.4 C

8

7 o

st

o

o

69.4 C

o

2 1 effect

o C2 52 C

69 C

4 322.3 kW

14

o

59.4 C

74.2 C

487.9 kW

110.8 kW

o

l2 (73 C) 10 o

o

69.4 C

83 C

0

484.5 kW

48.2 C rd

3 effect o

57 C 5.7 kW

490.2 kW o

Product

57 C 6 o

o

75.8 C

67 C

12

o

59.4 C

15

Figure 12: Evolved network for integrated MEE system


22

CU

o

V3 (57 C) o

l3 (57 C)

498.1kW

Energy Integration of Multiple Effect Evaporators ... - ACS Publications

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