20th European Symposium on Computer Aided Process Engineering – ESCAPE20 S. Pierucci and G. Buzzi Ferraris (Editors) © 2010 Elsevier B.V. All rights reserved.

Global Optimal Design of Mechanical Vapor Compression (MVC) Desalination Process Marian Marcovecchioa, Pio Aguirrea, Nicolas Scennaa, Sergio Mussatia

a INGAR Instituto de desarrollo y diseño, Avellaneda 3657, S3002GJC Santa Fe, Argentin, {mariangm; paguir; nscenna; mussati}@santafe-conicet.gob.ar

Abstract This paper deals with the optimal design of Mechanical Vapor Compression (MVC) desalination process. Precisely, a detailed mathematical model of the process and a deterministic global optimization algorithm are applied to determine the optimal design and operating conditions for the system. The resulting model involves the real-physical constraints for the evaporation process. Nonlinear equations in terms of chemical-physical properties and design equations (efficiencies, Non-Allowance Equilibrium, Boiling Point Elevation, heat transfer coefficients, momentum balances, among others) are used to model the process. The model has been solved by using a deterministic global optimization algorithm previously developed by the authors [7] and implemented in a General Algebraic Modeling System GAMS [1]. The generalized reduced gradient algorithm CONOPT 2.041 [2] is used as NLP local solver. The model was successfully solved for different seawater conditions (salinity and temperature) and fresh water production levels. The influence of the production requirements on the process efficiency as well as the algorithm’s performance is presented. Keywords: Vapor Compression (MVC) desalination, global optimization method.

1. Introduction Desalination of seawater is one of the main alternatives to overcome the problem of fresh water supply. Various types of desalination systems are known and are in use. Typically, such systems include a water pre-treatment system, a desalination unit and a post-treatment system. The desalination of seawater in such systems is achieved through thermal or membrane processes. The thermal processes for seawater desalination include multistage-flash distillation (MSF), multi effect distillation (MED) and vapor compression (VC). Further, the main membrane systems are reverse osmosis (RO) and electrodialysis (ED) processes. The product of a Vapor Compression system enjoys similar qualities to the other distillation processes. Its source of driving force is rotating mechanical energy, generally obtained from a motor. VC units tend to be small plants in isolated locations while the other processes are usually used for large fresh-water productions. Furthermore, certain desalination systems can employ renewable energy sources for powering the desalination system. In fact, a mechanical vapor compression (MVC) desalination system may be powered by a wind turbine. Typically, wind powering of a MVC desalination system may be achieved either by direct mechanical coupling of the turbine shaft to the compressor axle of the desalination system, or by generating electrical power that is utilized to drive the electrical compressor drive. However, the

M.Marcovecchio et al.

mechanical coupling does not provide any means for power regulation or speed control of the compressor drive. A brief outline of the articles focusing on mathematical modeling and analysis of single effect VC desalination units can be found in [3, 4, 5]. In the present work, a mathematical model recently developed by the authors [6] which was solved for local optimality is properly extended in order to get a more realistic design of the process. Mass, energy and momentum balances are included in the mathematical model. Rigorous correlations to compute Boiling Point Elevation, total heat transfer coefficient and physical-chemical properties of all streams, among others, are also considered. The model involves non-convex constraints like bilinear terms and logarithms which can lead to local optimal solutions. For this reason, a deterministic global optimization algorithm previously developed by the authors [7] is implemented in this paper to find the global optimum for the resulting mathematical model. The paper is outlined as follows. Section 2 briefly describes the process. Section 3 introduces the problem formulation. Section 4 summarizes the mathematical model. Section 5 presents applications of the developed model and results analysis. Finally, Section 6 presents the conclusions and future work.

2. Process description Figure 1 shows a Single-Effect Mechanical Vapor Compression (MVC) desalination process. As is shown, the energy input is entirely as mechanical power to drive the compressor. No live steam is required except for preliminary heating to raise the plant to working temperature. Vapor formed is recompressed and introduced to the evaporator. Two primary methods can be used for the compression of the vapor: 1) Thermal Vapor Compression (TVC) and, 2) Mechanical Vapor Compression (MVC). The main equipments used in the MVC desalting process are the evaporator, the compressor, pumps and pre-heaters.

Md , Preh Trec

Mf1 ; TF_out_HX1

Mf2 ; TF0 ; X

Wcomp

Mf ; Tf ; Xf MD ; Pboil ; Tv

HEX1

HEX2

Mb ; Tboil ; Xb

Md ; Td

MFo ; TF0 ; XF0

Fig. 1 Single-effect Mechanical Compression Vapor (MVC) desalination

Global Optimal Design of Mechanical Vapor Compression Desalination Process

As is shown in Fig. 1, the incoming seawater [Mf] is passed through two heat exchangers [HEX1 and HEX2] where it is preheated by the heat transferred from the discharged brine [Mb] and product [Md] streams. The sea water is then recycled and sprayed on the outside of a bundle where it boils and partially evaporates. Then, the produced steam is drawn through the demister to the centrifugal compressor [VC] which increases the pressure and temperature of the steam by compression. This steam is then discharged into the inside of the heat transfer tube bundle where it condenses into distillate [Md]. The compressor provides, through its suction, a pressure lower than the equilibrium of the brine facilitating the evaporation of the seawater. The energy performance of the system depends on the pressure increment in the mechanical compressor, on the thermodynamic efficiency of polytropic process and on the efficiency of the electric motor. MVC plants are in service with energy consumptions around 11 kWh/m3, and designs have been developed with power consumptions as low as 8 kWh/m3. This is the lowest energy consumption of any distillation so far developed and is competitive with seawater reverse osmosis including energy recovery. Capital and energy costs are significant factors on the total water production cost. The main energetic consumption of the MVC distillation unit is represented by the electricity which is mainly required to drive the compressor motor, while there is no steam requirement. The operation and maintenance of the compressor motor may be half of the total operating cost. The process includes pumps for the seawater, brine and product. In some designs, part of the discharge brine is recycled by using a recirculation pump. MVC unit ratings have so far been limited to about 1500 m3/d. The most disadvantages of MVC system are the maximum allowable tip velocity of the compressor blades and mechanical compressor which limit the fresh water production.

3. Problem formulation The optimization problem can be stated as follows: Given the water demand and seawater conditions, the goal is to determine the optimal operating conditions in order to minimize the electricity used by the compressor and total heat transfer area of the process. Another optimization problem could be formulated as follows: Given the total heat transfer area (evaporator and pre-heaters), the goal of the problem is to maximize the ratio of fresh water production to the electricity used by the compressor. Finally, other objective function may be the total annual cost of the process (minimization).

4. Assumptions and Mathematical Model The resulting mathematical model is based on the following assumptions: a) Product is pure water, b) Heat losses from the evaporator surface are negligible, c) No recycle is considered, and d) equal overall heat transfer coefficients in the two heat exchangers are assumed. Basically, the model involves real-physical constraints for the evaporation process and is derived from the rigorous energy, mass and momentum balances. Physical and chemicals properties of the seawater and fresh water are computed by detailed correlations. Next, the main equations of the model are presented. Total mass and energy balance:

dbf MMM += (1)

ddbbff XMXMXM += (2) The outside temperature at the compressor is computed as:

M.Marcovecchio et al.

γ−γ

=1

v

sobrec RpT

T (3)

where

rehboil PPRp = (4) The mechanical power consumed by the compressor is given by:

1TTTR

1M3600MWW

v

sobrecvdcomp −−γ

γ=η (5)

The energy balance on the evaporator is as follows:

( ) ( ) TvdTfTboilfTDdsat_vapsobrecd MHHMMHHM λ+−=λ+− (6) The energy balances on the two pre-heaters are given by:

( )dischbboilbHEX HHMQ _1 −= (7)

( )01_11 HHTFMQ HEXoutfHEX −= (8) The mass balance on the seawater spliter is:

2f1ff MMM += (9)

( )prodTdTddHEX HHMQ _2 −= (10)

( )SWHXoutTFfHEX THMQ −= 2__22 (11)

2HX_out_TF2f1HX_out_TF1fTFf HMHMHM += (12) The temperature differences on hot/cold sides of pre-heaters are computed as follows:

1__1 1 HEXoutTFTt boilHX −=Δ (13)

SWdisch1HX TTb2t −=Δ (14)

2TF_out_HEX1 2 −=Δ Tdt HX (15)

SW_2 T2 −=Δ proddHEX Tt (16) The logarithmic mean temperature differences to compute the heat transfer area of pre-heaters (LMTD) are given by:

j

j

jj

tt

tt

21

ln

21LMTDj

ΔΔΔ−Δ

= j = HEX1, HEX2 (17, 18)

Then, the heat transfer areas are given by: LMTD A U Q jjjj = j = HEX1, HEX2 (19, 20)

On the other hand, the evaporator area is calculated by:

( ) LMTD U

M)T - (T U

M A d

boildevap

TDdevap

boilrecv TTCp −+=

λ (21)

Global Optimal Design of Mechanical Vapor Compression Desalination Process

In total, the proposed mathematical model involves 41 variables and 36 constrains, most of them being non-convex. The model was solved for global optimization by applying the ME-D (Minimization of the Error and Discard) algorithm [7] implemented in the software GAMS. The tolerance for the global optimality was set at 0.001 which represents about 0.09% of the global optimal objective value.

5. Results and discussion In this section, the optimal solutions corresponding to three representative case studies are presented due to space limitation. Table 1 shows the optimal solutions obtained for different fresh water demand. As is mentioned in Section 3, the goal is to determine the optimal operating conditions to minimize the electricity consumption in order to satisfy the given fresh water demand. The seawater salinity and temperature are 45000 ppm and 298 K, respectively. Table I. Optimal values corresponding to different fresh water demands.

Md = 1000.00 [Kg/h]

Md = 800 [Kg/h]

Md = 700.00 [Kg/h]

W_comp [kW] 58.059 44.969 39.348 Rp ** 2.10 *** 2.10 *** 2.10 *** Td [K] 340.41 328.98 328.907 Tboil [K] 325.32 316.12 315.00 ## Tf [K] 317.30 306.59 306.59 Mb[Kg/h] 900.000 720.00 630.000 Mf [Kg/h] 1900.00 1520.000 1330.000 LMTD_HX1 [K] 12.287 8.30 5.156 LMTD_HX2 [K] 36.935 30.54 13.940

*** Variables reaching their upper bounds ## Variables reaching their lower bounds As is expected, the obtained results show that the electricity consumption as well as the flow-rate of streams increase with the fresh water demands. From a mathematical point of view, it should be mentioned that the same optimization problem was solved by using a local optimization algorithm (CONOPT) instead of a global optimization method. Despite that the simplicity of the proposed model, authors conclude that the non-convex constraints involved by the mathematical model such as logarithms to compute the logarithmic mean temperature differences (LMTD) and bilinear terms lead to local optimal solutions when a local optimization algorithm is used and the solutions depend strongly on the initial values. Consequently, authors remark the advantages and the importance of employing global optimization algorithm. In order to verify the accuracy of the proposed model, output results are compared to those reported previously by [4]. For comparison purposes, it was necessary to fix some optimization variables at the same values as in [4], in such way that the model had the functionality of a simulator. The obtained results agree satisfactorily to the reported in [4]. Then, the presented model represents adequately the process and can be used to optimize the design and operating condition, meanwhile the resolution method provides the best solution (global optimum).

M.Marcovecchio et al.

6. Conclusions A mathematical model for the optimal design of MVC desalination process was presented. The proposed model was successfully solved by using a deterministic global optimization method. Precisely, the ME-D algorithm developed by [7], within a very tight global optimality tolerance, was used to solve the model and the results agree satisfactorily with those reported by other authors. Different objective functions have been implemented and studied by the model and methodology proposed. As future work, the effect of the non-condensable gases on the process, the velocity of steam inside the evaporator and dimensions, among others, will be included into the model in order to get more realistic process designs.

7. Acknowledgements The authors acknowledge financial supports from ’Consejo Nacional de Investigaciones Científicas y Técnicas’ (CONICET) and ‘Agencia Nacional de Promoción Científica y Tecnológica’ (ANPCyT).

References [1] A. Brooke, , D. Kendrick, A. Meeraus, A. A. 1992, GAMS- A User's Guide (Release 2.25).

The Scientific Press. San Francisco, CA,. [2] A. Drud, 1996, CONOPT 2.041: A system for large scale nonlinear optimization. Reference

manual for CONOPT Subroutine Library, 69p, ARKI consulting and development A/S, Bagsvaerd; Denmark.

[3] Ettouney Hisham. 2006, Design of single effect Mechanical Vapor Compression. Desalination J. (190) 1-15.

[4] Helal A.M., Al-Malek S.A., 2006, Design of a solar-assited mechanical vapor compression (MVC) desalination unit for remote areas in the UAE, Desalination J. (197) 273-300.

[5] Aly Narmine H., El-Fiqi Adel, 2003, Mechanical vapor compression deslalination systems. A case study. Desalination J. (158) 143 – 150.

[6] S. Mussati, N. Scenna, E. Tarifa, S. Franco, J. Hernandez, 2009, Optimization of the mechanical vapor compression (MVC) desalination process by using mathematical programming, Desalination and Water Treatment, (5), 124-131.

[7] M. G. Marcovecchio, “Modelado de procesos y Métodos de optimización global aplicados a la síntesis de procesos de desalinización”, Tesis doctoral, Facultad de Ingeniería y Ciencias Hídricas. Universidad Nacional del Litoral, Santa Fe, 2007.