MSF MED
1.3 State of the Art in Process Optimization of MSF, RO and hybrid MSF-RO processes
1.3.1 MSF desalination processes
1.3.1.2 Simulation based analysis
In this chapter, total number of equations (EQ) and inequality constraints (IC) and dependent (DV) and independent variables (IV) were evaluated by counting the expressions provided in the relevant literature. Using a lumped parameter model, Mandil and Ghafour (1970) studied the optimality of MSF-BR process using unit water cost (minimization) as objective function.
The model was developed for constant physical properties of seawater composition and temperature, constant heat transfer coefficients and constant stage temperature drop. The optimization procedures are based on analytical approach based insights of mathematical formulation. The authors reported an optimal independent variable set of NR = 35, RH = 1.76 and thermal driving force (θ) =1.6738.
Introduction and Literature Review
Helal et al (1986) formulated a tri-diagonal matrix model for the simulation of MSF processes using a stage to stage model. Thereby, the model was solved using Thomas algorithm. The MSF model accounts for the nonlinear variation in temperature elevation and other physical properties as functions of temperature and seawater composition. Further, the MSF mode considered the temperature loss due to demister and polynomial expression for the evaluation of heat transfer coefficients (HTC) using appropriate fouling correlations. The model also accounted for very high temperature operation of the MSF plant (TS = 114 oC, T3
= 97.7 oC and TSea = 35 oC). The simulation based design parameters for MSF plant are WMR
= 14000 m3/h, WMCW = 12400 m3/h, WMF =12500 m3/h and TS = 114 °C.
Al-Mutaz and Soliman (1989) developed MSF model that was similar to that developed by Helal et al. (1986). The model was solved using orthogonal collocation method. Similarly, Abdulbary (1993) developed simulation model for MSF-BR process. The mathematical formulation is similar to that presented by Helal et al. (1986). The simulation model was eventually solved using neural network technique. The simulation based design parameters of the MSF plant are WMR = 14000 m3/h, WMCW = 12400 m3/h, WMF =12500 m3/h and T3 = 90
°C.
Rosso et al. (1997) conducted performance evaluations using MSF-BR simulation model that was solved using Thomas algorithm. The authors studied the effect of WS, TS, RH, MCW, TSea
and number of stages on the dependent variables. Based on extensive parametric analysis, the authors reported that WM = 5680 m3/h, WMBD = 4745.9 m3/h, WMCW = 12000 m3/h, WMF = 11300 m3/h and CMR=62921 ppm are the best.
Chapter 1 Thomas et al. (1998) carried out steady state and dynamic simulation of MSF-BR process.
The model is similar to that presented by Helal et al. (1986). The MSF-BR model has 34 EQ, 4 IEC and 4 IV. The steady state model is solved using Thomas algorithm. Based on simulation study, the authors reported that T3 = 80oC, WM = 5513 m3/h, CMF = 51500 ppm, NR
= 15 and Nj = 3 provided a good performance of the MSF process.
Abdel-jabbar et al. (2007) conducted performance evaluations using MSF-BR simulation model that was solved using Newton’s method. The MSF-BR model has 27 EQ, 9 IEC and 9 IV. Based on analysis, the authors reported that T3 = 30oC, PR = 9 are the best.
Hawaidi and Mujtaba (2010) conducted performance evaluations using MSF-BR simulation model that was solved using gPROMS model. The MSF-BR model has 28 EQ, 3 IEC and 3 IV. Based on analysis, the authors reported that WMF = 568 m3/h, WMBD = 474 m3/h, WMR = 1203 m3/h, WS = 134.8 m3/h are the best.
Tayyebi and Alishiri (2014) conducted performance evaluations using MSF-BR simulation model that was solved using artificial neural networks model. The MSF-BR model has 8 EQ.
Based on analysis, the authors reported that T3 = 83.16 oC, WMBD = 1752.59 m3/h are the best.
A summary of results obtained from the above research articles is presented in Table 1.6.
Introduction and Literature Review
Table 1.6: Summary of literature data for simulation based analysis of MSF desalination processes
S.No Authors Year Configuration
No of Equations Software Platform/
model
Method Best design parameters from simulation study
EQ IEC IV Simulation 1 Mandil and
Ghafour 1970 MSF-BR 26 3 3 Minimization of unit cost
lumped parameters model
- NR=35 , RH = 1.76, thermal driving force (θ) =1.6738
2 Helal et. al. 1986 MSF-BR 25 5 5 Performance calculations
Stage to stage model
Tridiagonal matrix (TDM) form which is solved by the Thomas algorithm (TA)
WMR = 14000 m3/h, WMCW = 12400 m3/h, WMF = 12500 m3/h and TS = 114 °C.
3 Al-Mutaz
and Soliman 1989 MSF-BR 20 - - Max production and brine temperature
Stage to stage calculations
ANN/
Orthogonal collocation
WMR = 14000 m3/h, WMCW = 12400 m3/h, WMF =12500 m3/h and T3 = 90 °C
4 Rosso et. al. 1997 MSF-BR 34 6 5 Performance calculations (GOR)
Stage to stage model
TDM form which is solved by TA
WM = 5680 m3/h, WMBD = 4745.9 m3/h, WMCW = 12000 m3/h, WMF = 11300 m3/h and CMR=62921 5 Thomas et.
al. 1998 MSF-BR 34 4 4 Max production Stage to stage
model
TDM form which is solved by the TA
T3 = 80oC, WM = 5513 m3/h, CMF
= 51500 ppm, NR = 15, Nj = 3
6 Abdel-
Jabbar et. al 2007 MSF-BR 27 9 9
Heating steam flow rate and the heat transfer area
Stage to stage
calculations Newton’s method NR = 24, T3 = 30oC, PR =9 7 Hawaidi and
Mujtaba 2010 MSF-BR 28 3 3 Min total operating
cost (TOC) gPROMS model -
WMF = 568 m3/h, WMBD = 474 m3/h, WMR = 1203 m3/h, WS = 134.8 m3/h.
8 Tayyebi
and Alishiri 2014 MSF-BR 8 - - Min Total annual cost (TAC)
Artificial neural
networks Simulink T3 = 83.16 oC, WMBD = 1752.59 m3/h
Nomenclature: NR= Number of stages in heat recovery stages , RH = Specific heat ratio (WMRCpR/WMFCpj ), WMR = Flow rate of recycle stream m3/h, WMCW = Flow rate of reject coolant stream in MSF process, m3/h, WMF = Feed flow rate in MSF process m3/h, TS = Steam temperature, °C, T3 = Top brine temperature, °C, WM = Flow rate of makeup stream in MSF process m3/h, WMBD = Flow rate of rejected stream in MSF process m3/h, CMR= Concentration of recycle stream (from splitter to heat recovery section), ppm , CMF = Feed (seawater) concentration, ppm , PR = Performance ratio, WS = Flow rate of steam fed to brine heater m3/h,
Introduction and Literature Review 1.3.1.3 Process optimality
Coleman (1971) studied the optimization of a single effect MSF process by targeting a stage to stage model. The model accounts for salinity effect on specific heat and boiling point elevation and involved the optimization of water cost objective function using Newton-Raphson search method and iterative approach. The independent optimization variables refer to process flow rates, heat transfer surface areas, flash temperature and number of stages. The model further assumes constant specific heat capacity (CP) of feed water in condenser, linear and simplified temperature elevation (TE) correlation in the chosen temperature range (112 < TE < 168 oC), very high steam operating temperature (268 oC), high feed (seawater) temperature (38 oC), constant heat transfer coefficient in the condenser and no scaling and fouling. The MSF model has 39 equations (EQ), 5 inequality constraints (IEC) and 5 independent variables (IV). The optimal solution set reported by the author are WFC = 28390.5 m3/h, WFC1 = 59829.5 m3/h, WMR = 48106.1 m3/h, T2 = 112.4 oC, TMD = 40.6 oC. The optimal water production cost is 34.26 ¢ per 1000 gallons of water.
Adopting direct search method, Beamer and Wilde (1971) studied single effect MSF plant using water production cost as objective function. The mathematical model is similar to that presented by Coleman (1971) and refers to unidirectional information flow by state inversion approach.
Thereby, the mathematical information flow is opposite to physical flow in the stage by stage calculation and refers to evaluations from cold end to hot end with brine heater as a last stage.
The MSF model has 19 EQ, 5 IEC and 4 IV. For an optimal water production cost of 27 ¢/1000 gallons, the authors reported optimal independent variable set values as WFC1 = 59829.5 m3/h,
Introduction and Literature Review
WMR = 48106.1 m3/h, T2 = 121.1 oC, TMD = 40.6 oC, PR = 6.8, Number of Vessels =30, pumping cost = 1.36¢/1000 gallons.
Emphasizing upon stage-to-stage calculations, El-Dessouky and Bingulac (1996) summarized a MSF process model which was solved using a iterative algorithm. The MSF model has about 70 EQ, 13 IEC and 11 IV. The model was validated using data available from a 6 MGD plant operating at Kuwait. The model was suggested for optimization studies but no results have been specifically presented with respect to the optimal set of independent and dependent variable values.
Mussati et al. (2001) developed a non-linear programming (NLP) model for the optimization of capital recovery factor (CRF) objective function. The authors adopted stage-to-stage evaluation approach and solved the NLP model using CONOPT 2.041 solver (Generalized Reduced Gradient (GRG) algorithm) in GAMS software platform. While several graphs were presented to indicate upon the role of independent variables on dependent variables, the authors opined that convergence of the model is not guaranteed for different sets of initial values for the independent variables.
Targeting the optimization of plant recovery factor (PRF) (expressed as the ratio of product flow rate to feed flow rate), Emad Ali (2002) reported the results obtained for a MSF plant with stage to stage calculation approach. The model has been evaluated to have 68 EQ, 13 IEC and 10 IV (with bounds). The solution of the optimization model is presented as PR = 7.87, LT = 0.6 m and
Chapter 1 TS = 98 oC. The author further addressed sensitivity analysis by targeting the effect of variation in parameters on the optimality of dependent and independent variable values.
Helal et al. (2003, 2004) studied the optimality of once through (OT) and brine recirculation (BR) configurations of MSF processes using cost as objective function. The authors adopted a stage to stage model to minimize heat transfer area by considering the non-linear variation of the thermo-physical properties of seawater and steam. The MSF model has about 9 IEC and 7 IV.
The solver tool available in MS-Excel (and hence GRG algorithm) has been adopted for the optimization studies. Based on extensive investigations, Helal (2004) concluded that significant in heat transfer area can be targeted by increasing the number of stages to 40 in the MSF-OT process. However, for the optimal sets of values for MSF-OT and MSF-BR, the author concluded that the OT designs could not save area costs by more than 1 %. The optimal set of independent variable value and objective function value are presented in Table 1.7.
Marcovecchio et al. (2005) studied the optimization of hybrid MSF-OT plant using cost as objective function. The authors considered the non-linearity of thermo-physical properties of seawater and steam. The MSF model has 25 EQ, 8 IEC and 4 IV. Thereby, the model was solved using CONOPT (GRG algorithm) in GAMS programming environment. The optimal independent variable set for the MSF-OT process refers to the values of WMF = 9073 m3/h, WL = 0.75 m, WW = 21.52, BVPH = 2.95 m/s and production cost 1.259 $/m3.
Considering energy consumption as the objective function, Al-shayji et al. (2005) studied the
Introduction and Literature Review
the simulation model for the MSF process simulation. The ANN modeling was facilitated with a feed forward architecture and back propagation algorithm. The optimization model involved a composite objective function that refers to maximization of distillate product, top brine temperature and minimization of steam consumed. The optimization model involved the optimization of 19 independent variables using sequential quadratic programming (SQP) algorithm. The authors further reported that the best solutions obtained with SQP have been reported with multiple initial guess values. However, the authors confirmed that the obtained solutions necessarily do not indicate the global optimum.
Mjalli et al. (2007) studied the optimality of MSF-BR process using ANN model and MATLAB built in optimization functions. The authors concluded that the optimal solution was strongly influenced by the initial guess values of the independent variables. The ANN solver was evaluated to reduce significantly the computational effort required for the simulation of the MSF- BR process.
Abdul-Wahab and Abdo (2007) studied the optimality of MSF-BR process using the combination of blow down rate (minimization) and distillate product (maximization). The two level factorial design approach is adopted to optimize sea water temperature, temperature difference, last stage level, first stage level and brine recycle pump flow. MSF model formulation had 5 EQ, 5 IEC and 5 IV. The optimal results correspond to TSea =, 30.36 oC, ΔT = 7.03 oC, last stage level = 50 mm, first stage level = 40 mm, and WMR = 11500 m3/h. Further, statistical analysis of the obtained data was conducted by the authors using Design-Ease software.
Chapter 1 Tanvir and Mujtaba (2008) formulated MINLP model for the optimization of MSF-BR process using total annualized cost as the objective function. The optimization model has several equations, 10 IEC and 5 IV. The MINLP model was solved using gPROMS. Based on the optimization study, the authors reported that the optimal variable values correspond to WMF = 11300 m3/h, NR = 24, WMR = 2190 m3/h, MMCW = 4490 m3/h , T3 = 90 °C, TS = 93 °C and WS = 54.7 m3/h.
Kumar et.al. (2009) studied the multi-objective approach based optimality of MSF-BR process using performance ratio (maximization) and start-up time (minimization). The optimization model was solved using genetic algorithm. The model had about 44 EQ, 5 IEC and 5 IV. The optimal set of results are T3 = 121 oC , WMR = 1350 m3/h, PR = 13.12 and start-up time = 265 min.
Abduljawad and Ezzeghni (2010) optimized MSF-M process by maximizing gained output ratio (GOR). The model had 20 EQ, 11 IEC and 4 IV. Excel solver (GRG algorithm) was used as optimization tool and the obtained optimal set of independent variable values are TSea = 28 oC, T2
= 99.3 oC, UR = 3.396 kW/m2K, UB = 3.77 kw/m2K and GOR=6.867.
Hawaidi and Mujtaba (2010) formulated a NLP model for the optimization of MSF-BR process using total annualized operating cost (TAC) as the objective function. The optimization model has several equality constraints, 3 IEC and 3 IV. The NLP model was solved using gPROMS model bulder 2.3.4. Thereby, the authors studied the effect of brine fouling factor and seasonal variation of seawater temperature on operating cost. The total monthly operation cost of MSF
Introduction and Literature Review
brine flow rate and steam temperature. Such an approach facilitated insights into the seasonal optimal operational policy for one whole year. Based on the optimization study, the authors reported that the optimal variable values (for min TAC in January) correspond to WM = 2450 m3/h, WMR = 4400 m3/h, TS = 110.3 °C and WS = 98.8 m3/h, monthly TAC = 4.52×105 $/month and annual TAC = 53.33 ×105 $/yr.
Marcovecchio et al. (2011) carried out the optimization of MSF-OT desalination process using total annualized operating cost as the objective function. The MINLP model was solved using DICOPT++ solver. The MSF-OT process optimization was carried out for comparative purposes along with other hybrid MSF-RO processes. The optimal variables correspond to CMBD = 67000 ppm and optimal cost of 1.1683 $/m3.
Manesh et.al. (2014) studied MSF-BR process by formulating objective functions as maximization of gained output ratio (GOR) and minimization of water cost. The MSF-BR model consists of several EQ, 10 IEC and 6 IV. The multi-objective optimization model was solved using GA and the optimal set of independent variable values are TS = 101oC, NR = 21, T3 = 98.14oC, WMD = 414 m3/h, WMBR = 11490 m3/h, CMR = 70000 ppm GOR = 7.59 and cost = 0.26$/m3. Further it is important to note that low grade heat source was useful to achieve very low cost for water production.
A summary of results obtained from the above research articles is presented in Table 1.7 of the thesis.
Introduction and Literature Review
Table 1.7: A summary of literature data available for the optimization of MSF desalination processes.
S.No. Authors Year Configuration Model summary Software Platform/
model
Method Optimal independent variable values
Optimal objective function value EQ IEC IV OF
1 Coleman 1971 MSF-BR 39 5 5 Minimization of
cost
Stage to stage model
Newton- Raphson search, iterative solution
WFC = 28390.5 m3/h, WFC1=59829.5 m3/h, WMR
= 48106.1 m3/h, T2 = 112.4 oC, TMD = 40.6 oC
Cost=34.26
¢/103 gallons
2 Beamer and
Wilde 1971 Single effect
MSF 19 5 4 Pumping cost Stage to stage
calculations
Direct search method
T2 = 121.1 oC, TMD = 40.6
°C, PR=6.8, Number of Vessels =30.
Pump
cost=1.36 ¢/103 gallons
3 Helal et. al. 2003 MSF-BR 32 9 7 Min cost SOLVER
tool
Newton- Raphsons
WM = 2.79×106, RH=1.0045, LT = 7.62, Uj
= 2.86 kW/m2k, UR = 3.44 kW//m2K, UB = 3.26 kW/m2K, NR = 18.
Cost = 1.104
$/m3
4 Marcovecchio
et. al. 2005 MSF-OT 25 8 4 Min cost - GAMS,GRG,
CONOPT
WMF = 9073 m3/h, WL = 0.75 m, WW = 21.52, BVPH = 2.95 m/s
Cost = 1.259
$/m3
5 Abdul-Wahab
and Abdo 2007 MSF-BR 5 5 5 Max product and
min blowdown - Design-Ease
software
TSea =, 30.36 oC ΔT = 7.03 oC
last stage level = 50 mm, first stage level = 40 mm, and WMR = 11500 m3/h
WMD = 1151.4 m3/h and WMBD
= 973.7 m3/h
WMF = 11300 m3/h, NR = 24, WMR = 2190 m3/h,
Introduction and Literature Review
Nomenclature: NR= Number of stages in heat recovery stages , RH = Specific heat ratio (WMRCpR/WMFCpj ), WMR = Flow rate of recycle stream m3/h, WMCW = Flow rate of reject coolant stream in MSF process, m3/h, WMF = Feed flow rate in MSF process m3/h, TS = Steam temperature, °C, T3 = Top brine temperature,
°C, WM = Flow rate of makeup stream in MSF process m3/h, WMBD = Flow rate of rejected stream in MSF process m3/h, CMR= Concentration of recycle stream (from splitter to heat recovery section), ppm , CMF = Feed (seawater) concentration, ppm , PR = Performance ratio, WS = Flow rate of steam fed to brine heater m3/h, WFC = Flow rate through the condensers, m3/h, T2 = Temperature of brine stream entering the brine heater in MSF process, oC LT = Tube length, m, Uj Overall heat transfer coefficient in rejection section, kW/m2k, UR = Overall heat transfer coefficient in recovery section kW//m2K, UB = Overall heat transfer coefficient in brine heater , kW/m2k, WL = Stage length, m, WW = Stage Width, m, CMBD = Concentration of reject stream leaving heat rejection section ppm,
7 Kumar et. al. 2009 MSF-BR 44 5 5
Max performance ratio (PR) and minimize the start- uptime.
- GA T3 = 121 oC, WMR = 1350 m3/h,
PR = 13.12 and Start-up time = 265 min
8 Abduljawad
and Ezzeghni 2010 MSF-M 20 11 4 Max gained output
ratio - SOLVER tool
Tsea = 28 oC, T2 = 99.3oC, UR = 3.396 kW/m2K, UB
= 3.77 kw/m2K GOR=6.867
9 Hawaidi and
Mujtaba 2010 MSF-BR 28 3 3 Min TAC gPROMS WM = 2450 m3/h, WMR =
4400 m3/h, TS = 110.3 °C.
TAC = 4.52×105
$/month TAC = 53.33
×105 $/y
10 Marcovecchio
et. al. 2011 MSF-OT 30 4 4 Min cost MINLP DICOPT++ CMBD = 67000 ppm Cost = 1.1683
$/m3
11 Manesh et.al 2014 MSF-BR - 10 6 Max GOR, Min
Water cost - Multi-
objectve/GA
TS = 101.2oC, NR = 21, T3
= 98.14oC, WMD = 414 m3/h, WMR = 11490 m3/h, CMR = 70000 ppm
GOR = 7.59 Cost = 0.26$/m3
Introduction and Literature Review 1.3.2 Reverse osmosis processes
Hatfield and Graves (1968) studied RO process optimality for the maximization of product flux using tubular membrane module. The mathematical formulation has 5 IV and was solved using conventional NLP solver.
For brackish water desalination, Wiley et.al. (1985) optimized RO process using total annualized cost as objective function. The RO model has 6 IV and was solved using Rosenbrook hill climbing method. The authors as well investigated the sensitivity of optimal design with respect to operating and cost parameters such as membrane cost, membrane permeability and power cost. The optimal set of independent variables refers to NC = 2640, CW = 0.12 m, Ch = 0.9 m, CL = 0.8m, P1F = 40.53 bar, Cd = 12.5 mm and cost = 1.21 $/m3.
Using Dupont B-10 RO membrane modules, Zhu et.al. (1997) optimized RO process using TAC as objective function. The mathematical formulation referred to MINLP model using state space representation. The MINLP process model was solved using LINGO software.
Later, the authors have also studied the scheduling of RO process networks. For the optimal TRO-RSR process that was identified from MINLP optimization studies, the optimal set of independent variables refer to P1F = 70.93 atm, NM1 = 54, NM2 = 40 and TRO-RSR model TAC = 0.518M $/m3.
Using CA membrane modules, Voros et al. (1997) studied RO process optimality using TAC as objective function. The mathematical formulation involved modification of the state representation presented by Zhu et al. (1997) and referred to an NLP formulation for a
Introduction and Literature Review
simplified process structure. Thereby, the authors have investigated several RO process configurations. The reformulation enabled a simpler NLP formulation which could be solved using E04UCF routine of the NAG Fortran library. Based on the superstructure optimization, the authors identified that TRO-RSR process as the optimal process. The optimal set of independent variables have been presented as WRORF = 63.43 m3/h, CRORF = 34800 ppm, NM1 = 66, NM2 = 38. Corresponding optimal TAC value is 0.253M $/m3.
See et al. (1999) studied the scheduling of membrane regeneration problem in RO process networks during sea water desalination. The authors used TAC as objective function for Dupont B-10 membrane modules. The mathematical formulation refers to MINLP formulation of 2038 continuous variables and 54 integer variables. The MINLP model was solved using GAMS modeling environment. From MINLP process optimization, TRO-RSR process has been identified as the optimal with optimal independent variable set values of NM1 = 65, NM2 = 40, TCU = 8, TCL = 4. Corresponding TAC value is about 0.763M $/m3.
Maskan et al. (2000) studied RO process optimality using profit as objective function for tubular membrane module. The mathematical formulation involved a NLP model that was solved using SQP algorithm. The authors studied SRO, TRO-RSR, TRO-RP, TRO-SRB-RR, TRO-SFRB, TRO-SFRR configurations based on a superset approach. The authors identified that among all processes, TRO-RSR and TRO-SFRR process configurations provided maximum profit. For the TRO-RSR process, the optimal profit is 0.0168 M $/m3. Corresponding optimal set of independent variables are P1F = 142 bar, P2F = 142 bar, Am1 = 37.8 m2, Am2 = 54.8 m2, NM1 = 3× 105, NM2 = 106. Similarly, for the TRO-SFRR process, the total profit is 0.0164 M $/m3. For the process, the optimal set of independent variable