Modelling and optimization of a multistage flash desalination process

Engineering Optimization Vol. 37, No. 6, September 2005, 591–607

Modelling and optimization of a multistage flash desalination process K. A. AL-SHAYJI†, S. AL-WADYEI† and A. ELKAMEL*‡ †Department of Chemical Engineering, College of Engineering and Petroleum, Kuwait University, P.O. Box 5969, Safat 13060, Kuwait ‡Department of Chemical Engineering, University of Waterloo, 200 University Avenue West, Waterloo, Ontario, Canada N2L 3G1 (Received 12 November 2003; revised 5 October 2004; in final form 17 November 2004) The multistage flash (MSF) desalination process is a widespread and vitally important process for satisfying the needs of citizens of arid land such as in the Middle East Countries. MSF processes are large and complex plants, and a number of simplifying assumptions must be used in order to provide first principle models for simulating and predicting their operation. This article describes the development and application of artificial neural networks (ANNs) as a modelling technique for simulating, analyzing, and optimizing MSF processes. Real operational data is obtained from an existing MSF plant during two modes of operation: a summer mode and a winter mode. ANNs based on a feed-forward architecture and trained by the backpropagation algorithm with momentum and a variable learning rate are developed. The networks can predict different plant performance outputs including the distilled water produced and top brine temperature. The inputs to the ANNs are based on engineering know-how of the operation of the plant. The predictions of the prepared networks were compared to actual measurements. Good agreements were obtained. In addition to their use as a training tool for new operators and for decision-making, the prepared networks were used to optimize the performance of the plant.A composite objective function that consists of the different plant performance measures was used in conjunction with the prepared ANNs within an optimization model. The ANN model serves as an accurate and more convenient replacement of first principle models or plant data. The decision variables over which optimization was carried out are subjected to constraints to ensure that maximum and minimum bounds are adhered to as well as safety considerations. Keywords: Optimization; Neural networks; MSF process; Desalination

1.

Introduction

Desalination of seawater is fast becoming a major source of potable water for long-term human survival in many parts of the world. Among all the seawater desalination processes, the multistage flash (MSF) process produces potable water much more successfully than any other process (Khan 1986, Al-Radif et al. 1991). In spite of its relatively high cost, the modular structure of an MSF plant is an obvious asset for a facility that must satisfy a variety of *Corresponding author. Email: [email protected]

Engineering Optimization ISSN 0305-215X print/ISSN 1029-0273 online © 2005 Taylor & Francis http://www.tandf.co.uk/journals DOI: 10.1080/03052150412331335801

592

K. A. Al-Shayji et al.

production demands. An additional advantage of an MSF plant is the capability of coupling it to a power generation plant as the heat source, thus making the process increasingly important for water and power production. The cost of MSF desalination can be reduced not only by advances in technology but also by operational advances. This article will focus on the latter. An artificial neural network (ANN) will be prepared and then used to optimize the operation of the plant. Optimization involves finding the optimum set points in the steady-state phase. A number of limited studies were based on semi-empirical equations to calculate set points (Husain et al. 1993a,b). No comprehensive study has been carried out so far. Some of the optimality objectives for desalination processes include the minimization of energy consumption (high performance ratio (PR)), the achievement of stable operation, the avoidance of equipment fouling (limiting top brine temperature (TBT) and tube side velocities), and the reduction of chemicals consumption. Desalination processes make good candidates for NN modelling due to their complexity, nonlinear behavior, and the presence of uncertainty. The development of the NN models is carried out in conjunction with engineering knowhow in order to determine the necessary variables for modelling. In contrast to several previous studies (Abdulbary et al. 1992, El-Hawary 1993, Selvaraj et al. 1995), the present work utilizes actual steady-state operating data. This data was collected during different seasons of the year from a large-scale (24-stage) MSF desalination plant operating in Kuwait. The overall objective is to model the process via ANNs and to develop an optimum operating strategy.

2.

Multistage flash distillation

The MSF distillation process involves boiling seawater and condensing the vapor to produce distilled water. It works on the principle that seawater will evaporate as it is introduced into the first evaporator (flash chamber) at a lower pressure than saturation pressure. It then condenses and cools down to a saturation temperature equivalent to the chamber pressure. Figure 1 shows a schematic diagram of the MSF desalination plant. The MSF plant consists of three sections: heat rejection, heat recovery, and heat input (brine heater). The heat

Figure 1.

Schematic diagram of the MSF desalination plant.

Multistage flash desalination

593

rejection and heat recovery sections consist of a number of flash chambers (stages) connected to one another. Seawater enters through the heat rejection section. This section uses the heat released during condensation to preheat the feed and to reject energy into the supplementary cooling water. The recirculating brine, which is formed by mixing part of the feed seawater (make-up) and a large mass of brine from the last stage, is circulated through heat-recovery tubes. In the heat-recovery section, the brine gets heated as it passes through the tubes from one stage to another by exchanging the thermal energy from the flashing vapor in each stage. Thus the heat released by the condensation of vapor is used to heat the recirculating brine. Passing through the last stage, the water enters the brine heater, where its temperature is raised to a certain temperature which is equal to the saturation temperature (i.e. TBT) for the system’s pressure. After heating the saturated brine to the TBT in the brine heater by the saturated or supersaturated steam coming from the boiler, the saturated brine enters the first stage of the heat-recovery section through an orifice or weir. As the brine runs into the first stage, it will become superheated and flashed-off to give pure vapor as a result of pressure reduction. The vapor then passes through the demisters, where the salt carried with the vapor is removed, condenses on the cooling tubes, and collected as distillate in the distillate tray. Figure 2 shows the crosssection of a single stage. The process is then repeated all the way down the plant as both brine and distillate enter the next stage at a lower pressure. The distillate is finally collected, disinfected, and treated for pH and hardness before going to storage vessels.

Figure 2. A single stage in the MSF desalination plant.

594

K. A. Al-Shayji et al.

Finally, and as mentioned earlier, part of the brine from the last stage is then recycled to the heat recovery tubes after adding make-up seawater to it. The brine gets heated as it passes through the tubes from one stage to another by exchanging the thermal energy from the flashing vapor in each stage, and the cycle is repeated again. The flashing flow system in the MSF process can be either a once-through system or with a recirculation. In the once-through system, all the brine left in the last stage after flashing is rejected to the sea. This means that no brine is circulated and there is no specific heatrejection section. The thermal rejection in this system is achieved by virtue of the temperature difference between the incoming feed stream and the outgoing brine and distillate streams. In the recirculation system, part of the brine from the last stage is recycled to heat recovery tubes before adding make-up seawater to it. The brine gets heated as it passes through the tubes from one stage to another by exchanging the thermal energy from the flashing vapor in each stage, and the cycle is repeated again.

3.

Modelling the MSF process with ANN

This section describes how ANNs are developed for modelling the MSF process. Two modes of operation are considered: a winter mode and a summer mode. In the winter mode, the MSF plant operates as a recirculation system in which a recycle of cooling water in the heat-rejection section is used for raising the inlet seawater temperature. In the summer mode, no seawater recycle is used. The desalination plant under consideration is first introduced. The necessary data used for modelling is illustrated, and the operational inputs and outputs are described. The data is first processed and analyzed. The steps and methodology used in preparing the NN models are given in detail. Two separate classes of models, as explained earlier (winter and summer modes), are prepared. The predictions of the models are compared to actual data. 3.1 MSF plant The MSF distillation plant under consideration was commissioned in late 1988 and is located at AZ-Zour, ∼100 km south of Kuwait city. Table 1 shows the design information of the unit. The plant uses a cross-type MSF evaporator with recirculating brine. The multistage condensers for the evaporator have two sections: a 21-stage heat-recovery section and a 3-stage heatrejection section. The plant consists of eight MSF-type desalting units and their common facilities. Each of the eight units has a daily output of 6.0 MGPD distillate, for a total of 48.0 MGPD. Anti-scaling chemicals treatment is used to prevent scale formation inside the condenser tubes. 3.2 Data collection In order to ensure the relevance of data collected, two inspections (before and after the overall annual maintenance) were carried out on the MSF unit. The final inspection report after the maintenance reveals that the unit is in very good condition. In addition, the data generated by the distillate control room was double checked against data from local instruments. The operating variables that affect the plant performance the most are given in table 2 (x1 , . . . , x16 ). Two sets of data were collected: one for winter operation (314 sets) and one for summer operation (300 sets). Three plant performance variables are considered: steam flowrate (STF), distillate produced (DP), and TBT. These are also listed in table 2 (y1 , y2 , and y3 ). Three parallel networks (one for each performance variable) are developed for each mode of operation.

Multistage flash desalination Table 1. Unit Manufacturer Year of commissioning Type Number of distillation units

595

Design information for AZ-Zour South distillation unit. AZ-Zour South distillation unit Sasakura Engineering Co. Ltd., Mitsubishi Heavy Industries and Mitsui and Company, Ltd. 1988 Cross-tube recirculating MSF Eight

Heat-input section (brine heater) Number of passes One Number of tubes 1367 Tube size 43.8 mm (O.D.) × 1.219 mm (avg. thickness) × 18,991 mm (length) Heat-transfer area Copper–nickel alloy Tube material 66% Cu, 30% Ni, 2% Mn, 2% Fe Heat-recovery section Number of passes Number of tubes Tube size Heat-transfer area Tube material: Stages 1 and 2 Stages 3–21 Heat-rejection section Number of passes Number of tubes Tube size Heat-transfer area Tube material

23 1451 43.8 mm (O.D.) × SWG. 18 (avg.) 77,206 m2 Copper–nickel alloy 66% Cu, 30% Ni, 2% Mn, 2% Fe Aluminum alloy 76% Cu, 22% Zn, 2% Al Three 1588 34.2 mm (O.D.) × SWG. 18 (avg.) 9444 m2 Copper–nickel alloy 66% Cu, 30% Ni, 2% Mn, 2% Fe

The ranges of the variables for the two modes of operation are shown in table 3. The operational variables x1 , . . . , x16 are used as the input variables to the NN models. These input variables are constantly monitored in the control room and are known to affect the plant performance the most. The input variable x3 (seawater recirculating flowrate (SWRF)) is used only in the winter operation mode. Figure 3 shows a schematic diagram of an MSF desalination plant in which all key input and output variables are labeled. The importance of these variables is discussed subsequently. The seawater temperature in the Arabian Gulf varies from 14 ◦ C in the winter to 35 ◦ C in the summer. The efficiency of the MSF desalination plant depends on the flash range, which is the difference between the TBT and the cooling water inlet (SWIT) temperature to the heatrejection section. At high seawater temperatures, the flash range will be the smallest. At low seawater temperatures, the thermodynamic situation of the whole evaporator changes. The seawater flowrate (SWF) is therefore reduced as the ambient temperature decreases in order to maintain the required seawater outlet temperature from the heat-rejection section. However, as flow is progressively reduced, a point is reached when it is not possible to maintain the required minimum velocity through the tubes. Therefore, scaling can occur. In such a situation, part of the rejected cooling water from the heat-rejection section is recirculated (SWRF) into the seawater line before its entry into the heat-rejection section. The SWRF ensures that the seawater meets the temperature and velocity requirements at the entry to the heat-rejection section. The TBT plays a crucial role in determining the performance of an MSF plant. It is usually expressed in terms of a PR, which is the ratio of the flowrate of the DP to the STF supplied

596

K. A. Al-Shayji et al. Table 2.

Input and output variables used within the prepared NN models.

Variable x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 y1 y2 y3

Variable name

Variable type

Nomenclature

Seawater flowrate Make-up flowrate Seawater recirculating flowrate Seawater inlet temperature Seawater outlet temperature Blow-down flowrate Brine inlet temperature Stage-24 brine temperature Brine-heater inlet temperature Stage-1 brine level Brine-heater shell pressure Brine-heater shell temperature Steam temperature Condensate temperature Condensate flowrate Recirculating brine flowrate Low-pressure STF to BH Distillate Produced Top brine temperature

Input Input Input Input Input Input Input Input Input Input Input Input Input Input Input Input Output Output Output

SWF MF SWRF SWIT SWOT BDF BIT S24BT BBT S1BL BHSP BHST STT CDT CDF RBF STF DP TBT

to the brine heater. The TBT directly affects the DP. A higher TBT leads not only to higher production but also to increased scale formation. Anti-scale chemicals can be employed to permit the use of higher TBT, but there is always an upper operational bound on its value. The recirculating brine flowrate (RBF) is one of the most important operational variables that could affect the performance of the MSF plant. Increasing RBF increases the DP, but adversely affects the PR (TBT). A compromise RBF must be obtained through a programed optimization approach as will be discussed in the next section.

Table 3.

Ranges of data collected for the two modes of operation. Minimum

Variable x1 x2 x3 x4 x5 x6 x7 x8 x9 x10 x11 x12 x13 x14 x15 x16 y1 y2 y3

Maximum

Summer mode

Winter mode

Summer mode

Winter mode

7570 3333 – 24.9 36.0 1999 34.9 35.0 98.0 362 1.40 109 109 109 113 12,060 128.39 1300 104.0

8380 3000 2074 26.0 33.8 1509 32.9 34.0 82.7 316 0.70 83.0 92.1 91.2 117.2 14,100 116.43 1101 87.4

9320 3550 – 30.8 40.5 2156 40.6 39.9 99.9 506 1.601 117.8 122.0 116.7 131.2 13,800 143.06 1450 107.8

12,140 3119 5821 29.2 38.1 1974 36.1 36.7 84.5 454 0.784 93.9 97.8 93.5 138.92 14,880 133.57 1215 89.1

Note: Flow is in kl/h, temperature is in ◦ C, pressure is in mmHg, and brine level is in mm.

Multistage flash desalination

Figure 3.

Schematic diagram of the MSF desalination plant depicting operational variables.

597

598

K. A. Al-Shayji et al.

As the make-up flowrate (MF) increases, the salt concentration in the brine stream decreases, which in turn will decrease the specific gravity of the brine and the boiling-point elevation. This lowers steam consumption and decreases blowdown salt concentration. Consequently, some increase in the PR can be expected.

3.3 Data analysis Real-life data often contains outliers, which are observations that do not reasonably fit within the pattern of the bulk of the data points and are not typical of the rest of the data. Some outliers are the result of incorrect measurements and can be immediately rejected and removed from the data set. Other outliers are observations resulting from unusual process performance that are of vital interest. Data requires careful inspection and examination in order to observe this distinction. Outliers are given particular attention in an NN and in a statistical analysis in order to determine the reasons behind large discrepancies between those points and the remainder of the data set. This inclusion of outliers in training data forces the network to consider a large solution space and can therefore reduce the overall precision of the resulting network. This is observed as occasional large differences between actual and predicted values of output variables. One of the simplest techniques for detecting outliers is to examine the frequency histogram of the data, plotting the number of occurrences of the observed data within a specific range of a selected variable. Figures 4 and 5 show the frequency distribution of the operational variables after removing the outliers for the summer mode and winter mode data sets, respectively. The frequency distributions are continuous and normally distributed with a bell shape, with the exception of a few outliers that are observations of unusual phenomena.

3.4 Training and testing ANNs can be thought of as ‘black box’ devices that accept inputs and produce outputs. They have been proved to be powerful in solving complex problems through their parallel distributive structure and their ability to learn and generalize (Bhagat 1990, Quantrille and Liu 1991, Spieker et al. 1993, Elkamel 1998). Several NN architectures can be employed. Figure 6 shows a typical feed-forward structure consisting of an input layer, a hidden layer, and an output layer. The input layer receives information from external sources and passes it to the hidden layer for processing. More than one hidden layer can be employed in the NN architecture. These hidden layers have no direct connection to the outside world (inputs or outputs). The output layer of neurons receives processed information from the hidden layer and sends output signals out of the system. Figure 6 shows also biases acting on hidden and output neurons. The function of these biases is to provide a threshold for the activation of neurons. As inputs enter the input layer from an external source, the input layer becomes ‘activated’ and emits signals to the immediate hidden layer neurons without any modification. These neurons in turn emit an output to their neighbors in the second hidden layer or in the output layer. Each input connection is associated with a weight factor. This weight measures the relative strength of the effect that one neuron can have on another. A neuron output is determined using a mathematical operation (transfer function) on the total activation of the neuron. This activation depends on the magnitude of the neuron internal threshold and the weighted input factor to the neuron.

Multistage flash desalination

Figure 4.

599

Frequency distribution for data used in training the NN models for the summer mode.

The number of input neurons in a given NN architecture corresponds to the number of input variables into the NN, and the number of output neurons is the same as the number of desired output variables. The number of neurons in the hidden layer(s) depends on the application at hand. In this work, the operational variables (x1 , . . . , x16 ) based on engineering know-how are used as inputs to a feed-forward NN. It was shown that engineering know-how is a far superior variable selection technique than factor and principal component analysis (Al-Shayji 1998). These latter techniques have always an inherent risk that significant input variables may be excluded if one does not utilize the exact functional relationship among the inputs. The weights in the NN are initially selected at random and a training algorithm is used to determine the weights that lead to the least sum squared error (SSE) between the actual outputs and the predicted outputs by the NN. In this work, the backpropagation algorithm with momentum and a variable learning rate is used in training the network (Elkamel 1998). Training the NN to get the best connection weights is performed on a given network architecture. One

600

K. A. Al-Shayji et al.

Figure 5.

Frequency distribution for data used in training the NN models for the winter mode.

usually starts with one hidden layer with a certain number of neurons. If the trained network does not perform well, the number of neurons in the hidden layer is increased systematically. If one hidden layer does not lead to the desired SSE, two or more hidden layers can be employed. More information on training the NN for predicting MSF plant performance is given subsequently. Before training, the data was normalized so that the inputs and outputs have the same order of magnitude and same significance. The normalization of a variable X was performed on the basis of the formula: Xn =

2(X − Xmin ) −1 (Xmax − Xmin )

(1)

where Xmin and Xmax represent the minimum and maximum values for variable X. Xn is the normalized variable that has a minimum of −1 and a maximum of 1.

Multistage flash desalination

Figure 6.

601

Structure of a typical multilayer NN.

Each of the data sets for the two modes of operation (summer and winter) was divided into two sets: a training set and a testing set. These sets were selected so that the data range in each encompasses all the operational range of the MSF plant. The training set was selected to comprise 80% of the data collected, whereas the testing set included the remaining 20%. Training was performed in order to find the best NN architecture that can achieve an SSE error goal of 10−5 . It was found that a one-hidden layer network of 30 neurons is able to achieve the earlier mentioned goal for the different modes of operation and for the different targets. A statistical analysis that calculates the minimum, maximum, and average errors along with the coefficient of regression is shown in table 4. A tan-sigmoid transfer function was used for the hidden layer neurons and a linear function for the output neurons. Figure 7 shows a comparison of the predicted and measured output variables for the two modes of plant operation. As can be seen, the performance of the trained networks is excellent. These networks are then checked against the testing data sets. The statistical results of this test are shown in table 4. Figure 8 shows a comparison of the predicted and actual outputs for these testing sets. As can be seen here also, the predictions of the networks are in good agreement with the actual measurements. This indicates that the NN models developed can generalize well over unseen data and can produce accurate estimates.

Table 4.

Statistical evaluation of the trained ANN models for predicting MSF plant performance.

Model output

Average % error

Maximum % error

Minimum % error

R2

Summer mode STF DP TBT

0.40847 0.41255 0.08936

3.06965 2.26931 1.68239

0.00019 0.00094 0.00004

0.92365 0.89890 0.89484

Winter mode STF DP TBT

1.01297 0.26098 0.02659

4.92923 2.21857 0.14043

0.00021 0.00065 0.00003

0.83055 0.91565 0.98631

602

K. A. Al-Shayji et al.

Figure 7.

4.

Comparison of predicted and measured output variables for the training data sets.

Optimum operation

Optimization of a physical process based on the NN model was discussed in detail by Elkamel (1998), Elgibaly and Elkamel (1999), and more recently by Nascimento et al. (2000). The basic idea is to replace the model equations or process data by an equivalent NN, and use this NN to support the required optimization. This uses the advantage of high-speed processing, because simulation with the NN involves only a few algebraic calculations. At this stage, two possible optimization approaches can be employed: a detailed grid search or an NLP-based approach. As the present problem has 16 variables, problems of dimensionality can arise and the NLP approach is more reliable. The NN models that were developed in the previous section are used to find the optimum operating conditions of the MSF plant. Optimization was first carried out using a single objective function consisting of one of the three plant performance variables: low-pressure STF to brine heater, DP, and TBT. Operationally, it is desired to minimize the STF and

Multistage flash desalination

Figure 8.

603

Comparison of the predicted and measured output variables for the testing data sets.

maximize the DP and TBT. Steam supplies energy to the MSF process and directly affects production. It is usually desirable to minimize the quantity of steam used but this will in turn have an adverse effect on DP and TBT. A compromise must therefore be reached and this leads us to the use of a composite objective function as follows:
 DP TBT STF max (2) + − DPU TBTU STFU In the earlier equation, the different terms are scaled by their upper bounds so that their values are all between 0 and 1 and unitless. Weighting factors can be used, if desired, in order to give more importance to a certain performance variable over the others. The optimal solution space is reduced by adding constraints. For example, upper and lower bounds are imposed on the variables either according to the range of the training data sets or according to the operational considerations. In this regard, the lower limit on SWF, for instance, can correspond to the requirement of a specific rate of evaporation in the heatrejection section. The upper limit is restricted by the maximum available pump flow of

604

K. A. Al-Shayji et al.

the seawater supply pump. For RBF, a lower limit must be fixed to avoid scaling problems caused by a low velocity of brine in the brine heater or brine boiling in the tubes. In addition, if the brine flowrate is low, sealing between stages may not be adequate. As a result, the plant will be unstable and operation will be inefficient. On the other hand, a high flowrate can cause product contamination because flooding can occur. Once contaminated, it takes a long time for the product salinity to drop. The upper limit is therefore imposed to avoid erosion and carryover of brine to the distillate. Similarly, limits must be imposed on TBT. TBT cannot be raised above a certain value due to scaling problems. This upper value depends on the type of chemicals used for feed treatment and on the brine concentration. A lower bound should also be imposed on TBT because too much reduction can cause the pressure difference to the vent condenser to become insufficient, which in turn causes an incomplete extraction of noncondensable gases, followed by instability and possible vaporside corrosion problems. Equality constraints are also imposed to indicate that some of the variables are fixed. For instance, the seawater inlet temperature (SWIT) is usually known a priori. The earlier model is a nonlinear-constrained optimization problem that can be recast as
 DP(x) TBT(x) STF(x) Minimize f (x) = − (3) − + DPU TBTU STFU s. t.

gi (x) = 0

i = 1, . . . , M

(4)

gi (x) ≤ 0

i = M + 1, . . . , N

(5)

where x is the vector of input variables to the NN model (table 2). The function f (x) is evaluated by first evaluating DP, TBT, and STF at each input vector x using the prepared NN models of the previous section and then the function is calculated according to equation (3). The values of gi represent the equality and inequality constraints of the model. Equality constraints are present in the case when it is not possible to manipulate all input variables, if some plant requirement is, for instance, known a priori or if only a subset of set points is to be adjusted. Inequality constraints can be due, as explained earlier, to the lower and upper bounds of the operational variables due to safety or capacity considerations. Minimization in the earlier model was achieved by simply multiplying the original maximization objective by −1. In order to solve the earlier optimization problem, a sequential quadratic programing algorithm due to Schittowski (1985) is used. The principal idea behind this algorithm is to formulate a quadratic programing subproblem of the original problem described by equations (3)–(5). This subproblem is based on a quadratic approximation of the Lagrangian L(x, λ) = f (x) + N i=1 λi gi (x) and for iteration k can be represented as 1 Minimize dkT Hk dk + ∇f (xk )T dk 2 ∇gi (xk )T dk + gi (xk ) = 0 ∇gi (xk )T dk + gi (xk ) ≤ 0

i = 1, . . . . . . , M

(6)

i = M + 1, . . . , N

where Hk is a positive definite matrix approximating the Hessian matrix at iteration k of the Lagrangian function and dk is the search direction. This subproblem can be solved for vector dk using any quadratic programing algorithm (Reklaitis et al. (1983)). The procedure proposed by Gill et al. (1984) is employed in this work. The solution for the subproblem produces a vector dk , which is used to calculate a new iteration xk+1 (xk+1 = xk + αk dk ), in which the Hessian matrix is updated using the formula of

Multistage flash desalination

605

Broyden (1970), Fletcher (1970), Golfarb (1970), and Shanno (1970). This formula is given as follows: qk q T H T Hk H k H = Hk + T k − T k (7) q k sk s k H k sk where sk = xk+1 − xk and qk = ∇f (xk+1 ) +

N 

(8)

 λi ∇gi (x)k+1 − ∇f (xk ) +

i=1

N 

 λi ∇gi (x)k

(9)

i=1

The parameter αk represents the step length and is updated by an approximate line search procedure (Han 1977). The optimization problem was solved for the two modes of MSF plant operation. The upper and lower bounds were imposed on the variables according to the minimum and maximum values given in table 3. Three distinct objective functions over each of the plant performance variables were first used. The results of the optimization are shown in table 5. The table shows five columns corresponding to current operation (column 2) and optimization over the three objective functions (columns 3–5). Each column shows two plant operation modes: winter and summer. In the winter mode, a seawater recirculation is used, whereas none is used during the summer operation mode. The SWIT was fixed a priori. The table gives the optimal operating vector of conditions for each objective function for each mode of operation. The steam savings and the extra DP in comparison with the nominal operation are also reported in the table (last two rows). As the different objectives are conflicting in nature, optimization leads sometimes to adverse effects. For instance, while optimizing over STF (minimize steam consumption), there was a reduction in distilled water produced for the winter mode. Similarly, optimization over Table 5. Nominal operation Variables STF DP TBT SWF MF SWRF SWIT SWOT BDF BIT S24BT BBT S1BL BHSP BHST STT CDT CDF RBF

Summer mode

Winter mode

Optimization over a single objective at a time.

Optimization over STF

Optimization over DP

Optimization over TBT

Summer mode

Summer mode

Summer mode

130.66 131.77 128.39 1336.0 1169.0 1428.77 105.6 88.8 104.01 9030.0 9570.0 8000.00 3440.0 3044.0 3399.99 – 3803 – 30.0 28.0 30.0 39.6 35.6 37.84 2083.0 1782.0 2050.0 39.8 34.8 38.02 38.7 35.6 36.99 99.6 84.0 99.22 387.0 354.0 400.00 1.514 0.777 1.450 111.8 93.5 112.99 113.1 95.4 114.97 111.1 93.2 111.97 125.0 133.54 119.99 12,830.0 14,530.0 12,999.99

Steam savings (kl/year) Extra DP (kl/year)

19,613 801,533

Winter mode

Winter mode

Winter mode

116.43 128.39 116.71 133.01 129.08 1110.82 1450.0 1215.0 1380.50 1206.91 88.27 104.00 87.45 107.8 89.1 10,000.00 7999.99 10,000.00 8000.00 10,000.00 3080.00 3399.99 3080.00 3400.00 3080.02 3999.99 – 3999.99 – 4000 28.0 30.0 28.0 30.0 28.0 35.99 38.01 35.99 37.97 35.19 1799.99 2050.0 1799.99 2050.0 1800.01 34.26 37.98 34.54 38.03 34.31 34.70 36.99 34.56 37.15 34.77 82.93 99.25 82.85 99.51 82.70 399.99 400.00 400.00 400.00 399.98 0.733 1.451 0.772 1.404 0.700 88.032 112.96 88.05 112.99 87.99 95.01 114.93 94.98 115.01 94.42 91.96 112.05 91.95 111.99 92.41 120.02 119.96 120.04 119.98 120.10 14,399.99 13,000.0 14,399.99 13,000.0 14,400.0 132,538 −502,675

19,613 94,960

130,118 397,440

−20,304 389,160

23,242 327,542

606

K. A. Al-Shayji et al. Table 6.

Optimization using a composite objective function. Optimal operation

Nominal operation

Objective value STF DP TBT SWF MF SWRF SWIT SWOT BDF BIT S24BT BBT S1BL BHSP BHST STT CDT CDF RBF

Case 1

Case 2

Summer mode

Winter mode

Summer mode

Winter mode

Summer mode

Winter mode

0.9877 130.66 1336.0 105.6 9030.0 3440.0 – 30.0 39.6 2083.0 39.8 38.7 99.6 387.0 1.514 111.8 113.1 111.1 125.0 12,830.0

0.9723 131.77 1169.0 88.8 9570.0 3044.0 3803.0 28.0 35.6 1782.0 34.8 35.6 84.0 354.0 0.777 93.5 95.4 93.2 133.54 14,530.0

1.1025 128.39 1449.99 107.8 8000.00 3399.99 – 30.00 38.253 2050.01 37.83 36.58 99.71 400.01 1.415 112.90 114.84 112.02 119.88 13,000.00

1.1283 116.43 1215.0 89.10 10,000.00 3080.02 3999.99 28.00 35.756 1799.99 34.94 34.59 82.93 399.99 0.736 88.02 94.72 91.91 120.07 14,399.99

1.1025 128.39 1449.99 107.80 7997.95 3376.81 – 30.00 39.60 1999.05 39.80 39.83 99.60 412.42 1.514 112.63 113.10 111.10 125.00 12,995.38

1.1212 116.43 1214.99 88.47 10,005.61 3098.30 3997.97 28.00 35.60 1841.95 34.80 34.14 84.00 376.01 0.777 93.90 95.40 93.20 133.54 14,411.57

Steam savings (kl/year) Extra DP (kl/year)

19,613 984,874

132,538 397,440

19,613 984,874

132,538 397,354

TBT leads to more steam consumption. For these reasons, we decided to adopt a composite objective function (equation (2)). The optimization results for this case are shown in table 6. Two cases were considered using two distinct operational strategies. In the first case (Case 1), optimization was carried out over all input variables. The results are shown in columns 3 and 4. Also shown are the steam savings and extra distilled water produced. There is now an improvement in all optimization criteria for both the summer and winter modes of operations. In Case 2, optimization was carried out over a subset of the variables. The inputs shown in bold for this case were fixed a priori and optimization was carried out over the remaining inputs. Discussions with plant operators indicated that these remaining inputs can be easily adjusted in practice. In this case, the optimization problem has fewer degrees of freedom. The achieved objective function value for the summer mode of operation is the same as for Case 1, but the achieved objective function for the winter mode of operation is less. It must be noted that the optimization problems discussed earlier were run several times with different starting guesses of the decision (input) variables. Multiple local optima were obtained. The reported values given in tables 5 and 6 represent the best local optima. There is no guarantee, however, that these optimum solutions are global optima.

5.

Conclusion

In this investigation, the use of ANNs for modelling and optimizing the MSF process has been successfully demonstrated. The complex MSF process was modelled using a single hidden layer NN. The backpropagation algorithm with a variable learning rate and with a momentum term was used for training the network. Two modes of plant operation were considered the

Multistage flash desalination

607

summer mode and the winter mode. During the summer mode, no seawater recirculation is employed in the plant, unlike during the winter mode. The predictions of the NN models were compared to actual measurements. It was found that the networks are very successful in predicting MSF plant performance outputs. The NN models were further validated using a testing data set that the network ‘did not see’ during training. The networks faired consistently well for this testing set. The NN models prepared can be used to train new operators of the MSF process, help in decision-making during operation, and optimize the operation of the process. In the latter case, the NN models serve as a simple replacement of complex phenomenological models or huge sets of plant data. An optimization procedure in terms of NLP was successfully applied in conjunction with the NN models. Different cases of plant operation were considered and the optimization approach was successful in obtaining the most efficient operating points. Different optimality criteria were used including a composite function that includes the different plant performance measurements. References Abdulbary, A.F., Lai, L.L., Al-Gobaisi, D.M.K. and Husain, A., Experience of using the neural network approach for identification of MSF desalination plants. Desalination, 1992, 92, 323–331. Al-Radif, A., Al-Gobaisi, D.M.K., El-Nashar, A. and Said, M.S., Review of design and specifications of the world largest MSF unit. Desalination, 1991, 84, 45–84. Al-Shayji, K.A., Modelling, simulation, and optimization of large-scale desalination plants. Ph.D. thesis, Virginia Polytechnique Institute and State University, 1998. Bhagat, P., An introduction to neural nets. Chem. Eng. Progr., 1990, 8, 55–60. Broyden, S., The convergence of a class of double-rank minimization algorithms. J. Inst. Math. Appl., 1970, 6, 76–90. Elgibaly, A. and Elkamel, A., Optimal hydrate inhibition policies with the aid of neural networks. Energy Fuels, 1999, 13, 105–113. El-Hawary, M.E., Artificial neural networks and possible applications to desalination. Desalination, 1993, 92, 125– 147. Elkamel,A.,An artificial neural network for predicting and optimizing immiscible flood performance in heterogeneous reservoirs. Comp. Chem. Eng., 1998, 22(1), 1699–1709. Fletcher, R., A new approach to variable metric algorithms. Comp. J., 1970, 13, 317–322. Gill, P.E., Murray, W., Saunders, M.A. and Wright, M.H., Procedures for optimization problems with a mixture of bounds and general linear constraints. ACM Trans. Math. Software, 1984, 10, 282–298. Golfarb, D., A family of variable metric updates derived by variational means. Math. Comput., 1970, 24, 23–26. Han, S.P., A globally convergent method for nonlinear programming. J. Optimiz. Theor. Appl., 1977, 22, 297. Husain, A., Hassan, A., Al-Gobaisi, D.M.K., Al-Radif, A., Woldai, A. and Sommarive, C., Modelling, simulation, optimization and control of multistage flashing (MSF) desalination plants. Part I: modelling and simulation. Desalination, 1993a, 92, 21–41. Hussain, A., Al-Gobaisi, D.M.K., Hassan, A., Kesou, A., Kurdali, A. and Podesta, S., Modelling, simulation, optimization and control of multistage flashing (MSF) desalination plants. Part II: optimization and control. Desalination, 1993b, 92, 43–55. Khan,A.H., Desalination Processes and Multistage Flash Distillation Practice, 1986 (Elsevier Publishers: NewYork). Nascimento, C.A.O., Giudici, R. and Guardani, R., Neural network based approach for optimization of industrial chemical processes. Comp. Chem. Eng., 2000, 24, 2303–2314. Quantrille, T.E. and Liu, Y.A., Artificial Intelligence in Chemical Engineering, 1991 (Academic Press: New York). Reklaitis, G.V., Engineering Optimization: Methods and Applications, 1983 (John Wiley and Sons: New York). Schittowski, K., A Fortran subroutine for solving constrained nonlinear programming problems. Oper. Res., 1985, 5, 485–400. Selvaraj, R., Deshpande, P.B., Tanbe, S.S. and Kulkarni, B.D. Neural networks for the identification of msf desalination plants. Desalination, 1995, 101, 185–193. Shanno, D.F., Conditioning of quasi-newton methods for function minimization. Math. Comput., 1970, 24, 647–656. Spieker, A., Najim, K., Chtourou, M. and Thibault, J., Neural network synthesis for thermal processes. J. Prod. Control, 1993, 3(4), 233–239.