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BACKGROUND ON COMPLEX COOLING WATER SYSTEMS
Introduction
This chapter presents a review on the work done by Gololo and Majozi (2011) on synthesis and optimization of cooling water systems consisting of multiple cooling towers. This work forms basis and motivation for the current work. Gololo and Majozi (2011) developed a comprehensive cooling water system model consisting of the cooling tower model and the cooling water network model. Their work accounts for the interaction between the cooling towers and the cooling water network.
Cooling water system model
Cooling water systems consist of cooling water network and cooling towers. There is a strong interaction between the two components thus their performances are related. Bernier (1994) showed that the cooling tower coefficient of performance can be improved by increasing the cooling tower inlet temperature while decreasing the cooling tower inlet flowrate. Hence, the comprehensive model developed by Gololo and Majozi (2011) included both cooling water network and cooling towers.
Cooling water network model
The cooling water network model was based on a superstructure in which all possible cooling water reuse were explored. The cooling water reuse was only possible in the case where the limiting heat exchanger inlet temperature is above the cooling water supply temperature. Therefore, if the outlet temperature of the cooling water from one heat exchanger is at least DT min lower than the process temperature in any heat exchanger, it could be reused to supply that heat exchanger. The cooling water reuse philosophy results in cooling water network with series-parallel combination of heat exchangers. This renders the system more flexible compared to the traditional parallel arrangement.
The model for cooling water network was developed considering the following two practical cases:
Case I. Any cooling tower can supply any cooling water using operation whilst the cooling water using operation can return to any cooling tower.
Case II. This is similar to Case I except that the geographic constrains were taken into account. A particular cooling tower can only supply a particular set of cooling water using operations and these cooling water using operations can only return water to the same supplier.
The optimum cooling water network was synthesized by minimizing the total cooling tower inlet flowrates. The model was solved using GAMS platform.
Case I
In this case there is no dedicated source or sink for any cooling water using operation. The water using operation can be supplied by one or more cooling towers. The maximum cooling water return temperatures to the cooling towers are also specified. This situation arises when packing material inside the cooling tower is sensitive to temperature and any cooling tower can supply any water using operation and the water using operation can return to any cooling tower.
Design constraints
The equipments within the cooling water system have the maximum allowable flowrates and temperatures. The design constraints ensure that all the equipments are operated within their specified design limits.
Constraints (3-12) and (3-13) ensure that the cooling towers are operated below their maximum throughputs and the maximum allowable temperatures respectively.
Case II
In this case the source and sink for any cooling water using operation are the same. This implies that no pre-mixing or post-splitting of cooling water return is allowed. A set of heat exchanger can only be supplied by one cooling tower. Furthermore, the return cooling water from cooling water using operation must supply the source cooling tower. However, reuse of water within the network is still allowed. All the constraints in Case I are still applicable. Few constraints needed to be added to control the source and the sink.
Constraints (3-34) and (3-35) prevent pre-mixing. Constraint (3-34) ensures that the supply flowrate from any cooling tower to operation i cannot exceed the maximum flowrate. Constraint (3-35) ensures that cooling water using operation i can only be supplied by a maximum of one cooling tower.
Cooling tower model
Gololo and Majozi (2011) used the cooling tower model developed by Kröger (2004) to study the interaction between the cooling water network and the cooling towers. One cooling tower model was used for all cooling towers in the cooling water system. The only distinction in the cooling towers was the correlations for the cooling tower coefficient of performance.
The governing equations that predict the thermal performance of a cooling tower are given by equations (3-40), (3-41) and (3-42). Equations (3-40) and (3-41) define the mass and energy balance for the control volume, respectively. Equation (3-42) defines the air enthalpy change through the cooling tower fill.
The model predicted the outlet water temperature, effectiveness, evaporation, makeup and blowdown for each cooling tower. This model was solved using MATLAB.
To synthesize the overall cooling water system, both the cooling tower model and the heat exchanger network model should be solved simultaneously. The algorithm for synthesizing the overall cooling water system is given in the following section.
Solution procedure
The cooling tower model and the cooling water network model were simultaneously solved using the procedure shown in Figure 3-2. The first step was to optimize the cooling water network model without the cooling towers. The results from the first iteration, which are cooling water return (CWR) temperatures and flowrates, become the input to the cooling tower models. Each cooling tower model then predicts the outlet water temperatures and flowrates. This was done by first assuming the outlet water temperature of a cooling tower. The assumption is done by subtracting from the given cooling tower inlet temperature. The governing mass and heat transfer equations were then solved numerically using forth order Runge_Kutta method starting from the bottom of the cooling tower moving upwards at stepsize Dz . When the maximum height is reached, the temperature at this point will be compared with the CWR temperature. If the two agree within a specified tolerance, the cooling tower model will stop and the outlet temperature will be given as the assumed temperature, else the inlet temperature will be adjusted until the CWR temperature agrees with the calculated temperature. The predicted outlet cooling tower temperatures and flowrates then become the input to the heat exchanger network model. If the outlet temperature of the cooling tower model agrees with the previous inlet temperature to the heat exchanger network model, the algorithm stops which implies that final results have been obtained. Otherwise the iteration continues. The procedure used to connect MATLAB and GAMS was adopted from Ferris (2005).
Conclusions
The mathematical technique for optimization and synthesis of cooling water systems with multiple cooling towers has been presented in this chapter to demonstrate the benefit of a comprehensive approach to cooling water system design. The detailed mathematical framework consisting of the cooling towers and the cooling water network models was developed considering two practical cases. Case I involves a cooling water system with no dedicated cooling water sources and sinks. This implies that a set of heat exchangers can be supplied by any cooling tower and return the cooling water to any cooling tower. Case II involves a cooling water system with dedicated cooling water sources and sinks. This implies that a set of heat exchangers can only be supplied by one cooling tower. No pre-mixing or post- splitting of cooling water return is allowed. However, reuse of water within the network is still allowed. The formulations for Case I yield nonlinear programming (NLP) structure whilst Case II yield mixed integer nonlinear programming (MINLP) structure.
The proposed technique debottlenecked the cooling towers by decreasing the total circulating water flowrate. This implies that a given set of cooling towers can manage an increased heat load. From the case study, 22% and 20% decrease in circulating water flowrate was realized for Case I and Case II respectively. A decrease in the overall circulation water has an added benefit of decreasing the overall power consumption of the circulating pumps.
An improvement of up to 4% overall cooling towers effectiveness was realized by applying the proposed technique in a case study. This improvement was due to a decrease in circulating water flowrate with an increase in return cooling water temperature. When the return cooling water temperature is high, the driving forces between air and water are improved thus more heat is removed from the cooling water.
This technique is more holistic because it caters for the effect of cooling tower performance on cooling water network. The results obtained using this technique are more practical, since all components of the cooling water system are included in the analysis. The comparison between Gololo and Majozi (2011), and Kim and Smith (2001) technique shows that better results could be achieved by considering the interaction of all cooling water networks.
Although the mathematical technique by Gololo and Majozi (2011) is holistic, they are few setbacks. The topology of the debottlenecked cooling water network is more complex due to the additional reuse streams. The network also consists of series-parallel combination of heat exchanger thus prone to higher network pressure drop. Therefore, it is imperative to consider cooling water network pressure drop when synthesizing and optimizing cooling water systems. Another setback is the solution procedure. The global optimality cannot be guaranteed because two platforms were used to model different components of the cooling water systems. The authors used MATLAB to solve the cooling tower model and GAMS to optimize the cooling water network. This approach does not simultaneously optimize the whole cooling water system. Better results could be obtained by using one platform approach.
1 INTRODUCTION.
1.1 Background
1.2 Basis and objectives of this study
1.3 Thesis scope
1.4 Thesis structure
References
2 LITERATURE REVIEW
2.1 Introduction
2.2 Heat integration
2.3 Mass Integration
2.4 Utility Systems
2.4.1 Steam Systems
2.4.2 Cooling Water Systems
2.5 Conclusions
References
3 BACKGROUND ON COMPLEX COOLING WATER SYSTEMS
3.1 Introduction
3.2 Cooling water system model
3.2.1 Cooling water network model
3.2.2 Cooling tower model
3.2.3 Solution procedure
3.3 Case studies
3.3.1 Base case
3.3.2 Case I
3.3.3 Case II
3.3.4 The overall effectiveness for multiple cooling towers
3.3.5 Single source approach
3.4 Conclusions
References
4 MODEL DEVELOPMENT
4.1 Introduction
4.2 Cooling Tower Model
4.2.1 Coefficient of performance
4.2.2 Makeup and blowdown
4.2.3 The overall effectiveness of the cooling towers
4.3 Heat Exchanger Network Model
4.3.1 Mathematical formulation
4.3.2 Solution Procedure
4.4 Debottlenecking the cooling water systems with no considering pressure drop
4.5 Conclusions
References
5 CASE STUDIES
5.1 Introduction
5.2 Base case
5.3 Debottlenecking the cooling water systems considering pressure drop
5.3.1 Case I
5.3.2 Case II
5.3.3 The overall effectiveness for multiple cooling towers
5.4 Integrated approach
5.5 Conclusions
References
6 CONCLUSIONS
6.1 Debottlenecking the cooling water systems considering pressure drop
6.2 Integrated approach
6.3 Overall effectiveness for multiple cooling towers
7 RECOMMENDATIONS
7.1 Environment
7.2 Costs
7.3 Integrated approach vs two platform approach
NOMENCLATURE
APPENDIX A: LINEARIZATION
APPENDIX B: MATLAB AND GAMS CODE
