反渗透海水淡化网络系统的优化研究
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摘要
反渗透技术广泛应用于海水和苦咸水淡化当中。相对于其他海水淡化技术，它的主要优势在于无相变、能耗低、模块化，因此近年来发展较快，市场占有率高。但目前反渗透工程设计仍主要采用基于工程经验的传统的设计方法，在技术可行的基础上并不能保证最优结果。因此进行反渗透系统优化研究是十分必要的。本文系研究反渗透海水及苦咸水淡化系统的优化问题，以降低吨水成本和能耗为目标开展以下工作。
首先针对采用功（压力）交换器的反渗透系统，建立了基于有限差分传质的反渗透系统超结构模型。该模型考虑了功（压力）交换器内盐水混合状况，得到的混合整数非线性规划（MINLP）采用外部逼近法求解。加入限制条件使得优化结果中压力容器以及压力容器内膜元件的个数为整数解。利用该模型对不同盐度进料海水的反渗透系统进行优化研究，产水水质小于500mg/L，结果表明：进料海水盐度升高，吨水成本升高，反渗透系统工艺也随之变化。当进料海水盐度在32000mg/L以上，最优化的反渗透方案为一段反渗透工艺。当进料水盐度低于28000mg/L时，反渗透系统采用带段间增压泵的两段式工艺，当进料盐度不同时采用的膜元件型号也不同。随着产水水质含盐量需求下降，吨水成本呈上升趋势。对于进料海水盐度为35000mg/L、产水水质要求在300~500mg/L范围时，单级反渗透系统可以满足产水水质的需求。当产水水质要求在50~100mg/L范围时，选用两级反渗透工艺。
其次，采用ε-限制算法对基于有限差分传质模型的反渗透系统进行多目标优化，吨水成本和吨水能耗同时优化得到非劣解（Pareto最优集），决策者可以根据不同的设计要求选择合适的反渗透配置工艺。以吨水成本和能耗分别为优化目标，对有无能量回收的反渗透系统进行单目标优化，无能量回收装置与采用透平的反渗透系统均采用带段间增压泵的两段式反渗透工艺，而以PX型作为能量回收装置的反渗透系统采用单段式工艺。以无能量回收装置来比较，采用透平式的反渗透方案其吨水成本下降不大；而采用PX型的反渗透方案，吨水成本最低。对采用PX型的反渗透系统，进行多目标优化设计，优化得到的反渗透方案的吨水成本在US$0.52—$0.69/m3之间，吨水能耗在2.30—2.79kW h/m~3之间，吨水成本与吨水能耗的变化趋势相反，一级反渗透方案能同时满足较低的制水成本和吨水能耗。当进料海水盐度升高时，多目标最优化设计的非劣解曲线向右上方平移，最低吨水成本和最低吨水能耗均有上升。
最后，采用广义析取模型对反渗透系统进行优化。用传质模型来描述压力容器内膜元件传质过程，对于超结构内不存在的膜元件则视为单纯的输入输出操作而没有传质过程，反渗透级做同样处理，得到的广义析取模型采用逻辑外部逼近法求解。相对于混合整数非线性规划，广义析取模型可以避免在计算过程中超结构中不存在的反渗透级以及物流为零的变量引起的不可行解，使得非线性规划子问题能更快收敛。利用该模型研究了电价、膜元件价格和海水温度等因素对海水淡化设计结果的影响。电价的变化对反渗透系统吨水成本影响较大。当电价升高时，可以通过降低系统的操作压力或增加膜面积来降低海水淡化的成本。相对于电价，膜元件价格的变化对反渗透系统吨水成本影响处于第二位。当进料海水温度升高时，所需要的操作压力逐渐减小，所需的膜面积减少，反渗透的吨水成本呈下降趋势。
本文开展了反渗透系统优化研究，考虑了由于系统内功（压力）交换器盐水混合引起的盐度升高，加入限制条件使得压力容器的个数以及压力容器内膜元件的个数为整数解。优化研究表明本文的结果可用于对实际的反渗透工程设计或系统评估。
The reverse osmosis (RO) has been widely used for seawater and brackish waterdesalination. The main advantages of RO over other desalination processes are its nophase change, energy saving, modularity, etc. Therefore, RO developed rapidly andits market share increased recently. However, it is still necessary to develop asystematic optimization method for RO process. In this paper, studies on optimizationof RO networks for desalination of seawater and brackish water to reduce cost andpower consumption of desalted water are carried out.
First, an optimization model of RO networks with pressure exchanger (PX) isestablished based on finite difference membrane transport model, and salinity increasecaused by volumetric mixing in PX is considered. The optimum design problem canbe solved as a mixed-integer nonlinear problem (MINLP) using outer-approximationalgorithm. Discrete numbers constraints are added to make sure the number ofmembrane elements in each PV and PVs employed in the RO stage are integers. Thevariation of salinity of feed seawater is studied using the RO super-structure model,and the maximum product concentration is500mg/L, the results show that when thefeed water salinity increases, the desalted water cost increases correspondingly, andsystem processes also change. For the feed seawater concentration higher than32000mg/L, single-stage RO system is favored. When the feed seawater concentration isbelow28000mg/L, two-stage RO system with inter-stage pump is the better choice.Different types of membrane modules are selected for different feed seawater salinity.The desalted water cost increases with the decreases of permeate concentrationrequirement. For the looser permeate concentration requirement range form300~500mg/L, single-pass configuration can meet the required quality of desalted water. Whenthe lower permeate quality requirement of concentration from50~100mg/L, two-passsystem is selected.
Secondly, multi-objective optimization (MOO) of RO networks based on finitedifference membrane transport model is solved by ε-constraint algorithm, and non-inferior solutions (Pareto optimal set) are obtained. Decision-makers can chooseproper RO design configuration process for different design requirement. RO systems with or without ERD are optimized and compared as single objective optimizationusing desalted water cost and unit energy cost as the optimization objective,respectively. Two-stage RO system with inter-stage pump is favored for RO systemswith turbine or without energy recovery device (ERD). For RO system with PX, asimple single-stage system is favored. The desalted water cost of the RO system withturbine dose not decline much comparing with the system without ERD, and thedesalted water cost of the RO system with PX is the lowest. For a specific RO projectusing PX as the ERD, the MOO optimal process configurations achieve to producepotable water with a desalted water cost between US$0.52—0.69/m3and powerconsumption between2.30—2.79kW h/m3. The variation of the power consumptionis contrary to the desalted water cost. One-stage layout is proved to minimizesimultaneously the power consumption and the desalted water cost. With increasingthe feed water salinity, the pareto curve shift to the upper right, and the lowestdesalted water cost and the lowest power consumption of the RO system are bothincrease.
Finally, a generalized disjunctive programming (GDP) approach is established forthe optimization of RO networks. The nonlinear model based on GDP is proposed thatrelies on the identification and application of mass balances and equilibrium equationsfor existence membrane modules in PV. For non-existing or inactive modules, theequations considered are simply input-output relations in which no mass transfer takesplace. RO stage takes similar treatment. A variant of the logic-based outerapproximation algorithm is proposed to solve the problem. It would be desirable notonly to reduce the size of the NLP sub-problems, but also to avoid infeasibilities thatare due to the non-existing RO stage and linearization at zero flows in the ROsuperstructure. RO seawater projects are studied using the proposed logic-based outerapproximation algorithm, and several factors such as electricity price, membranemodule price, average seawater temperature, etc, are concerned. The desalted watercost is very sensitive to electricity price. When the electricity price increases, thedesalted water cost can be decrease through increasing operating pressure orincreasing membrane area. The desalted water cost is more sensitive to changes inelectricity price than membrane price. If the seawater temperature increases, theoperation pressure required by the RO system decreases and the total membrane areareduces, so the desalted water cost decreases.
Study on the optimization of RO networks is carried out, taking into account thesalinity increase caused by volumetric mixing in PX, and discrete numbers constraintsare added to make sure the number of membrane elements in each PV and PVsemployed in the RO stage are integers. Optimization researches show that the resultsin this paper could be utilized in the actual engineering design of RO process orsystem evaluation.
首先针对采用功（压力）交换器的反渗透系统，建立了基于有限差分传质的反渗透系统超结构模型。该模型考虑了功（压力）交换器内盐水混合状况，得到的混合整数非线性规划（MINLP）采用外部逼近法求解。加入限制条件使得优化结果中压力容器以及压力容器内膜元件的个数为整数解。利用该模型对不同盐度进料海水的反渗透系统进行优化研究，产水水质小于500mg/L，结果表明：进料海水盐度升高，吨水成本升高，反渗透系统工艺也随之变化。当进料海水盐度在32000mg/L以上，最优化的反渗透方案为一段反渗透工艺。当进料水盐度低于28000mg/L时，反渗透系统采用带段间增压泵的两段式工艺，当进料盐度不同时采用的膜元件型号也不同。随着产水水质含盐量需求下降，吨水成本呈上升趋势。对于进料海水盐度为35000mg/L、产水水质要求在300~500mg/L范围时，单级反渗透系统可以满足产水水质的需求。当产水水质要求在50~100mg/L范围时，选用两级反渗透工艺。
其次，采用ε-限制算法对基于有限差分传质模型的反渗透系统进行多目标优化，吨水成本和吨水能耗同时优化得到非劣解（Pareto最优集），决策者可以根据不同的设计要求选择合适的反渗透配置工艺。以吨水成本和能耗分别为优化目标，对有无能量回收的反渗透系统进行单目标优化，无能量回收装置与采用透平的反渗透系统均采用带段间增压泵的两段式反渗透工艺，而以PX型作为能量回收装置的反渗透系统采用单段式工艺。以无能量回收装置来比较，采用透平式的反渗透方案其吨水成本下降不大；而采用PX型的反渗透方案，吨水成本最低。对采用PX型的反渗透系统，进行多目标优化设计，优化得到的反渗透方案的吨水成本在US$0.52—$0.69/m3之间，吨水能耗在2.30—2.79kW h/m~3之间，吨水成本与吨水能耗的变化趋势相反，一级反渗透方案能同时满足较低的制水成本和吨水能耗。当进料海水盐度升高时，多目标最优化设计的非劣解曲线向右上方平移，最低吨水成本和最低吨水能耗均有上升。
最后，采用广义析取模型对反渗透系统进行优化。用传质模型来描述压力容器内膜元件传质过程，对于超结构内不存在的膜元件则视为单纯的输入输出操作而没有传质过程，反渗透级做同样处理，得到的广义析取模型采用逻辑外部逼近法求解。相对于混合整数非线性规划，广义析取模型可以避免在计算过程中超结构中不存在的反渗透级以及物流为零的变量引起的不可行解，使得非线性规划子问题能更快收敛。利用该模型研究了电价、膜元件价格和海水温度等因素对海水淡化设计结果的影响。电价的变化对反渗透系统吨水成本影响较大。当电价升高时，可以通过降低系统的操作压力或增加膜面积来降低海水淡化的成本。相对于电价，膜元件价格的变化对反渗透系统吨水成本影响处于第二位。当进料海水温度升高时，所需要的操作压力逐渐减小，所需的膜面积减少，反渗透的吨水成本呈下降趋势。
本文开展了反渗透系统优化研究，考虑了由于系统内功（压力）交换器盐水混合引起的盐度升高，加入限制条件使得压力容器的个数以及压力容器内膜元件的个数为整数解。优化研究表明本文的结果可用于对实际的反渗透工程设计或系统评估。
The reverse osmosis (RO) has been widely used for seawater and brackish waterdesalination. The main advantages of RO over other desalination processes are its nophase change, energy saving, modularity, etc. Therefore, RO developed rapidly andits market share increased recently. However, it is still necessary to develop asystematic optimization method for RO process. In this paper, studies on optimizationof RO networks for desalination of seawater and brackish water to reduce cost andpower consumption of desalted water are carried out.
First, an optimization model of RO networks with pressure exchanger (PX) isestablished based on finite difference membrane transport model, and salinity increasecaused by volumetric mixing in PX is considered. The optimum design problem canbe solved as a mixed-integer nonlinear problem (MINLP) using outer-approximationalgorithm. Discrete numbers constraints are added to make sure the number ofmembrane elements in each PV and PVs employed in the RO stage are integers. Thevariation of salinity of feed seawater is studied using the RO super-structure model,and the maximum product concentration is500mg/L, the results show that when thefeed water salinity increases, the desalted water cost increases correspondingly, andsystem processes also change. For the feed seawater concentration higher than32000mg/L, single-stage RO system is favored. When the feed seawater concentration isbelow28000mg/L, two-stage RO system with inter-stage pump is the better choice.Different types of membrane modules are selected for different feed seawater salinity.The desalted water cost increases with the decreases of permeate concentrationrequirement. For the looser permeate concentration requirement range form300~500mg/L, single-pass configuration can meet the required quality of desalted water. Whenthe lower permeate quality requirement of concentration from50~100mg/L, two-passsystem is selected.
Secondly, multi-objective optimization (MOO) of RO networks based on finitedifference membrane transport model is solved by ε-constraint algorithm, and non-inferior solutions (Pareto optimal set) are obtained. Decision-makers can chooseproper RO design configuration process for different design requirement. RO systems with or without ERD are optimized and compared as single objective optimizationusing desalted water cost and unit energy cost as the optimization objective,respectively. Two-stage RO system with inter-stage pump is favored for RO systemswith turbine or without energy recovery device (ERD). For RO system with PX, asimple single-stage system is favored. The desalted water cost of the RO system withturbine dose not decline much comparing with the system without ERD, and thedesalted water cost of the RO system with PX is the lowest. For a specific RO projectusing PX as the ERD, the MOO optimal process configurations achieve to producepotable water with a desalted water cost between US$0.52—0.69/m3and powerconsumption between2.30—2.79kW h/m3. The variation of the power consumptionis contrary to the desalted water cost. One-stage layout is proved to minimizesimultaneously the power consumption and the desalted water cost. With increasingthe feed water salinity, the pareto curve shift to the upper right, and the lowestdesalted water cost and the lowest power consumption of the RO system are bothincrease.
Finally, a generalized disjunctive programming (GDP) approach is established forthe optimization of RO networks. The nonlinear model based on GDP is proposed thatrelies on the identification and application of mass balances and equilibrium equationsfor existence membrane modules in PV. For non-existing or inactive modules, theequations considered are simply input-output relations in which no mass transfer takesplace. RO stage takes similar treatment. A variant of the logic-based outerapproximation algorithm is proposed to solve the problem. It would be desirable notonly to reduce the size of the NLP sub-problems, but also to avoid infeasibilities thatare due to the non-existing RO stage and linearization at zero flows in the ROsuperstructure. RO seawater projects are studied using the proposed logic-based outerapproximation algorithm, and several factors such as electricity price, membranemodule price, average seawater temperature, etc, are concerned. The desalted watercost is very sensitive to electricity price. When the electricity price increases, thedesalted water cost can be decrease through increasing operating pressure orincreasing membrane area. The desalted water cost is more sensitive to changes inelectricity price than membrane price. If the seawater temperature increases, theoperation pressure required by the RO system decreases and the total membrane areareduces, so the desalted water cost decreases.
Study on the optimization of RO networks is carried out, taking into account thesalinity increase caused by volumetric mixing in PX, and discrete numbers constraintsare added to make sure the number of membrane elements in each PV and PVsemployed in the RO stage are integers. Optimization researches show that the resultsin this paper could be utilized in the actual engineering design of RO process orsystem evaluation.
引文
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