Optimal control theory is applied to dynamic operation of batch reverse osmosis (RO) for seawater desalination and batch pressure retarded osmosis (PRO) for power generation. It is proved that the water flux should be constant during the entire operation in order to minimize specific energy consumption (SEC) in RO or to maximize specific energy production (SEP) in PRO. A dimensionless parameter γ = A_mL_pπ₀t_f/V₀, similar to that used in continuous osmotic membrane processes, is proposed to characterize the energy performance. While the SEC in RO is a monotonic function of recovery and γ, the SEP in PRO is solely a monotonic function of γ. It is shown that batch RO/PRO excels continuous RO/PRO because it mitigates the spatial variation of flux in a long pressure vessel observed in the latter. The batch operation provides an elegant way to implement continuous multistage RO with interstage pumps and an energy recovery device as well as continuous multistage PRO with interstage turbines. Some trade-off between the energy efficiency and flux is deemed necessary. A preliminary cyclic diagram to operate the batch PRO is proposed.

中文翻译：

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批量反渗透和批量压力延迟渗透的动态运行

最优控制理论应用于海水淡化的间歇式反渗透（RO）和发电的间歇式减压渗透（PRO）的动态运行。事实证明，在整个操作过程中，水通量应保持恒定，以使RO中的比能耗（SEC）最小化或PRO中的比能量产生（SEP）最大化。无量纲参数γ=阿_米大号_p π ₀吨_˚F / V ₀与在连续渗透膜过程中使用的类似，被提出来表征能量性能。RO中的SEC是恢复和γ的单调函数，而PRO中的SEP仅是γ的单调函数。结果表明，批量RO / PRO优于连续RO / PRO，因为它减轻了在后者中观察到的长压力容器中助焊剂的空间变化。批处理操作为实施带级间泵和能量回收装置的连续多级RO以及带级间涡轮机的连续多级PRO提供了一种绝妙的方法。能源效率和通量之间必须进行权衡。提出了操作批生产PRO的初步循环图。