<p dir="ltr">Reverse osmosis (RO) is emerging as the world’s leading desalination technology due to its superior energy efficiency and the shift towards renewable electrification. However, RO systems need to further improve efficiency, increase operating flux, reach higher salinities (>7.5% w.t.), and minimize component complexity. Treating RO as a dynamical system, this dissertation invents new processes for high-efficiency desalination that achieve milestones for low downtime and high final salinity. It also introduces modeling methods that include more detail (e.g. salt retention, time-varying salinity, concentration polarization, salt transport, temporal multi-staging, etc.) and the first use of certain optimization methods in RO.</p><p dir="ltr">Batch RO is an unsteady, pressure driven process that efficiently desalinates a saline feed volume over time by continuously recirculating the brine through the membrane module. A tank houses the concentrating feed and mediates the streams entering and leaving the membrane module. Most studies so far have concentrated on the high-pressure tank design that requires finite downtime at the end of each stroke. A scalable pressure exchanger batch RO (PX-BRO) configuration using atmospheric tanks that practically has zero downtime and produces permeate even while flushing is first described in this dissertation.</p><p dir="ltr">To achieve high recovery at nominal RO pressures, osmotically assisted RO processes have both sides of the membrane saline and the streams usually in counterflow. The first unsteady osmotically assisted process based on the high-pressure piston tank design, batch counterflow RO (BCFRO) is introduced which dramatically reduces the energy needs. To address the issue of high component count in spatial multi-staging, the first “temporally multi-staged” BCFRO process is also introduced. The new process uses the pressure ex- changer and atmospheric pressure tank design for scalability and operational flexibility.</p><p dir="ltr">For membranes with low salt rejection, it becomes imperative to integrate the salt trans- port dynamics for deciding operating and initial conditions. Trajectory optimization is used to match salinity and volume between stages of temporally multi-staged BCFRO. Treating the process as an optimal control problem, a framework for obtaining time varying flux pro- files that minimize the specific energy consumption is also developed. Both reduced order and discretized models are developed to analyze these new batch RO configurations.</p>