Water scarcity is a dilemma facing much of the global population. Cation intercalation desalination (CID) cells, which use intercalation host compounds (IHCs) in combination with ion-exchange Membranes (IEMs), could aid in addressing this challenge by treating saline water sources. Originally, the performance of such cells was predicted utilizing continuous flow of saline water through porous IHC electrodes. Here, we use two-dimensional porous-electrode theory with concentrated solution transport to evaluate the performance of various cell architectures where flow occurs through open flow channels (OFCs) when two IHC electrodes comprised of nickel hexacyanoferrate (NiHCF) are used to store Na* ions. We show that, when two OFCs are used, cation exchange membranes (CEMs) are adjoined at flowchannel/electrode interfaces, and an anion exchange membrane (AEM) is arranged between flow channels, salt removal increases relative to the original design with flow -through (FT) electrodes. The IEM stacking sequence within such a membrane flow -by (MFB) cell is the fundamental repeat unit for electrodialysis (ED) stacks using many IEMs (CEM/AEM/ /CEM/AEM/CEM) with Many diluate streams. Accordingly, we simulate the performance of such ED stacks rising NiHCF IHCs, and we predict that salt adsorption capacity (per unit NiHCF mass) is amplified by twenty -fold relative to MFB and FT cells, while simultaneously decreasing 0.7 M NaCI feed water to 0.2-0.3 M within diluate streams. The generality of these findings is further supported by simulations using Na0.44MnO2 IHC instead of NiHCF. Thus, we propose the use of cation IHCs as alternatives to the gas -evolution reactions used in conventional ED. (C)2017 Elsevier Ltd. All rights reserved.