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A simple, yet effective, approach to estimate the effect of parasitic phenomena inside the stack is the definition of the current utilisation factor (or current efficiency) 𝜁, defined as the ratio between the ideal current calculated from the salt depletion in the diluate channel and the actual current passing though the stack: 𝜁 = ( 𝐶 𝑄 − 𝐶 𝑄 ) ∙ 𝐹 𝐼 (45) Typical values of 𝜁 range from 0.5 to 0.95, with the lower end indicating a significant adverse effect of parasitic phenomena such as salt counter-diffusion, low IEMs perm-selectivity, presence of parasitic currents in the manifolds, etc., particularly detrimental when high concentrations are reached. The current utilisation factor is often adopted in simplified models and design tools (see Section 5.3) for a quick calculation of operating current in industrial ED stacks, and 𝜁 values are generally based on empirical equations or practical experience of process designers and operators. ED models often neglect the pumping power [174, 199], although in some operating conditions this may be significant (see Section 4.4.5). RED models, instead, normally take into account the pumping power [6, 141, 254, 297] because of the relative low gross power densities producible. In both cases, the pumping power per cell pair can be calculated as 𝑃 = 𝑄 ∆ 𝑝 + 𝑄 ∆ 𝑝 ( 4 6 ) 𝜒 where Q is the flow rate, ∆𝑝 is the total (in-out) pressure drop pressure drop, 𝜒 is the pump efficiency, and the subscripts C and D refer to the concentrate and diluate channels, respectively. ∆𝑝 includes the pressure drop along the channel and the concentrated pressure drop within the manifolds. It can be predicted by in-out pressure drops measurements used as fitting data [254], or by CFD tools providing distributed pressure drops [6, 141, 297], along with experimental data or simulation results on the friction losses through the manifolds [6, 297]. 5.3 Simplified models for the simulation and design of ED systems The last class of models reported in the literature is characterized by a simplified structure [226, 351, 360]. This approach has been mainly followed in order to implement models aiming at the preliminary design of ED units. In 2002 Lee et al. [226] presented a design tool based on a number of simplifying assumptions and simple equations allowing to estimate the main features of an ED stack such as electric current and required membrane area for a fixed applied voltage. In particular, the main assumptions are: 63PDF Image | Electrodialysis for water desalination
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