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Firstly it is shown that the effective thickness of the membrane is the sum of the actual thickness, k 0 /U L and ! where k 0 is the thermal conductivity of the membrane matrix, λ is the latent of vaporization of water, C is a parameter (defined as flux per unit thickness of membrane per unit of temperature driving force) and U L is a coefficient combining the feed side and permeate side film heat transfer coefficients. For typical conditions the sum of the additional terms exceeds 100µm which clearly shows that the flux is not inversely proportional to membrane thickness. Also to a first approximation the thermal efficiency is independent of membrane thickness. This work and the development of an overall mass transfer coefficient for direct contact membrane distillation build upon the pioneering work of Giulio Sarti. Secondly a re-assessment of the traditional method for combining the Knudsen diffusion coefficient and the molecular diffusion coefficient suggests that the traditional sum of resistances approach engages in some double counting and thereby overestimates the resistance and consequently underestimates the flux.

Highlights-An Effectiveness-NTU (number of heat transfer units) method is developed for DCMD-This method can be used to either size or rate co-and counter-current DCMD modules-Production rate of DCMD module can be estimated within 6% accuracy-The computational cost is minor compared with discretised models Abstracts An equivalent effectiveness-number of heat transfer units (ε-NTU MD) method was developed for direct contact membrane distillation. Efficient performance rating and design sizing for individual DCMD modules can be rapidly made based upon limited experimental data. Using this method, the construction of a specific finite element model and their associated costs, involving both time and expenditure, are avoided. Instead the module performance or sizing requirements can be estimated efficiently using a set of expressions based on the conventional ε-NTU expressions used for the design of heat exchangers. The outlet temperatures are also predicted which is useful for the design of the overall DCMD process and module cascading networks. The ε-NTU MD method was validated against an experimentally validated discretized model of a flat sheet DCMD module, built using MATLAB. A correction function is included in the ε-NTUMD method proposed which results in 100% of the data having an accuracy of better than 6%. Method validation was done for both co-and countercurrent flow, with a range of module dimensions, flowrates and membrane permeabilities.

This research develops a technoeconomic analysis to study the profitability of ethanol production from CO 2 electroreduction. A HYSYS simulation is used to calculate the separation costs, a challenge in previous models available in literature. The profitability of a 10 000 kg per day CO 2 electroreduction plant to produce ethanol is studied. An optimization of the pressure swing adsorber and distillation tower, which greatly influence the total cost of the plant (≈20% of total cost), is carried out, obtaining a total cost of separation of £1.94 × 10 6 . The study demonstrates that reducing the voltage applied to values around 0.5 V, i.e., by increasing the pH up to 12 makes the process economically feasible with a current density over 15 mA cm −2 . It also shows that the process is economically feasible using a current density of 5 mA cm −2 if the electricity cost from renewable sources drops to 2.0 × 10 −2 £ kWh −1 . Finally, it is proved that if catalyst stability is not considered, some catalysts currently available in the literature can be used with a positive economic income. The results of this research show that the industrial electroreduction of ethanol can be feasible and can attract interest in the industrial adoption of the technology.

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