Prediction models to analyse the performance of a commercial-scale membrane distillation unit for desalting brines from RO plants

Abstract

Desalting brines from Reverse Osmosis (RO) plants is one of the most promising applications of Membrane Distillation (MD) systems. The development of accurate models to predict MD system performances plays a significant role in the design of this kind of industrial applications. In this paper, a commercialscale Permeate Gap Membrane Distillation (PGMD) module was modeled by means of two different approaches: Response Surface Methodology (RSM) and Artificial Neural Networks (ANN). Condenser inlet temperature, evaporator inlet temperature, feed flow rate and feed water salt concentration were selected as inputs of the model, while permeate flux and Specific Thermal Energy Consumption (STEC) were chosen as responses. The prediction abilities of both RSM and ANN models were compared with further experimental data by using the Analysis of Variance (ANOVA) and the Root Mean Squared Error (RMSE). The results show that the ANN model is able to predict in a more precise way the behaviour of the module for the whole range of input variables. Thus, ANN model was used to find the optimal operating conditions, for the module operating at feed water salinity of 70 and 105 g/L, concentrations that can be reached when desalting RO brines.

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“…, w 1,n ). Second, the weighted inputs are added together with bias signal b to obtain a value [21]:…”

“…First n-elements of the input vector (z1, z2, …, zn) are multiplied by weights (w1,1, w1,2, …, w1,n). Second, the weighted inputs are added together with bias signal b to obtain a value [21]: Finally, the output signal is a function of a, the weighted sum of the inputs. The purpose of an activation function is to ensure that the input space is mapped to a different space in the output.…”

“…The purpose of an activation function is to ensure that the input space is mapped to a different space in the output. Linear, sigmoid and hyperbolic transfer functions are generally used in ANNs [21,22].…”

“…There are many different topologies; however, the Multi-Layer feedforward Perceptron (MLP) is the most commonly used. The MLP topology can be characterized by the same number of network inputs and outputs, equal to the number of input and output variables of the system to be modelled [21]. There are no specific rules for finding the best topology of the network, and therefore different methods such as trial and error or evolutionary algorithms (e.g., genetic algorithm) can be used for this purpose [23].…”

“…Once the topology is obtained, the network should be trained. We used a back-propagation algorithm using Stochastic Gradient Descent (SGD) with an adaptive learning rate algorithm [21]. There are many parameters that need to be tuned for ANN, the most important ones include the number of layers, number of neurons in each layer, type of transfer function and regularization terms (L1 and L2), which prevent overfitting and improve generalization, were considered for a grid search.…”