Dynamic analysis and modeling of direct contact membrane distillation for water desalination during startup using linear system theory

Abstract

The transient performance of direct contact membrane distillation during startup was investigated using experimental data and theoretical modeling. The primary input, inlet hot temperature, caused a minor time delay in the output variable's dynamics because the dynamic of the former is not instantaneous. The minor input, inlet cold temperature, can cause disturbances in the system dynamics if it is not well controlled. Reaction curve methods revealed that the time constant of the outlet permeate temperature varied from 2 to 6 min as the operating temperature increased from 50 to 80 °C. The dynamic of the outlet hot temperature was found to be slower, with the time constant changing from 40 to 16 min under the same operating conditions. Modeling the outlet permeate temperature with a first-order transfer function produced results that closely followed the measured transient response. The lead-lag transfer function was found insufficient for capturing the dynamics of the outlet hot temperature. The choice of a high order transfer function for the hot temperature led to improved tracking of the measured time response. The static version of the transfer functions provided an enhanced prediction of the mass flux at steady state via improved approximation of the bulk temperatures.