Mathematical Analysis of Sub-Atmospheric Vapor Pipeline (SAVP) Transmission for Seawater Desalination

Abstract

Seawater desalination by sub-atmospheric vapor pipeline transfer (known as SAVP) is one of the innovative seawater desalination methods that could be used in lands and industries. SAVP systems works based on the temperature difference between a hot source and a cold environment; this method can provide users with a variety of advantages in industrial and field applications. The temperature of the hot and cold sources, as boundary conditions, can be considered as a function of time in natural and industrial environments; therefore, it affects the process of convection and diffusion significantly. In such a case, new and interesting challenges arise; such as reviewing and simplifying the basic convection-diffusion equation through obtaining the temperature profile in the pipeline by using advanced engineering mathematics. Two mathematical approaches can be developed to solve the temperature differential equation; one is through Eigen functions and the other one uses Green’s equation based on the length of the pipeline for SAVP. In this study, vapor’s temperature will be formulated as a function of time and length in accordance with the given assumptions and information. Mathematical simulations were performed for a field-scale spanning between Bandar Abbas and Geno (two places on the south coast of Iran) biosphere reserve. Also, an industrial scale in a vapor transfer device with a heat source capacity of about 200 liters was assembled. The results showed an acceptable range of accuracy in the proposed methods.