Технические науки/12. Автоматизированные системы управления на производстве.

Ladiyeva L., Dovbnia S.

NTUU «Igor Sikorsky Kyiv Polytechnic Institute»

Mathematical model of the contact membrane distillation of desalination process

The aim is to study the potential for membrane distillation desalination, particularly developed detailed mathematical model allowing to investigate membrane distillation for the purpose of control.

In order to promote this model is considered three separate sections of the process before bring them together (Fig. 1). The process was divided into paroridynnyy distribution, mass transfer, heat transfer [1].

Fig. 1. The contact membrane distillation

– The temperature of the hot solution; – Temperature permeate; – Temperature of cold water.

Powered following formulas Description: (1) the equation channel solution, (2) permeate channel equation, the equation cold water channel respectively [2].

, (1)

, (2)

, (3)

, – the cost of input solution and cold water, respectively;

– Flow solution at the outlet;

, – Concentration of the solution at the inlet and cold water, respectively;

, – Concentration of the solution at the outlet and cold water, respectively;

, – Temperature at the inlet solution and cold water;

, , – The temperature of the solution, the permeate and cold water outlet, respectively;

– The flow of vapor through the membrane;

– The rate of transmission through the membrane;

– Transfer coefficient through the wall.

In membrane distillation hydrophobic membrane for water vapor. The membrane ensures the passage of only a couple but not the solution. This leads to the presence of steam-liquid distribution on the inputs and outputs of the membrane pores, in the place where the liquid and vapor in contact with each other. [3]

Evaporation and condensation of liquid vapor is a function of temperature, pressure and the corresponding concentration of water and salt. Mathematical equations representing this part of the process have been developed based on the equation coefficients and Antoine.

Mass transfer in membrane distillation is a number of the following stages: water from the volumetric flow of sea water must pass through a very thin boundary layer on the side of the supply membrane to evaporate on the surface of the membrane, the steam then passes through the pores of the membrane, and condenses on the surface of the membrane to permeatniy side of the membrane . Then the condensate must move through another boundary layer before connecting the permeate flow rate and gather as a product. There have been developed mathematical equations describing this part of the process based on the theory of boundary and model dusty gas.

Heat transfer in membrane distillation rozbyvavsya by heat exchange between the different sections of membrane distillation. This part of the process modeled by developing mathematical equations that describe the amount of heat transferred between each section and then combine them.

We found concordance between the results of the model and the actual results of the experiment. Using this model we can calculate the contours of regulation. In the future, thanks to cheap energy and membrane distillation can get a clean, cheap water wherever it is needed.

References:

1. Close E. Modeling of direct contact membrane distillation for desalination / Edward Close, Eva Sorensen // 20th European Symposium of Computer Aided Process Engineering, 6–9 June 2010 : abstracts and presentations. – Naples : Elsevier, 2010. – P. 534-539.

2. Ettouney, H. M. Fundamentals of Salt Water Desalination, Elsevier : textbook / H. M. Ettouney, H. T. El Dessouky. – Amsterdam : ELSEVIER SCIENCE B.V., 2002. – 670 p.

3. Termpiyakul, R. Heat and mass transfer characteristics of a direct contact membrane distillation process for desalination / R. Termpiyakul, R. Jiraratananon, S. Srisurichan // Desalination. – 2005. – Vol. 177, №2. – P. 133-141.