Solution of mathematical model for supercritical fluid extraction with finite difference method

Experiments for science and engineering have a very important place. Some experiments can be very long and costly. But without the experimental studies of the problem, by solving the generated mathematical model it can be get some idea about the success of the experiment and the approximate obtaining of some parameters. If the mathematical has a complex structure, it is difficult or impossible to find an analytical solution. Applied mathematics is used at this stage. It can provide ease of use of numerical methods in science and engineering fields. In this thesis, it is aimed to present a numerical solution for supercritical fluid extraction which is a chemical engineering subject. The mathematical model used in the solution of supercritical fluid extraction which has experimental results in the thesis corresponds to a system of partial differential equations. Reasonable results have been achieved by solving the system with finite differences and comparing with the existing experimental results. The study consists of four chapters. The first chapter covers literature summary, the aim and hypothesis of the thesis. This chapter is an explanation of the literature from the beginning to the end of the thesis study. The second chapter responds the question of "What is supercritical fluid extraction?". Accordingly, experimental stages and mathematical model are mentioned. In the last part of this chapter, mathematical model has been dimensionless in order to start a numerical solution. Numerical solution stages of the system of partial differential equations corresponding to dimensionless mathematical model are given in the third chapter. Firstly, Crank-Nicolson method which is the solution method has been mentioned then, the equations are replaced by finite difference expressions instead of derivatives in the system of partial differantial equations with the help of this system. Thus, algebraic equation system has been obtained and this system is solved using the Thomas algorithm method. The fourth chapter is section where numerical results are examined. Firstly, experimental and numerical results are given by using graphs according to temperature, pressure, solvent flow rate and partical size. Then, numerical results were compared with experimental results. After reaching the results, the relations between the coefficients were examined. The results and recommendations section of the thesis are given in the last section.