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This work extends the development of backmixing-diffusion model by further removal of some assumptions from the previous works. The model covers for steady and unsteady state conditions in continuous countercurrent extraction and will be available for simulation purpose for reversing continuous countercurrent extractor (RCCE) in a more realistic ways, especially in beverage juice production. Solution of the modeling was carried out by numerical method, namely, an implicit finite difference. For the unsteady state condition, the Crank-Nicholson method was selected for calculation due to its stability; for the steady state one, the selected numerical method was center-difference formula with second order of magnitude of error, cooperated with Richardsons extrapolation. Matrix inversions were done by Gauss Jordan method. Considerable verification was made by assuring the accuracy and stability of numerical method for both steady and unsteady state conditions in a practical range. It was found that the solution obtained from the developed model with aforementioned numerical method compared well with the well-established analytical solution whenever they are available. Generally, the numerical solutions gave high accuracy for the steady state condition, while still being acceptable for practical purpose.

Mathematical Simulation of Solid-Liquid Diffusion in Continuous Countercurrent Extraction Process, Part I - Modeling Development