Counter current solid liquid extraction

Counter-current solid-liquid extraction is a widely employed technique in chemical engineering, known for its efficiency and operational simplicity. This study aims to present an analytical solution and calculation method for a cascade of perfectly mixed batch extractors operating counter-currently with variable parameters for each extractor. The methodology includes the assessment of spherical solid particles and takes into account diverse factors such as diffusivity, adsorption isotherm constants, and apparent density of the solution. An extensive literature review indicates that while numerous studies have addressed various aspects of solid-liquid extraction, a rigorous analytical framework has been deficient. By establishing certain assumptions—such as constant diffusivity, linear adsorption isotherm, and negligible mass transfer resistance—the study offers an initial approximation to the problem of extraction dynamics. The results demonstrate that the proposed method yields favorable agreement with experimental data, provided that adequate average values of the diffusivity are adopted for each extractor. This analytical approach presents a valuable contribution to solid-liquid extraction design, highlighting the possibility of achieving efficiency through a systematic consideration of extractor parameters.