It is known that efficiency of washing/extraction can be increased by implementing cascade washing/extraction instead of using all the solvents at one time. How do I calculate the optimum number of cascade steps?
There exist several ways in which a product can be washed or extracted.
In the attached .pdf file I worked out the equations and a graph to calculate a multi-stage cross flow solid/liquid extraction (see attached .pdf file, including worked examples). In the presented multi-stage cross flow solid/liquid extraction, a mass of L kg of the product is washed (“extracted”) with a fixed mass V kg of solvent; the spent product then is drained to obtain the original mass of L kg and an extract 1 of V kg. The L kg spent solid is again washed with V kg of fresh solvent, drained, etc. This can be repeated N times; N = the number of extraction steps. Sometimes at the end all extracts are mixed to get a TOTAL extract, which will be very dilute.
I could also have worked out equations and a graph on a multi-stage counter current extraction.
Or even on a multi-stage counter current extraction in which the product increases in mass after the first extraction step.
If the multi-stage cross flow solid/liquid extraction attached was not what you asked for, could you please specify the required extraction (wash) process in more details?
I really appreciate that you both provided lot of detailed the information on extraction. As this is a new filed for me, I had no idea where to start. Your information will help me to get started.
In addition to my previous contribution of 6 days ago, I now also have included equations and worked examples regarding washing/extraction/leaching for products which increase in mass during extraction. This is frequently the case with dried foods such as tea leaves, ground coffee, etc. By the simple soaking action to increase the mass (swelling) prior to the first extraction step, all Kremser equations and graph can be applied, assuming that the swollen mass of the product is the mass to be extracted.