OBM with continuous addition of melt

Fluid addition may be a one-time event or a continuous process. For the situation of continuous process, the total amount of fluids increases with the degree of melting. Thus, we can assume (Ozawa and Shimizu, 1995) 

Note that for one-time metasomatism, is not related to the degree of melting. 

The concentration in the melt is related to the concentration in the solid by a bulk partition coefficient 

We now need to find the variation of the bulk partition coefficient D as a function of the degree of melting. Mass balance of mineral i gives 

Note that we chose L instead of because mineral i does not 

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