Negative saturation problem
In some cases and due to the instabilities created by the IMPES Method we observe that after certain time of extraction of liquid, the saturation could be negative or superior to one which is incompatible with our definition of the saturation.
Then we added a criteria on the saturation to avoid having negative saturation. The criteria stops the well production if there is a negative saturation in one or several cells of the well.
To resolve saturation superior to one problem, one of the solution is to decrease gradually the source term (flow rate) when the saturation goes below certain values fixed by the operator. This could help to delay the apparition of saturation superior to one.