For example, a simple 1D porous flow problem in a reservoir. On the left of the model, there is a production well. So how should I deal with this production well? Adding a Neumann boundary condition at the left? Will it change the physical problem that I am trying to simulate? since if there is a production or injection well, it should be a source term in the mathematical model.
Wells are, of course, sources. The interesting point is that it is useful to transform a problem with non-zero sources and Dirichlet or Neumann boundary conditions to one with vanishing sources, a technique known as ``homogenization'', in which case it's the result of the calculation what the appropriate boundary conditions turn out to be.
These might be useful:
http://www.cmap.polytechnique.fr/~allaire/homog/lect2.pdf
Preprint Higher order homogenized boundary conditions for flows over ...
http://www.diva-portal.org/smash/get/diva2:999907/FULLTEXT01.pdf
https://pastel.archives-ouvertes.fr/pastel-00866253/document
it is possible to impose a flow condition on the wells, whether it is an injection or production well. the difference between the two kinds of sinks lies in the sign of the imposed flux. You can also impose a pressure on each well, then calculate the fluix of the well by using the pressure difference between the imposed pressure and the pressure of the mesh crossed by the well. you can consult this paper for dertail:
(PDF) Modeling and Simulation of Compressible Three-Phase Flows in an Oil Reservoir: Case Study of Tsimiroro Madagascar (researchgate.net)
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