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lotusquantum

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I am working on tracer in the oil field. In attempt to understand the analytical solution of tracer breakthrough in 5-spot pattern I'm reading the paper of Brigham and Abbasadez. For obtaining of potential field, they used some mapping methods from z plane to w plan, with w=sn(z,n). But I don't understand how to convert the Jacobi Elliptic functions from z plane to one half of w plan. So I hope anybody will help me or show me some related articles to clarify this point.

Another thing, If we have 2 points (one source and one sink) with different elevation (considering of gravity), then how can we modify the complex potential and the stream function as well??

Hope to hear from all of you soon. Thank you very much!