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Hello, guys
We all know that near-wellbore production pressure gradient for radial flow is delta P/delta r|r=rw = -q*mu/2*pi*rw*k*h.
How can we calculate that the production pressure gradient delta P/ delta x for bilinear flow in to the well? Do we need to use the formula such as delta P/delta x= -q*mu*/0.001127*k*A?
Will be great if you give some links to above question or give comprehensive answer.
Thanks
'Normal' radial flow - of the sort you describe in the first equation - is omnidirectional, that is, it does not matter which direction you look at. Bilinear flow by it's very nature is highly directional.
Think of bilinear flow in a hydraulic fractured case - You have linear flow from the reservoir, entering the fracture wing perpendicular to it, and then linear flow along the fracture wing into the wellbore. See the problem? When you ask for an equation to describe deltaP with delta r, it also depends upon which direction you are looking at and also at what time, as this flow regime is usually transitory on the way to pseudo radial flow