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- TL;DR Summary
- I wish to learn how to model the radial pressure gradient across a cylindrical, permeable strata and possibly develop tighter ranges for estimated porosity and permeability.

I was asked to give an estimate for a three dimensional permeate problem and I need an assist in how to setup a model equation.

Picture a 6" underground cylindrical bore. The depth of the cylindrical bore is 150 feet. The bore is sealed at the bottom and the permeability below the bore bottom in a horizontal plane is zero. Likewise there is a similar impermeable, horizontal layer at the top of the 150' bore, except there is a pipe leaving the bore where the permeate leaves and its size only offers negligible resistance to flow by comparison to the much lower permeability of the strata composition surrounding the bore.

How do I set up an equation to model the gradient pressure radiating out from the cylindrical bore?

All comments and suggestions are most welcome!

Best regards,

B

Picture a 6" underground cylindrical bore. The depth of the cylindrical bore is 150 feet. The bore is sealed at the bottom and the permeability below the bore bottom in a horizontal plane is zero. Likewise there is a similar impermeable, horizontal layer at the top of the 150' bore, except there is a pipe leaving the bore where the permeate leaves and its size only offers negligible resistance to flow by comparison to the much lower permeability of the strata composition surrounding the bore.

- Viscosity of the permeate is 0.0111 cP.
- The porosity of the surrounding strata is homogeneous estimated between 3-7%.
- Permeability of the strata over the 150' cylinder depth is estimated to be between 100 and 1000 micro-Darcy.
- Strata pressure at a very long, but unknown, distance from the bore is uniformly 45 PSIG in all directions surrounding the bore.
- Free permeate pressure inside the cylinder is 30 PSIG for a differential pressure of 15 psi.
- The measured flow rate is 4 cubic feet per hour in actual volume at 30 psig.

How do I set up an equation to model the gradient pressure radiating out from the cylindrical bore?

All comments and suggestions are most welcome!

Best regards,

B