Injectivity index II = qi/Dp Productivity index PI = qp/Dp Rate is proportional to the pressure drop for any flow geometry Darcy’s law: n=1, x
Steady state flow towards well Flux of incompressible fluid via the contour with the radius r is: Separation of variables and integration give: where C is a constant
Setting the pressure values at well radius rw and at the contour radius Rc results in the Dupui formula Drainage radius of production/injection well Let us rewrite the Dupui formula as
Well radius is usually around 0.1 m. Contour radius can vary from 5 m to 500 m. So, the ratio Rc/rw can vary from 50 to 5000. The variation of permeability k, well rate q, reservoir net pay h and viscosity can be 3-4 orders of magnitude in real reservoirs. Nevertheless, the right hand side of the equality varies from 4.0 to 8.5. It allows to fix any Rc value for well rate calculations.
Impedance – Reciprocal to Injectivity index Injectivity index
Mud filtrateinvasion Damage Caused by Drilling Fluid
p < pb p > pb Damage Caused by Production
“dirty”water incompatiblewater Damage Caused by Injection
Bulk formation Altered zone k ka h rw ra Reservoir Model of Skin Effect
2000 1500 Pressure, psi 1000 Dps 500 1 10 100 1000 10000 Distance from center of wellbore, ft Reservoir Pressure Profile
rw kdp rdp rp kR Lp kd rd After McLeod, JPT (Jan. 1983) p. 32. Completion Skin
Gravel Pack Skin Cement Lg
Introduction of skin factor For dimensionless pressure P=2kp/qµ:
Skin factor in a damaged well – definition: What is a skin factor if II for damaged well is 10 times lower than that of undamaged well? In damaged zone with rd=0.2 m permeability decreased 10 times if compared with initial permeability. Calculate skin for rw=0.1 and Rc=500 m.
Well boundary condition for unsteady state flow in damaged formation dimensional dimensionless