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## Injectivity index II = q i / D p

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**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