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Drawdown = P R - P wf. Inflow Performance Relationship (IPR) 1.Straight-line IPR q o = C(P 2 R – P 2 wf ) n q o = J(P R – P wf ) Open-flow potential IPR Calculation Methods Concepts Productivity Index, J 2. non-linear IPR Vogel’s Method

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IPR Calculation Methods 3. Fetkovich’s qoqo q o(max) 1 - P wf PRPR = 2 n For case of n =1, based on field observations for saturated oil wells. normalization qoqo q o(max) 1 - P wf PRPR = 2 q o = C(P 2 R – P 2 wf ) n Developed from: Observations of the American Bureau of Mines consider the effect of high velocity (non-Darcy, turbulent flow) slightly different from Vogel’s, somewhat more conservative

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Exercise: Back Pressure, Vogel’s & Fetkovich’s Methods Data from a multirate test for a well producing from a pay zone in a field is given in Table Q1. 1.Calculate the productivity index, J based on the lowest four flow rates. Find q max based on the straight IPR. 2.Plot the data in Table Q1 on the Cartesian paper. Use only point 10 to determine q max with the Vogel’s equation. Plot and tabulate the calculated rates predicted by Vogel’s against corresponding bottomhole flowing pressures given in Table Q1. 3.Repeat step 2 using Fetkovich’s method. 4.Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find q max. Table Q1

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Solution q P r - P wf Productivity Index = J = stb/d.psi q max (based the straight IPR) J = q P r - P wf 0 q max = J P r q max = (1600 psi) (5.38 stb/d.psi) = 8608 stb/d 1.Calculate the productivity index, J based on the lowest four flow rates. Find q max based the straight IPR psi =

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2.Plot the data on the Cartesian paper. Use only point 10 to determine q max with the Vogel’s equation. Plot and tabulate the Vogel’s rates corresponding to the bottomhole flowing pressures given in Table Q1. Vogel’s equation q max = 3706 stb/d Plot of observed rates vs. P Point 10, q = 1260 psi P wf = 1267 psi psi =

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Plot of observed & Vogel’s rates vs. P wf Vogel’s Observed Field Data vs. Vogel’s

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3. Repeat step 2 using Fetkovich’s method/ special normalized Back Pressure. qoqo q o(max) 1 - P wf PRPR = 2 q o(max) = qoqo 1 - P wf PRPR 2 q max = Point 10, q = 1260 psi, P wf = 1267 psi

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Field Data vs. Fetkovich Observed Backpressure

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4. Use the Backpressure Equation to tabulate the calculated rates corresponding to the bottomhole flowing pressures given in Table Q1. Find q max. n & C ? Backpressure Equation q o = C(P 2 R – P 2 wf ) n

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C = 0.08 (plugging a value on the line into) n = 1/slope = ~0.7 q o = C(P 2 R – P 2 wf ) n

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Field Data vs. Backpressure Backpressure Observed

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A plot of the measured data compared with Vogel’s equation, the Backpressure equation & Fetkovich’s equation

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Many oil wells produce from reservoirs with pressure above P b but with P wf below P b q o = J(P R – P wf ) P b P wf P r IPR curve is characteristic of reservoirs with a solution gas drive q o = J(P R – P wf ) + (P 2 b – P 2 wf ) J 2Pb2Pb P wf P b P r

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QUIZ: IPR A well produces oil at a rate of 108 stb/d with a bottomhole flowing pressure of 1980 psia. The PVT analysis of the core samples and recombined reservoir fluids suggested that the bubble point pressure to be at 1825 psia at a temperature of 195 o F. An initial reservoir pressure of 3620 psia was recorded during the 48-hour buildup following the flow test. i.Calculate the productivity index, J if flowing bottomhole pressure is greater than bubble point pressure. ii.Calculate the production rate if bottomhole flowing pressure is held at the bubble-point pressure to avoid the blockage in the near wellbore region. iii.Calculate the maximum production rate that can be expected from the well. iv.Plot the IPR curve for the entire range of wellbore flowing pressures, both above and below the bubble point.

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Solution i.J = stb/d/psia. ii. q ob = stb/d/psia. iii. q max = stb/d/psia. (P wf = 0)

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