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TO: T.E Petroleum Class FROM: Dr. Abdul Majeed DATE: January 25, 2017 SUBJECT: PE-306_HW/Assignment #4 Date of submission: 01st February Wednesday, 2017 Perform calculations for the following oil-well data: (a) Calculate the absolute open flow potential and draw the inflow performance relationship curve (b) calculate the Productivity Index. Data Permeability, ko = 30 md Pay thickness, h = 40 ft Average reservoir pressure, pr = 3000 psig Reservoir temperature, T = 200°F Well spacing, A = 160 acres (43,560 ft2/acre) Drilled hole size, D = 12-1/4 in. (open hole) Formation volume factor, Bo = 1.2 (bbl/STB) Oil viscosity, mo = 0.8 cp (assume skin = 0 and no turbulence) Perform calculations for the following oil-well data: Make a completion sensitivity study for the following well: k = 20 md pr = 3000 psia re = 2000 ft h = 25 ft hp = 20 ft rp = 0.021 ft Lp = 0.883 ft kp = 0.4 x k md rc = 0.063 ft rw = 0.365 ft API = 35° gg = 0.65 Bo = 1.2 (res bbl/STB) uo = 1 cp 1. Calculate the pressure loss through perforations for 2, 4, 8, 12, 20, and 24 spf in the flow rate range from 100 to 1200 STB/D. 2. Plot completion sensitivities q versus Dp.

Theory:

Completion System Most oil and gas wells are completed with casing. The annulus behind the casing is normally cemented. Once the casing is cemented, it is hermetically insulated from the formation. To produce any fluid from the formation, the casing is perforated using perforation guns. Perforated completions provide a high degree of control over the pay zone, because selected intervals can be perforated, stimulated and tested as desired. It is also believed that hydraulic fracturing and sand control operations are more successful in perforated completions. However, the perforations impose restrictions to flow from the formation to the wellbore in the form of additional pressure losses. Consequently, if not adequately designed and understood, perforations may substantially reduce the flow rates from a well. Shaped-charge perforating is the most common and popular method of perforating. A typical cross section of a shaped charge is shown in Fig. 24. As the shaped charge is detonated, the various stages in the jet development are shown in Fig. 25a and Fig. 25b. The velocity of the jet tip is in excess of 30,000 ft/sec, which causes the jet to exert an impact of some four million psi on the target. Every shaped charge manufacturer provides a specification sheet for charges regarding the length of penetration and diameter of the entrance hole in addition to other API required specifications.

Pressure Loss in Perforations The effect of perforations on the productivity of wells can be quite substantial. Therefore, much work is needed to calculate the pressure loss through perforation tunnels. A brief review of the background work in the area was presented by Karakas and Tariq (1988). Most of the calculations on perforation pressure losses are based on single-phase gas or liquid flow. It is generally believed that if the reservoir pressure is below the bubble point, causing two-phase flow through the perforations, the pressure loss may be an order of magnitude higher than that for single-phase flow. Perez and Kelkar (1988) presented a new method for calculating twophase pressure loss across perforations. Two methods of calculating the pressure loss in perforations are provided here with appropriate examples. These methods were proposed by McLeod (1983) and Karakas and Tariq (1988). McLeod Method Pressure loss in a perforation is calculated using the modified Jones, Blount, and Glaze equations proposed by McLeod. McLeod treated an individual perforation tunnel as a miniature well with a compacted zone of reduced permeability around the tunnel. It is believed that the compacted zone is created due to the impact of the shaped charge jet on the rock. However, there is no physical means to actually calculate the permeability of the compacted zone. McLeod suggested from his experience that the permeability of the compacted zone is: 1. 10% of the formation permeability, if perforated overbalanced 2. 40% of the formation permeability, if perforated underbalanced. These numbers may be different in different areas. The thickness of the crushed zone is assumed to be 0.5 in. The massive reservoir rock surrounding a well perforation tunnel renders it feasible to assume a model of an infinite reservoir surrounding the well of the perforation tunnel. Thus, in the application of Darcy's law, -0.75 in the denominator can be neglected. A cross section of McLeod's perforation flow model is provided in Fig. 26. The pressure loss equations through perforations are: Oil Well

where the constants a and b are defined below. Note that the flow qo in this equation is not the well production rate but the flow rate through an individual perforation.

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Theory:

Completion System Most oil and gas wells are completed with casing. The annulus behind the casing is normally cemented. Once the casing is cemented, it is hermetically insulated from the formation. To produce any fluid from the formation, the casing is perforated using perforation guns. Perforated completions provide a high degree of control over the pay zone, because selected intervals can be perforated, stimulated and tested as desired. It is also believed that hydraulic fracturing and sand control operations are more successful in perforated completions. However, the perforations impose restrictions to flow from the formation to the wellbore in the form of additional pressure losses. Consequently, if not adequately designed and understood, perforations may substantially reduce the flow rates from a well. Shaped-charge perforating is the most common and popular method of perforating. A typical cross section of a shaped charge is shown in Fig. 24. As the shaped charge is detonated, the various stages in the jet development are shown in Fig. 25a and Fig. 25b. The velocity of the jet tip is in excess of 30,000 ft/sec, which causes the jet to exert an impact of some four million psi on the target. Every shaped charge manufacturer provides a specification sheet for charges regarding the length of penetration and diameter of the entrance hole in addition to other API required specifications.

Pressure Loss in Perforations The effect of perforations on the productivity of wells can be quite substantial. Therefore, much work is needed to calculate the pressure loss through perforation tunnels. A brief review of the background work in the area was presented by Karakas and Tariq (1988). Most of the calculations on perforation pressure losses are based on single-phase gas or liquid flow. It is generally believed that if the reservoir pressure is below the bubble point, causing two-phase flow through the perforations, the pressure loss may be an order of magnitude higher than that for single-phase flow. Perez and Kelkar (1988) presented a new method for calculating twophase pressure loss across perforations. Two methods of calculating the pressure loss in perforations are provided here with appropriate examples. These methods were proposed by McLeod (1983) and Karakas and Tariq (1988). McLeod Method Pressure loss in a perforation is calculated using the modified Jones, Blount, and Glaze equations proposed by McLeod. McLeod treated an individual perforation tunnel as a miniature well with a compacted zone of reduced permeability around the tunnel. It is believed that the compacted zone is created due to the impact of the shaped charge jet on the rock. However, there is no physical means to actually calculate the permeability of the compacted zone. McLeod suggested from his experience that the permeability of the compacted zone is: 1. 10% of the formation permeability, if perforated overbalanced 2. 40% of the formation permeability, if perforated underbalanced. These numbers may be different in different areas. The thickness of the crushed zone is assumed to be 0.5 in. The massive reservoir rock surrounding a well perforation tunnel renders it feasible to assume a model of an infinite reservoir surrounding the well of the perforation tunnel. Thus, in the application of Darcy's law, -0.75 in the denominator can be neglected. A cross section of McLeod's perforation flow model is provided in Fig. 26. The pressure loss equations through perforations are: Oil Well

where the constants a and b are defined below. Note that the flow qo in this equation is not the well production rate but the flow rate through an individual perforation.

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