# TAMU PETE 662 - hw 2 sol f14 (10 pages)

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- School:
- Texas A&M University
- Course:
- Pete 662 - Production Engineering

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PETE 662 HW 2 Solution Fall 2014 Question 1 The input parameters required are summarized in Table 1 Table 1 Input Values for all models Net pay ft h Reservoir Pressure psi pe Wellbore Pressure psi pwf Fluid viscosity cp Volume Factor B0 Drainage length ft Drainage width ft Wellbore length ft L Wellbore Radius ft rw Horizontal Permeability md kH Vertical Permeability md kV a 50 3000 1500 8 1 1 4000 3000 5000 0 25 2 1 Joshi Economides model can not be applied to a fully penetrated well as the model assumed an elliptical horizontal flow and elliptical horizontal flow can not exist at the end of the drainage region if the well extends to the end of drainage region b Furui et al model can be used as shown below Distance to the reservoir boundary yb 1500 ft see Fig 1 Fig 1 Furui et al Model geometry of horizontal well in reservoir The mean permeability k k y k z 1 1 0 md Skin s 0 assumed as there is no mention of any formation damage Page 1 of 10 PETE 662 HW 2 Solution Fall 2014 kL pe p wf q hI ani y b 141 2 Bo ln 1 224 s rw I ani 1 hI ani For Pwf 1500 psi q 1 5000 3000 1500 50 2 1500 141 2 8 1 1 ln 1 224 0 2 0 25 2 1 50 118 8 STB d Production rate for different bottomhole pressure s are calculated and shown in IPR curve below Fig 2 Fig 2 IPR curve for Furui et al model c Babu and Odeh model can be applied as shown below Table 2 Input Values for Babu and Odeh Model see Fig 3 Drainage length ft b Drainage width ft a Position in width direction ft x0 Position in Length direction ft y1 Position in Length direction ft y2 Position in height direction ft z0 Page 2 of 10 5000 3000 1500 0 5000 25 PETE 662 HW 2 Solution Fall 2014 Fig 3 Babu and Odeh Model of horizontal well in reservoir First we calculate the shape factor CH ln CH 6 28 2 a 1 x0 x0 z ln sin 0 I ani h 3 a a h a 0 5ln 1 088 I ani h 2 3000 3000 1 1500 1500 25 1 088 12 914 ln C H 6 28 ln sin 0 5 ln 2 50 3 3000 3000 50 2 50 Now since the well is fully penetrating the reservoir partial penetration skin factor sR 0 The drainage area of horizontal well A a h 150000 ft2 Production rate for Pwf 1500 psi is calculated q k y k z b p p wf A0 5 ln C H 0 75 s R s 141 2 Bo ln rw 309 38 STB d Production rate for different bottomhole pressure s are calculated and shown in IPR curve below Fig 4 Page 3 of 10 PETE 662 HW 2 Solution Fall 2014 Fig 4 IPR curve for Babu and Odeh model Now we compare the resulting IPR s Fig 5 Fig 5 IPR curves of Furui et al and Babu Odeh models As we can see from Fig 5 the production rate of Babu and Odeh model is always higher than Furui et al model and their differences increases as the pressure difference driving flow increases Babu and Odeh model gives a higher production rate as it is for pseudo steady state however we are using the same average reservoir pressure as the pressure at the boundary Average reservoir pressure should be smaller than drainage boundary pressure As we use the same value obviously Babu and Odeh model gives higher production rate due to higher driving force Page 4 of 10 PETE 662 HW 2 Solution Fall 2014 Question 2 The input parameters for this problem are summarized in Table 3 Table 3 Input Values for all models Net pay ft h Reservoir Pressure psi pe Wellbore Pressure psi pwf Fluid viscosity cp Volume Factor B0 Drainage length ft Drainage width ft 50 3000 1500 8 1 1 5000 3000 Wellbore length ft L Wellbore Radius ft rw Horizontal Permeability md kH Vertical Permeability md kV 2500 0 25 2 0 5 a Joshi Economides model can be used as shown below I ani kH 2 kV a 2500 ft one half of the reservoir extent in the direction of the well see Fig 6 L 2500 ft Drainage Length 5000 ft Fig 6 Joshi Economides Model Skin s 0 assumed as there is no mention of any formation damage pwf 2 2 141 2qBo a a L 2 I ani h I ani h pe ln ln s kH h L 2 L rw I ani 1 Page 5 of 10 PETE 662 HW 2 Solution Fall 2014 For a Pwf of 1500 psi the production rate q 79 81 STB d Production rate for different bottomhole pressure s are calculated and shown in IPR below Fig 7 Fig 7 IPR curve for Joshi Economides model b The geometry for the Furui et al model is based on fully penetrating horizontal wells However this restriction can be relaxed by incorporating partial penetration effects This is done using a partial penetration skin factor which accounts for the extra pressure drops due to the flow pattern developing around the entrance to the well Identical to adding a skin factor for formation damage partial penetration skin sR can be directly added to the inflow equation resulting in Page 6 of 10 PETE 662 HW 2 Solution kL pe pwf q Fall 2014 hI ani yb 141 2 Bo ln 1 224 s sR r I 1 hI ani w ani The actual pressure drop components of the partial penetration skin effect can be determined as done in Babu and Odeh model Distance to the reservoir boundary yb 1500 ft as before The mean permeability k k y k z 4 2 md Skin s 0 assumed as there is no mention of any formation damage For the partial penetration skin sR we use the Babu and Odeh model method As the reservoir is longer compared to width we apply the second case however case 1 method can also be used if it applies Case 2 5000 2 b ky 1 33 a 1 33 3000 2 kx h kz 50 0 5 3535 2827 72 70 71 Since above comparisons are true then case 2 applies hence s R Pxyz Pxy Py k z b h Pxyz 1 ln 0 25ln x ln sin 0 kz h L rw Py 6 28b 2 ah 1 84 3 80 2 kx kz 1 ymid ymid L L 2 3 16 35 ky 3 b 24 b b b 2 1 x0 x0 b 6 28a Pxy 1 k z k x 2 15 70 L h 3 a a Hence sR 35 86 Page 7 of 10 PETE 662 HW 2 Solution Fall 2014 For pwf 1500 psi production rate is q kL pe pwf 69 66 STB D hI ani yb 141 2 Bo ln …

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