# TAMU PETE 662 - Ch 2 (26 pages)

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## Ch 2

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- Pages:
- 26
- School:
- Texas A&M University
- Course:
- Pete 662 - Production Engineering

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PETE 662 Production Engineering Chapter 2 Production from Undersaturated Oil Reservoirs Undersaturated Oil Reservoirs pe pwf pbubble point single phase flow in reservoir rock Undersaturated Oil Reservoirs Darcy s Law for Single Phase Radial Flow kA dp q 2 1 dr where q flow rate k permeability A cross sectional area perpendicular to flow fluid viscosity p pressure r radial distance from center of well Undersaturated Oil Reservoirs Diffusivity Equation 1 k p p r c r r r t where fluid density c system compressibility k permeability porosity fluid viscosity p pressure r radial distance from center of well t time Diffusivity equation describes the pressure profile in the reservoir during production Undersaturated Oil Reservoirs Single phase Flow under Steady State Condition A well draining from a reservoir with an open boundary where the fluid withdraw from the well is balanced exactly by fluid entry across the open boundary p p wf q r ln 2 4 2 kh rw Skin Effects The Near Wellbore Damage The additional pressure drop required to achieve a given flow rate caused by the skin effect can be expressed as p s q s 2 5 2 kh Including skin effect with oil field units Eq 2 4 becomes pe p wf 141 2qB re ln s 2 8 kh rw Table 1 1 Typical Units for Reservoir and Production Engineering Calculations Variable Oilfield Units SI Conversion Multiply Oilfield Unit Area acre m2 4 04 103 Compressibility psi 1 Pa 1 1 45 10 4 Length ft m 3 05 10 1 Permeability md m2 9 9 10 16 Pressure psi Pa 6 9 103 Rate oil STB d m3 s 1 84 10 6 Rate gas MSCF d m3 s 3 28 10 4 Viscosity cp Pa s 1 10 3 Skin Effects Effective Wellbore Radius pe p wf 141 2qB re ln s 2 8 kh rw pe p wf r 141 2qB ln e s 2 11 kh rw e Define effective wellbore radius rw as rw rw e s 2 12 Eq 2 11 can be written as pe p wf 141 2qB re ln kh rw Impact of Skin Effects on Effective Wellbore Radius rw rw e s 2 12 Example s 10 rw 4 5 10 5 rw In contrast s 6 rw 403rw Positive skin factor decreases effective wellbore radius Negative skin factor increases effective wellbore radius Impact of Skin Effects on Well Productivity Oil well productivity index is defined as J q kh J D 1 6 p p wf r B For steady state flow to a vertical well JD 1 1 2 14 re re ln s ln rw rw Positive skin factor decreases effective wellbore radius Smaller effective wellbore radius results in lower well productivity Stimulation e g acidizing fracturing etc reduces skin thereby increasing effective wellbore radius and well productivity Undersaturated Oil Reservoirs Well Flowing Pressure Profile under Constant Rate Production Undersaturated Oil Reservoirs Single phase Flow under Transient Condition During the initial pressure decline from p pi the pressure response in the reservoir is not affected by the outer boundary The system appears infinite in extent For radial flow of a slightly compressible constant viscosity fluid in an infinite acting reservoir the pressure profile can be described by 2 p 1 p ct p 2 20 2 r r r k t Undersaturated Oil Reservoirs Single phase Flow under Transient Condition 2 p 1 p ct p 2 20 2 r r r k t Solving Eq 2 20 for constant flow rate in field units yields pwf pi k 162 6qB 2 6 t log log 3 23 2 24 2 kh c r t w For constant bottom hole pressure in field units 1 kh pi p wf k 2 25 log t log 3 23 q 2 162 6 B ct rw Incorporating skin factor yields 1 kh pi p wf k 2 26 log t log q s 3 23 0 87 162 6 B ct rw2 Undersaturated Oil Reservoirs Single phase Flow under Pseudosteady State Condition The total effect of outer boundary has been felt Usually applicable to reservoirs with no flow boundaries which have been producing for some time Undersaturated Oil Reservoirs Single phase Flow under Pseudosteady State Condition From the radial diffusivity equation the pressure p at any point r in a reservoir of radius re under pseudosteady state is given by p p wf r2 141 2qB r ln 2 2 28 kh rw 2re At r re 141 2qB re 1 ln 2 29 kh rw 2 Since pe is usually unknown and the average reservoir p can be obtained from pressure buildup tests a more useful expression for pseudosteady state with skin effect s included would be pe p wf p p wf 141 2qB 0 472re ln s 2 34 kh rw Undersaturated Oil Reservoirs Wells Draining Irregular Patterns For pseudosteady state flow p p wf 141 2qB 1 4A s 2 44 ln 2 kh 2 C A rw Shape factors CA accounts for irregular drainage shapes or asymmetrical positioning of wells Undersaturated Oil Reservoirs Inflow Performance Relationship IPR IPR is the relationship between bottomhole pressure pwf and well flow rate q IPR combines what the reservoir can deliver q pwf 0 and what the imposed wellbore hydraulic would allow q pwf 0 Transient IPR in field units 1 kh pi p wf k 2 26 log t log 3 23 0 87 q s 162 6 B ct rw2 Pseudosteady State IPR in field units p p wf 141 2qB 0 472re ln s 2 34 kh rw Steady State IPR in field units pe p wf 141 2qB re ln s 2 8 kh rw Example 2 7 Transient IPR Using the well and reservoir data in Appendix A construct transient IPR curves for 1 6 and 24 months Assume zero skin and transient flow Solution For transient flow 1 kh pi p wf k 2 26 log t log q s 3 23 0 87 ct rw2 162 6 B From Appendix A k 8 2 md h 53 ft pi 5651 psi B 1 1 rb STB 1 7 cp 0 19 ct 1 29 10 5 psi 1 rw 0 328 ft Substituting into Eq 2 26 and rearranging yields q 2 16 5651 p wf log t 4 25 2 50 Next plot pwf vs q at different t in hours t one month 30 24 720 hours t two month 2 30 24 1 440 hours t three month 3 30 24 2 160 hours Example 2 8 Steady State IPR Influence of Skin Effect Assume that the reservoir described in Appendix A is flowing under steady state condition and pi pe 5651 psi Draw IPR curves for s 0 5 10 and 50 respectively Use a drainage radius re of 2980 ft Solution For steady state flow pe p wf 141 2qB re ln s 2 8 kh rw From Appendix A k 8 2 md h 53 ft pi 5651 psi B 1 1 rb STB 1 7 cp 0 19 ct 1 29 10 5 psi 1 rw …

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