TAMU PETE 662 - Ch 5 (40 pages)

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Ch 5



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Ch 5

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Pages:
40
School:
Texas A&M University
Course:
Pete 662 - Production Engineering
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PETE 662 Production Engineering Chapter 5 Production from Horizontal Wells Vertical Well Flow Pattern re pwf pe Top View Cross Sectional View Radial drainage pattern Horizontal Well Flow Patterns Heel Toe Combination of radial linear and elliptical drainage patterns Horizontal Wells Advantages Over Vertical Wells Larger and more efficient drainage pattern leading to increased overall hydrocarbon recovery efficiency Increased production rate due to greater wellbore length exposed to the pay zone Reduced water and gas coning resulting from reduced drawdown in the reservoir for a given production rate Reduced pressure drop around the wellbore Lower fluid velocities around the wellbore A general reduction in sand production from reduced pressure drop around the wellbore and the resulting low fluid velocities around the wellbore Horizontal Wells Important Factors Affecting Well Productivity Vertical permeability low vertical permeability or discontinuities detrimental to productivity Permeability anisotropy in horizontal plane higher well productivity from horizontal wells drilled normal to the large horizontal permeability direction Direction of maximum horizontal stress direction of maximum horizontal permeability the same as that of maximum horizontal stress Horizontal Wells Steady State Inflow Performance Joshi Model z y z plane x y qv x y plane qh Horizontal Wells Steady State Inflow Performance Joshi Model Integrating flow long the x y plane over the thickness h yields qh 2 k p a a L 2 Bo ln L 2 2 2 5 1 Assumptions made in deriving Eq 5 1 elliptical drainage area with length of major axis 2a constant pressure at the drainage boundary Horizontal Wells Steady State Inflow Performance Joshi Model Integrating flow long the y z plane over the well length L yields qv 2 k p 5 2 h Bo ln 2rw Assumptions made in deriving Eq 5 2 Radial flow from the vertical boundary located 2 h from the well Pressure at the boundary pressure at the elliptical horizontal boundary Horizontal Wells Steady State Inflow Performance Joshi Model p q p q v p q h From Eq 5 1 and Eq 5 2 for an isotropic formation we obtain q 2 k H h p a a 2 L 2 2 Bo ln L 2 h h ln L 2rw 5 3 Horizontal Wells Steady State Inflow Performance For an anisotropic formation Eq 5 3 becomes Economides et al k H h pe p wf q a a 2 L 2 2 141 2 Bo ln L 2 where I ani I h I h ani ani ln L rw I ani 1 5 4 kH 5 5 kV Note Eq 5 4 was derived assuming the horizontal well is centered in the drainage volume Horizontal Wells Steady State Inflow Performance Rearranging Eq 5 4 we obtain the following IPR equation based on Joshi s Model p wf 2 141 2qBo a a 2 L 2 pe ln kH h L 2 I h I h 5 7 ani ani ln r I 1 L w ani To account for that the ends of the horizontal well are the foci of the ellipse in the horizontal plane by equating the areas of the ellipse to that of a cylinder of radius re Joshi developed the following equation to relate with re 4 0 5 L r a 0 5 0 25 eH 2 L 2 0 5 5 6 Example 5 1 Well Performance with Joshi Model A 2000 ft horizontal lateral is producing from a 100 ft thick reservoir where kH 10 md kV 1 md The lateral has an rw 3 in draining from a region 4000 ft in the direction of the well where pe 4000 psi o 5 cp Bo 1 1 Determine q when pwf 2000 psi Solution p wf 2 141 2qBo a a 2 L 2 pe ln kH h L 2 I ani a I h I h ani ani ln 5 7 L rw I ani 1 kH 10 3 162 5 5 kV 1 4000 2000 ft 2 Substituting in Eq 5 7 and consolidate yields p wf 4000 1 74q 5 9 From Eq 5 9 q 1149 STB d when pwf 2000 psi Example 5 1 Well Performance with Joshi Model Solution cont d p wf 4000 1 74q 5 9 Horizontal Wells Steady State Inflow Performance Furui et al Model In the cross sectional area perpendicular to the wellbore Furui Model assumes radial flow in the near wellbore region and linear flow beyond that Horizontal Wells Steady State Inflow Performance Furui et al Model p r p r p l r 2 I ani q 5 11 ln t 2 kL rw I ani 1 where k k H kV 5 12 rt y t 2 pl 2 I ani h 5 14 2 q 2 y b y l 5 13 kI ani hL p p r pl 5 10 Horizontal Wells Steady State Inflow Performance Furui et al Model p r p l p p r pl 5 10 Combining consolidating Eqs 5 11 5 12 5 13 514 and substituting into Eq 5 10 yields p 2hI ani q ln y b h I ani 2 5 17 2 kL rw I ani 1 I ani Horizontal Wells Steady State Inflow Performance Furui et al Model Defining skin factor as p skin q s 5 18 2 kL With skin included Eq 5 17 becomes p 2hI ani q ln y b h I ani 2 s 5 19 2 kL rw I ani 1 I ani Solving for q using field units we obtain q kL pe p wf hI ani y 141 2 Bo ln L 1 224 s rw I ani 1 hI ani 5 20 Including partial penetrating skin sR Eq 5 20 becomes q kb pe p wf hI ani y 141 2 Bo ln b 1 224 s s R rw I ani 1 hI ani where b is the total length of the reservoir 5 21 Example 5 2 Well Performance with Furui et al Model A 2000 ft horizontal lateral is producing from a 100 ft thick h 100 ft reservoir where kH 10 md kV 1 md The lateral has an rw 3 in draining from a region 4000 ft in the direction of the well where pe 4000 psi o 5 cp Bo 1 1 Determine q when pwf 2000 psi Solution q kb pe p wf hI ani y 141 2 Bo ln b 1 224 s s R rw I ani 1 hI ani 5 21 k k H kV 10 1 3 162 md kH 10 3 162 kV 1 I ani 2 2 2 2 b L 4000 ft 2000 ft yb 1732 ft 2 2 2 2 q 912 STB d Horizontal Wells Pseudosteady State Inflow Performance Babu and Odeh Model z x y The well can be in any arbitrary location in the reservoir provided that it lies in the x direction and not too close to any boundary Horizontal Wells Pseudosteady State Inflow Performance Babu and Odeh Model z x y Babu and Odeh Inflow Equation q k y k Z b p p wf A0 5 ln C H 0 75 s …


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