Introduction to Well Stimulation

Transcription

1 Introduction to Well Stimulation PNGE 691A Ali Takbiri-Borujeni West Virginia University Fall 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 1 / 46

2 What is well stimulation? Main purpose Increase well productivity Increase ultimate recovery Approach Decrease damage Change the flow pattern Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 2 / 46

3 Production in high permeability formations Production behavior in a high permeability formation. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 3 / 46

4 Production behavior in low-permeability formations Production behavior in a low-permeability formation. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 4 / 46

5 Techniques Matrix treatment Removing the damage using acid and other chemicals Hydraulic fracturing Change the flow pattern using acid or proppant fracturing Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 5 / 46

6 Skin factor Skin factor: S = ( k k s 1)ln( rs ) Pressure drop caused by skin: P s = qbsµ kh Effective wellbore radius:,eff = e s Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 6 / 46

7 Skin factor Skin factor: S = ( k k s 1)ln( rs ) Pressure drop caused by skin: P s = qbsµ kh Effective wellbore radius:,eff = e s Skin does not mean damage. It means change in permeability in the vicinity of the wellbore. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 6 / 46

8 Productivity index Productivity index is the ratio of the rate of production to the pressure drawdown, J = q p, where, Therefore, q = kh µb (p e p w ) ln( re ) + s (steady state). J = kh µb(ln( re ) + s) (steady state flow) J = kh µbln( 0.472re ) + s (semi-steady state flow) Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 7 / 46

9 Flow efficiency, Ef Flow efficiency, E f, is defined as the ratio of the actual productivity index of the well (including skin) to the ideal productivity index (zero skin factor). E f = J Actual J ideal = kh µb(ln( re rw )+s) kh µb(ln( re rw )) = ln( re ) ln( re ) + s (steady state flow) E f = J Actual J ideal = kh µb(ln( 0.472re )+s) rw kh µb(ln( 0.472re )) rw = 0.472re ln( ) ln( 0.472re ) + s (semi-steady state) E f of 1 indicates an undamaged well and a E f < 1 indicates a damaged well. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 8 / 46

10 Matrix acidizing for productivity index improvement Effect of damage on well productivity. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 9 / 46

11 Example 1: Steady state reservoir flow Wellbore radius: Permeability of the reservoir: Permeability of the damaged zone: Damaged zone extension: Flow rate and thickness: Viscosity: Formation volume factor: ft 50md 10md 6 in 800 STBD and 50ft 0.7cp 1.1RB/STB Calculate the skin factor Calculate the apparent wellbore radius Calculate P s Flow efficiency if r e is 700ft Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 10 / 46

12 Solution to Example 1: Skin: S = ( k k s 1)ln( r s ) What is r s? Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 11 / 46

13 Solution to Example 1: Skin: What is r s? S = ( k k s 1)ln( r s ) r s = + ( 6 ) = = S = ( )ln( ) = 3.7 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 11 / 46

14 Solution to Example 1: Skin: What is r s? S = ( k k s 1)ln( r s ) r s = + ( 6 ) = = S = ( )ln( ) = 3.7 Effective wellbore radius:,eff = e s Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 11 / 46

15 Solution to Example 1: Skin: What is r s? S = ( k k s 1)ln( r s ) r s = + ( 6 ) = = S = ( )ln( ) = 3.7 Effective wellbore radius:,eff = e s,eff = 0.328e 3.7 = ft Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 11 / 46

16 Solution to Example 1: P s = qbµ kh s Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 12 / 46

17 Solution to Example 1: P s = P s = qbµ kh s = 128.7psi Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 12 / 46

18 Solution to Example 1: P s = P s = qbµ kh s = 128.7psi E f = re ln( ) ln( re ) + s Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 12 / 46

19 Solution to Example 1: P s = P s = qbµ kh s = 128.7psi E f = E f = re ln( ) ln( re ) + s ln( ) ln( ) = 0.67 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 12 / 46

20 Example 2: Semi-steady state reservoir flow Having the same well as the Example 1 but semi-steady state flow, we acidize the well to restore the original permeability of the skin zone. What is the folds of increase in J? Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 13 / 46

21 Example 2: Semi-steady state reservoir flow Having the same well as the Example 1 but semi-steady state flow, we acidize the well to restore the original permeability of the skin zone. What is the folds of increase in J? FOI = J stimulated J damaged = 0.472re ln( ) s ln( 0.472re ) 0.75 FOI = 1.53 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 13 / 46

22 Example 2: Semi-steady state reservoir flow Having the same well as the Example 1 but semi-steady state flow, we acidize the well to restore the original permeability of the skin zone. What is the folds of increase in J? FOI = J stimulated J damaged = 0.472re ln( ) s ln( 0.472re ) 0.75 FOI = 1.53 What if after the stimulation, skin equals -1? Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 13 / 46

23 Example 2: Semi-steady state reservoir flow Having the same well as the Example 1 but semi-steady state flow, we acidize the well to restore the original permeability of the skin zone. What is the folds of increase in J? FOI = J stimulated J damaged = 0.472re ln( ) s ln( 0.472re ) 0.75 FOI = 1.53 What if after the stimulation, skin equals -1? FOI = 700 ln( ) ln( ) = 1.79 What is k s in this case? Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 13 / 46

24 Example 2: Semi-steady state reservoir flow Having the same well as the Example 1 but semi-steady state flow, we acidize the well to restore the original permeability of the skin zone. What is the folds of increase in J? FOI = J stimulated J damaged = 0.472re ln( ) s ln( 0.472re ) 0.75 FOI = 1.53 What if after the stimulation, skin equals -1? FOI = 700 ln( ) ln( ) = 1.79 What is k s in this case? 1 = ( 50 k s 1)ln( ) k s = 625 md Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 13 / 46

25 Productivity index for gas reservoirs Flow equation in a gas reservoir: kh( p 2 p 2 w ) q = 1424 µ ZT ln( re ) + s J = q g µ Z p 2 pw 2 q = kh(m( p) m(p w f )) 1424T (ln( re ) + s) m = p p R p µz dp Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 14 / 46

26 Example 3 Suppose an undersaturated oil reservoir that k=5md, h=75ft, p e =5,000psi, B=1.1RB/STB, µ=0.7cp, r e =1,500ft, and =0.328ft. Develop a family of curves for productivity index ratio for k s /k ranging from 0.1 to 1 for damaged zone thickness from 1 to 12 inches. Develop a family of curves for productivity index ratio for k s /k ranging from 1 to 20 for damaged zone thickness from 1 to 50 ft (semi-log graph). Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 15 / 46

27 Solution Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 16 / 46

28 Matrix acidizing Matrix acidizing works very well for removing the damages, and increasing the productivity index by factors 2, 4,... However, stimulation of an undamaged well does not substantially increase the productivity index ratio. To increase the productivity index ratio of undamaged wells, we use hydraulic fracturing to change the flow pattern from radial to pseudoradial (elliptical) flow pattern. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 17 / 46

29 Hydraulic fracturing Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 18 / 46

30 Preliminary Post-Fracture Production Estimates The initial step for estimating the post-treatment oil and gas production is to use pre-treatment formation evaluation data. The procedure is to use a combination of propped fracture penetrations and fracture conductivities that optimize post-fracture production behavior. Estimating post-fracture production can be done using Type curves (FOI charts for semi-steady state reservoir flow or transient reservoir flow type curve charts) Reservoir simulation/stimulation software Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 19 / 46

31 Graphical representation of FOI They provide a visual perspective about the interdependence and relative effects of parameters. This approach is used to determine fracture conductivity and fracture penetration design targets that optimize post-fracturing production. They are important for understanding the fundamentals of reservoir behavior from a well that has been fracture treated. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 20 / 46

32 Essential parameters Formation permeability Effective propped fracture penetration, i.e., from wellbore to tip (half-length) Effective fracture conductivity: K f w fp Dimensionless penetration ratio: I x = 2X f X e Dimensionless conductivity ratio:c D = K f w fp KX f Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 21 / 46

33 Production estimates for semi-steady-state reservoir flow These charts can provide initial guidelines for determining approximate treatment size, materials, and other treatment variables, such as injection rates and proppant staging schedule. Prats Holditch McGuire & Sikora Tinsley Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 22 / 46

34 Tannich and Nierode Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 23 / 46

35 All charts are applicable to Single, palanar fractures that propagate symmetrically about the wellbore Fracture conductivity over the entire net pay Assumptions concerning the shape of the reservoir Radial reservoir flow for Prats and Tinsley Flow from square reservoir for McGuire & Sikora and Holditch Conditions/assumptions pertinent to applying the charts Normalized on net pay Fracture conductivity vertical extent equals net pay vertical extent Semi-steady state, radial flow No near-wellbore formation damage Only Tannich and Nierode applies to non-darcy fracture flow Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 24 / 46

36 All charts are applicable to Single, palanar fractures that propagate symmetrically about the wellbore Fracture conductivity over the entire net pay Assumptions concerning the shape of the reservoir Radial reservoir flow for Prats and Tinsley Flow from square reservoir for McGuire & Sikora and Holditch Conditions/assumptions pertinent to applying the charts Normalized on net pay Fracture conductivity vertical extent equals net pay vertical extent Semi-steady state, radial flow No near-wellbore formation damage Only Tannich and Nierode applies to non-darcy fracture flow None of these charts apply to well production during transient reservoir flow. Their applicability to oil formation permeability lower than 0.1 md and gas formation permeability below 0.01 md is questionable because it takes a long time before the wells to reach semi-steady sate flow. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 24 / 46

37 Insights: Tinnsley chart As reservoir permeability decreases, relative capacity increases, and higher values of FOI can be acheived with deeper penetration ratios. For relative capacity > 100, FOI is governed by fracture penetration. for relative capacity > 500, FOI remains constant. As reservoir permeability increases, relative capacity decreases, and fracture conductivity dominates. Effect of fracture penetration is minute on FOI and maximum acheivable values are FIO=2 or lower. Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 25 / 46

38 Prats chart J stim J orig = ln( re ) ln( re,eff ) If the dimensionless fracture conductivity is equal to 10 or greater, the hydraulic fracture will essentially act as if it is an infinitely conductive fracture. A well with x f = 50 ft will produce as if the well had been drilled with a 50 ft diameter drill bit. Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 26 / 46

39 Example 4 k f w x f k r e 2000 md 0.2 ft 200 ft 1 md 660 ft 0.5 ft What is C fd? What is effective radius wellbore? What is FOI? Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 27 / 46

40 Solution to Example 4 C fd = k f W kx f Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 28 / 46

41 Solution to Example 4 C fd = k f W kx f C fd = 1 200,eff 0.3 x f,eff = 60ft = 2 Therefore, FOI = Xe ln( ) ln( Xe,eff ) = ln( ) ln( ) 3 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 28 / 46

42 McGuire Sikora graph for determining FOI For a low permeability reservoir, k f w k is large, productivity can be increased by increasing the fracture length but not the fracture conductivity. For a high permeability reservoir, k f w k is low, increasing the fracture length does not help much! You can change the proppant type to increase the fracture permeability and increase the fracture conductivity and get higher FOI. Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 29 / 46

43 Proppant number Dimensionless Proppant Number, N prop, is a more appropriate way to express the relative size of a given treatment. N prop = 2K f V p KV r = I 2 x C fd where, V p is the propped fracture volume V r is the reservoir volume N prop represents the amount of resources spent on the treatment. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 30 / 46

44 Proppant number 1 q = J D = q = J P ( ) 2πKh J D p Bµ 1 ln (r e / ) s 1 Economides, M. J. and Martin, T.: Modern Fracturing, Enhancing Natural Gas Production, (hardbound) Energy Tribune Publishing, Houston, 2007 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 31 / 46

45 Proppant number Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 32 / 46

46 Proppant number Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 33 / 46

47 Optimum fracture geometry by proppant number The optimum fracture geometry is given by V f = hw p x f x f = C fd = k f w p kx f ( ) Kf V 1/2 2 wings,prop 2C fd,opt Kh ( CfD,opt kv 2 wings,prop w p = 2K f h ) 1/2 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 34 / 46

48 Application example 2 Place 240,000 lbm of proppant (pack porosity=0.35, specific gravity=2.65, and equivalent permeability = 60,000 md) into a 65ft-thick formation of 1.5-md effective permeability. Assume that 50% of the proppant goes to pay because of some height growth of the fracture to the adjacent shales. r e is 2,100 ft is ft s pre is 5 (s pre : skin factor before fracturing) Determine the maximum possible folds of increase and the optimum propped length and width. 1 Romero, D. J., Valko, P. P., & Economides, M. J. (2002, January 1). The Optimization Of The Productivity Index And The Fracture Geometry Of A Stimulated Well With Fracture Face And Choke Skins. Society of Petroleum Engineers. doi: /73758-ms Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 35 / 46

49 Solution The volume of proppant reaching the pay is 50% of the 240,000-lbm proppant volume: 1 240, 000 Mass of propp.(lb) 1 2 ( ) (1 0.35) The proppant number is Mass of propp. Vol. of proppant lb (ft 3 ) Vol. of proppant Bulk Volume = 1, 116ft 3 2(60, 000md) N prop = (1.5md ft 2 (1, 116ft) = π 65 ft) J D,max = FOI = J post J pre = J D,post = J D,max J 1 D,pre ln 0.474re rw +s pre = 6.1 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 36 / 46

50 Solution The volume of proppant reaching the pay is 50% of the 240,000-lbm proppant volume: 1 240, 000 Mass of propp.(lb) 1 2 ( ) (1 0.35) The proppant number is Mass of propp. Vol. of proppant lb (ft 3 ) Vol. of proppant Bulk Volume = 1, 116ft 3 2(60, 000md) N prop = (1.5md ft 2 (1, 116ft) = π 65 ft) J D,max = FOI = J post J pre = J D,post = J D,max J 1 D,pre ln 0.474re rw +s pre = 6.1 ( 0.5(1116 ft 3 ) 1/2 )(60, 000 md) x f = = 463ft 1.6(65 ft)(1.5 md) ( 0.5(1, 116 ft 3 ) ) w = = ft = 0.222in (65 ft)(463 ft) Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 36 / 46

51 Remarks from the proppant number graphs Reservoirs with low permeability (k 1md) ( ) kf V 1/2 ( 2 wings,prop CfD,opt kv 2 wings,prop x f =, w = 2C fd,opt kh k f h ) 1/2 Reservoirs with high permeability (k 1md) ( ) Kf V 1/2 ( 2 wings,prop CfD,opt KV 2 wings,prop x f =, w = 2C fd,opt Kh K f h ) 1/2 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 37 / 46

52 Post-fracture production: transient reservoir flow FOI terminology is not commonly used for fracturing tight formations. Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 38 / 46

53 Transient reservoir flow: Example Fracture penetration ranges from 500 to 2,500 ft, and fracture conductivity ranges from 500 to 2,000 md-ft in an oil producing reservoir. The fluid and reservoir properties are listed below: Property Value K 0.01md h 100ft φ 0.15 p e 5, psi p wf 1, psi Average flowing pressure (p a ) 3,01465 psi Oil properties Oil gravity 30 API Producing gas gravity 0.65 Producing GOR 100 ft 3 /STB Bubble point pressure 1000 psi Total compressibility /psi viscosity p e 2 cp viscosity p a 2.2 cp B 1.1RB/STB t D = K(md)t(hrs) φµ(@p e )C(1/psi)X f (ft 2 ) C r = w f K f (md ft) πx f (ft)k(md) 1 q D = K(md)h(ft)(p e p w ) 141.3q(BOPD)µ(@p a )B Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 39 / 46

54 Solution Fracture length = 500ft Time = 360 hrs Fracture conductivity = 500 md-ft t D = 9.6E-04 C D = 32 1/q D = 1.0E-01 q = 86 BOPD Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 40 / 46

55 Candidate selection for hydraulic fracturing The most important parameters for choosing the best candidate for stimulation: formation permeability fluid viscosity in situ stress distribution skin factor reservoir pressure reservoir depth condition of the wellbore formation thickness Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 41 / 46

56 Other benefits from well stimulation Connection to the natural fractures. Minimize pressure drawdown around the wellbore, which minimizes: Sand production Water and gas coning Well instability Paraffin and asphaltene generation Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 42 / 46

57 Homework: Due next week For a undersaturated oil reservoiith steady-state reservoir flow: Variable Value K 0.5md h 75ft p e 5000psi B 1.1RB/STB µ 0.7cp r e 1500ft 0.328ft 2000 psi p wf Calculate the post fracturing production rate with C D = 5and X f = 500ft. Compare the results with a pre-treatment skin of 10. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 43 / 46

58 Homework: Due next week Semi-steady state flow calculations: Calculate FOI and post-fracture production using Prat, McGuire & Sikora, Holditch, and Tinsley charts. Variable Value Pre-fracture production rate q 100 BOPD Well spacing A 160 acres Formation permeability K 0.5md In-situ closure stress 4,900 psi Formation temperature T f 150 F proppant size 20/40 mesh proppant type Ottawa sand Proppant concentration 2.5 lb/ft 2 Propped fracture width W fp ft Undamaged fracture permeability K f 80 Darcys Fracture permeability damage factor 50% Propped fracture conductivity K fp W fp 910 md-ft Propped fracture half-length X fp 1,000ft Propped fracture height H fp Entire vertical net pay Reservoir static pressure P e 5000psi Formation volume factor B 1.1RB/STB r e 1,489ft 0.5ft Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 44 / 46

59 Homework: Due next week Semi-steady state flow calculations: Calculate FOI and post-fracture production using Tanich and Nierode chart. Data are the same as previous homework. Following additional data applies to gas reservoir: Variable Value Pre-fracture production rate q 100 MCFD Reservoir static pressure P e 3,500 psig Wellbore producing pressure P w 3,000 psig Gas compressibility factor Z Gas specific gravity γ g 0.65 Gas viscosity µ cp Fracture non-darcy factor (atm.s 2 /gm) β b/(k f ) a a 1.54 b 2.65 In equation β = b/(k f ) a, K f must be in Darcies. Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 45 / 46

60 References Essentials of Hydraulic Fracturing, Veatch, King, and Holditch, PennWell, 2018 SPE 1618-G SPE 1575-G SPE SPE 6838-PA SPE 1900-PA Ali Takbiri-Borujeni PNGE 691A: Introduction to Well Stimulation 46 / 46