Mass‐Balance in the Fracture Efficiency η = Vfrac/Vinj Vinj = Vfrac + Vloss Vpad 1 ‐ η = Vinj 1 + η Vpad = Vloss ‐ Vfrac 2 Design Parameters to find: ww= 2RΔPnet πE Pnet,w E R3 = ηV E’ ΔPnet E’ = 4(1 – ν2) h f efficiency η Exercise 3‐1 ΔP tc Fluid‐Efficiency, η: from closure Θme Fracture Height from sonic log or assume Radial fracture: H=2L 6 Total Volume and Pad volume ¥ Determine opΘmum fracture length based on S= ‐5 = ln(2rw/Lf) ¥ Calculate Volume to be pumped to achieve L 2ΔP 3ΔP hL R net E’ net or V = V = R = ηV inj inj ηE’ ηE’ ΔPnet Calculate Pad Volume Vpad 1 ‐ η = Vinj 1 + η 7 Proppant stage ¥ Calculate Fracture Volume = proppant Volume η = Vfrac/Vinj 1 gallon sand = 13.5 lbs 1 m3 sand = 1610 kg Calculate proppant ramp ‐ Nolte 8 C f What happens if the fracture is ‘full’ ¥ Stop pumping Ð Job done ¥ ConΘnue pumping sand ‐> ‘Tip Screen‐out’ Ð If you need more width Ð Pressure will increase KW‐13 Step Down Test 7000 6000 5000 4000 3000 2000 1000 0 25 27 29 31 33 35 37 20 Group Exercise Day 4 Near Wellbore Issues Pretend we have no BHP data! Use file: Day 4‐1 Group exercise tab: step down test Start with KW‐13; repeat with KW12 Fill‐in red dark blue cells Determine slope YES/NO? Check with BHP step Rate test; last tab 21 Group Exercise Day 4 Near Wellbore Issues ¥ Use file Day 4 exercise KW‐13 Minifrac: tab 1st step down test. ¥ Plot pump rate vs BHP‐ISIP ‐> slope? BHP THP Pump rate 22 Group Exercise Day 4 Near Wellbore Issues For KW‐13 a sand slug has been pumped! Use file: Day 3 Exercise 1‐1 tab: 2st step down test Fill‐in red dark blue cells Determine slope YES/NO? What did you see? Check with BHP data 23 Well KW‐13 2850 Depth (m) 2860 2870 2880 2890 2900 0.8 0.7 0.6 Stress gradient (psi/φ) 24 Well KW‐12 25 Stress Profile well KW‐13 2850 Depth (m) 2860 2870 2880 2890 2900 0.8 0.7 0.6 Stress gradient (psi/φ) Stress Profile well KW‐12 ‐ 2900 ‐ 3000 ‐ 3050 0.7 0.6 0.5 psi/φ Depth (m) Depth (feet) ‐ 2950 Proppant properΘes 28 Nolte (SPE 12941) Simplified PKN model to include a fracture efficiency factor η and a fluid‐loss Θme funcΘon g(tD). For a small radial fracture: 2RΔPnet πE’ ww= E’ R3 = ηV ΔPnet Vpad 1 ‐ η = Vinj 1 + η E E’ = 4(1 – ν2) “SoluΘon” 1. Find OpΘmum Frac Length assume S=‐5 S=ln(2rw/Lf) L 2. Find minimum frac width FCD=kfwf/krL >10 3. EsΘmate efficiency from closure Θme 4. Find Pnet from minifrac 5. Compute pump Volume for opΘmum Length from mass balance with Pnet 6. Es>mate fracture width for this Pnet. Is this enough? 7. Calculate pad Volume from efficiency 8. Calculate proppant ramp and Volume in lbs if 1 gal of sand weights 13.5 lbs 9. Recommend strategy to solve near well bore issues “SoluΘon KW‐12” 1. Find OpΘmum Frac Length IPR curve Skin L Skin = ‐5 = ln(2rw/Lf) 2rw/Lf =e‐5 Lf = 100 m = 300 Σ 2. Find minimum frac width FCD=kfwf/krL >10 Wf = 10krL/kf = 0.012 Σ = 0.15” = 0.4 cm = 1.2 lb/Σ2 for 20/40 mesh sand 3. EsΘmate efficiency from closure Θme tc = 11 min tp = 18 min tc/tp = 0.6 η = 0.33 4. Find Pnet from minifrac Pnet= 200 psi = 1.4Mpa 5. Compute pump Volume for opΘmum Length from mass balance with Pnet V = hL2 Pnet/η E’ = 100x1002 1.4/0.33 9000 = 470m3 =3000 bbl 6. Es>mate fracture width for this Pnet. Is this enough? w = 2RPnet/πE’ = 1 cm 7. Calculate pad Volume from efficiency Vpad= (1‐η /1+η ) Vinj = 0.50 x 470= 235m3 = 1500 bbl 8. Calculate proppant ramp and Volume in lbs Cp(t) = Cf(t‐tpad)/(ti‐tpad) ε Vprop= ηVi = 0.33 x 120 = 1660 gal = 23285 lbs No tortuosity issues in KW‐12 1 gallon of sand = 6.25 kg = 13.7 lbs “SoluΘon KW‐13” 1. Find OpΘmum Frac Length IPR curve Skin L Skin = ‐5 = ln(2rw/Lf) Lf = 100 Σ = 33 m 2. Find minimum frac width FCD=kfwf/krL >10 Wf = 10krL/kf = 0.05 Σ = 0.6” = 1.5 cm = 4.6 lb/Σ2 for 20/40 mesh sand 3. EsΘmate efficiency from closure Θme tc = 12 min tp = 12 min tc/tp = 1 η = 0.42 4. Find Pnet from minifrac Pnet= 300 psi = 2.0 Mpa 5. Compute pump Volume for opΘmum Length from mass balance with Pnet V = R3 Pnet/η E’ = 333 2.0/0.42 9000 = 20m3 = 130bbl 6. Es>mate fracture width for this Pnet. Is this enough? w = 2RPnet/πE’ = 0.5 cm 7. Calculate pad Volume from efficiency Vpad= (1‐η /1+η ) Vinj = 0.42 x 20= 8.5m3 = 55bbl 8. Calculate proppant ramp and Volume Cp(t) = Cf(t‐tpad)/(ti‐tpad) ε Vprop= ηVi = 0.42 x 130 = 2300 gal = 31000 lbs Tortuosity issues in KW‐13. include sand slug in prepad KW‐12 Pumping Schedule 16 14 Prop Conc. (ppg) 12 10 8 6 4 2 0 0 2 4 6 8 10 Elapsed Time (min) 12 14 16 18 20 WK-13 Main Fracjob 9000 140 8000 120 THP (psi) 7000 100 5000 80 4000 60 3000 40 2000 20 1000 time (min) 0 50 10 100 20 150 25 200 30 35 250 40 300 Pump Rate(bpm) 6000 ... 20 58 19 12 0 0 .16 0 .50 0.334 4 .5 0. 25 0.42 28.0 35 5. 30 0 .12 0.78 0.334 5 0. 25 4 .5 0. 65 0. 619 1. 93 4.72 0.606 2.0 1. 8 0.606 2 .13 2.99 0.6 15 2.29 2. 91 10 0 10 00 750 ... 400 53 0 0.334 2. 15 0. 25 E‐06 (/psi) E+03m3/d E+03m3/d KW 13 313 0 2672 222.2 0. 65 32 45 1 .50 0. 15 0.79 0.334 5 0. 25 4 .5 0. 65 15 19 KW 13 Step Down Test 7000 6000 50 00 ... Well PotenΘal‐Pre frac 11 /29/ 15 m tvd m tvd bara o C m m md fract fract φ E+6psi/‐ KW‐07 2926 4790 85 KW‐02 2 750 2700 40 KW 12 313 0 2620 239.4 10 4 10 9 11 0 10 0 2 50 360 0 .12 0.80