Lesson 9 Gasified Liquid Hydraulics

Lesson 9 Gasified Liquid Hydraulics - PETE 689...

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Unformatted text preview: PETE 689 Underbalanced Drilling (UBD) Lesson 9 Lesson 9 Gasified Liquid Hydraulics Read: UDM Chapter 2.7 Pages 2.131­ 2.179 Harold Vance Department of Petroleum Engineering Gasified Liquid Hydraulics Gasified Liquid Hydraulics Reynolds number. Multi­phase flow. Pressure prediction: Hole static pressure. Circulating pressure. Bit pressure drop. Hole Cleaning. Harold Vance Department of Petroleum Engineering Reynolds Number Reynolds Number In practice the flow of gasified liquid is almost always turbulent (Reynolds number > 4,000). Example water flowing up an 8½” hole with 5” drillpipe. Harold Vance Department of Petroleum Engineering Reynolds Number Reynolds Number Annular velocity of 7 ft/min would be sufficient for turbulent flow. AV’s > 100 ft/min are common in gasified liquid drilling. Harold Vance Department of Petroleum Engineering Reynolds Number Re = 15.47 DhρwVan 15.47 D µ 2 .58 Where: Dh hydraulic diameter of the annulus (the difference between the hole and pipe diameters) (inc). ρw liquid density (ppg). Van average annular velocity (ft/min). μ liquid viscosity (cP). Harold Vance Department of Petroleum Engineering Reynolds Number The consequences of turbulence in the annulus is that the rheology of gasified fluids has little effect on the annular pressure profile. This is at least true with un­ viscosified base fluid and annular velocities are high. Harold Vance Department of Petroleum Engineering Multi­phase Flow Multi­phase Flow At least three phases are present in the wellbore annulus. Liquid, gas and solids (cuttings). Liquids could be: Mud. Oil. Water. Harold Vance Department of Petroleum Engineering Flow Regimes Flow Regimes Bubble Flow Slug Flow Churn Flow Annular Flow Flow Regimes for Two­Phase, vertical, Upward Fluid Flow Harold Vance Department of Petroleum Engineering Flow Regimes Flow Regime Map for Water/Air Mixture in Upward Flow Harold Vance Department of Petroleum Engineering Flow Regimes Horizontal flow patterns GAS (a) Bubble (a) Bubble GAS (e) Slug GAS GAS (f) Semi­Annular (b) Plug GAS GAS (c) Stratified (g) Annular GAS (h) Spray (d) Wavy Harold Vance Department of Petroleum Engineering Pressure Prediction Pressure Prediction HSP Annular friction. Bit pressure drop. Mud. Gasified mud. Drillstring pressure drop. Mud. Gasified mud. Harold Vance Department of Petroleum Engineering HSP HSP 144 ∫ P1 P2 VdP + h = 0 2.59 Where: V specific volume of the fluid (ft3/lbm) P pressure (psia) P1 pressure at the top of the column (psia). P2 pressure at the bottom of the column (psia). H height (feet) Harold Vance Department of Petroleum Engineering HSP In oilfield units, assuming ideal gas behavior 14.7S (Tavg + 460) Vm = 5.61 + 520P 2.60 M = 42MW + 0.0764GS 2.61 Where: Vm total volume (ft3) of gas/bbl liquid at pressure. P pressure (psia). Tave average temperature (oF). M mass of mixture (lbm/bbl) of liquid. S volume of gas (scf/bbl) of mud. G gas gravity. MW mud weight (ppg). Harold Vance Department of Petroleum Engineering HSP HSP For a static column of mixed gas and liquid in a well of depth, h, Equation 2.59 can be rewritten as: 1 2117S (Tavg + 460)dP 1 P1 P1 h = 808dP + M P2 M 520P P2 ∫ ∫ 2.62 Harold Vance Department of Petroleum Engineering Gas Volume Gas Volume This can be integrated an re­ arranged to find S, the volume of gas (scf/bbl of liquid) S = 808 (Pb – Ps) – 42 hMW 0.0764h – 4.071 (Tavg + 460)ln (Pb/Ps) Where: 2.63 Ps surface pressure (psia). Pb desired bottomhole pressure (psia). Harold Vance Department of Petroleum Engineering Friction Forces Friction Forces When the fluid column is flowing up the annulus, work is done against friction between the fluid and the annular walls (the hole wall, the casing’s inside surface, and the drillstring). Neglecting acceleration, the pressures at the top and bottom of a vertical flowing column of fluid are related to the fluid’s specific volume, the height of the column and the energy lost to friction, Wf , by: ∫ P1 144 VdP + h + Wf = 0 P2 2.64 Harold Vance Department of Petroleum Engineering Fanning Friction Factor Fanning Friction Factor Poettmann and Bergman related Wf to a fanning friction factor, f: Wf = 2.85 x 10­9fQ2V2mavg (Dh + Ds)2 (Dh – Ds)3 2.65 Where: Q flow rate of liquid (gpm). Vmavg integrated average of Vm between the surface and the bottomhole pressures (ft3/bbl). Dh hole diameter (inches). Ds drillstring diameter (inches). Harold Vance Department of Petroleum Engineering This relationship implies that an average friction This Factor is taken to represent frictional effects up the full length Of the annulus. Substituting Equation (2.65) into Equation (2.64) and integrating, the following relationship between well depth, surface and bottomhole pressures is obtained: 808 (Pb­Ps)+4.071(Tavg+460)ln(Pb/Ps) h= 2.85x10­9fQ2Vmavg2 (42MW+0.0764GS) 1+ (Dh+Ds)2(Dh­Ds)3 Harold Vance Department of Petroleum Engineering Reduced Reynolds Number Reduced Reynolds Number Poettman and Carpenter, 1952 15, determined the friction factor, f, using a correlation with a reduced Reynolds number for flow of gas and liquid mixtures up gas wells. The reduced Reynolds number, RePC was defined (in oil field units) as: 5.16x10­6MQ RePC = Dh + Ds 2.67 Where: Q liquid flow rate, stock tank (gpm). Harold Vance Department of Petroleum Engineering Reduced Reynolds Number 100 Friction Factor, f 10 1 0.1 0.01 0.001 1 10 100 Reduced Reynolds Number, RePC Correlation between friction factor, f, and the reduced Reynolds number, RePC (after Poettmann and Carpenter, 195215). Harold Vance Department of Petroleum Engineering Gas Volume Gas Volume This correlation and equation 2.66 were used to compute the required air injection rate to give a BHP of 2,497 psi at 6000’ in an 8½” X 4½” annulus at 350 gpm. Required 14.9 scf/bbl Harold Vance Department of Petroleum Engineering Gas Volume Equation 2.63 was used to calculate the volume of air to give the same BHP static. Required 13.4 scf/bbl. Poettmann and Bergman concluded that the difference is insignificant and a reasonable calculation of air rate for the desired BHP could be done assuming a static fluid column. Harold Vance Department of Petroleum Engineering CUBIC FEET OF AIR AT 14.7 PSIA AND 600F PER BARREL OF NUC 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 AVERAGE FLUID COLUMN TEMPERATURE 1000 F (75­125) W’ =Actual Fluid Weight Pounds Per Gallon W = Desired Effective Fluid Weight Pounds Per Gallon 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Drilling Depth in Feet Air volumes required to achieve desired mud weight reductions; average fluid temperature 1000F (Poettmann and Bergman, 195514). Harold Vance Department of Petroleum Engineering Bit Pressure Drop Bit Pressure Drop Mud Red book Gasified Mud Harold Vance Department of Petroleum Engineering Bit Pressure Drop Bit Pressure Drop Gasified Mud G2 1 1 Pa = Pb + ­ gcA2n ρb ρa 2.68 Where: G mass flow rate of drilling fluid (lbm/s). An total flow area of the nozzles (feet). gc gravitational conversion factor (32.17 ft­lbm/lbf­s 2). ρ s fluid’s density above the bit (lbm/ft3). ρb fluid’s density below the bit (lbm/ft3). Pa pressure above the bit (psfa). Pb bottomhole pressure below the bit (psfa). This relationship neglects any energy loss through the nozzles due to frictional effects and any change in potential energy. Harold Vance Department of Petroleum Engineering Bit Pressure Drop Bit Pressure Drop Gasified Mud Substituting equation 2.44 for the density of a lightened fluid this becomes G2Fgo Po Po Pa = Pb + ­ gcAn2ρo Pb Pa 2.69 Where: Fgo volume fraction of gas in the liquid under standard conditions. ρo density of the fluid under standard conditions (pressure, Po) (lbm/ft3). Harold Vance Department of Petroleum Engineering Predicted Bottomhole Pressure (psia) 2000 1800 1600 1400 1200 Specifications Depth: 6000 feet Hole Diameter: 8 ½ inches Drill Pipe: 4 ½ inches Drill Collars: 6 ¼ inches Standpipe Injection 1000 800 600 400 200 0 0 100 200 300 400 500 600 700 800 900 1000 Air Rate (scf/bbl) Influence of gas and liquid injection rates on predicted bottomhole pressures. Harold Vance Department of Petroleum Engineering Oil Injection @ 200 Liters/min 139.7 m m (5­1/2”) Int. casing 120.7 m m (4­3/4”) Main Hz Hole 12 10 (1000kPa) Annular Bottomhole Pressure @ 2100m. 14 Optimum Point Minimum Achievable bottom Hole Pressure for Specific Liquid Rate 8 6 4 2 0 Hydrostatic Dominated Unstable Large Pressure Changes Gas Influx Reduces BHP Friction Dominated Nitrogen Wasting­Inefficient More Stable system Higher N2 rates or Gas Influx Increases BHP 0 10 20 30 40 50 Nutrition rate (stm3/min) Pressure Dominance in a Multiphase Fluid System (Saponja, 1995) Harold Vance Department of Petroleum Engineering Oil Injection 139.7 m m (5­1/2”) Int. Casing 120.7 m m (4 ¾”) Main Hz Hole 12 10 (1,000kPa) Annular Bottomhole Pressure @ 2,100m. 14 8 6 4 2 0 Optimum Points 0 10 20 30 40 50 Nitrogen Rate (m3/min) Optimum Condition for Different Liquid Circulation Rates (Saponja, 1995) Harold Vance Department of Petroleum Engineering Predicted Bottomhole Pressure (psia) 2500 2000 1500 Specifications Liquid Rate: 350 gpm Depth: 6,000 feet Drilled Diameter: 8½ inches Drillpipe: 4½ inches Drill Collars: 6¼ inches Parasite string at 2,000 feet 1000 500 0 0 100 200 300 400 500 600 700 800 900 1000 AirRate (scf/bbl) Comparison of bottomhole pressure predicted for drillstring (standpippe) and annular (parasite string) gas injection. Harold Vance Department of Petroleum Engineering 10 1 0.9 8 0.8 7 0.7 6 0.6 5 0.5 4 0.4 3 0.3 2 0.2 1 0.1 0 0 0 1000 2000 3000 4000 5000 6000 Gas Fraction Equivalent Circulating Density (ppg) 9 Measured Depth (feet) Predicted Equivalent circulating densities and gas volume fractions as functions of depth. Harold Vance Department of Petroleum Engineering 8000 7500 7000 6500 Annular Pressure (kPa) 6000 5500 Wiper Trip 5000 4500 4000 Hole Problems Hole cleaning Inadequate Hole Packed Off Not inidicated by Surface Pressure Bottomhole Pressure 3500 3000 2500 2000 1500 1000 500 0 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 1800 1900 Time (min) Comparison of dowhole and surface pressures (after Saponja, 1995 7). To convert from kPa to psi, multiply by 0.145. Harold Vance Department of Petroleum Engineering Hole Cleaning Hole Cleaning Settling velocity. Critical velocity. Settling velocity. Cuttings transport ratio. Harold Vance Department of Petroleum Engineering Settling Velocity Settling Velocity Vt = 92.6 dc ρc – ρf ρf 2.70 Where: ρc cutting’s density (ppg). ρb drilling fluid’s average density, at the prevailing temperature and pressure (ppg). Harold Vance Department of Petroleum Engineering Critical Velocity Guo assumed that the cuttings Guo concentration in the annulus should not exceed some critical value if hole cleaning problems were to be avoided. Vc = ROP/60Cc vc critical velocity, ft/min ROP rate of penetration, ft/hr Cc cuttings concentration, fraction Harold Vance Department of Petroleum Engineering Critical Velocity Taking the critical concentration as 4%, cuttings would need to travel uphole with a velocity 25 times greater than the penetration rate. For a penetration rate of 30 ft/hour, this corresponds to a velocity of 12.5 ft/min. Harold Vance Department of Petroleum Engineering 350 Mud Flow Rate (gpm) 300 250 200 150 100 50 0 0 1000 2000 3000 4000 5000 6000 7000 8000 Air Injection Rate (cfm) Gas and liquid injection rates required for efficient cuttings transport (after Guo et al.,199312) . Harold Vance Department of Petroleum Engineering Settling Velocity Settling Velocity With a large annulus, the AV may not be such that turbulent flow can be achieved. We would then need to alter the viscosity of the fluid. (ρc – ρf) 0.667 Vt = 175dc (ρf µ)0.333 2.72 Where: Vt terminal velocity (ft/m) dc average cutting's diameter (inches) ρc cutting’s density (ppg) ρ f fluid’s density above the bit (lbm/ft3) μ fluid’s effective viscosity (i.e. accounting for annular flow, cP) Harold Vance Department of Petroleum Engineering Settling Velocity Settling Velocity For a 0.25” cutting with a density of 21 ppg falling through a fluid of density of 5 ppg. Maximum AV = 15 ft/min. Settling velocity would have to be restricted to 17.4 ft/min at a penetration rate of 30 ft/hr. This would require an effective viscosity of 160 cP. Harold Vance Department of Petroleum Engineering Cuttings Transport Ratio Cuttings Transport Ratio CTR = Vt / Va Or Where: CTR cuttings transport radio / V ) CTR = 1 – (Vsl a Vt transport velocity, or velocity of the cuttings (ft/sec) Va cutting’s density (ppg) Vsl fluid’s density above the bit (lbm/ft3) Harold Vance Department of Petroleum Engineering Cuttings Transport Ratio The velocity of the system is normally the The mean velocity in the annulus determined by dividing the total flow rate of the various phases of the fluid by the cross­sectional area of the annulus. Va = M / (A) (ρf) Where: M = mass flow rate of fluid, lb/sec. A = cross­sectional area of the annulus, ft2 ρf = density of the fluid, lbm/ft3 Note: Harold Vance Department of Petroleum Engineering These units are for this equation only Cuttings Transport Ratio The CTR should be calculated throughout the annulus to ensure that adequate hole cleaning takes place at all points and that the cuttings are not packing off in the hole somewhere. A CTR of 1.0 implies perfect hole cleaning. If CTR>0 cuttings are moving upward. CTR should be >0.55 Harold Vance Department of Petroleum Engineering Example Example The following example suggested by Guo et all illustrates how the Charts can be used to arrive at an optimum solution for hydraulics. Example: Gasified­Fluid Hydraulics Solution Depth: 5,000 ft Hole size: 7 7/8­inc Max. ROP: 60 ft/hr Rotary Speed: 48 rpm D.P Diameter: 4½­inc Min. BHP (to avoid collapse):1,250 psi Harold Vance Department of Petroleum Engineering Example 1. Determine BHP requirements (given as 1,250 psi in this example). 2. Determine expected cutting size. ds = ROP/rpm = {(60 ft/hr)(12 in/ft)(1 hr/60 min)} / …. …{48 rev/min} = ¼ in. 3. Enter the figure 3­3­10 at BHP = 1,250 psi, and read the resulting intersection points with the curves for the four liquid flow rates to arrive at four combinations of liquid and gas rates that will give a BHP of 1,250 psi. Harold Vance Department of Petroleum Engineering 2500 H = 5.000 ft., Dh =7­7/5”, Cp = 4­½” Pbh, psi 2000 1500 1000 500 0 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 Qg. 1000 cfpm Flowing Bottomhole Pressure vs. Gas Injection Rate at 5.000 ft. (Guo et al., 1993). Harold Vance Department of Petroleum Engineering NOTE: A family of curves exists, each NOTE: member of which covers a different set of conditions. The additional curves are published in the Appendix of this manual along with the curve above, as Figures 3­ 3­10a through 3­3­10g. Mud Rate, gpm 100 200 300 400 Air Rate, scfm 400 1,000 2,000 4,000 Harold Vance Department of Petroleum Engineering 4. Plot the intersection points 4. determined in Step 3 on Figure 3­3­11. Connect the plotted points and determine the resultant intersection with the curve for ¼­in. diameter cuttings to be 230­gpm mud rate and 1,300­scfm air injection rate. Harold Vance Department of Petroleum Engineering MUD FLOW RATE. GPM 500 DEPTH 5000”, HOLE 7­7/5”, PIPE 4­1/2” 400 300 200 100 0 0 1 2 3 4 5 AIR INJECTION RATE, 1000 CFPM Mud Flow Rate vs. Air Injection Rate at 5,000 ft. (Guo et al., 1993). Harold Vance Department of Petroleum Engineering NOTE: A family of curves similar to NOTE: that above, each member of which describes a different set of conditions, has been published in the Appendix of this manual as Figures 3­3­11a through 3­3­11h. The flow and injection rates determined in Step 4 represent the circulation rates that should be employed to maintain a flowing BHP of 1,250 psi in this well while cleaning the hole adequately. Harold Vance Department of Petroleum Engineering THE END THE END Harold Vance Department of Petroleum Engineering ...
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