Fundamentals of Drilling Engineering

Conversions and Constants Considerations Nomenclature 2 3 1 kPa = 0.1450 psi 1 in = 2.54 cm 1 acre = 43,560 ft 1 m = 6.2898 bbl R = 459.67 + °F 1 lbm = 453.59 g Fluid Pressure Gradient Filtration Rate – API Tests Adjusting Weight with Barite Common Variables 2 2 3 1 MPa = 10 bar 1 ft = 0.3048 m 1 m = 10.764 ft 1 bbl = 5.6146 ft K = 273.15 + °C 푂퐷, 퐼퐷 = outer, inner diameter 1 bbl = 42 US gal °F = 1.8 °C + 32 훻푃 = 휌Τ144 [=] 푝푠𝑖Τ푓푡 푉30 = 2 푉7.5 − 푉푠푝 + 푉푠푝 푚퐵푎 = 42 푉푓 − 푉푖 휌퐵푎[=]푙푏푚 1 atm = 14.696 psi 1 mile = 5,280 ft 휌 = mud density[=]푝푝푔 3 푚 1 atm = 1.013 bar 1 ft = 7.4805 gal 1 cp = 1.0 mPa-s 휌[=] 푙푏 Τ푓푡3 푚 푉30 = API vol. collected at 30 mins 휌퐵푎 − 휌푖 푞 = flow rate[=] 푔푎푙Τ푚𝑖푛 6 2 푉푓 = 푉푖 [=]푏푏푙 휌퐵푎 = 35푝푝푔 1 bar = 1 x 10 dynes/cm 1 lbmΤgal = 0.052 psiΤft Standard Pressure = 14.696 psia 휌퐵푎 − 휌푓 훻푃Τ0.052 [=] 푙푏푚Τ푔푎푙 푉7.5 = volume collected at 7.5 mins 휎푦 = min. yield strength[=]푝푠𝑖 5 −3 2 1 Newton = 1 x 10 dynes 1 mD/cp = 6.33 x 10 ft /psi−day Standard Temperature = 60°F 퐸 = Young′s modulus Rotational Viscometer 푉푠푝 = spurt vol. collected at 0 mins Mud Quality Control −6 −9 2 3 6 1 dyne = 2.248 x 10 lbf 1 Darcy = 9.8692 x 10 cm Gas Constant = 10.732 psia ⋅ ft Τlbmol ⋅ R 푓 휌 − 휌 − 휌 + 휌 − 푓 휌 − 휌 퐸 = 30푥10 푝푠𝑖 for steel 휇 = 휃 − 휃 [=]푐푝 푉2 − 푉1 푠 퐵푎 푤 푚 푤 표 푤 표 Τ 3 600 300 푉 = 푉 − 푡 푓푙푔 = 3 3 1 hp = 0.7457 kw Water density at SC = 62.37 lbm ft 푠푝 1 1 휌퐵푎 − 휌푙푔 퐼 = moment of inertia 1 g/cm = 62.428 lbm /ft 푡2 − 푡1 푙푏푓 퐽 = polar moment ofinertia 1 hp = 33,000 ft ⋅ lbfΤmin Molar Mass of Air = 28.966 g/ 휏 = 휃 − 휇[=] 푓 = 푓 − 푓 휌 = 21.7푝푝푔 푦 300 100 푓푡2 When conducting HPHT test, 퐵푎 푠 푙푔 푙푔 1 kgΤl = 8.347 lbmΤgal VIG = 379.3 scfΤlbmol @ 14.696 psia 푆퐹 = safety factor 1 BTU = 778 ft ⋅ lbf M 푉푠푝 & 푉30 must be multiplied by WBM Maximum Solids Fraction Casing Design Rig Power Requirements Viscosity is Newtonian 4 due to smaller HPHT filter cell 퐷퐹 = design factor if yield point is zero, if 푓푠,푚푎푥 = 0.0289휌푚 − 0.139 푡 = pipe wall thickness[=]𝑖푛 not it’s plastic viscosity Recommended Clearance Ratio Hoisting Power Typical WBM In general, the OBM 푓푠,푚푎푥 is about 30% Drilling Fluid Considerations Hoisting Efficiency Clearance between 푊푣푏 퐶 퐼퐷표푢푡 − 푂퐷푖푛 Plastic Viscosity Limits 휃# = reading at # rpm tube centered in 0.13 ≤ ≤ 0.18 퐶 = 푃푖푛푝푢푡 = [=]ℎ푝 n E VAPI Limits for Yield Point 푂퐷 2 퐸(33,000) larger tube 푖푛 6 0.874 휇푚푎푥 = 2.94exp(0.164휌푚) Typical OBM/SBM −1.15 휏푦 = yield point 휏푦,푚푎푥 = 353휌푚 휏푦,푚푖푛 = 0.07휌푚 − 0.45 푊 = hook load[=]푙푏푓 8 0.841 푂퐷 = inside tube 푂퐷 퐼퐷 = outer tube 퐼퐷 푉푠푝 푚퐵푎 = Barite mass to add 푖푛 표푢푡 휇푚푖푛 = 1.58exp(0.171휌푚) 푣푏 = velocity ofblocks[=] 푓푡Τ푚𝑖푛 10 0.810 Altering suspended low 훾 solids normally keeps 휌퐵푎 = Barite density Mud Window and Casing Point Selection 퐸 = hoisting efficiency 12 0.770 휇 [=]푐푝 time mud parameters within recommended ranges 14 0.740 휌푖 = initial mud density[=]푝푝푔 Equivalent Mud Density 푛 = number of lines strung through blocks Routine Pipe Calculations Well Trajectory Surface Casing 휌푓 = final mud density[=]푝푝푔 Rotating Power Pumping Power Capacity and Volume Definitions 푓푙푔 = low gravity solids fraction DF 푤푇 푞푃푑 2 2 2 N = 0° N 푃 = [=]ℎ푝 퐻 = [=]ℎ푝 퐼퐷 푂퐷 − 퐼퐷 DF = Derrick Floor 휌푤 = base water [=]푝푝푔 푇 푖푛푝푢푡 퐶 = 퐶 = 33,000 1714휂 푝푖푝푒 푎푛푛푢푙푎푟 휌 = oil density[=]푝푝푔 1029.4 1029.4 270° 90° 표 휀 훼1 Intermediate Casing 푤 = 2휋푁[=] 푟푎푑Τ푚𝑖푛 푞 = flow rate[=] 푔푎푙Τmin 푀퐷1 푓 = fraction of total solids Τ 푠 푁 = rotary speed[=]푟푝푚 푃 = discharge pressure[=]푝푠𝑖 퐶[=] 푏푏푙 푓푡 푉[=]푏푏푙 퐼퐷, 푂퐷[=]𝑖푛 퐿[=]푓푡 180° Depth 푑 휀 = azimuth TVD 훼 = inclination 푓표 = oil fraction 푇 = rotary torque[=]푓푡 ⋅ 푙푏 휂 = overall pump efficiency 2 2 2 푓 퐼퐷 퐿 푂퐷 − 퐼퐷 퐿 KOP = Kick-Off Point 휌푙푔 = drilled low gravity solids 푉 = 푉 = 훼2 푃 = torque horespower normally 휂 = 0.9 푝푖푝푒 푎푛푛푢푙푎푟 2 푇 1029.4 1029.4 훽 = Dog Leg Angle 푀퐷2 휏푦,푚푎푥, 휏푦,푚푖푛 [=] 푙푏푓Τ100 푓푡 Pumps Production Casing Using Pipe Weight OD 푅 Rig Power Requirements KOP 푐 Pore Pressure Gradient Single Acting Pumps 2 푊 ID 훽 THD 푤 = angular velocity ”Bottom-Up” Casing Selection 푂퐷 푝푖푝푒 푅푐 Pore Pressure + Trip Margin 퐶푝푖푝푒 = − THD = Departure can also do 2 Well Trajectory Fracture Gradient 푞 = 0.0034 푑 푁 퐿 푁휂 [=] 푔푎푙Τ푚𝑖푛 1029.4 5.615휌푝푖푝푒 “Top-Down” Casing Selection 푝 푝 푠 푣 N Frac Gradient – Kick Margin 푅푐 = radius ofcurvature 푙푏푓 푙푏푚 5729.6 deg. BHL 푑푝 = plunger diameter[=]𝑖푛 푁푝 = number of plungers 퐷퐿푆 = [=] 푊푝푖푝푒[=] 휌푝푖푝푒[=] 3 푇푉퐷 = true vertical depth Common Bit Sizes Conventional Casing Strings 푓푡 푓푡 푅푐 100 푓푡 푁 = pump speed[=] 푠푡푟표푘푒푠Τ푚𝑖푛 퐿푠 = stroke length[=]𝑖푛 푀퐷 = measured depth 퐷퐿푆 = Dog Leg Severity Casing Size Common Bit CSG BIT 2 DF Departure

(OD in.) Sizes (in.) in. in. 휂푣 = volumetric efficiency which is usually between 0.8 − 0.9 푂퐷 푊푝푖푝푒 푇퐻퐷 = total horizontal distance Annular Space Annular 퐼퐷 = 24 − AnnularSpace 훼2 − 훼1 휀2 − 휀1 1 11 24 휋휌푝푖푝푒 훽 = 2arcsin sin2 + sin훼 sin훼 sin2 퐵퐻퐿 = bottom hole location 4 2 6,6 ,684 Down Hole Motors 2 1 2 2 1 3 Routine Pipe Calculations 5 624 ,6 7 6 1 7 8 Output Shaft Torque Cement 1 73 2 푊푝푖푝푒 = pipe air weight 5 2 7 ,888 푞휂푣훥푃 Leak-Off Test – Good Cement 731 5 푇 = 3.064 [=]푓푡 ⋅ 푙푏푓 Common Properties 24 Hour Compressive Strength (psi) Pumps 6 7,8,8882 8 8 푁 5 1 53 API Class A H Curing Temperature and Pressure (psi) 푞 = flow rate under load 훥푃 6 8 8,8,8284 훥푃 = 훥푃 through motor 푁[=]푟푝푚 휂 = volumetric efficiency Desired Pressure 7 1 푣 Reached Water (%) by 531 9 8 11 12 4 46 38 60°F 80°F 95°F 110°F 140°F Down Hole Motors 7 88 ,8 4 ,9 2 Cement Weight Key Notes on Motors Class A 0 0 800 1600 3000 5 75 푁 = shaft speed 7 8 9,10,1188 - Motor provides torque at the bit depending on 푞 and 훥푃 Water Cement 5.19 4.29 3000 4050 5500 6700 8400 5 1 (gal/sack) Drill String Considerations 8 8 1 1, 1 2 4 - A motor is a speed multiplier, adding to top drive or rotary speed 1 95°F 110°F 140°F 170°F 200°F 퐹 = drag due to friction 9 5 12,141 3 15 17 2 Slurry Density 퐷 8 44 - Torque from the motor helps the bit drill in highly deviated 15.6 16.4 Class H 800 1600 3000 3000 3000 (ppg) 푊 = traveling equipment 3 sections where it’s difficult to apply WOB Pressure Pipe Drill 푇퐸 10 4 15 Cement Slurry Yield 615 1905 2085 2925 5050 13 3 17 1 - 푞, 훥푃, and 푁 are interrelated and depend on how motor is made Pumping Shut-in & Bleed-off 1.18 1.06 푊퐵,퐷푆 = buoyed drill string 8 2 ft3Τsack 16 26 - If motor cannot supply the required torque to break rock, the 0 Time (mins) 20 훼 = hole inclination[=]deg 20 2 4 ,2 6 motor will stall and motor damage can occur Casing Loads 푇 = rotating torque Drill String Considerations 푊푐푟 = critical weight on bit Collapse Pressure Burst Pressure Worst Case Scenario for Collapse and Burst Casing Loads Weight Indicator Buoyed Pipe Weight Collapse: Lost Circulation During Drilling 푃푐 = 푆퐹 푃푒 − 푃푖 + 푃푇 푃푏 = 푆퐹 푃푖 − 푃푒 + 푃푇 푃푒 = external pressure 푊푖푛푑 = 푊퐵,퐷푆 + 퐹퐷 + 푊푇퐸[=]푙푏푓 푊퐵 = 푊 − 푊푓[=] 푙푏푓Τ푓푡 푊퐵 = 푊 1 − 휌푚Τ휌푝푖푝푒 푆퐹 = 1.125 푃푐 = 푆퐹 0.052휌푚 퐷 퐷 = csg shoe depth = 푓푡 푃퐵푅 = burst resistance 푃푖 = internal pressure 퐹 − value moving down 퐹 + value moving up Collapse resistance 퐷 퐷 푊 = pipe air weight 푊 = fluid weight 푊 = 푊 1 − 0.0153휌 Burst: Gas Kick Fills Casing 푓 퐵 푚 determined by four 2휎푦푡 푃푇 = 푃 due to temp change 푃 = 퐷퐹 Required Drill Collar Length different eqns based 퐵푅 Pressure high enough to fracture rock at shoe of the casing 퐹 = tensile load 푊퐵 = buoyed pipe weight 휌푚 [=]푝푝푔 휌푠푡푒푒푙 = 65.5 푝푝푔 푂퐷 푡 Τ 푆퐹 ⋅ 푊푂퐵 on the 푂퐷 푡 ratio 푃 = 푃 − 푃 푃 = 푃 inside casing at the surface 퐷퐹 = 0.875 푂퐷, 푡 = 𝑖푛 푖푆 푖퐷 푔 푖푆 푊 = casing air weight 퐿퐷퐶 = [=]푓푡 Buckling – Vertical Hole (more info: API Bulletin 5C3) 푊퐵,퐷퐶cos훼 퐷 = depth below bend 푃푖퐷 = 푃푓푟푎푐 + 훥푃푓푟푖푐 푃푖퐷 = pressure inside casing at D 푏 푊 = 1st order buckle = 1.94푚푊 [=]푙푏 Casing in Tension 푊퐵,퐷퐶 = buoyed drill collar 푊푂퐵 = weight on bit 푐푟,1 퐵,퐷퐶 푓 3 퐸퐼 퐹푇 = force due to temp change 훥푃푓푟푖푐 ≈ 0.015퐷 푃푓푟푎푐 = fracture pressure at D 푚 = 퐹푡 = 푆퐹 푊 퐷푏 + 퐹푇 + 퐹퐵[=]푙푏푓 푆퐹 = 1.8 퐹 = force due to bending Linear Pipe Drag 푊퐵,퐷퐶 퐵 푊푐푟,2 = 2nd order buckle = 3.75푚푊퐵,퐷퐶[=]푙푏푓 푃 훾 푃 = estimated 퐶퐻 gas column 푃 6퐾퐿 퐿 = 푓푡 푖퐷 푔 푔 4 퐷퐿푆 = dogleg severity 퐹 = 휇푁 = 휇퐹sin훼 퐹 = 퐹 − 푊 푗 푗 푃푔 = 0.0187퐷 퐷 푎푥 퐵 Critical WOB for deviated hole usually outside 휋 퐹퐵 = 64(퐷퐿푆)(푂퐷)푊 푇퐷 푇 = temperature at D[=]푅 퐼 = 푂퐷4 − 퐼퐷4 tanh 6퐾퐿 퐾[=]𝑖푛−1 퐷 퐾 = bending constant 푁 = normal force 퐹 = axial force 푗 푎푥 recommended range for effective drilling 64 Τ 퐾 = 푊퐷푏 퐸퐼 푇퐷 = 퐷훼푇 + 푇푠푢푟푓푎푐푒 훼푇 = local temperature gradient 퐿푗 = joint length 휇 = friction coefficient and is usually 0.15 − 0.6 Maximum Pull on Pipe Depth to Stuck Point Well Control 훥푃푓푟푖푐 = 푃 to overcome friction Rotational Pipe Drag 휎푦 훾 = gas specific gravity 퐹 = 퐴[=]푙푏 훥푙 Pressure Balance Kick Indicators Kick Control Methods 푔 푂퐷 max 푓 퐿 = 퐸 퐴[=]푓푡 푆퐹 훥퐹 - Flow rate/pit volume increase Driller’s Method Well Control 푇 = 휇 퐹sin훼[=]𝑖푛 ⋅ 푙푏푓 푃 = 푃 + 0.052휌 푇푉퐷 2 퐵퐻 푑푝 푚 푙푏푚 - Two circulations 휎푦 = pipe min. yield strength[=]푝푠𝑖 훥푙 = drill pipe stretch[=]푓푡 휌푚[=] - Pump pressure decrease along 푃퐵퐻 = 푃 at depth TVD = 푝푠𝑖 When rotating pipe up or down while 푃 = 푃 + 0.052휌 푇푉퐷 푔푎푙 with pump stroke increase 1. Circulate out kick 휋 퐵퐻 푐푠푔 푚 2. Kill the well 푃푑푝 = shut−in drill pipe 푃 circulating mud, the overall drag is 퐴 = 푂퐷2 − 퐼퐷2 [=]𝑖푛2 훥퐹 = incremental force pulled - Improper hole fill-up on trips normally reduced and not additive 4 against stuck drill pipe[=]푙푏푓 Weight & Wait 푃푐푠푔 = shut−in casing 푃 Post-Kick Calculations - Change in drill string weight - One circulation 훼 = average inclination angle 퐶푎푛푛푢푙푎푟 푏푏푙 Von Mises Effective Stress Criterion ℎ = = 푓푡 퐶 [=] - Unexpected drilling rate increase 1. Circulate out kick and kill well 푘푖푐푘 푉 푎푛푛 푓푡 푇푉퐷 = true vertical depth 2 푝푖푡 Circulating Pressures Equivalent Circulating Density 휋 2 휋 2 2 2 푚 = Barite mass to add 퐹푎푥 + 훥푃 퐼퐷 훥푃 푂퐷 퐹푎푥 + 훥푃 퐼퐷 훥푃 푂퐷 푇 푂퐷 푉푝푖푡 = mud pit gain[=]푏푏푙 퐵푎 휎 < 0.8휎 휎 = 4 − 4 + + 3 푃 = 푃 + 푃 푒 푦 푒 휋 휋 푖푐 푑푝 푐푠푟 훻푃 ⋅ 푇푉퐷 + 훥푃퐴푛푛 푃푟푠푣푟 = formation 푃 = 푝푠𝑖 푂퐷2 − 퐼퐷2 2푡 푂퐷2 − 퐼퐷2 2푡 2퐽 ℎ′ = ℎ cos훼 퐸퐶퐷 = [=]푝푝푔 4 4 푘푖푐푘 푘푖푐푘 푃푓푐 = 푃푐푠푟 휌푘푖푙푙Τ휌푚 0.052푇푉퐷 휌푘푖푙푙 = kill mud density 4 ℎ′ = true vertical height of kick 훥푃 = pump pressure to overcome pipe friction and bit nozzle losses[=]푝푠𝑖 퐽 = 2퐼[=]𝑖푛 푘푖푐푘 푉 = volume increase 푃푐푠푟 = circulating pressure Effective mud weight during 푖푛푐 at slow pump rate dynamic circulating conditions Hydraulics 푃푑푝 − 푃푐푠푔 푃푖푐 = initial circulating 푃 휌 = 휌 + [=]푝푝푔 푘푖푐푘 푚 ′ 푃 = final circulating pressure Pump Pressure Viscosity Hole Cleaning 0.052ℎ푘푖푐푘 Number of Pump Strokes 푓푐 훻푃 = mud pressure gradient If fluid is a Bingham Plastic, This eqn estimates the added mass of rock 푉푑푝 + 푉푑푐 푉[=]푏푏푙 푉푑푝,푎푛푛 + 푉푑푐,푎푛푛 2 2 푃푟푠푣푟 = 푃푑푝 + 0.052휌푚푇푉퐷 휌 푞 푣ҧ 퐿 calculate apparent viscosity 푆푇퐾푑푝 = 푆푇퐾푎푛푛 = 42푞 푞 [=] 푔푎푙Τ푠푡푟표푘푒 42푞 훥푃퐴푛푛 = frictional 푃 loss in 푃푝 = 4 + ෎ 푓휌 [=]푝푠𝑖 푚푟 = 푅푂푃 퐴푏휌푟표푐푘 1 − 휙 푝 푝 푝 6704 푑 25.8 퐷 휏 퐷 푃푟푠푣푟 annulus above point ofinterest 푒 푦 휌 ≥ [=]푝푝푔 1 휇푎 = 휇푝 + 6.66 푚푟 [=]rock mass per time 푘푖푙푙 푛 ൗ2 푣ҧ 0.052푇푉퐷 Pressures During Driller’s Method 푉푑푝 = drill pipe volume 2 푅푂푃 = rate of penetration[=] 푓푡Τℎ푟 Gas Kick circulated 푑 = equivalent nozzle diameter = ෍푑 푉푑푐 = drill collar volume 푒 푖 Reynold’s Number 푉 휌 휌 − 휌 across choke Drillstring 푖=1 2 3 푚 퐵푎 푘푖푙푙 푚 퐴푏 = bit area[=]푓푡 휌푟표푐푘 [=] 푙푏푚Τ푓푡 푚 = [=]푙푏 푞푝 = pump output 퐵푎 휌 − 휌 푚 Volume Annulus Volume 푑푖 = bit nozzle diameter[=]𝑖푛 퐷푣휌 퐵푎 푘푖푙푙 푃푖푐 푁Re = 928 If cuttings from shaker cleaned and 푆푇퐾푑푝 = strokes to fill drill pipe 휌[=]푝푝푔 푞[=] 푔푎푙Τ푚𝑖푛 푣ҧ[=] 푓푡Τ푠푒푐 퐿[=]푓푡 퐷[=]𝑖푛 휇 weighed as a function of time, a rough idea 푉푚 = total system mud volume = 푔푎푙 푃푐푠푟 푉푑푐,푎푛푛 = drill collar annular 푉 *units same as Pump Pressure of the state of cleaning can be obtained Optimizing Bit Hydraulics 푉푚 휌푘푖푙푙 − 휌푚 푃푐푠푔 푉푑푐,푎푛푛 = drill collar annular 푉 - Normally it’s only possible to optimize bit hydraulics 푁Re < 2100 : Laminar Flow Factors Influencing Deviated Hole Cleaning 푉푖푛푐 = [=]푏푏푙 42 휌퐵푎 − 휌푘푖푙푙 푆푇퐾 = strokes to fill annulus if drilling without a motor 푃 푎푛푛 푁 > 2100 : Turbulent Flow Pipe Flow Rate 푑푝 Re Eccentricity Hole 푃푓푐 - Adjust bit nozzle diameters to consume 64% of total Deviation Pipe Post-Kick Important Actions Hydraulics Mud Density Rotation Kick circulated 푃푝 across the bit to maximize hydraulic power Friction Factor - Record shut-in drill pipe pressure out of the well 푣ҧ = avg. fluid velocity in pipe Cuttings Hole Size Fluid - Adjust bit nozzles to consume 46% of total pump 푓 = friction factor 푓 = 푎푁−푏 Density Rheology - Record shut-in casing pressure 푃 pressure across bit to maximize jet impact force Re 푓푐 Pressure Annulus Volume 퐿 = pipe segment length - Record mud pit volume gain 훥푃푏푖푡푞 1.273퐻푃푏푖푡 ℎ푝 Laminar Turbulent ROP/Cuttings Generation Rate 퐷 = flow conduit diameter 퐻푃푏푖푡 = 퐻푆퐼 = 2 [=] 2 - If shut-in pressures increase over time, 1714 푑푒 𝑖푛 푎 = 16 푎 = 0.0791 Cuttings Size Sweeps reservoir fluid is gas 2nd Circulation 2nd Circulation 휇푎 = apparent viscosity[=]푐푝 Influence on Hole Cleaning Hole on Influence First Circulation Phase 푏 = 1 푏 = 0.25 푞[=] 푔푎푙Τ푚𝑖푛 퐻푃푏푖푡 = bit hydraulic horsepower Active Control in Field Practice (SPE 132372, 2010) - If not, kick is liquid Phase 1 Phase 2 휌푟표푐푘 = rock grain density Created by James Riddle with guidance from Dr. Paul Bommer and Dr. Matthew T. Balhoff Contact [email protected] with comments/suggestions Fundamentals of Production Engineering

Nomenclature Flow in Pipes Corrosion Corrosion Mechanical Energy Balance Friction Factor Reduces metal thickness which leads to a reduction in collapse, burst, and tensile forces 훥푚푎푠푠 = mass lost Liquid Flow Moody correlations based Corrosion Influences Approximate Material Selection Monitoring – Corrosion Coupon on Reynolds Number Consistent Units 1000 훥푡 = test duration Max Temp Corrosion Rate 2 푞휌 In general, hard metal ) Max Temp 392°퐹 25Cr- 휌 = coupon density 8푞 1 1 푔 퐿 100 482°퐹 푐 2 푁Re = 1.478 with large 휎푦 will corrode 50Ni-6Mo 훥푚푎푠푠 푚𝑖푙 푚𝑖푙 𝑖푛푐ℎ − + 푔퐿sin휃 + 푃2 − 푃1 + 2푣ҧ 푓 = 0 푎푡푚 25 Cr 퐴 = coupon surface area 휋2 퐼퐷4 퐼퐷4 휌 퐼퐷 퐼퐷휇 ( 25Cr-35Ni-3Mo Max Temp 퐶푅 = [=] = 푠 2 1 quicker than softer metal 10 13 Cr 휌 퐴 훥푡 푦푟 푦푟 1000 푦푟 with a smaller 휎 25 Cr 20Cr-35Ni-5Mo 572°퐹 푐 푠 Flow in Pipes 훾푔푞푠푐 푦 13 Cr duplex Kinetic energy Potential energy Expansion or Energy of 푁 = 20.09 1 duplex Τ Re 퐼퐷휇 22Cr-42Ni-3Mo 퐶푅[=] 푡ℎ𝑖푐푘푛푒푠푠 푙표푠푠 푡𝑖푚푒 푓 = friction factor vertical flow 휃 = 90° Compression friction Increases Corrosion Rate pressure 0.1 J-55 Pitting Rate 퐼퐷 = internal diameter[=]𝑖푛 Gas Flow Laminar Flow - Following variables increase L-80 Cr 0.01 N-80 Max Temp Τ Τ 퐿 = pipeline length[=]푓푡 Consistent Units partial C-90 푃푅 = 푑 훥푡 [=] 푚𝑖푙 푦푟 푃2 - Salt concentration 2 P-110 Cr-Mo 300°퐹 if 2 푁Re ≤ 2100 O 1E−3 T-95 not noted 푑 = deepest pit depth 훥푡 = test duration 훾 = gas specific gravity - Dissolved gas C 푔 푧푅푇 32푓퐿 푞푠푐 푧푇푃푠푐 Flow in pipes Q-125 - Dissolved CO 푀푊 = molar mass of air ඲ 푑푃 + 푔퐿sin휃 + 2 5 = 0 16 2 CR 푚𝑖푙Τ푦푟 PR 푚𝑖푙Τ푦푟 Severity 푎푖푟 훾 푀푊 푃 휋 퐼퐷 푃푇 훥퐾퐸 negligible 푓 = 1E−4 1E−3 0.01 0.1 1 10 100 1000 푔 푎푖푟 푠푐 - Dissolved H2S 휇 = fluid viscosity[=]푐푝 horizontal 푁Re H S partial pressure (푎푡푚) <1.0 <5.0 Low 푃1 휃 = 0° - Temperature 2 ′ 1.0−4.9 5.0−7.9 Moderate 푁Re = Reynold s number ത 2 푃 = 푧 푃 푃 = 푃 퐻 푆 푝푝푚Τ1푥106 Horizontal 훾푔푧ҧ푇푞푠푐 Turbulent Flow 퐶푂2 퐶푂2 퐵퐻 퐻2푆 퐵퐻 2 5.0−10.0 8.0−15.0 Severe 푃 = inlet pressure[=]푝푠𝑖 2 2 −4 Τ - Decrease in pH 1 푃2 − 푃1 = 1.0068푥10 5 푓퐿 + 퐼퐷ln 푃1 푃2 (in a smooth tube) >10.0 >15.0 Very Severe Gas Flow 퐼퐷 푧퐶푂2 = CO2 fraction 푃퐵퐻 = static bottom hole 푃[=]푎푡푚 푃 = outlet pressure[=]푝푠𝑖 2 푁 > 2100 푞 = liquid rate[=] 푏푏푙Τ푑푎푦 Inclined Gas Flow Re Scale 푞 = gas rate[=] 푀푠푐푓Τ푑푎푦 푓 푧ҧ푇ത푞 −0.0375훾푔퐿sin휃 0.0791 푠푐 2 푠 2 −3 푠푐 푠 푠 = 푓 = Calcium Carbonate Scale Sulfate Scale Tendencies 3 푃2 = 푒 푃1 + 2.685푥10 5 푒 − 1 0.25 휌 = fluid density[=] 푙푏푚Τ푓푡 퐼퐷 sin휃 푧ҧ푇ത 푁Re Calculate the Langelier Saturation Index (LSI) to predict scale Calculate the solubility (S) of the ion to predict scale 푇ത = avg. flowing temp[=]푅 Flow Control at the Surface 푝퐻 = pH at saturation 퐿푆퐼 = 푝퐻 − 푝퐻 푝퐻 = actual pH 2 푣ҧ = avg. velocity[=] 푓푡Τsec 푠 푠 푆 = 푋 + 4퐾푠푝 − 푋 푋 = 퐶 − 퐴 [=] 푚표푙Τ퐿 푧ҧ = avg. z-factor Liquid Flow – Choke Gas Flow Through a Choke Isothermal, steady-state 훾퐻 푝퐻푠 = 0.1log10 푇퐷푆 − 13.12log10 푇 − log10 퐻푎푟푑 퐴푙푘 + 44.15 푆 = ion solubility[=] 푚표푙Τ퐿 퐶 = cation molarity መ 훾 − 1 Flow Control mechanical energy balance specific 퐶푝푀푊푎푖푟훾푔 critical 2 퐻 훾 ≈ CV = 푇퐷푆 = total dissolved solids[=] 푚푔Τ퐿 푇 = temperature[=]퐾 퐾푠푝 = equilibrium coefficient 퐴 = anion molarity 퐻 → value 퐷c = choke diameter[=]𝑖푛 heat ratio 퐶መ푃푀푊푎푖푟훾푔 − 1.99 훾퐻 + 1 1 2 2 푃1 − 푃2 Compute equivalents per liter for cation and anion 퐼퐷푝 = upstream diameter[=]𝑖푛 푣2 − 푣1 = 푔 퐻푎푟푑 = hardness = 1000 푀푊퐶푎퐶푂 퐶푎 + 푀푔 [=] 푚푔Τ퐿 2 휌 푃 3 Compare solubility to minimum value 훥푃 = 훥푃 across choke[=]푝푠𝑖푎 푃2 2 uses measured 푃2 ≤ CV > CV 퐴푙푘 = alkalinity[=] 푚푔Τ퐿 푀푊 = 100.09 푔Τ푚표푙 𝑖표푛 [=] 푚표푙Τ퐿 መ 2 푃 푃1 pressures from well 푃 퐶푎퐶푂3 퐶푃 = constant pressure specific 8081.7퐶 퐷푐 훥푃 1 푚 푚 1 푚 𝑖표푛 푚푔Τ퐿 𝑖표푛 푐ℎ푎푟푔푒 푒푞 heat capacity[=] 퐵푇푈Τ푙푏푚°퐹 푞 = [=] 휌 Critical flow 푃1 = upstream pressure Critical flow 퐴푙푘 = 500 푀푊퐶푎퐶푂 퐻퐶푂3 + 2 퐶푂3 + 푂퐻 + 퐻 퐻 is negligible 1000(푀푊푖표푛) 퐿 퐷 4 3 퐷64 = 64 퐷푐 [=] 𝑖푛Τ64 푐 achieved NOT achieved 1 − 푃2 = downstream pressure 퐼퐷푝 Scale is likely to form if 퐿푆퐼 ≥ 0 Scale is likely to form if 푆 ≤ 푒푞Τ퐿 푇1 = upstream temp[=]푅 2 훾퐻 + 1 Pipeline Design Discharge Coefficient 퐶 훾 훾 Pipeline Design 훾퐻 CV 퐻 − CV 퐻 휎 = min. yield strength[=]푝푠𝑖 푞 = 0.238퐶퐷2 푃 푦 actual flow rate 64 1 훾 푇 훾 − 1 General Design Steps 푡 = wall thickness[=]𝑖푛 퐶 = 푔 1 퐻 theoretical rate 1. Determine proper regulatory policy 5. Calculate 푃 and 푃 6. Determine test pressure 7. Final burst rating check 푂퐷 = outer diameter[=]𝑖푛 푖 푀푇 Critical Flow Not Achieved - Do not proceed until established - As specified by correct Empirical Estimate 2 푆퐹 휎 푡 2휎푦푡 푃푖 = internal pressure[=]푝푠𝑖 - Design engineer’s responsibility 푦 regulatory policy 2 훾퐻+1 푃푖 = 푆퐹 = 0.875 푃푑 = 퐹퐸푇 퐷푐 훾 훾 푂퐷 푃푀푇 = mill test pressure[=]푝푠𝑖 훾퐻 푃2 퐻 푃2 퐻 푂퐷 퐶 = 퐶1 − 6.53 2 푃푑 and 푃푡푒푠푡 < 0.85푃푀푇 푃 = burst pressure[=]푝푠𝑖 퐼퐷푝푁Re 푞 = 0.238퐶퐷64푃1 − 2. Determine pipe diameter 푃푡푒푠푡 = 1.5푀퐴푂푃 표푟 1.25푃푑 푏 훾푔푇1 훾퐻 − 1 푃1 푃1 푃푀푇 ≅ 0.8푃푖 푃푖 [=] 푃푏 푚 푚 - Based on flow rate and exit pressure whichever is greater Example using ASME B31.8 푃푑 = design pressure[=]푝푠𝑖 퐶1 = 0.9975 Construction Type F Joint Type Flowing Temp T IPR Inflow Performance Relation (IPR) 3. Determine 푀퐴푂푃 for pipeline E Private right of way (PROW) 0.72 < 250 °F 1.0 푞푠푐 = oil rate[=] 푆푇퐵Τ푑푎푦 - Maximum allowed operating pressure Threaded seamless 1.0 표 250 − 300 °F 0.967 Oil Productivity Index Single-Phase Oil IPR Gas Productivity Index PROW on fringe of populated areas 0.6 Threaded ERW 1.0 푃푒 = boundary pressure[=]푝푠𝑖 푠푐 Decreasing 푠푐 4. Estimate pipe 휎푦 and 푡 300 − 350 °F 0.933 푃 = flowing wellbore[=]푝푠𝑖 푞표 푆푇퐵 푞푔 푀푠푐푓 Sparsely populated residential areas 0.5 Furnace lap welded 0.8 푤푓 퐽 = [=] 푃푒 over time 퐽 = [=] 2휎 푡 350 − 400 °F 0.900 표 푃 − 푃 푝푠𝑖 ⋅ 푑푎푦 푔 푃2 − 푃2 푝푠𝑖2 ⋅ 푑푎푦 푦 푘표 = oil permeability[=]푚퐷 푒 푤푓 푒 푤푓 1.5 푀퐴푂푃 = 퐹퐸푇 Populated areas and public roads 0.4 Furnace butt welded 0.6 400 − 450 °F 0.867 푡1 1 푂퐷 ℎ = reservoir thickness[=]푓푡 Steady-state & radial flow 푝푠𝑖 − Apply steady-state & radial flow 퐽표 Predicting Gas Production Flow Assurance 푤푓 푡 퐵표 = oil FVF[=] 푅퐵Τ푆푇퐵 3 −4 0.00708푘 ℎ 푃 7.0225푥10 푘푔ℎ 표 퐽 = - Gas decline curves are harder to predict due to the Common Issues 휇표 = oil viscosity[=]푐푝 퐽표 = 0 푔 푟 푟푒 1 0 푠푐 푒 1 high expansivity of gas 푟 = drainage radius[=]푓푡 퐵표휇표 ln − + 푠 푞표 푆푇퐵Τ푑푎푦 휇ҧ푔푧ҧ푇 ln − + 푠 Damage Type Detection Methods Prevention Methods Removal Methods 푒 푟푤 2 푟푤 2 If 퐵 ,휇 ,푘 relatively constant, - Can lead to an overestimation of total recovery 푟푤 = wellbore radius[=]푓푡 표 표 표 Calcium Water analysis Scale inhibitor Only good for single phase flow 퐽 is a constant Gas properties evaluated at 푃ത HCl acid job 푠 = skin factor 표 - Can use a P/z plot as another predictor Carbonate Scale Physical sample Scale squeeze ത Gas IPR Curves 푃 = avg. reservoir 푃[=]푝푠𝑖 Two-Phase IPR 푃 < 푃퐵푃 - Developed from the Real Gas Law Barium Water analysis Mechanical removal Scale inhibitor 푘 = gas permeability[=]푚퐷 Decreasing 푃푒 over time Sulfate Scale Physical sample Re-perforation 푔 Empirical correlation (Vogel, 1968) Decreasing 푃ത over time 푠푐 P/z Plot – OGIP Estimation 푞푔 = gas rate[=] 푀푠푐푓Τ푑푎푦 푞 Sodium Water analysis Reduce pressure drop Fresh H2O circulation 표 2 푝푠𝑖 = 1 − 0.2훸 − 0.8훸 푡1 Absolute Pത 휇ҧ푔 = avg. gas viscosity[=]푐푝 푝푠𝑖 Chloride Physical sample to reduce gas cooling Re-perforation 푞표,푚푎푥 푡2 Water influx 푡1 푤푓 Open Flow

푇 = reservoir temp[=]푅 ത 푃 z 훸 = 푃푤푓Τ푃 푤푓 푡2 푡3 i No water influx Emulsions Physical sample Emulsion Emulsion breaker 푃 푡3 and Sludge Lab analysis breaker Mutual Solvent Predicting Gas Production ത 0 0 Can replace 푃 with 푃푒 0 푠푐 Τ 0 푠푐 Τ 퐺 = cumulative gas produced 푞표 푆푇퐵 푑푎푦 푞푔 푀푠푐푓 푑푎푦 ഥ Liquid Block Well history Limit pressure 푃 퐏 Mutual solvents Gas Well Lab analysis drop at wellbore 퐺푟 = recoverable gas Vertical Lift Performance Decline Curve Analysis 퐳 퐺 = original gas in place 1000 Physical sample Inhibitors Inhibitors - Vertical lift performance can be developed Asphaltenes Hyperbolic Decline 푏 = 0 푏 = 0.5 푏 = 1 Oil analysis Application of heat by using the mechanical energy balance Gab = Gr Application of heat Decline Curve Analysis (Arps, 1940) ഥ - VLP displays bottom hole pressure required P Physical sample Inhibitors Inhibitors 푏 = hyperbolic exponent 100 Paraffin to flow to surface at varying flow rates 0 < 푏 < 1 z G = OGIP Oil analysis Application of heat Application of heat 푞 = future rate [=] 푝푟표푑Τ푡𝑖푚푒 ab VLP & IPR 푞 Formation Limit production rate Re-perforation 푞푖 = initial rate[=] 푝푟표푑Τ푡𝑖푚푒 푞 = 푖 10 Physical sample 2.375” tbg 2.875” tbg 3.5” tbg IPR 1Τ푏 퐆퐏 Fines Gravel/frac pack Small frac job 푡 = time 1 + 푏퐷푖푡 As b-factor increases, well’s

Production Rate (q)Rate Production economic life increases 5 Clay Lab analysis Don’t introduce Re-perforation 퐷 = decline rate[=] 1Τ푡𝑖푚푒 Smaller 퐼퐷 requires 푏 1 퐺 0 푃ത 푃ത 푃ത 1 푟 4 more pressure 1 푞푖 Time 푅퐹 = Swelling Production rate drop incompatible water Small frac job 퐷푖 = initial decline[=] 1Τ푡𝑖푚푒 푡 = − 1 = − 퐺푃 퐺 1000 퐷푖푏 푞 푧 푧 푧 퐺 Physical sample Don’t introduce 푁푝 = cumulative production Τ 3 ถ푖 푖 Recovery Bacteria Bacteriacides

푝 Lab culture bacteria laden water

푝푠𝑖 intercept slope factor 2 푏 1−푏 푁

Need more 푃푤푓 푞푖 − 푞푖 푞 푤푓

푃퐼푃 = pump intake 푃 푃 than well provides 푁푝 = Artificial Lift 1 퐷푖(1 − 푏) EL 푃퐷푃 = pump discharge 푃 Common Issue Rod Pump ESP Beam Lift

0 푏 Recovery EL 훥푃푆푉 = 훥푃 thru standing valve 0 1000 2000 3000 4000 푞 Sand Fair Fair Excellent 푞푠푐 푆푇퐵Τ푑푎푦 푏 = 0 푏 = 0.5 푏 = 1 Pressure Differential Across Plunger Rod Loads 푃푠,푡푏푔 = tbg surface pressure 표 퐷 = 퐷푖 0 Paraffin Poor Good Poor IPR < VLP need artificial lift to flow to surface 푞푖 0 Time High GOR Fair Fair Excellent 훥푃 = 푃퐷푃 − 푃퐼푃 + 훥푃푆푉 푃퐼푃 = 푃푤푓 푃푃푅퐿 = 푊푟푓 + 퐹표 + 푊퐷,푢푝 훻푃푡푏푔 = tbg fluid 푃 gradient Deviated Hole Poor Fair Good 푆 = surface stroke length = 𝑖푛 Packer Forces 푃퐷푃 = 훻푃푡푏푔퐷푝푢푚푝 + 푃푠,푡푏푔 + 푃푓푟푖푐 푀푃푅퐿 = 푊푟푓 − 푊퐷,푑표푤푛 Corrosion Good Fair Fair 푠푡푏푔 = tubing stretch = 𝑖푛 Tubing Movement Piston Forces Pump Displacement 휌푓 푊 = buoyed High Volume Poor Excellent Good 푊 = 푊 1 − 푟푓 휋 푟푓 푟표푑 휌 rod weight 푠푟표푑 = rod stretch = 𝑖푛 If tbg free to 2 2 푞 = 0.1166푁푑2푆 휂 [=] 푏푏푙Τ푑푎푦 푟표푑 퐹푎 = 퐹푆푂 + 푃푎 푂퐷푏 − 푂퐷푠 Depth Fair Fair Good 푝 푝 푝 푀푃푅퐿 = min. polish road load move, need to 4 make sure pkr Simple Design Yes Yes No 푁 = pump speed[=]푠푝푚 휂푝 = pump efficiency 푆푉푙표푎푑 = 푊푟푓 푇푉푙표푎푑 = 퐹표 + 푆푉푙표푎푑 푃푃푅퐿 = peak polish rod load stays sealed 푃푎 = 푃푠,푎푛푛 + 퐷푝푘푟훻푃푎푛푛 Casing Size Fair Good Good 푑푝 = plunger diameter[=]𝑖푛 Pump Slippage (Patterson, et al, 2007) 퐹표 = fluid weight[=]푙푏푓 Flexibility Fair Poor Good 퐹푆푂 = slacked off tubing weight Effective Stroke Length 푑 훥푃푐1.52 푏푏푙 푊퐷 = dynamic load[=]푙푏푓 Total Production Scale Good Poor Fair 푝 푝 푂퐷푏 = packer bore diameter[=]𝑖푛 푞 = 1 + 0.14푁 453 [=] 훥퐿 Movement 푠 퐿 = plunger seal length[=]𝑖푛 푆푝 = 푆 + 푠푝표 − 푠푡푏푔 − 푠푟표푑 = 𝑖푛 퐿푝휇푓 푑푎푦 푝 푂퐷푠 = metal seal tube 푂퐷[=]𝑖푛 Onshore Usage 84% 2% 11% Packer Forces 퐷푝푘푟 = packer true vertical depth Gas Lift much higher % offshore 푠푝표 = plunger overtravel 푠푡푏푔 = 0 tbg anchored 푐푝 = plunger clearance = 𝑖푛 휇푓[=]푐푝 푃 = surface pressure in annulus 푃푎 = 푃 above the packer 푠,푎푛푛 Resource Economics 푃 = 푃 below the packer 훻푃 = annulus fluid pressure gradient 푏 푎푛푛 Reserve Classification – Common Acronyms Time Value of Money 퐼퐷푠 = seals 퐼퐷[=]𝑖푛 휋 Landed Piston Buckling Ballooning Temp 퐹 = −푃 푂퐷2 − 퐼퐷2 1. PDP: Proved Developed Producing – well is online and producing 푏 푏 푏 푠 푃푉 = present value 푃푉 = 퐹푉 퐷퐹 퐷푅 = discount rate 퐴푝푘푟 = cross sectional area length 4 2. PDNP: Proved Dev. Non-Producing – reserves are behind pipe, well is 훴퐹 푀퐷 퐹푉 = future value −푡푛 퐷푅[=] 푑푒푐𝑖푚푎푙Τ푦푟 훥푃푎푛푛 = avg. 훥푃 in annulus 푃푏 = 푃푠,푡푏푔 + 퐷푝푘푟훻푃푡푏푔 shut-in, or waiting on necessary equipment installation to produce 퐷푅 훴퐹 = 퐹푏 + 퐹푎 + 퐹푏푢 + 퐹푏푎 + 퐹푇 훥퐿 = [=]푓푡 퐷퐹 = 1 + 훥푃푡푏푔 = avg. 훥푃 in the tubing 퐴푡푏푔 퐸 퐷퐹 = discount factor 푡 = time in years Permanent Buckling 3. PUD: Proved Undeveloped – offsetting wells or existing wells that 푛 훿 = linear thermal expansion 퐹푎 = force acting on seals from above 푀퐷 = pkr measured depth would require a major recompletion 푛 = discounting periods per year 퐹푏푢 = 퐴푝푘푟 훥푃푎푛푛 − 훥푃푡푏푔 Resource Economics 퐹푏 = force acting on seals from below 퐴푡푏푔 = cross sectional area Economic Limit Converting Production into Cash Flow 퐷푝푘푟훻푃푎푛푛 푁푅퐼 = net revenue interest 훥푃 = 훥푃 + 푂푃퐸푋[=] $Τ푡𝑖푚푒 Net Revenue Tax Cash Flow Disc. Cash Flow - If tbg cannot move, need to check tensile strength of pkr and tbg 푎푛푛 푠,푎푛푛 2 푂푃퐸푋 푊퐼 푝푟표푑 푂푃 = oil price 푊퐼 = working interest 퐸퐿 = [=] 퐺푅 푁푅퐼 푁푅 푆푇 + 퐴푉푇 푁푅 − 푂푃퐸푋 − 푇퐴푋 퐶퐹 퐷퐹 퐹푡표푝 = 푀퐷 푊퐵 − 퐹푇 − 퐹푏푎 − 퐹푆푂 퐷 훻푃 푁푃 푁푅퐼 푡𝑖푚푒 퐴푉푇 = ad valorem tax 푝푘푟 푡푏푔 푁푃 = net price 퐺푅 = gross revenue = production grossprice 퐹 = force at top of tubing 푊 = buoyed tbg weigh푡[=] 푙푏 Τ푓푡 훥푃푡푏푔 = 훥푃푠,푡푏푔 + 퐺푃 = gas price 푡표푝 퐵 푓 2 Evaluating Potential Investments 푁푃표 = 푂푃 1 − 푆푇표 − 퐴푉푇 + 퐺푃 퐺푂푅 1 − 푆푇푔 − 퐴푉푇 퐺푂푅 = gas−oil ratio Temperature Change (for steel) Tubing Ballooning Disc. Return on Investment Disc. Rate of Return Undiscounted Payout Discount rate that Time required to return 푁푃 = net gas price 퐸 = 30 푥 106 푝푠𝑖 휋 푁푃푔 = 퐺푃 1 − 푆푇푔 − 퐴푉푇 + 푂푃 푂푌 1 − 푆푇표 − 퐴푉푇 퐷퐶퐹 푔 퐹 = 퐴 훥푇 퐸훿 = 207퐴 훥푇 2 2 퐷푅푂퐼 = yields a net present initial investment using 푇 푡푏푔 푡푏푔 −6 −1 퐹푏푎 = 0.6 훥푃푎푛푛푂퐷푡푏푔 − 훥푃푡푏푔퐼퐷푡푏푔 퐼푛푣푒푠푡푚푒푛푡 퐷퐶퐹 = discounted cash flow 훿 = 6.9 푥 10 °퐹 4 푁푃표 = net oil price 푆푇 = severance tax 푂푌 = oil yield value of zero undiscounted cash flow Created by James Riddle with guidance from Dr. Paul Bommer and Dr. Matthew T. Balhoff Contact [email protected] with comments/suggestions