Drilling Calculations Course Common Units and symbols parameter Unit Symbol length Feet,inches or Mtr Ft ,inor M Area Square feet, Square inches or square meters Volume Cubic feett, cubic centimeters cubic meters or Cuft. Cu In or Meters cube Capacity US barrels,US gallons, Cubic ft bbl, gal(US), cuft Mass Pounds,Short tons lbs, Sh tn Force (weight) Pounds-force lbf Presure Ppounds –force per square inch psi Density (mudweight) Pounds per gallon, pounds per cubic ft Ppg ,pcf torque Foot pounds ftlbs AREAS Areas Length • Area of a square breadth Area of a Square = length X breadth Length This same expression is applicable to a rectangle and parallelogram breadth base Area of a triangle = Height Height Area of a Triangle base Base x Height 2 Area of a Circle Diameter Area of a circle = Π x radius x radius Where r= radius of the circle Π = 3.142 Since diameter= 2 x radius Area of circle= Π x Diameter x Diamater 4 Radius VOLUMES Annular area d D Annular or cross sectional area = Π {(D x D)-(d x d)} 4 This can be used to calculate annular areas of the wellbore or Cross sectional areas of tubulars Volumes hieght Volume of a cube length Volume of a cube = length x breadth x height Height Cylindrical Capacities Area Volume of a cylinder = Area x Height = Π x Diameter x Diameter x Height 4 This is the basis for all volume the capaciy calculations in well control Capacity Calculations Rule of thumb: Capacity of a cylinder in bbls/ft= Diamater x Diameter 1029.4 Multiply this by the Height of the cylinder ( or length of the hole) gives the volumetric capacity in barrels HVolume = Diameter x Diameter x height(or length) 1029.4 This expression is generally used on the rig for volume and capacity calculations Annular volume calculations Top view d D Annular Volume in bbls {(D x D)-(d x d)}xlenght 1029.4 Hole volume calculations ANNULAR VOLUME AROUND DP = [( D3² - D1² ) / 1029.4] x L1 ANNULAR VOLUME AROUND DC = [( D3² - D2² ) / 1029.4] x L2 Hole volume calculations example Using the following data, calculate the total annular volume. L1 = 4000 ft L2 = 800 ft D1 = 5 in D2 = 6.5 in D3 = 8.5 in Hole volume calculations ANNULAR VOLUME AROUND DP = [( 8.5² - 5² ) / 1029.4] x 4000 = 183.6 bbls ANNULAR VOLUME AROUND DC = [( 8.5² - 6.5² ) / 1029.4] x 800 = 23.31 bbls Total Annular Volume =183.6 + 23.31 = 206.91 bbl D Pump displacement volumes L The same expression for calculation od hole volumes can also be used for the calculation of mud pump displacements Triplex Pump displacement in bbls/ft = D² x L x e x3 1029.4 x 12 x100 Where D= liner size in inches L= Stroke length in inches e= Volumetric efficiency in % D Pump displacement volumes example L Where D= 7 inches L= 11 inches e = 97% Pump displacement= 7 x 7 x 97 x 11 x 3 1029.4 x 12 x 100 = 0.127 bbls/ stroke Weight on bit • Drill collars and/or heavy wall drill pipes are uses to put weight on the bit • Drill collars are also used to keep the string in tension and prevent it from buckling • There is a point in the drill collars where compression stops and tension starts this point is called the neutral point • Weight on bit is usually about 75-90%of the buoyed drill collar weight compression Neutral point Tension Bouyancy factor The apparent loss of weight when an object Is immersed in a fluid Is calculated using the expression: 65.44-mw or 1 - mw 65.44 65.44 This factor must be multiplied by the weight in air to calculate the buoyed weight Buoyed weight= weight in air x buoyancy factor Apparent or buoyed weight WB = WA x fluid density Steel density Where: WB = weight of tubulars in fluid WA = Weight of tubulars in air Fluid density = Density of fluid in ppg Steel Density =Density of Steel in PPG Example • A drill string weighs 180000 lbs in air how much will it weigh in 11.5ppg mud? Buoyed weight = weight in air X buoyancy factor Bouyancy factor= 65.44-mw 65.44 = 65.44-11.5 = 0.8242 65.44 Buoyed weight = 180,000 X 0.8242 = 148 356 lbs A practical application of this is expression is when calculating the number of drill collars to give a desired weight on bit Example Find the maximum weight on bit if a drill string has 20 drill collars each 8 inch by 2.5 inch and 30ft in length and weight 154 lbs/ft The density of the drilling fluid is 13.4ppg and 90% of the buoyed weight will be utilized Answer Weight of drill collars in air=20x30x154= 92400 lbs Bouyancy factor= 65.44-13.4 = 0.795 65.44 Effective drill collar wt in fluid = 92400 x =0.795 =73458lbs 90% of available drill collar weight =0.9x73458=66112 lbs Example Find the maximum weight on bit if a drill string has 30 drill collars each 6.5 inch by 3 inch and 30ft in length and has a nominal wt of 88.88 pounds per foot The density of the drilling fluid is 12.4 ppg and 80% of the buoyed weight will be utilized Example Find the maximum weight on bit available if a drill string has 15 drill collars each 9.5 inch by 2.75 inch and 30ft in length The density of the drilling fluid is 13 ppg and 80% of the buoyed weight will be utilized WET AND DRY TRIPPING Tripping Dry When a length of pipe is pulled from the hole, the mud level will fall. Tripping Dry The volume of fall is equal to the volume of steel pulled from the hole. The trip tank is then used to fill up the hole. If 1 barrel of steel is removed from the hole, then using the trip tank, we have to add 1 barrel of mud. Tripping Dry 1- Calculate the volume of steel pulled: Length x Metal Displacement Example: DP Metal Disp = 0.00764 bbls/ft Length Pulled 93 feet Volume Of Steel Pulled: 93 x 0.00764 = 0.711 bbls Tripping Dry 2- Fill up the hole: You must pump 0.711 barrel of mud from the trip tank. You must investigate ( flow check) if more mud or less mud is needed. Tripping Dry 3- NO FILL UP: If you fail to fill up the hole, the mud level will drop by the volume of steel pulled. It will drop inside the pipe and in the annulus. Tripping Dry 3- NO FILL UP: Example: Volume Of Steel Pulled: 93 x 0.00764 = 0.711 bbls DP Capacity: 0.01776 bbl/ft Annular Capacity: 0.0504 bbl/ft The mud will drop inside the pipe and the annular: 0.01776 + 0.0504 = 0.06816 bbl/ft Tripping Dry 3- NO FILL UP: Example Cont’d: The volume of drop is 0.711 bbls and will drop in a volume of 0.06816 bbl / ft, then the length of drop will be: 0.711 / 0.06816 = 10.43 feet. If 93 feet are pulled with no fill up, the mud level will drop by 10.43 feet. Tripping Wet When a length of pipe is pulled from the hole, the mud level will fall. Tripping Wet The volume of fall is equal to the volume of steel pulled from the hole plus the volume of mud inside this pipe. The trip tank is then used to fill up the hole. If 3 barrels of steel and mud are removed from the hole, then using the trip tank, we have to add 3 barrels of mud. Tripping Wet 1- Calculate the volume of steel pulled: Length x Metal Displacement Example: DP Metal Disp = 0.00764 bbls/ft Length Pulled 93 feet Volume Of Steel Pulled: 93 x 0.00764 = 0.711 bbls Tripping Wet 2- Calculate the volume of mud pulled: Length x DP Capacity Example: DP Capacity = 0.01776 bbls/ft Length Pulled 93 feet Volume Of Mud Pulled: 93 x 0.01776 = 1.65 bbls Tripping Wet 3- Calculate the total volume of steel and mud pulled: 1.65 + 0.711 = 2.36 barrels Tripping Wet 4- Fill up the hole: You must pump 2.36 barrels of mud from the trip tank. You must investigate ( flow check) if more mud or less mud is needed. Tripping Wet 5- NO FILL UP: If you fail to fill up the hole, the mud level will drop by the volume of steel and mud pulled. It will drop inside the annulus. Tripping Wet 5- NO FILL UP: Example: Volume Of Steel and Mud Pulled: 93 x (0.00764+0.01776) = 2.36 bbls Annular Capacity: 0.0504 bbl/ft The mud will drop inside the annular by: 2.36 / 0.0504 = 46.84 feet Mud Weight The Mud weight is the density ( mass per unit volume ) of a drilling fluid. Mud Weigth can be expressed in: Pound per Gallon ( ppg ) Pound per Cubic Feet ( pcf ) Specific Gravity ( sg ) Pressure The pressure is a force or weight per unit area exerted by a gas or liquid against the walls of a vessel, hole, or object inserted into said gas or liquid. Pressure can be expressed in: Pounds per square inches ( psi ) OR Kilograms per square centimeters ( kg / cm²) Derivation of 0.052 A cubic foot contain 7.48 US gallons. If the fluid used to fill the cube weights 1 ppg, then the cube would weight 7.48 pounds. The base of the cube has: 12x12=144 square inches. 7.48/144=0.05194 A 1 foot column of 1ppg fluid exerts a pressure of 0.052 psi Pressure or Mud Gradient Since the pressure is measured in psi and depth is measured in feet, it is convenient to convert mud weights from ppg to a pressure gradient in psi/ft. The conversion factor is 0.052 Pressure gradient (psi/ft) = Fluid Density (ppg) x 0.052 Example: A fluid having a mud weight of 10 ppg will have: 10 x 0.052 = 0.52 psi ft as a pressure gradient. A 1 foot column of 10 ppg mud will have a pressure of 0.52 psi Hydrostatic Pressure Hydrostatic Pressure is the pressure exerted by a column of fluid ( at rest )and is calculated by multiplying the gradient of the fluid by the True Vertical Depth at which the pressure is being measured: Hyd Pressure(psi) = Fluid gradient (psi/ft) x TVD Example: What is the hydrostatic pressure at 10,000 ft for a mud gradient of 0.52 psi /ft ? Hyd Pressure(psi) = 0.52 x 10,000 Hyd Pressure = 5,200 psi Hydrostatic Pressure It is the vertical height/depth of the fluid column that matters, its shape is unimportant Hydrostatic Pressure Using the formula for the pressure gradient and for the hydrostatic pressure: Pressure gradient (psi/ft) = Fluid Density (ppg) x 0.052 Hyd Pressure(psi) = Fluid gradient (psi/ft) x TVD We can write: Hyd Pressure(psi) = Fluid Density (ppg) x 0.052 x TVD Hydrostatic Pressure It is usefull to visualize the well as a U-tube. One column is for the pipe in the well and the other column is for the annulus. If the same fluid is used is both columns, hydrostatic would be equal and the fluid would be static on both sides of the tube. Mud Hydrostatic in the string Mud Hydrostatic in the annulus Well bore hydraulics Well bore pressure losses 2600 psi 2500 psi 0 psi 100 psi 400 psi 300 psi 80 SPM 2100 psi 500 psi 1600 psi 1300 psi 300 psi Hydraulic horsepower = PxQ 1714= Where P= Pressure loss V= Quantity of flow in Gallons per minute Annular velocity= Pump output (bbls/min) Annular capacity (bbls/ft) Example • What is the hydraulic horsepower delivered by a pump at 400 gallons per minute at 3000psi 3000 x 400 1714 =700HP Annular Velocity Annular velocity is the speed with which the fluid travels up the annulus. It is an indication of the amount of HHP available in the annulus Annular Velocity Annular velocity = pump output (bbls/min) Annular capacity (bbls/str) Pump pressure vs pump rate Pump pressure increased as pump speed increases P2 =P1x SPM2 2 SPM1 Where: P1=old pump pressure P2=new pump pressure SPM1=Old pump rate SPM2= New pump rate Pump pressure vs fluid density • Pump pressure also increases with fluid density P2= P1 x MW2 MW1 Where P1=old pump pressure P2=new pump pressure MW1= Old mud wdensity MW2 new mud density Example At 100 spm the pumping pressure is 2850 psi with 13 ppg What is the new pressure if the pumps are decreased to 65 spm? What is the new pressure if the mud weight is then decreased to 10.5 ppg? Solution: 2850 x 65 x 65 x 10.5 100 x 100 13 = 973 psi The new pump pressure will be 973 psi approximately Work Done by the Drilling line Each time the block are raised and lowered during the drilling process a certain amount of work is done by the drilling line Work done = Force X Distance = Ton X Miles Tin mile calculations are used to determine the actual slip and cut off programs for the rig Varieties of Ton-Miles Calculations • • • • Round Trip Ton Miles Drilling Ton miles Casing Ton miles Coring Ton miles Drilling Ton Miles Dtm=3X(RTtm2-RTtm1) Where: Dtm =Drilling Ton Miles between Trips RTtm2 =Ton miles at depth when bit is run RTtm1 =Ton miles at depth when bit is pulled Round trip Ton Mile calculations RTtm = Wp X (Lp+D) +2XDX(2Wb+Wc) 5280 X 2000 Where: RTtm =Round trip Ton Miles Wp= Buoyant weight of drill pipe in mud D=Depth of the hole Lp=average stand length Wb=Weight of travelling block assembly Wc=Buoyant weight of drill collars minus the buoyant weight of the same length of drill pipe Example Depth 7000 ft. Drilling fluid density 10 ppg Drill pipe 5 inch diameter x 19.5 lb/ft. Collars 500 ft of 8 inch OD x 3 inch ID x 147 lb/ft. Travelling block assembly 15000 lbs. Calculate the Round Trip ton miles at 7000 ft. Answer: From Drilling Data Handbook table the buoyancy factor = 0.848 The WP Buoyant weight of drill pipe = 19.5 x 0.848 = 16.53 lb/ft. Wc,the Buoyant weight of drill collars = (500 x 147 x 0,848) - (500 x 16,53)= 62328 - 8265 = 54063 lbs Take average length of 1 stand = 90 ft. RTtm = WP x D x ( LP + D ) + 2 x D x ( 2 Wb + Wc ) 5280 x 2000 and with the numbers entered into the formula RTt= 16,53 x 7000 x ( 90 + 7000 ) + 2 x 7000 x ( 2 x 15000 x 54063 ) 5280 x 2000 = 189 TM Casing Ton Miles • Ctm= D xWcx(Lc +D)+4 x D xWb 5280 x2000x2 Where:Ctm= casing ton miles Wc=Submerged wt of casing in mud (lbs/ft) Lc=Average lenght of 1 joint f casing Wb=weight of travelling block assembly Ton miles for coring Coring =2x(RT -RT ) tm tm2 tm1 Where:RTtm1=Ton miles for trip where core barrel was run :RTtm2=Ton miles for trip where core barrel was pulled Stuck pipe calculations Free point determination L=M xexA 12 xP Where: L= lenght of free pipe M=Modulus of elasticity of steel e =Strech in drill pipe A=cross sectional area of drill åpipe in sq inches P= difference betweem maximum and minimum pull on pipe Example A 10000 ft string of 4½" and 16,6 lb/ft drill pipe is stuck. Maximum pull of 250000 lbs and a minimum pull of 180000 lbs gave a stretch figure of 45 inch. The cross sectional area of 4½" drill pipe is 4.4 sq.in. Calculate the position of the free point. M = 30000000 e = 45 inch A = 4.4 sq.in P = 250000 - 180000 = 70000 lbs Length of free pipe = L = M x e x A = 30000000 x 45 x 4.4 12 x P 12 x 70000 = 7071 ft below the rotary table Accummulator Volumetric requirements Definitions • Stored Hydraulic Fluid. The fluid volume recoverable from the accumulator system between the maximum designed accumulator operating pressure and the precharge pressure. • Usable Hydraulic Fluid. The hydraulic fluid recoverable from the accumulator system between the maximum accumulator operating pressure and minimum calculated operating pressure or 200 psi above precharge pressure whichever is greatest. • Minimum Calculated Operating Pressure. The minimum calculated pressure to effectively close and seal a ram-type BOP against a wellbore pressure equal to the maximum rated working pressure of the BOP divided by the closing ratio specified for that BOP. • Component Minimum Operating Pressure Recommended by the Manufacturer. The minimum operating pressure to effectively close and seal ram-type or annular-type preventers under normal operating conditions, as prescribed by the manufacturer. Boyles Law Pressure X Volume is constant Or P1V1=P2V2 At constant temparature If the volume of an enclosed gas bubble is doubled them the presure is reduced by half and if the pressure of a gas bubble is doubled the volume is halved Example Accumulator bottle size 10 gallons. Precharge pressure 1.000 psi Initial condition with only gas : Pressure x Volume = Constant 1.000 x 10 = 10.000 The pump system is started and hydraulic fluid is pumped into the accumulator bottle until maximum operating pressure is reached at 3.000 psi : P1 x V1 = P2 x V2 1.000 x 10 = 3.000 x V2 V2= 1000 X10 3000 = 3.33 gallon gas Stored hydraulic fluid = 10 - 3.33 = 6.67 gal 1.000 psi 3.000 psi 1.200 psi 1.500 psi 2.110 psi 10 gal 3.33 gal 8.33 gal 6.66 gal 4.74 gal 6.66 gal 1.66 gal 3.33 gal 5.26 gal Fig 58 b Gas Fig 58 c Fig 58 d Fluid Fig 58 e Fig 58 a The pump system is isolated and the BOP’s functioned until accumulator pressure reach precharge pressure + 200 psi: P1 x V1 = P2 x V2 1.000 x 10 = 1.200 x V2 V2= 10 X10000 =8.33 gallons gas 1200 Usable hydraulic fluid = 8.33 - 3.33 = 5 gal If the minimum operating pressure recommended by the manufacture is 1.500 psi as for Shaffer Annular Preventer with pipe size smaller than 7” the usable hydraulic fluid would be : P1 x V1 = P2 x V2 1.000 x 10 = 1.500 x V2 V2= 10 X10000 =6.66 gallons gas 1500 Usable hydraulic fluid = 6.66 - 3.33 = 3.33 gal Well Control Mud Weight The Mud weight is the density ( mass per unit volume ) of a drilling fluid. Mud Weight can be expressed in: Pound per Gallon ( ppg ) Pound per Cubic Feet ( pcf ) Specific Gravity ( sg ) Pressure The pressure is a force or weight per unit area exerted by a gas or liquid against the walls of a vessel, hole, or object inserted into said gas or liquid. Pressure can be expressed in: Pounds per square inches ( psi ) Kilograms per square centimeters ( kg / cm²) Hydrostatic Pressure Using the formula for the pressure gradient and for the hydrostatic pressure: Pressure gradient (psi/ft) = Fluid Density (ppg) x 0.052 Hyd Pressure(psi) = Fluid gradient (psi/ft) x TVD We can write: Hyd Pressure(psi) = Fluid Density (ppg) x 0.052 x TVD Hydrostatic Pressure It is usefull to visualize the well as a U-tube. One column is for the pipe in the well and the other column is for the annulus. If the same fluid is used is both columns, hydrostatic would be equal and the fluid would be static on both sides of the tube. Mud Hydrostatic in the string Mud Hydrostatic in the annulus Hydrostatic Pressure If the pipe or the annulus are not kept full, then the hydrostatic pressure in reduced. Pipe is not full Annulus is not full HP is reduced HP is reduced Balanced Balanced when Hydrostatic Pressure = Formation Pressure Under Balanced Under Balanced when HP < FP Over Balanced Over Balanced when HP > FP Kill Sheet The kill sheet is a tool used to kill the well. It gathers all the informations needed and help you to perform the calculations. The first section to fill is the well data. Kill Sheet The pump displacement must be entered and the Slow Circulating Rate must be recorded. Kill Sheet This section is used to calculate all the hole volumes, to convert them in strokes and in time. Drillpipe Internal volume Heavy weight dril pipe Internal Volume Dril Collars Internal Volume Drill Collar open hole annular volume Drill pipe- Open hole annular volume Drill pipe-Casing annular volume Kill Sheet The formulas are used to calculate the kill mud, Initial Circulating Pressure, Final Circulating Pressure and to prepare the graph. Kill Sheet The graph will be followed to maintain a constant Bottom Hole Pressure. Pumping a Slug It is useful to pump a slug before tripping. The slug weight being heavier than the mud, a length of pipe will be empty. The HP is not reduced because the heavier mud will compensate for the empty pipe. Pumping a Slug The total HP is the same on both sides of the pipe. HP kmw HP mud HP mud Pumping a Slug Example: If 20 bbls of 12 ppg slug are pumped in a 10,000 ft hole containing 10 ppg mud, what will be the height of empty pipe? DP capacity = 0.01776 bbl/ft 1- Calculate the height of the slug: 20 / 0.01776 = 1126 ft Pumping a Slug 2- Calculate the HP of the slug: 1126 x 12 x 0.052 = 702.6 psi 702.6 psi Pumping a Slug 2- Calculate the HP of the mud in the annulus: 10,000 x 10 x 0.052 = 5,200 psi 702.6 psi 5,200 psi Pumping a Slug 3- The total hydrostatic beeing the same on both sides, calculate the HP of the mud below the slug: 5,200 - 702.6 = 4497.4 psi 702.6 psi 4497.4 psi 5,200 psi Pumping a Slug 4- Calculate the height of mud needed to give 4497.4 psi as a HP: TVD = 4497.4 / ( 10 x 0.052 ) = 8648.8 feet 1,126 ft 8648.8 ft 10,000 ft Pumping a Slug 4- Calculate the height of empty pipe 10,000 - 8648.8 - 1,126 = 225.2 ft 225.2 ft 1,126 ft 8648.8 ft 10,000 ft Practical Exercise 3- If 28 bbls of 14 ppg slug are pumped in a 12,000 ft hole containing 11 ppg mud, what will be the height of empty pipe? DP capacity = 0.01776 bbl/ft MUD WEIGHT CHANGE • A well is being drilled using 10 ppg mud. At 80 spm the total circulating system pressure losses are 2600 psi. • It is decided to increase the mud weight to 11 ppg. 2600 psi 80 spm Mud wt 10 ppg MUD WEIGHT CHANGE • It is a good drilling practice to calculate the new circulating pressure before changing the mud weight. • The way we calculate this change in pressure is to use the following formula; • New Mud ppg • Old Mud ppg x Old psi. • 11 ppg 10 ppg x 2600 = 2860 psi • The new pump pressure would be approximately 2860 psi. 2860 psi 80 spm Mud wt 11 ppg MUD WEIGHT CHANGE Final Circulating Pressure • The formula that was just used to calculate the pressure change due to a change in mud weight, is also the formula used to calculate the Final Circulating Pressure. Kill Mud ppg Old Mud ppg x Slow Pump psi. PUMP STROKE CHANGE • A well is being drilled using 10 ppg mud. At 80 spm the total circulating system pressure losses are 2600 psi. • It is decided to increase the pump speed from 80 spm to 100 spm. 2600 psi 80 spm Mud wt 10 ppg PUMP STROKE CHANGE • It is a good drilling practice to calculate the new circulating pressure before changing the pump speed. • The way we calculate this change in pressure is to use the following formula; New SPM 2 Old psi x Old SPM • 2600 x 100 spm 2 80 spm = 4063 psi • The new pump pressure would be approximately 4063 psi. 4063 psi 100 spm Mud wt 10 ppg Height of Influx Pit gain(bbls) = (ft.) hi = annuluscapacity(bbls/ft.) Gi = G m - P sia - P sidp psi / ft hi Influx gradient P sia - P sidp psi / ft Gi = G m hi Where: Gi=Influx Gradient Gm= Mud Gradient hi= Hieght of influx DEPTH 0 1 Gas grad. 0.07 psi/ft 2 Oil grad. 0.30 psi/ft 3 Fresh W. grad 0.433 psi/ft 4 Salt W. grad 0.465 psi/ft 5 10 ppg grad. 0.52 psi/ft 2500 6 15 ppg grad. 0.7785 psi/ft 7 21 ppg grad. 1.091 psi/ft 5000 1000 2000 3000 4000 5000 PRESSURE