Example No. 1: Capacity, Volumes and Strokes
Example No. 2: Drill String Design (Limitations)
Example No. 3: Cementing Calculations
Example No. 4: Pressure Requirement to Break Circulation
Example No. 5: Drilling Fluids - I
Example No. 6: Drilling Fluids - II
Example No. 7: Drilling Fluids - III
Example No. 8: Pressure Analyses
Example No. 9: Bit Nozzle Selection – Optimized Hydraulics
Example No. 10: Critical Annular Velocity and Critical Flow Rate

Capacity of Drill Pipe, Heavy Weight Drill Pipe (HWDP), Casing or Open Hole in bbl/ft

Capacity of Casing or Open Hole between Drill Pipe, HWDP or Casing in bbl/ft

Capacity of Drill Pipe, HWDP, Casing or Open Hole in ft/bbl

Capacity of Casing or Open Hole between Drill Pipe, HWDP or Casing in ft/bbl

Volume of Drill Pipe, HWDP, Drill Collar or Casing in bbl

Volume between Drill Pipe, HWDP or Casing and the Casing or Open Hole in bbl

♦ Rule of Thumb: Hole Volume

Example: Determine volumes and strokes for following:

Item	Size, Inches	Weight per foot	Length, Feet
Riser	18 ¾ (ID)		5075
Intermediate Casing	13 5/8 x 12 ¼	88,2	8425
Open Hole	9 7/8		4000

Item	Size, Inches	Weight per foot	Length, Feet
DP	6 5/8 x 5,965	25,2	15900
HWDP	6 5/8 x 4 ½	63,2	1000
DC	8 ½ x 2 13/16	172	600

Item	Size, Inches	Efficiency, %	Output, bbl/stk	SPM
Hole Pumps	5 ½ x 14	97	0,100	210
Booster Pump	6 x 6	97	0,051	180

Step 1: Calculate the drill string volume:

1. Drill Pipe Volume:
   
2. Heavy Weight Drill Pipe (HWDP) Volume:
   
3. Drill Collars Volume:
   
4. Total Drill String Volume:
   

Step 2: Calculate the Annular Volume:

1. Drill Pipe/Riser Annular Volume:
   
2. Drill Pipe/Casing Annular Volume:
   
3. Open Hole/Drill Pipe Annular Volume:
   
4. Open Hole/HWDP Annular Volume:
   
5. Open Hole/Drill Collars Annular Volume:
   
6. Total Annular Volume:
   
7. Total Volume of Hole System:
   

The following will be determined:

Length of bottom hole assembly (BHA) necessary for a desired weight on bit (WOB).

Feet of drill pipe that can be used with a specific bottom hole assembly.

Step 1: Calculate the Buoyancy Factor:

Step 2: Calculate the Length of BHA Necessary for Desire Weight on the Bit

Example: Calculate the BHA length necessary for desired WOB:

Step 1: Calculate the Buoyancy Factor:

Step 2: Calculate the Length of the BHA Necessary for this Weight on Bit:

Step 1: Calculate the Buoyancy Factor:

Step 2: Calculate the Maximum Length of Drill Pipe that can be Run into the Hole with a Specific BHA Assembly:

Step 3: Calculate the Total Depth that can be Reached with a Specific BHA in ft:

Example:

Result: D_T = 26,013 ft

Step 1: Calculate the Weight of Additive per Sack of cement in lb:

Step 2: Total Water Requirement for each Sack of Cement in gal/sk:

Step 3: Calculate the Volume of the Cement Slurry in gal/sk:

Step 4: Calculate the Yield of the Cement Slurry in ft³/sk:

Step 5: Calculate the Cement Slurry Density in lbm/gal:

Example: using a Class A cement plus 4% bentonite with normal mixing water, calculate the following:

1. Amount of bentonite to add in lb/sk,
2. Total water volume requirement for the slurry in gal/sk,
3. Slurry yield in ft³/sk,
4. Slurry weight in lbm/gal.

Step 1: Calculate the Weight of the Bentonite Additive:

Step 2: Calculate the Total Water Requirement per Sack of Cement Used:

Step 3: Calculate the Total Volume of the Cement Slurry:

Step 4: Calculate the Yield of the Cement Slurry:

Step 5: Calculate the Cement Slurry Density:

Water Requirements

Step 1: Calculate the Weight of Cement Additive Materials in lb/sk:

Step 2: Calculate the Water Requirement for the Slurry using Material Balance Equation:

D₁ V₁ = D₂ V₂

Example: Using a Class H cement plus 6% bentonite to be mixed at 14,0 lb/gal, calculate the following:

1. Bentonite requirement in lb/sk,
2. Water requirement in gal/sk,
3. Slurry yield in ft³/sk,
4. Check the slurry weight in lbm/gal.

Step 1: Calculate the Weight of Cement Additive Materials

Step 2: Calculate the Volume of Cement Slurry

Step 3: Calculate the Water Requirement using the Material Balance Equation

Step 4: Calculate the Yield of the Cement Slurry

Step 5: Recheck the Cement Slurry Density

RESULT: 14,0 lb/gal

Step 1: Calculate the Pressure Requirement to Break the Mud´s Gel Strength inside the Drill String

Step 2: Calculate the Pressure Required to Break the Mud´s Gel Strength in the Annulus:

Step 3: Calculate the Total Pressure Required to Break Circulation:

Example: Calculate the pressure required to break circulation in the well with this data:

Gel strength (10 or 30 minute) = 18 lb/100 ft²

Drill string = 6 5/8 x 5,965 in.

Hole size = 12 ¼ in.

Depth (MD) = 15000 ft

Step 1: Calculate the Pressure Required to Break the Mud´s Gel Strength inside the Drill String:

Step 2: Calculate the Pressure Required to Break the Mud´s Gel Strength in the Annulus:

Step 3: Calculate the Total Pressure Required to Break Circulation:

Calculate the Effective Gel Strength Based on the Actual Pressure Required to

Break the Circulation

Example: Calculate the effective gel strength with the following data:

Pressure required to break circulation = 475 psi

Drill string length = 15000 ft

Hole size = 12 ¼ in.

Drill string size = 6 5/8 x 5,965 in.

RESULT: τ_egs = 27,5 lb/100 ft²

1. Short formula for mud weight increase:
   
   where:

   W_M = number of 100 lb sacks of weight material required for 100 bbls of mud,
   ρ₀ = original mud weight in ppg,
   ρ_n = new mud weight in ppg.
2. Volume increase based on the amount of weight material
   
   where:

   V_i = volume increase in bbls,
   SG_wm = specific gravity of weight material.

   Examples: Calculate the number of sacks of 4,2 ASG of barite required to increase the density of 100 bbls of 12,0 ppg (ρ₀) mud to 14,0 ppg (ρ_n) and the resultant volume increase:

   W_M = 5·14,0·(14,0-12,0)

   W_M = 140 sacks of barite required for 100 bbls of 12,0 ppg mud

   

   V_i = 9,5 bbls volume increase

3. Increase mud weight:
   
   where:

   350 = weight of 1 barrel of fresh water in lbs,
   8,34 = mud weight of fresh water in lb/gal (ppg),
   SG_wm = specific gravity of weight material, gm/cc.
4. Volume increase with 100 lb sacks of weight material based on the change in mud weight:
   
   where:

   V_i = volume increase in bbls.

   Example: Calculate the number of sacks of 4,2 ASG barite required to increase the density of 100 barrels of 12,0 ppg (ρ₀) mud to 14,0 ppg (ρ_n):

   RESULT: V_i = 9,5 bbls volume increase

Example: Determine the number of barrels of fresh water weighing 8,34 ppg required to reduce the mud weight of 100 bbls of water – base mud (WBM) from 14,0 ppg to 12,0 ppg:

Example: Determine the number of barrels of base oil weighing 6,7 ppg required to reduce the mud weight of 100 bbls of synthetic – base mud (SBM) from 14,0 ppg to 12,0 ppg:

RESULT: V_a = 37,7 bbls of oil are required

Mixing Fluids of Different Densities (The Material Balance Formula)

where: V_f = final volume in bbls, gals, etc.,

ρ_f = final mud weight in ppg, lb/ft³, etc.,

V₁ = volume of fluid 1 in bbls, gals, etc.,

Ρ₁ = mud weight of fluid 1 in ppg, lb/ft³, etc.,

V₂ = volume of fluid 2 in bbls, gals, etc.,

Ρ₂= mud weight of fluid 2 in ppg, lb/ft³, etc.

Example: A limit is placed on the desired volume:

Determine the volume of 11,0 ppg mud and 14,0 ppg mud required to build 300 bbl of 11,5 ppg mud:

300 · 11,5 = ((300 – x) · 11,0) + 14,0 · x

3450 = (3300 – 11,0 x) + 14,0 · x

3450 – 3300 = 3,0 x

150 = 3,0 x

x = 50 bbls of 14,0 ppg mud

300 – 50 = 250 bbls of 11,0 ppg required

To check the volumes are corrected:

300 · 11,5 = 250 · 11,0 + 50 · 14,0

3450 = 2750 + 700

3450 = 3450

To check the final mud weight:

300 x = 250 · 11,0 + 50 · 14,0

300 x = 2750 + 700

x = 3450/300 = 11,5 ppg

Example: No limit is placed on volume:

Determine the final mud weight when the following two muds are mixed together:

Given: 400 bbl of 11,0 ppg mud and 400 bbl of 14,0 mud

RESULT: ρ_f = 12,5 ppg

NOTE: Steps 1 – 4 are performed on high salt content muds. For low – chloride muds, begin with Step 5.

Step 1: Calculate the Volume of Salt water in Percent (%):

Step 2: Calculate the Volume of the Suspended Solids in Percent (%):

Step 3: Calculate the Average Specific Gravity (ASG) of the Salt Water:

Step 4: Calculate the Average Specific Gravity of the Solids Suspended in the Mud:

Step 5: Calculate the Average Specific Gravity of Solids without Salt in Water Phase:

Step 6: Calculate the Volume of Low Gravity Solids (LSG) in percent (%):

Step 7: Calculate the Amount of LGS in lb/bbl:

Step 8: Calculate the Volume of the Weight Material in Percent (%):

Step 9: Calculate the Amount of High Specific Gravity Weight Material in Pounds (lbs):

Step 10: Calculate the Amount of Bentonite (High – quality LGS) in the Mud:

• If the cation exchange capacity (CEC) of the formation clays and the methylene blue test (MBT) of the mud are know:
  
  
  1. Calculate the Amount of Bentonite in the Mud in lb/bbl:
     
     where:

     B_ppb = amount of bentonite in the mud in lb/bbl,
     F_CEC = CEC of the formation solids,
     M_MBT = MBT of the mud.
  2. Calculate the Volume of Bentonite in the Mud in Percent (%):
     
     where:

     B_% = amount of bentonite in the mud in %.
• If the cation exchange capacities (CEC) of the formation clays are not know:
  
  
  1. Calculate the Volume of Bentonite in Percent (%):
     
  2. Calculate the Amount of Bentonite in the Mud in lb/bbl:
     

Step 11: Calculate the Volume of Drill Solids in Percent (%):

Step 12: Calculate the Amount of Drill Solids in the Mud in lb/bbl:

Example:

Step 1: Calculate the volume of salt water in %:

Step 2: Calculate the volume of suspended solids in %:

Step 3: Calculate the average specific gravity (ASG) of the salt water:

Step 4: Calculate the average specific gravity of the solids suspended in the mud:

Step 5: Because a high chloride example is being used, Step 5 is omitted.

Step 6: Calculate the volume of low gravity solids (LGS) in percent (%):

Step 7: Calculate the amount of LGS in lb/bbl:

Step 8: Calculate the volume of the weight material in percent (%):

Step 9: Calculate the amount of high specific gravity weight material in pounds (lb/bbl):

Step 10: Calculate the amount of bentonite in the mud in lb/bbl:

Step 11: Calculate the volume of bentonite in the mud in percent (%):

Step 12: Calculate the volume of drill solids in percent (%):

Step 13: Calculate the amount of drill solids in the mud in lb/bbl:

Basic gas low:

Basic gas law plus compressibility factor:

Shortened gas expansion equation:

• With pipe in the wellbore:
  
  Example:
  D_h – 9 5/8 in. casing – 43,5 lb/ft
  D_p
  Mud weight

  = 8,755 in. ID
  = 5,0 in. OD
  = 10,5 ppg
  
• With no pipe in the wellbore:
  
  Example:
  D_h – 9 5/8 in. casing – 43,5 lb/ft
  Mud weight

  = 8,755 in. ID
  = 10,5 ppg
  

• Determine formation pressure from equation:
  psi = formation pressure equivalent mud weight, ppg · 0,052 · TVD, ft
• Determine oil hydrostatic pressure:
  psi = oil specific gravity · 0,052 · TVD, ft
• Determine surface pressure:
  Surface pressure, psi = formation pressure, psi – oil hydrostatic pressure, psi

  Example: Oil bearing sand at 12500 ft with a formation pressure equivalent to 13,5 ppg. If the specific gravity of the oil is 0,5, what will be the static surface pressure during a drill stem test?

• Determine formation pressure, psi:
  FT, psi = 13,5 ppg · 0,052 · 12500 ft = 8775 psi
• Determine oil hydrostatic pressure:
  psi = (0,5 · 8,33) · 0,052 · 12500 ft = 2707
• Determine surface pressure:
  Surface pressure, psi = 8775 psi – 2707 psi = 6068 psi

These series of formulas will determine the correct jet sizes when optimizing for jet impact or hydraulic horsepower and optimum flow rate for two or three nozzles.

1. Nozzle area, sq. in.:
   
2. Bit nozzle pressure los, psi (Pb):
   
3. Total pressure losses except bit nozzle pressure loss, psi (Pc):
   
4. Determine slope of line M:
   
5. Optimum pressure losses (Popt):
   1. For impact force:
      
   2. For hydraulic horsepower:
      
6. For optimum flow rate (Qopt):
   1. For impact force:
      
   2. For hydraulic horsepower:
      
7. To determine pressure at the bit (Pb):

   Pb = Pmax – Popt

8. To determine nozzle area, sq. in.:
   
9. To determine nozzles, 1/32 in, for three nozzles:
   
10. To determine nozzles, 1/32 in. for two nozzles:
    

Example: Optimize bit hydraulics on a well with the following:

Select the proper jet size for impact force and hydraulic horsepower for 2 and 3 jets:

1. Nozzle area, sq. in.:
   
2. Bit nozzle pressure loss, psi (Pb):
   
   
3. Total pressure losses expect bit nozzle pressure loss (Pc), psi:

   Pc₁ = 3000 psi – 478 psi = 2522 psi

   Pc₂ = 1300 psi – 205 psi = 1095 psi

4. Determine slope of line (M):
   
5. Determine optimum pressure losses, psi (Popt):
   1. For impact force:
      
   2. For hydraulic horsepower:
      
6. Determine optimum flow rate (Qopt):
   1. For impact force:
      
   2. For hydraulic horsepower:
      
7. To determine pressure at the bit (Pb):
   1. For impact force:

      Pb = 3000 psi –1511 psi = 1489 psi

   2. For hydraulic horsepower:

      Pb = 3000 psi –1010 psi = 1990 psi

8. To determine nozzle area, sq. in.:
   1. For impact force:
      
   2. For hydraulic horsepower:
      
9. To determine nozzles, 1/32 in, for three nozzles:
   1. For impact force:
      
   2. For hydraulic horsepower:
      

      Note: usually the nozzles size will have a decimal fraction. The fraction times 3 will determine how many nozzles should be larger than that calculated.

   3. For impact force:

      0,76 · 3 = 2,28 rounded to 2

      so:

      1 jet
      2 jets

      = 10/32
      = 11/32
   4. For hydraulic horsepower:

      0,03 · 3 = 0,09 rounded to 0

      so:

      3 jets

      = 9/32 in.
10. To determine nozzles, 1/32 in. for two nozzles:
    1. For impact force:
       
    2. For hydraulic horsepower:
       

1. Determine n:
   
2. Determine K:
   
3. Determine x:
   
4. Determine critical annular velocity:
   
5. Determine critical flow rate:
   

Nomenclature:

Example:

1. Determine n:
   
2. Determine K:
   
3. Determine x:
   
4. Determine critical annular velocity:
   
5. Determine critical flow rate: