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**PETE 411 Well Drilling Lesson 13 Pressure Drop Calculations**

API Recommended Practice 13D Third Edition, June 1, 1995

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**Homework HW #7. Pressure Drop Calculations Due Oct. 9, 2002**

The API Power Law Model

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**Contents The Power Law Model The Rotational Viscometer**

A detailed Example - Pump Pressure Pressure Drop in the Drillpipe Pressure Drop in the Bit Nozzles Pressure Drop in the Annulus Wellbore Pressure Profiles

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Power Law Model K = consistency index n = flow behaviour index

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**Fluid Flow in Pipes and Annuli**

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**Fluid Flow in Pipes and Annuli**

Laminar Flow Turbulent LOG (SHEAR STRESS) (psi) n 1

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**Rotating Sleeve Viscometer**

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**Rotating Sleeve Viscometer**

(RPM * 1.703) SHEAR RATE sec -1 5.11 170.3 511 1022 VISCOMETER RPM 3 100 300 600 ANNULUS BOB DRILL STRING SLEEVE API RP 13D

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**API RP 13D, June 1995 for Oil-Well Drilling Fluids**

API RP 13D recommends using only FOUR of the six usual viscometer readings: Use 3, 100, 300, 600 RPM Readings. The 3 and 100 RPM reading are used for pressure drop calculations in the annulus, where shear rates are, generally, not very high. The 300 and 600 RPM reading are used for pressure drop calculations inside drillpipe, where shear rates are, generally, quite high.

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**Example: Pressure Drop Calculations**

Example Calculate the pump pressure in the wellbore shown on the next page, using the API method. The relevant rotational viscometer readings are as follows: R3 = (at 3 RPM) R100 = 20 (at 100 RPM) R300 = 39 (at 300 RPM) R600 = 65 (at 600 RPM)

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**Pressure Drop Calculations**

PPUMP Q = gal/min r = lb/gal PPUMP = DPDP + DPDC + DPBIT NOZZLES + DPDC/ANN + DPDP/ANN + DPHYD

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**Pressure Drop In Drill Pipe**

OD = 4.5 in ID = in L = 11,400 ft Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity in Pipe (Vp):

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**Pressure Drop In Drill Pipe**

OD = 4.5 in ID = in L = 11,400 ft Effective Viscosity in Pipe (mep): Reynolds Number in Pipe (NRep):

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**Pressure Drop In Drill Pipe**

OD = 4.5 in ID = in L = 11,400 ft NOTE: NRe > 2,100, so Friction Factor in Pipe (fp): So,

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**Pressure Drop In Drill Pipe**

OD = 4.5 in ID = in L = 11,400 ft Friction Pressure Gradient (dP/dL)p : Friction Pressure Drop in Drill Pipe : DPdp = 665 psi

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**Pressure Drop In Drill Collars**

OD = 6.5 in ID = 2.5 in L = 600 ft Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity inside Drill Collars (Vdc):

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**Pressure Drop In Drill Collars**

OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars Effective Viscosity in Collars(mec): Reynolds Number in Collars (NRec):

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**Pressure Drop In Drill Collars**

OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars NOTE: NRe > 2,100, so Friction Factor in DC (fdc): So,

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**Pressure Drop In Drill Collars**

OD = 6.5 in ID = 2.5 in L = 600 ft Pressure Drop In Drill Collars Friction Pressure Gradient (dP/dL)dc : Friction Pressure Drop in Drill Collars : DPdc = 227 psi

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**Pressure Drop across Nozzles**

DN1 = 11 32nds (in) DN2 = 11 32nds (in) DN3 = 12 32nds (in) DPNozzles = 1,026 psi

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**Pressure Drop in DC/HOLE Annulus**

Q = gal/min r = lb/gal 8.5 in DHOLE = 8.5 in ODDC = 6.5 in L = 600 ft

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**Pressure Drop in DC/HOLE Annulus**

DHOLE = 8.5 in ODDC = 6.5 in L = 600 ft Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity in DC/HOLE Annulus (Va):

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**Pressure Drop in DC/HOLE Annulus**

DHOLE = 8.5 in ODDC = 6.5 in L = 600 ft Effective Viscosity in Annulus (mea): Reynolds Number in Annulus (NRea):

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**Pressure Drop in DC/HOLE Annulus**

DHOLE = 8.5 in ODDC = 6.5 in L = 600 ft NOTE: NRe < 2,100 Friction Factor in Annulus (fa): DPdc/hole = 31.6 psi So,

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**Pressure Drop in DP/HOLE Annulus**

q = gal/min r = lb/gal DHOLE = 8.5 in ODDP = 4.5 in L = 11,400 ft

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**Pressure Drop in DP/HOLE Annulus**

DHOLE = 8.5 in ODDP = 4.5 in L = 11,400 ft Power-Law Constant (n): Fluid Consistency Index (K): Average Bulk Velocity in Annulus (Va):

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**Pressure Drop in DP/HOLE Annulus**

Effective Viscosity in Annulus (mea): Reynolds Number in Annulus (NRea):

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**Pressure Drop in DP/HOLE Annulus**

NOTE: NRe < 2,100 Friction Factor in Annulus (fa): DPdp/hole = psi So, psi

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**Pressure Drop Calculations - SUMMARY -**

PPUMP = DPDP + DPDC + DPBIT NOZZLES + DPDC/ANN + DPDP/ANN + DPHYD PPUMP = ,026 PPUMP = 1, = 2,103 psi

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**PPUMP = 1,918 + 185 = 2,103 psi PPUMP = DPDS + DPANN + DPHYD**

DPDS = DPDP + DPDC + DPBIT NOZZLES = ,026 = 1,918 psi P = 0 DPANN = DPDC/ANN + DPDP/ANN = = 185 DPHYD = 0 PPUMP = 1, = 2,103 psi

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**What is the BHP? BHP = 7,985 psig BHP = 185 + 7,800**

BHP = DPFRICTION/ANN + DPHYD/ANN BHP = DPDC/ANN + DPDP/ANN * 12.5 * 12,000 = ,800 = 7,985 psig BHP = ,800 BHP = 7,985 psig

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**DRILLPIPE DRILL COLLARS BIT NOZZLES ANNULUS**

2103 DRILL COLLARS BIT NOZZLES ANNULUS

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BHP DRILLSTRING ANNULUS

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CIRCULATING 2103 STATIC

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**DRILLSTRING ANNULUS BIT**

2103 DRILLSTRING ANNULUS (Static) BIT

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Pipe Flow - Laminar In the above example the flow down the drillpipe was turbulent. Under conditions of very high viscosity, the flow may very well be laminar. NOTE: if NRe < 2,100, then Friction Factor in Pipe (fp): Then and

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**Annular Flow - Turbulent**

In the above example the flow up the annulus was laminar. Under conditions of low viscosity and/or high flow rate, the flow may very well be turbulent. NOTE: if NRe > 2,100, then Friction Factor in the Annulus: Then and

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**Critical Circulation Rate**

Example The above fluid is flowing in the annulus between a 4.5” OD string of drill pipe and an 8.5 in hole. The fluid density is 12.5 lb/gal. What is the minimum circulation rate that will ensure turbulent flow? (why is this of interest?)

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**Critical Circulation Rate**

In the Drillpipe/Hole Annulus: Q, gal/min V, ft/sec Nre ,044 ,154 ,446 ,756 ,086 ,099 ,100

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**Optimum Bit Hydraulics**

Under what conditions do we get the best hydraulic cleaning at the bit? maximum hydraulic horsepower? maximum impact force? Both these items increase when the circulation rate increases. However, when the circulation rate increases, so does the frictional pressure drop.

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n = 1.0

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**Importance of Pipe Size**

Eq. 4.66e or, *Note that a small change in the pipe diameter results in large change in the pressure drop! (q = const.) Decreasing the pipe ID 10% from 5.0” to 4.5” would result in an increase of frictional pressure drop by about 65% !!

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Dpf = v 1.75 turbulent flow Dpf = 9.11 v laminar flow Use max. Dpf value

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