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Well Control Equations

Browse 82 well control petroleum engineering equations with formulas, inputs, outputs, units, and sources.

Well control calculators support hydrostatic pressure, shut-in pressure interpretation, circulating pressure schedules, MAASP, and kick tolerance checks.

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Drilling EngineeringWell Control

Accumulator Bottles Required for BOP Function Volume

Nbottles=⌈VrequiredVusable,bottle⌉N_{bottles}=\left\lceil\frac{V_{required}}{V_{usable,bottle}}\right\rceil
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Drilling EngineeringWell Control

Accumulator Nitrogen Gas Volume from Boyle Law

VN2=PpreVbottlePsystemV_{N2}=\frac{P_{pre}V_{bottle}}{P_{system}}
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Drilling EngineeringWell Control

Actual Gas Migration Rate from Casing Pressure Increase

RGM=(Pcsg2−Pcsg1)/Δt0.052MWRGM=\frac{(P_{csg2}-P_{csg1})/\Delta t}{0.052MW}
View formula
Drilling EngineeringWell Control

Additional Mud Returned by Slug

Vadd=(WsWm−1)VsV_{add}=\left(\frac{W_s}{W_m}-1\right)V_s
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Drilling EngineeringWell Control

Breakover Point Between Stripping and Snubbing

Lds=Ldc+LbpL_{ds}=L_{dc}+L_{bp}
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Drilling EngineeringWell Control

Brine Fluid Density to Mix for Temperature Correction

ρmix=ρavg+(Tavg−Tsurface)WL\rho_{mix}=\rho_{avg}+(T_{avg}-T_{surface})WL
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Drilling EngineeringWell Control

Bullhead Pump Speed to Exceed Gas Migration

SPMbh=(RGM/60)CtbgPOSPM_{bh}=\frac{(RGM/60)C_{tbg}}{PO}
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Drilling EngineeringWell Control

Bullheading Formation Fracture Pressure from Gradient

Pfrac=GfracTVDperfP_{frac}=G_{frac}TVD_{perf}
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Drilling EngineeringWell Control

Bullheading Initial Average Fluid Density

ρinit=Ph,init0.052TVDperf\rho_{init}=\frac{P_{h,init}}{0.052TVD_{perf}}
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Drilling EngineeringWell Control

Bullheading Initial Hydrostatic Pressure from Formation Pressure

Ph,init=Pform−SITPP_{h,init}=P_{form}-SITP
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Drilling EngineeringWell Control

Bullheading Maximum Final Surface Pressure

Psurf,final,max=Pfrac−KFW 0.052TVDperfP_{surf,final,max}=P_{frac}-KFW\,0.052TVD_{perf}
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Drilling EngineeringWell Control

Bullheading Maximum Initial Surface Pressure

Psurf,init,max=Pfrac−Ph,initP_{surf,init,max}=P_{frac}-P_{h,init}
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Drilling EngineeringWell Control

Bullheading Volume to Perforations

Vbh=Vlines+Vsurface→EOT+VEOT→top+Vtop→bottomV_{bh}=V_{lines}+V_{surface\to EOT}+V_{EOT\to top}+V_{top\to bottom}
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Drilling EngineeringWell Control

Casing Pressure After Subsea Start-Up

Pstart=SICP−PclP_{start}=SICP-P_{cl}
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Drilling EngineeringWell Control

Casing Pressure Increase from Stripping Into Influx

P=H(G−Gi)P=H(G-G_i)
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Drilling EngineeringWell Control

Casing Pressure Increase Rate from Gas Migration

Pinc=RGM MWGP_{inc}=RGM\,MWG
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Drilling EngineeringWell Control

Closed-Ended Pipe Buoyed Weight with No Fluid Inside

Wbuoyed,closed=Wair−OD2FW24.5W_{buoyed,closed}=W_{air}-\frac{OD^2FW}{24.5}
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Drilling EngineeringWell Control

Constant Bottomhole Pressure Bleed Volume for Rising Gas

Vbleed=ΔPstepCaGV_{bleed}=\frac{\Delta P_{step}C_a}{G}
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Drilling EngineeringWell Control

Dry Pipe Pulled Before Fill-Up for Pressure Drop

Ldry=ΔP(Cann+Cdp)0.052MWDdpL_{dry}=\frac{\Delta P(C_{ann}+C_{dp})}{0.052MWD_{dp}}
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Drilling EngineeringWell Control

Equivalent Mud Weight from Surface Pressure

EMW=Psurf0.052TVD+MWEMW=\frac{P_{surf}}{0.052TVD}+MW
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Drilling EngineeringWell Control

Final Circulating Pressure

FCP=SCRPKWMOMWFCP=SCRP\frac{KWM}{OMW}
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Drilling EngineeringWell Control

Formation Integrity Test Pressure

PFIT=(FIT−MW)0.052TVDP_{FIT}=(FIT-MW)0.052TVD
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Drilling EngineeringWell Control

Height Gain from Stripping Into Influx

H=LstrippedCdp+DdpCaH=L_{stripped}\frac{C_{dp}+D_{dp}}{C_a}
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Drilling EngineeringWell Control

Hydraulic Force from Pressure and Diameter

F=PD2(0.7854)F=PD^2(0.7854)
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Drilling EngineeringWell Control

Hydrostatic Pressure Decrease Due to Gas-Cut Mud

Ploss=MGCVP_{loss}=\frac{MG}{C}V
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Drilling EngineeringWell Control

Hydrostatic Pressure Drop per Foot Pulling Dry Pipe

ΔPdry/ft=0.052MWDdpCann+Cdp\Delta P_{dry/ft}=\frac{0.052MWD_{dp}}{C_{ann}+C_{dp}}
View formula
Drilling EngineeringWell Control

Hydrostatic Pressure Drop per Foot Pulling Wet Pipe

ΔPwet/ft=0.052MWCdp+DdpCann\Delta P_{wet/ft}=0.052MW\frac{C_{dp}+D_{dp}}{C_{ann}}
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Drilling EngineeringWell Control

Hydrostatic Pressure from Mud Weight

HP=0.052MW⋅TVDHP = 0.052 MW \cdot TVD
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Drilling EngineeringWell Control

Hydrostatic Pressure in Annulus Due to Slug

P=VaVs(Ws−Wm)0.052P=V_aV_s(W_s-W_m)0.052
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Drilling EngineeringWell Control

Initial Circulating Pressure

ICP=SCRP+SIDPPICP=SCRP+SIDPP
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Drilling EngineeringWell Control

Kick Analysis - Formation Pressure With Well Shut-In

Pfp=SIDPP+MW⋅0.052⋅hP_{fp} = SIDPP + MW\cdot0.052\cdot h
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Drilling EngineeringWell Control

Kick Analysis - Height of Influx

hi=PGACh_i = \frac{PG}{AC}
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Drilling EngineeringWell Control

Kick Analysis - Influx Density

I=MW−SICP−SIDPPhi⋅0.052I = MW - \frac{SICP - SIDPP}{h_i\cdot0.052}
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Drilling EngineeringWell Control

Kick Analysis - Maximum Pit Gain From Gas Kick

MPG=4PVCKWMMPG = 4\sqrt{\frac{PVC}{KWM}}
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Drilling EngineeringWell Control

Kick Analysis - Shut-In Drill Pipe Pressure

SIDPP=Pfp−MW⋅0.052⋅hSIDPP = P_{fp} - MW\cdot0.052\cdot h
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Drilling EngineeringWell Control

Kick Tolerance Bottomhole Gas Volume

KT=min⁡(Vinitial,Vbottom,shoe)KT=\min(V_{initial},V_{bottom,shoe})
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Drilling EngineeringWell Control

Kill Weight Mud Determination - Moore Equation

KWM=SIDPP0.052TVD+OMWKWM=\frac{SIDPP}{0.052TVD}+OMW
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Drilling EngineeringWell Control

Level Drop After Pumping a Slug

Ldrop=(Ws/Wm−1)VsCdpL_{drop}=\frac{(W_s/W_m-1)V_s}{C_{dp}}
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Drilling EngineeringWell Control

Maximum Allowable Annular Surface Pressure from Shoe EMW

MAASP=(MWmax−MW)0.052TVDshoeMAASP=(MW_{max}-MW)0.052TVD_{shoe}
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Drilling EngineeringWell Control

Maximum Allowable Mud Weight From Leak-Off Pressure

MWmax=MW+Pl0.052TVDMW_{max} = MW + \frac{P_l}{0.052TVD}
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Drilling EngineeringWell Control

Maximum Allowable Surface Pressure Governed by Casing Burst

MASP=PbcS−(Wu−Wo)0.052HMASP = P_{bc}S - (W_u - W_o)0.052H
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Drilling EngineeringWell Control

Maximum Surface Pressure From Gas Kick in Water-Based Mud

MSP=0.2PVKWMCMSP=0.2\sqrt{\frac{PVKWM}{C}}
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Drilling EngineeringWell Control

Minimum Surface Pressure Before Stripping

Pmin=WcLstandDc2(0.7854)P_{min}=\frac{W_cL_{stand}}{D_c^2(0.7854)}
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Drilling EngineeringWell Control

Mud Pressure Gradient from Mud Weight

MWG=0.052MWMWG=0.052MW
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Drilling EngineeringWell Control

New MAASP After Kill Mud Weight

MAASPkill=(MWmax−KMW)0.052TVDshoeMAASP_{kill}=(MW_{max}-KMW)0.052TVD_{shoe}
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Drilling EngineeringWell Control

New Pump Pressure with Mud Weight Change

Pnew=PcurrentMWnewMWoldP_{new}=P_{current}\frac{MW_{new}}{MW_{old}}
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Drilling EngineeringWell Control

Open-Ended Pipe Buoyed Weight

Wbuoyed,open=WairBFW_{buoyed,open}=W_{air}BF
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Drilling EngineeringWell Control

Pore Pressure Gradient - Rehm and McClendon

gp=0.398log⁡10(dcn−dco)+0.86g_p=0.398\log_{10}(d_{cn}-d_{co})+0.86
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Drilling EngineeringWell Control

Pore Pressure Gradient - Zamora

gp=gndcndcog_p=g_n\frac{d_{cn}}{d_{co}}
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Drilling EngineeringWell Control

Pressure by Each Barrel of Mud in Casing

Pbbl=1029.4⋅0.052MWDh2−Dp2P_{bbl}=1029.4\cdot0.052\frac{MW}{D_h^2-D_p^2}
View formula
Drilling EngineeringWell Control

Rectangular Tank Capacity per Foot

Crect,ft=LW(0.178)C_{rect,ft}=LW(0.178)
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Drilling EngineeringWell Control

Rectangular Tank Capacity per Inch

Crect,in=LW(0.0148)C_{rect,in}=LW(0.0148)
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Drilling EngineeringWell Control

Rectangular Tank Volume

Vtank=LWH5.615V_{tank}=\frac{LWH}{5.615}
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Drilling EngineeringWell Control

Riser Hydrostatic Loss on Disconnect

ΔPriser=0.052MW(WD+AG)−0.052SW WD\Delta P_{riser}=0.052MW(WD+AG)-0.052SW\,WD
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Drilling EngineeringWell Control

Riser Margin from Hydrostatic Loss

RM=ΔPriser0.052(TVD−WD−AG)RM=\frac{\Delta P_{riser}}{0.052(TVD-WD-AG)}
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Drilling EngineeringWell Control

Shut-In Pressure Increase from Gas Migration Time

ΔP=RGM MWG Δt\Delta P=RGM\,MWG\,\Delta t
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Drilling EngineeringWell Control

Specific Gravity to Fluid Weight

FW=8.33SGFW=8.33SG
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Drilling EngineeringWell Control

Stored Hydraulic Fluid Volume in Accumulator Bottle

Vfluid=Vbottle−PpreVbottlePsystemV_{fluid}=V_{bottle}-\frac{P_{pre}V_{bottle}}{P_{system}}
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Drilling EngineeringWell Control

Subsea Choke Line Pressure Loss

CLPL=0.000061MWLQ1.86ID4.86CLPL=\frac{0.000061MWLQ^{1.86}}{ID^{4.86}}
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Drilling EngineeringWell Control

Subsea Choke Line Pressure Loss Adjusted for Mud Weight

CLPL=WnCLPLoWoCLPL=\frac{W_n CLPL_o}{W_o}
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Drilling EngineeringWell Control

Subsea Choke Line Velocity

V=24.5QID2V=24.5\frac{Q}{ID^2}
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Drilling EngineeringWell Control

Subsea Maximum Allowable Mud Weight from Leakoff Test

Wmax=Plo0.052H+WuW_{max}=\frac{P_{lo}}{0.052H}+W_u
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Drilling EngineeringWell Control

Subsea Stack Casing Burst Pressure

CBP=YPc−HP+HPswCBP=YP_c-HP+HP_{sw}
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Drilling EngineeringWell Control

Surface Pressure During Drill Stem Test

P=0.052h(EMW−SG⋅8.33)P = 0.052h(EMW - SG\cdot8.33)
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Drilling EngineeringWell Control

Surface Test Pressure Required to Frac the Formation

PST=FGD−0.052ρmDP_{ST}=FGD-0.052\rho_mD
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Drilling EngineeringWell Control

Surface-to-Bit Strokes for Wait and Weight Schedule

Sbit=CdpTDPOS_{bit}=\frac{C_{dp}TD}{PO}
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Drilling EngineeringWell Control

Time to MAASP During Gas Migration

tlimit=MAASP−SICPcurrentRGM MWGt_{limit}=\frac{MAASP-SICP_{current}}{RGM\,MWG}
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Drilling EngineeringWell Control

Total Mud Returned by Slug

Vreturn=WsWmVsV_{return}=\frac{W_s}{W_m}V_s
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Drilling EngineeringWell Control

Total Usable Fluid Volume from Accumulator Bank

Vtotal=NbottlesVusable,bottleV_{total}=N_{bottles}V_{usable,bottle}
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Drilling EngineeringWell Control

Trip Margin from Yield Point and Annular Clearance

TM=YP11.7(Dh−Dp)TM=\frac{YP}{11.7(D_h-D_p)}
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Drilling EngineeringWell Control

Tubular Buoyed Weight with Different Internal and Annular Fluids

Wbuoyed,diff=Wair+ID2FWtbg24.5−OD2FWann24.5W_{buoyed,diff}=W_{air}+\frac{ID^2FW_{tbg}}{24.5}-\frac{OD^2FW_{ann}}{24.5}
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Drilling EngineeringWell Control

Usable Fluid Volume per Surface Accumulator Bottle

Vusable=Vfluid,operating−Vfluid,minV_{usable}=V_{fluid,operating}-V_{fluid,min}
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Drilling EngineeringWell Control

Vertical Cylindrical Tank Capacity per Foot

Ccyl,ft=D27.148C_{cyl,ft}=\frac{D^2}{7.148}
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Drilling EngineeringWell Control

Vertical Cylindrical Tank Volume

Vcyl=Ccyl,ftHV_{cyl}=C_{cyl,ft}H
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Drilling EngineeringWell Control

Volumetric Mud Bleed from Allowed Pressure Rise

Vbleed=ΔPallowFp/bblV_{bleed}=\frac{\Delta P_{allow}}{F_{p/bbl}}
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Drilling EngineeringWell Control

Wait and Weight Drill Pipe Pressure at Schedule Strokes

Pdp=ICP−(ICP−FCP)SschedSbitP_{dp}=ICP-\frac{(ICP-FCP)S_{sched}}{S_{bit}}
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Drilling EngineeringWell Control

Wait and Weight Pressure Drop over Stroke Interval

ΔPinterval=(ICP−FCP)SintervalSbit\Delta P_{interval}=\frac{(ICP-FCP)S_{interval}}{S_{bit}}
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Drilling EngineeringWell Control

Wait and Weight Pressure Drop per Stroke

ΔPstk=ICP−FCPSbit\Delta P_{stk}=\frac{ICP-FCP}{S_{bit}}
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Drilling EngineeringWell Control

Wet Pipe Pulled Before Fill-Up for Pressure Drop

Lwet=ΔP Cann0.052MW(Cdp+Ddp)L_{wet}=\frac{\Delta P\,C_{ann}}{0.052MW(C_{dp}+D_{dp})}
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Drilling EngineeringWell Control

Workover Buoyancy Factor from Fluid Weight

BF=65.4−FW65.4BF=\frac{65.4-FW}{65.4}
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Drilling EngineeringWell Control

Workover Kill Fluid Weight from Bottomhole Pressure

KFW=BHP0.052TVDKFW=\frac{BHP}{0.052TVD}
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Drilling EngineeringWell Control

Workover Kill Fluid Weight from Shut-In Tubing Pressure

KFW=SITP0.052TVDperf+OFWKFW=\frac{SITP}{0.052TVD_{perf}}+OFW
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