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Surge pressure prediction for wellbore flow: Difference between revisions

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An exceptional flow case is the operation of running pipe or [[Casing and tubing|casing]] into the wellbore. Moving pipe into the wellbore displaces fluid, and the flow of this fluid generates pressures called surge pressures.
An exceptional flow case is the operation of running pipe or [[Casing_and_tubing|casing]] into the wellbore. Moving pipe into the wellbore displaces fluid, and the flow of this fluid generates pressures called surge pressures.


==Overview==
== Overview ==


When the pipe is pulled from the well, negative pressures are generated, and these pressures are called swab pressures. In most wells, the magnitude of the pressure surges is not critical because proper [[Casing design|casing design]] and mud programs leave large enough margins between fracture pressures and formation-fluid pressures. Typically, dynamic fluid flow is not a consideration, so a steady-state calculation can be performed. A certain fraction of wells, however, cannot be designed with large surge-pressure margins. In these critical wells, pressure surges must be maintained within narrow limits. In other critical wells, pressure margins may be large, but pressure surges may still be a concern. Some operations are particularly prone to large pressure surges (e.g., running of low-clearance liners in deep wells). The reader is referred to papers on dynamic surge calculations,<ref name="r1"/><ref name="r2"/>and the article on [[Dynamic wellbore pressure prediction|dynamic pressure calculation]] gives a taste of this type of calculation.
When the pipe is pulled from the well, negative pressures are generated, and these pressures are called swab pressures. In most wells, the magnitude of the pressure surges is not critical because proper [[Casing_design|casing design]] and mud programs leave large enough margins between fracture pressures and formation-fluid pressures. Typically, dynamic fluid flow is not a consideration, so a steady-state calculation can be performed. A certain fraction of wells, however, cannot be designed with large surge-pressure margins. In these critical wells, pressure surges must be maintained within narrow limits. In other critical wells, pressure margins may be large, but pressure surges may still be a concern. Some operations are particularly prone to large pressure surges (e.g., running of low-clearance liners in deep wells). The reader is referred to papers on dynamic surge calculations,<ref name="r1">Lubinski, A., Hsu, F.H., and Nolte, K.G. 1977. Transient Pressure Surges Because of Pipe Movement in an Oil Well. Revue de I’lnst. Fran. du Pet (May/June): 307.</ref><ref name="r2">Mitchell, R.F. 1988. Dynamic Surge/Swab Pressure Predictions. SPE Drill Eng 3 (3): 325-333. SPE-16156-PA. http://dx.doi.org/10.2118/16156-PA.</ref>and the article on [[Dynamic_wellbore_pressure_prediction|dynamic pressure calculation]] gives a taste of this type of calculation.


==Surge analysis==
== Surge analysis ==


The surge pressure analysis consists of two analytical regions: the pipe-annulus region and the pipe-to-bottomhole region ('''Fig. 1'''). The fluid flow in the pipe-annulus region should be solved using techniques already discussed, but with the following special considerations: frictional pressure drop must be solved for flow in an annulus with a moving pipe, and in deviated wells, the effect of annulus eccentricity should be considered. The analysis of the pipe-to-bottomhole region should consist of a static pressure analysis, with pressure boundary condition determined by the fluid flow at the bit, or pipe end if running casing. The pipe-annulus model and the pipe-to-bottomhole model then are connected through a comprehensive set of force and displacement compatibility relations.
The surge pressure analysis consists of two analytical regions: the pipe-annulus region and the pipe-to-bottomhole region ('''Fig. 1'''). The fluid flow in the pipe-annulus region should be solved using techniques already discussed, but with the following special considerations: frictional pressure drop must be solved for flow in an annulus with a moving pipe, and in deviated wells, the effect of annulus eccentricity should be considered. The analysis of the pipe-to-bottomhole region should consist of a static pressure analysis, with pressure boundary condition determined by the fluid flow at the bit, or pipe end if running casing. The pipe-annulus model and the pipe-to-bottomhole model then are connected through a comprehensive set of force and displacement compatibility relations.


<gallery widths=300px heights=200px>
<gallery widths="300px" heights="200px">
File:Devol2 1102final Page 130 Image 0001.png|'''Fig. 1—Surge-pressure calculation regions.'''
File:Devol2 1102final Page 130 Image 0001.png|'''Fig. 1—Surge-pressure calculation regions.'''
</gallery>
</gallery>


==Boundary conditions==
== Boundary conditions ==


The following conditions describe the flow for a surge or swab operation.
The following conditions describe the flow for a surge or swab operation.


===Surface boundary conditions===
=== Surface boundary conditions ===


There are six variables that can be specified at the surface:
There are six variables that can be specified at the surface:


''P''<sub>1</sub> = pipe pressure.
''P''<sub>1</sub> = pipe pressure.
''v''<sub>1</sub> = pipe fluid velocity.


''P''<sub>2</sub> = annulus pressure.  
''v''<sub>1</sub> = pipe fluid velocity.


''v''<sub>2</sub> = annulus fluid velocity.  
''P''<sub>2</sub> = annulus pressure.
 
''v''<sub>2</sub> = annulus fluid velocity.


''v''<sub>3</sub> = pipe velocity.
''v''<sub>3</sub> = pipe velocity.
Line 33: Line 33:
A maximum of three boundary conditions can be specified at the surface. For surge without circulation, the following boundary conditions hold:
A maximum of three boundary conditions can be specified at the surface. For surge without circulation, the following boundary conditions hold:


''P''<sub>1</sub> = atmospheric pressure.  
''P''<sub>1</sub> = atmospheric pressure.


''P''<sub>2</sub> = atmospheric pressure.  
''P''<sub>2</sub> = atmospheric pressure.


''v''<sub>3</sub> = specified pipe velocity.
''v''<sub>3</sub> = specified pipe velocity.
Line 41: Line 41:
For a closed-end pipe, the following boundary conditions hold:
For a closed-end pipe, the following boundary conditions hold:


''v''<sub>1</sub> = ''v''<sub>3</sub> , and fluid velocity equals pipe velocity.  
''v''<sub>1</sub> = ''v''<sub>3</sub> , and fluid velocity equals pipe velocity.


''P''<sub>2</sub> = atmospheric pressure. ''v''<sub>3</sub> = specified pipe velocity.
''P''<sub>2</sub> = atmospheric pressure. ''v''<sub>3</sub> = specified pipe velocity.
Line 47: Line 47:
For circulation with circulation rate ''Q'', the boundary conditions are
For circulation with circulation rate ''Q'', the boundary conditions are


''v''<sub>1</sub> = ''v''<sub>3</sub> <nowiki>+</nowiki> ''Q''/''A''<sub>1</sub> (i.e., fluid velocity equals pipe velocity plus circulation velocity).
''v''<sub>1</sub> = ''v''<sub>3</sub>
 
<nowiki>+</nowiki>
''P''<sub>2</sub> = atmospheric pressure.  
''Q''/''A''<sub>1</sub> (i.e., fluid velocity equals pipe velocity plus circulation velocity).
''P''<sub>2</sub> = atmospheric pressure.


''v''<sub>3</sub> = specified pipe velocity.
''v''<sub>3</sub> = specified pipe velocity.


===End of pipe boundary conditions===
=== End of pipe boundary conditions ===


There are 11 variables that can be specified at the moving pipe end (see '''Fig. 2'''):
There are 11 variables that can be specified at the moving pipe end (see '''Fig. 2'''):


<gallery widths=300px heights=200px>
<gallery widths="300px" heights="200px">
File:Devol2 1102final Page 131 Image 0001.png|'''Fig. 2—Balance of mass at the bit.'''
File:Devol2 1102final Page 131 Image 0001.png|'''Fig. 2—Balance of mass at the bit.'''
</gallery>
</gallery>


''P''<sub>1</sub> = pipe pressure.  
''P''<sub>1</sub> = pipe pressure.


''v''<sub>1</sub> = pipe velocity.  
''v''<sub>1</sub> = pipe velocity.


''P''<sub>2</sub> = pipe annulus pressure.  
''P''<sub>2</sub> = pipe annulus pressure.


''v''<sub>2</sub> = pipe annulus velocity.  
''v''<sub>2</sub> = pipe annulus velocity.


''P''<sub>''n''</sub> = pipe nozzle pressure.  
''P''<sub>''n''</sub> = pipe nozzle pressure.


''v''<sub>''n''</sub> = pipe nozzle velocity.  
''v''<sub>''n''</sub> = pipe nozzle velocity.


''P''<sub>''r''</sub> = annulus return area pressure.  
''P''<sub>''r''</sub> = annulus return area pressure.


''v''<sub>''r''</sub> = annulus return area velocity.  
''v''<sub>''r''</sub> = annulus return area velocity.


''P'' = pipe-to-bottomhole pressure.  
''P'' = pipe-to-bottomhole pressure.


''v'' = pipe-to-bottomhole velocity.  
''v'' = pipe-to-bottomhole velocity.


''v''<sub>3</sub> = pipe velocity.
''v''<sub>3</sub> = pipe velocity.
Line 85: Line 86:
A total of seven boundary conditions can be specified at the moving pipe end with bit (see '''Fig. 3'''). For the surge model, three mass balance equations and four nozzle pressure relations were used.
A total of seven boundary conditions can be specified at the moving pipe end with bit (see '''Fig. 3'''). For the surge model, three mass balance equations and four nozzle pressure relations were used.


<gallery widths=300px heights=200px>
<gallery widths="300px" heights="200px">
File:Devol2 1102final Page 132 Image 0001.png|'''Fig. 3—Balance of mass for cross-sectional area change.'''
File:Devol2 1102final Page 132 Image 0001.png|'''Fig. 3—Balance of mass for cross-sectional area change.'''
</gallery>
</gallery>
Line 91: Line 92:
''Pipe-to-Bottomhole Mass Balance.''
''Pipe-to-Bottomhole Mass Balance.''


[[File:Vol2 page 0132 eq 001.png]]
[[File:Vol2 page 0132 eq 001.png|RTENOTITLE]]


''Pipe Annulus Mass Balance''
''Pipe Annulus Mass Balance''


[[File:Vol2 page 0132 eq 002.png]]
[[File:Vol2 page 0132 eq 002.png|RTENOTITLE]]


''Pipe Mass Balance''
''Pipe Mass Balance''


[[File:Vol2 page 0133 eq 001.png]]
[[File:Vol2 page 0133 eq 001.png|RTENOTITLE]]


''Pipe Nozzle Pressures''
''Pipe Nozzle Pressures''


[[File:Vol2 page 0133 eq 002.png]]
[[File:Vol2 page 0133 eq 002.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 003.png]]
[[File:Vol2 page 0133 eq 003.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 004.png]]
[[File:Vol2 page 0133 eq 004.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 005.png]]
[[File:Vol2 page 0133 eq 005.png|RTENOTITLE]]


''Annulus Return Pressures''. The boundary conditions are greatly simplified for a pipe without a bit.
''Annulus Return Pressures''. The boundary conditions are greatly simplified for a pipe without a bit.


[[File:Vol2 page 0133 eq 006.png]]
[[File:Vol2 page 0133 eq 006.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 007.png]]
[[File:Vol2 page 0133 eq 007.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 008.png]]
[[File:Vol2 page 0133 eq 008.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 009.png]]
[[File:Vol2 page 0133 eq 009.png|RTENOTITLE]]


The boundary condition imposed by a float is the requirement that
The boundary condition imposed by a float is the requirement that


[[File:Vol2 page 0133 eq 010.png]]
[[File:Vol2 page 0133 eq 010.png|RTENOTITLE]]


If the solution of the boundary conditions does not satisfy this condition, the boundary conditions must be solved again with the new requirement:
If the solution of the boundary conditions does not satisfy this condition, the boundary conditions must be solved again with the new requirement:


[[File:Vol2 page 0133 eq 011.png]]
[[File:Vol2 page 0133 eq 011.png|RTENOTITLE]]




===Change of cross-sectional area===


Changes in the cross-sectional area of the moving pipe generate an additional term in the balance of mass equations because of the fluid displaced by the moving pipe (see '''Fig. 3''').  
=== Change of cross-sectional area ===
 
Changes in the cross-sectional area of the moving pipe generate an additional term in the balance of mass equations because of the fluid displaced by the moving pipe (see '''Fig. 3''').


The following was already inserted:
The following was already inserted:


[[File:Vol2 page 0133 eq 012.png]]
[[File:Vol2 page 0133 eq 012.png|RTENOTITLE]]


[[File:Vol2 page 0133 eq 013.png]]
[[File:Vol2 page 0133 eq 013.png|RTENOTITLE]]


where
where


[[File:Vol2 page 0133 eq 014.png]]
[[File:Vol2 page 0133 eq 014.png|RTENOTITLE]]


and
and


[[File:Vol2 page 0134 eq 001.png]]
[[File:Vol2 page 0134 eq 001.png|RTENOTITLE]]


The superscript – denotes upsteam properties, and the superscript <nowiki>+</nowiki> denotes downstream properties.
The superscript – denotes upsteam properties, and the superscript
 
<nowiki>+</nowiki>
==Surge pressure solution==
denotes downstream properties.
== Surge pressure solution ==


Because of the complex boundary conditions, the solution of a steady-state surge pressure is most easily solved with a computer program. For closed-pipe and circulating cases, the flow is defined so that pressures can be calculated from the annulus exit to the standpipe, as discussed previously. For open-pipe surges, the problem is finding how the flow splits between the pipe and the annulus, so that the pressures for both the pipe and the annulus match at the bit. One strategy for solving this problem is given next.
Because of the complex boundary conditions, the solution of a steady-state surge pressure is most easily solved with a computer program. For closed-pipe and circulating cases, the flow is defined so that pressures can be calculated from the annulus exit to the standpipe, as discussed previously. For open-pipe surges, the problem is finding how the flow splits between the pipe and the annulus, so that the pressures for both the pipe and the annulus match at the bit. One strategy for solving this problem is given next.


1. Calculate all pressures with all flow in the annulus. Then, check pressures at the bit; annulus pressure will be lower because of [[Fluid friction|fluid friction]].
1. Calculate all pressures with all flow in the annulus. Then, check pressures at the bit; annulus pressure will be lower because of [[Fluid_friction|fluid friction]].


2. Calculate all pressures with all flow in the pipe. Then, check pressures at the bit; pipe pressure will be lower because of fluid friction.
2. Calculate all pressures with all flow in the pipe. Then, check pressures at the bit; pipe pressure will be lower because of fluid friction.
Line 162: Line 165:
4. Repeat Step 3 until the two pressures match within an acceptable tolerance.
4. Repeat Step 3 until the two pressures match within an acceptable tolerance.


The efficiency of this calculation will depend on the method chosen for Step 3. With modern computers, this is not a particularly critical problem, so a simple interval halving technique would work. For the ''i''th iteration of Step 3, ''f''<sub>''i''</sub> is the fraction of flow in the pipe, and (1 – ''f''<sub>''i''</sub> ) is the fraction in the annulus. Previous steps show that ''f''<sub>''p''</sub> gives a higher annulus pressure and ''f''<sub>''m''</sub> gives a lower annulus pressure. Our new choice for ''f''<sub>''i''</sub> is ½(''f''<sub>''p''</sub> <nowiki>+</nowiki> ''f''<sub>''m''</sub>). We perform the pressure calculation and find that the annulus pressure is higher, so we assign ''f''<sub>''p''</sub> = ''f''<sub>''i''</sub> . If the pressure difference is less than our tolerance, which we chose to be 1 psi, then the calculation is complete. Otherwise, we try another step. How do we establish ''f''<sub>''p''</sub> and ''f''<sub>''m''</sub>? The initial two steps in the solution step should give us ''f''<sub>''p''</sub> = 0 and ''f''<sub>''m''</sub> = 1, respectively. In some cases, such as small nozzles or restricted flow around the bit, fluid must flow into either the pipe or annulus, or the fluid level must fall. For these cases, ''f'' may be negative or greater than one. It may be necessary to repeat Steps 1 and 2 to establish the initial set ''f''<sub>''m''</sub> and ''f''<sub>''p''</sub>.
The efficiency of this calculation will depend on the method chosen for Step 3. With modern computers, this is not a particularly critical problem, so a simple interval halving technique would work. For the ''i''th iteration of Step 3, ''f''<sub>''i''</sub> is the fraction of flow in the pipe, and (1 – ''f''<sub>''i''</sub> ) is the fraction in the annulus. Previous steps show that ''f''<sub>''p''</sub> gives a higher annulus pressure and ''f''<sub>''m''</sub> gives a lower annulus pressure. Our new choice for ''f''<sub>''i''</sub> is ½(''f''<sub>''p''</sub>
<nowiki>+</nowiki>
''f''<sub>''m''</sub>). We perform the pressure calculation and find that the annulus pressure is higher, so we assign ''f''<sub>''p''</sub> = ''f''<sub>''i''</sub> . If the pressure difference is less than our tolerance, which we chose to be 1 psi, then the calculation is complete. Otherwise, we try another step. How do we establish ''f''<sub>''p''</sub> and ''f''<sub>''m''</sub>? The initial two steps in the solution step should give us ''f''<sub>''p''</sub> = 0 and ''f''<sub>''m''</sub> = 1, respectively. In some cases, such as small nozzles or restricted flow around the bit, fluid must flow into either the pipe or annulus, or the fluid level must fall. For these cases, ''f'' may be negative or greater than one. It may be necessary to repeat Steps 1 and 2 to establish the initial set ''f''<sub>''m''</sub> and ''f''<sub>''p''</sub>.
== Nomenclature ==


==Nomenclature==
{| cellspacing="0" cellpadding="4" width="60%"
{|cellspacing="0" cellpadding="4" width="60%"
|''A''
|=
|flow area (see subscripts), m<sup>2</sup>
|-
|-
|''c''
| ''A''
|=  
| =
|average concentration of cuttings overall
| flow area (see subscripts), m<sup>2</sup>
|-
|-
|''c''<sub>''a''</sub>
| ''c''
|=  
| =
|cuttings concentration in annular region
| average concentration of cuttings overall
|-
|-
|''c''<sub>''o''</sub>  
| ''c''<sub>''a''</sub>
|=  
| =
|feed concentration of cuttings
| cuttings concentration in annular region
|-
|-
|''c''<sub>''p''</sub>  
| ''c''<sub>''o''</sub>
|=  
| =
|cuttings concentration in plug region
| feed concentration of cuttings
|-
|-
|''C''  
| ''c''<sub>''p''</sub>
|=  
| =
|compressibility
| cuttings concentration in plug region
|-
|-
|''C''<sub>d</sub>
| ''C''
|=  
| =
|discharge coefficients for the flow through an area change, dimensionless
| compressibility
|-
|-
|''C''<sub>''D''</sub>  
| ''C''<sub>d</sub>
|=  
| =
|drag coefficient, dimensionless  
| discharge coefficients for the flow through an area change, dimensionless
|-
|-
 
| ''C''<sub>''D''</sub>
|''d''<sub>''s''</sub>  
| =
|=  
| drag coefficient, dimensionless
|particle diameter, m
|-
|-
|''D''  
| ''d''<sub>''s''</sub>
|=  
| =
|characteristic length in Reynolds number, m  
| particle diameter, m
|-
|-
|''D''<sub>''e''</sub>
| ''D''
|=  
| =
|special equivalent diameter for yield power law fluid, m  
| characteristic length in Reynolds number, m
|-
|-
|''D''<sub>eq</sub>  
| ''D''<sub>''e''</sub>
|=  
| =
|equivalent diameter, m  
| special equivalent diameter for yield power law fluid, m
|-
|-
|''D''<sub>hyd</sub>  
| ''D''<sub>eq</sub>
|=  
| =
|hydraulic diameter, m  
| equivalent diameter, m
|-
|-
|''D''<sub>''h''</sub>  
| ''D''<sub>hyd</sub>
|=  
| =
|wellbore diameter, m  
| hydraulic diameter, m
|-
|-
|''D''<sub>''i''</sub>  
| ''D''<sub>''h''</sub>
|=  
| =
|inside diameter, m  
| wellbore diameter, m
|-
|-
|''D''<sub>''o''</sub>  
| ''D''<sub>''i''</sub>
|=  
| =
|outside diameter, m  
| inside diameter, m
|-
|-
|''D''<sub>''p''</sub>  
| ''D''<sub>''o''</sub>
|=  
| =
|drillpipe outside diameter, m  
| outside diameter, m
|-
|-
|''D''<sub>plug</sub>  
| ''D''<sub>''p''</sub>
|=  
| =
|plug diameter, m  
| drillpipe outside diameter, m
|-
|-
|''g''  
| ''D''<sub>plug</sub>
|=  
| =
|acceleration of gravity, m/s<sup>2</sup>
| plug diameter, m
|-
|-
|''G''  
| ''g''
|=  
| =
|mass flow rate density of mixture, kg/m<sup>3–s</sup>  
| acceleration of gravity, m/s<sup>2</sup>
|-
|-
|''G''<sub>''s''</sub>
| ''G''
|=  
| =
|mass flow rate density of solids, kg/m<sup>3–s</sup>  
| mass flow rate density of mixture, kg/m<sup>3–s</sup>
|-
|-
|''h''  
| ''G''<sub>''s''</sub>
|=  
| =
|specific enthalpy, J/kg
| mass flow rate density of solids, kg/m<sup>3–s</sup>
|-
|-
|''h''  
| ''h''
|=  
| =
|total friction pressure drop, Pa/m
| specific enthalpy, J/kg
|-
|-
|''''
| ''h''
|=  
| =
|mass flow rate, kg/s
| total friction pressure drop, Pa/m
|-
|-
|''ṁ''<sub>''s''</sub>
| ''ṁ''
|=  
| =
|mass flow rate of solid, kg/s  
| mass flow rate, kg/s
|-
|-
|''P''  
| ''''<sub>''s''</sub>
|=  
| =
|pressure, Pa
| mass flow rate of solid, kg/s
|-
|-
|''Q''  
| ''P''
|=  
| =
|heat transferred into volume, W
| pressure, Pa
|-
|-
|''R''  
| ''Q''
|=  
| =
|ideal gas constant, m<sup>3</sup> Pa/kg-K
| heat transferred into volume, W
|-
|-
|''t''  
| ''R''
|=  
| =
|time, s
| ideal gas constant, m<sup>3</sup> Pa/kg-K
|-
|-
|''T''  
| ''t''
|=  
| =
|absolute temperature, °K
| time, s
|-
|-
|''u''  
| ''T''
|=  
| =
|radial displacement, m
| absolute temperature, °K
|-
|-
|''v''<nowiki>*</nowiki>
| ''u''
|=  
| =
|characteristic velocity for turbulent flow calculations, m/s
| radial displacement, m
|-
|-
|''v''  
| ''v''<nowiki>*</nowiki>
|=  
 
|average velocity, m/s  
| =
| characteristic velocity for turbulent flow calculations, m/s
|-
|-
|Δ''P''  
| ''v''
|=  
| =
|pressure drop, Pa
| average velocity, m/s
|-
|-
|Δ''t''  
| Δ''P''
|=  
| =
|time increment, s
| pressure drop, Pa
|-
|-
|Δ''v''  
| Δ''t''
|=  
| =
|change in velocity, m/s  
| time increment, s
|-
|-
|Δ''z''  
| Δ''v''
|=  
| =
|length of flow increment, m  
| change in velocity, m/s
|-
|-
|''ρ''  
| Δ''z''
|=  
| =
|fluid density, kg/m<sup>3</sup>
| length of flow increment, m
|-
| ''ρ''
| =
| fluid density, kg/m<sup>3</sup>
|}
|}


Line 337: Line 343:


''r'' = properties in annulus outside bit, surge calculations
''r'' = properties in annulus outside bit, surge calculations


'''Superscripts'''
'''Superscripts'''
Line 343: Line 348:
- = upstream properties
- = upstream properties


==References==
== References ==


<references>
<references />
<ref name="r1">Lubinski, A., Hsu, F.H., and Nolte, K.G. 1977. Transient Pressure Surges Because of Pipe Movement in an Oil Well. ''Revue de I<nowiki>’</nowiki>lnst. Fran. du Pet'' (May/June): 307.</ref>


<ref name="r2">Mitchell, R.F. 1988. Dynamic Surge/Swab Pressure Predictions. ''SPE Drill Eng'' '''3''' (3): 325-333. SPE-16156-PA. http://dx.doi.org/10.2118/16156-PA.</ref>
== See also ==
</references>


== See also ==
[[Fluid_mechanics_for_drilling|Fluid mechanics for drilling]]
[[Fluid mechanics for drilling|Fluid mechanics for drilling]]


[[Fluid friction]]
[[Fluid_friction|Fluid friction]]


[[Dynamic wellbore pressure prediction]]
[[Dynamic_wellbore_pressure_prediction|Dynamic wellbore pressure prediction]]


[[PEH:Fluid Mechanics for Drilling|PEH:Fluid Mechanics for Drilling]]
[[PEH:Fluid_Mechanics_for_Drilling|PEH:Fluid Mechanics for Drilling]]


== Noteworthy papers in OnePetro ==
== Noteworthy papers in OnePetro ==
Freddy Crespo and Ramadan Ahmed, SPE, University of Oklahoma, and Arild Saasen, SPE: Surge and Swab Pressure Predictions for Yield-Power-Law Drilling Fluids. 138938-MS. http://dx.doi.org/10.2118/138938-MS.


R.F. Mitchell, Enertech Engineering & Research: Dynamic Surge/Swab Pressure Predictions. 16156-PA. http://dx.doi.org/10.2118/16156-PA.
Freddy Crespo and Ramadan Ahmed, SPE, University of Oklahoma, and Arild Saasen, SPE: Surge and Swab Pressure Predictions for Yield-Power-Law Drilling Fluids. 138938-MS. [http://dx.doi.org/10.2118/138938-MS http://dx.doi.org/10.2118/138938-MS].
 
R.F. Mitchell, Enertech Engineering & Research: Dynamic Surge/Swab Pressure Predictions. 16156-PA. [http://dx.doi.org/10.2118/16156-PA http://dx.doi.org/10.2118/16156-PA].


== External links ==
== External links ==
[[Category: 1.7.5 Well control]]
 
==Category==
[[Category:1.7.5 Well control]] [[Category:YR]]

Latest revision as of 15:50, 26 June 2015

An exceptional flow case is the operation of running pipe or casing into the wellbore. Moving pipe into the wellbore displaces fluid, and the flow of this fluid generates pressures called surge pressures.

Overview

When the pipe is pulled from the well, negative pressures are generated, and these pressures are called swab pressures. In most wells, the magnitude of the pressure surges is not critical because proper casing design and mud programs leave large enough margins between fracture pressures and formation-fluid pressures. Typically, dynamic fluid flow is not a consideration, so a steady-state calculation can be performed. A certain fraction of wells, however, cannot be designed with large surge-pressure margins. In these critical wells, pressure surges must be maintained within narrow limits. In other critical wells, pressure margins may be large, but pressure surges may still be a concern. Some operations are particularly prone to large pressure surges (e.g., running of low-clearance liners in deep wells). The reader is referred to papers on dynamic surge calculations,[1][2]and the article on dynamic pressure calculation gives a taste of this type of calculation.

Surge analysis

The surge pressure analysis consists of two analytical regions: the pipe-annulus region and the pipe-to-bottomhole region (Fig. 1). The fluid flow in the pipe-annulus region should be solved using techniques already discussed, but with the following special considerations: frictional pressure drop must be solved for flow in an annulus with a moving pipe, and in deviated wells, the effect of annulus eccentricity should be considered. The analysis of the pipe-to-bottomhole region should consist of a static pressure analysis, with pressure boundary condition determined by the fluid flow at the bit, or pipe end if running casing. The pipe-annulus model and the pipe-to-bottomhole model then are connected through a comprehensive set of force and displacement compatibility relations.

Boundary conditions

The following conditions describe the flow for a surge or swab operation.

Surface boundary conditions

There are six variables that can be specified at the surface:

P1 = pipe pressure.

v1 = pipe fluid velocity.

P2 = annulus pressure.

v2 = annulus fluid velocity.

v3 = pipe velocity.

A maximum of three boundary conditions can be specified at the surface. For surge without circulation, the following boundary conditions hold:

P1 = atmospheric pressure.

P2 = atmospheric pressure.

v3 = specified pipe velocity.

For a closed-end pipe, the following boundary conditions hold:

v1 = v3 , and fluid velocity equals pipe velocity.

P2 = atmospheric pressure. v3 = specified pipe velocity.

For circulation with circulation rate Q, the boundary conditions are

v1 = v3 + Q/A1 (i.e., fluid velocity equals pipe velocity plus circulation velocity). P2 = atmospheric pressure.

v3 = specified pipe velocity.

End of pipe boundary conditions

There are 11 variables that can be specified at the moving pipe end (see Fig. 2):

P1 = pipe pressure.

v1 = pipe velocity.

P2 = pipe annulus pressure.

v2 = pipe annulus velocity.

Pn = pipe nozzle pressure.

vn = pipe nozzle velocity.

Pr = annulus return area pressure.

vr = annulus return area velocity.

P = pipe-to-bottomhole pressure.

v = pipe-to-bottomhole velocity.

v3 = pipe velocity.

A total of seven boundary conditions can be specified at the moving pipe end with bit (see Fig. 3). For the surge model, three mass balance equations and four nozzle pressure relations were used.

Pipe-to-Bottomhole Mass Balance.

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Pipe Annulus Mass Balance

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Pipe Mass Balance

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Pipe Nozzle Pressures

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Annulus Return Pressures. The boundary conditions are greatly simplified for a pipe without a bit.

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The boundary condition imposed by a float is the requirement that

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If the solution of the boundary conditions does not satisfy this condition, the boundary conditions must be solved again with the new requirement:

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Change of cross-sectional area

Changes in the cross-sectional area of the moving pipe generate an additional term in the balance of mass equations because of the fluid displaced by the moving pipe (see Fig. 3).

The following was already inserted:

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where

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and

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The superscript – denotes upsteam properties, and the superscript + denotes downstream properties.

Surge pressure solution

Because of the complex boundary conditions, the solution of a steady-state surge pressure is most easily solved with a computer program. For closed-pipe and circulating cases, the flow is defined so that pressures can be calculated from the annulus exit to the standpipe, as discussed previously. For open-pipe surges, the problem is finding how the flow splits between the pipe and the annulus, so that the pressures for both the pipe and the annulus match at the bit. One strategy for solving this problem is given next.

1. Calculate all pressures with all flow in the annulus. Then, check pressures at the bit; annulus pressure will be lower because of fluid friction.

2. Calculate all pressures with all flow in the pipe. Then, check pressures at the bit; pipe pressure will be lower because of fluid friction.

3. Calculate a division of flow between the pipe and annulus that will equalize the pressures at the bit.

4. Repeat Step 3 until the two pressures match within an acceptable tolerance.

The efficiency of this calculation will depend on the method chosen for Step 3. With modern computers, this is not a particularly critical problem, so a simple interval halving technique would work. For the ith iteration of Step 3, fi is the fraction of flow in the pipe, and (1 – fi ) is the fraction in the annulus. Previous steps show that fp gives a higher annulus pressure and fm gives a lower annulus pressure. Our new choice for fi is ½(fp + fm). We perform the pressure calculation and find that the annulus pressure is higher, so we assign fp = fi . If the pressure difference is less than our tolerance, which we chose to be 1 psi, then the calculation is complete. Otherwise, we try another step. How do we establish fp and fm? The initial two steps in the solution step should give us fp = 0 and fm = 1, respectively. In some cases, such as small nozzles or restricted flow around the bit, fluid must flow into either the pipe or annulus, or the fluid level must fall. For these cases, f may be negative or greater than one. It may be necessary to repeat Steps 1 and 2 to establish the initial set fm and fp.

Nomenclature

A = flow area (see subscripts), m2
c = average concentration of cuttings overall
ca = cuttings concentration in annular region
co = feed concentration of cuttings
cp = cuttings concentration in plug region
C = compressibility
Cd = discharge coefficients for the flow through an area change, dimensionless
CD = drag coefficient, dimensionless
ds = particle diameter, m
D = characteristic length in Reynolds number, m
De = special equivalent diameter for yield power law fluid, m
Deq = equivalent diameter, m
Dhyd = hydraulic diameter, m
Dh = wellbore diameter, m
Di = inside diameter, m
Do = outside diameter, m
Dp = drillpipe outside diameter, m
Dplug = plug diameter, m
g = acceleration of gravity, m/s2
G = mass flow rate density of mixture, kg/m3–s
Gs = mass flow rate density of solids, kg/m3–s
h = specific enthalpy, J/kg
h = total friction pressure drop, Pa/m
= mass flow rate, kg/s
s = mass flow rate of solid, kg/s
P = pressure, Pa
Q = heat transferred into volume, W
R = ideal gas constant, m3 Pa/kg-K
t = time, s
T = absolute temperature, °K
u = radial displacement, m
v* = characteristic velocity for turbulent flow calculations, m/s
v = average velocity, m/s
ΔP = pressure drop, Pa
Δt = time increment, s
Δv = change in velocity, m/s
Δz = length of flow increment, m
ρ = fluid density, kg/m3

Subscripts

1 = properties inside pipe, surge calculations

2 = properties inside annulus, surge calculations

3 = properties of moving pipe, surge calculation

c = concentric

e = eccentric

n = properties in bit nozzle, surge calculations

o = upstream, initial, or inlet

r = properties in annulus outside bit, surge calculations

Superscripts

- = upstream properties

References

  1. Lubinski, A., Hsu, F.H., and Nolte, K.G. 1977. Transient Pressure Surges Because of Pipe Movement in an Oil Well. Revue de I’lnst. Fran. du Pet (May/June): 307.
  2. Mitchell, R.F. 1988. Dynamic Surge/Swab Pressure Predictions. SPE Drill Eng 3 (3): 325-333. SPE-16156-PA. http://dx.doi.org/10.2118/16156-PA.

See also

Fluid mechanics for drilling

Fluid friction

Dynamic wellbore pressure prediction

PEH:Fluid Mechanics for Drilling

Noteworthy papers in OnePetro

Freddy Crespo and Ramadan Ahmed, SPE, University of Oklahoma, and Arild Saasen, SPE: Surge and Swab Pressure Predictions for Yield-Power-Law Drilling Fluids. 138938-MS. http://dx.doi.org/10.2118/138938-MS.

R.F. Mitchell, Enertech Engineering & Research: Dynamic Surge/Swab Pressure Predictions. 16156-PA. http://dx.doi.org/10.2118/16156-PA.

External links

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