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# Difference between revisions of "Plunger lift design and models"

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− | [[Plunger lift]] systems can be evaluated using rules of thumb in conjunction with historic well production, or with a mathematical plunger model. Because plunger lift systems typically are inexpensive and easy to install and test, most are evaluated by rules of thumb. | + | [[Plunger_lift|Plunger lift]] systems can be evaluated using rules of thumb in conjunction with historic well production, or with a mathematical plunger model. Because plunger lift systems typically are inexpensive and easy to install and test, most are evaluated by rules of thumb. |

− | ==GLR and buildup pressure requirements== | + | == GLR and buildup pressure requirements == |

− | The two minimum requirements for plunger lift operation are: | + | The two minimum requirements for plunger lift operation are: |

− | *Minimum gas-liquid ratio ([[ | + | |

+ | *Minimum gas-liquid ratio ([[Glossary:GLR|GLR]]) | ||

*Well buildup pressure | *Well buildup pressure | ||

− | Plunger lift operation requires available gas to provide the lifting force, in sufficient quantity per barrel of liquid for a given well depth. The minimum GLR requirement is approximately 400 scf/bbl per 1,000 ft of well depth and is based on the energy stored in a compressed volume of 400 scf of gas expanding under the hydrostatic head of 1 bbl of liquid.<ref name="r1"/> One drawback to this rule of thumb is that it does not consider line pressures. Excessively high line pressures relative to buildup pressure might increase the requirement. The rule of thumb also assumes that the gas expansion can be applied from a large open annulus without restriction, but slimhole wells and wells with packers that require gas to travel through the reservoir or through small perforations in the tubing will cause a greater restriction and energy loss, which increase the minimum GLR requirement to as much as 800 to 1,200 scf/bbl per 1,000 ft. | + | Plunger lift operation requires available gas to provide the lifting force, in sufficient quantity per barrel of liquid for a given well depth. The minimum GLR requirement is approximately 400 scf/bbl per 1,000 ft of well depth and is based on the energy stored in a compressed volume of 400 scf of gas expanding under the hydrostatic head of 1 bbl of liquid.<ref name="r1">Ferguson, P.L. and Beauregard, E. 1983. Will Plunger Lift Work In My Well? Proc., Thirtieth Annual Southwestern Petroleum Short Course, Lubbock, Texas, 301–311.</ref> One drawback to this rule of thumb is that it does not consider line pressures. Excessively high line pressures relative to buildup pressure might increase the requirement. The rule of thumb also assumes that the gas expansion can be applied from a large open annulus without restriction, but slimhole wells and wells with packers that require gas to travel through the reservoir or through small perforations in the tubing will cause a greater restriction and energy loss, which increase the minimum GLR requirement to as much as 800 to 1,200 scf/bbl per 1,000 ft. |

− | Well buildup pressure is the bottomhole pressure just before the plunger begins its ascent (equivalent to surface casing pressure in a well with an open annulus). In practice, the minimum shut-in pressure requirement for plunger lift is equivalent to one and a half times the maximum sales-line pressure, although the actual requirement might be higher. This rule of thumb works well in intermediate-depth wells (2,000 to 8,000 ft) with slug sizes of 0.1 to 0.5 bbl/cycle. It does not apply reliably, however, to higher liquid volumes, deeper wells (because of increasing friction), and excessive pressure restrictions at the surface or in the wellbore. | + | Well buildup pressure is the bottomhole pressure just before the plunger begins its ascent (equivalent to surface casing pressure in a well with an open annulus). In practice, the minimum shut-in pressure requirement for plunger lift is equivalent to one and a half times the maximum sales-line pressure, although the actual requirement might be higher. This rule of thumb works well in intermediate-depth wells (2,000 to 8,000 ft) with slug sizes of 0.1 to 0.5 bbl/cycle. It does not apply reliably, however, to higher liquid volumes, deeper wells (because of increasing friction), and excessive pressure restrictions at the surface or in the wellbore. |

− | An improved rule of thumb for minimum pressure is that a well can lift a slug of liquid when the slug hydrostatic pressure (phs) equals 50 to 60% of the difference between shut-in casing pressure (pcs) and maximum sales-line pressure: | + | An improved rule of thumb for minimum pressure is that a well can lift a slug of liquid when the slug hydrostatic pressure (phs) equals 50 to 60% of the difference between shut-in casing pressure (pcs) and maximum sales-line pressure: |

− | [[File:Vol4 page 0851 eq 001.png]] ........................(1a) | + | [[File:Vol4 page 0851 eq 001.png|RTENOTITLE]] ........................(1a) |

− | or | + | or |

− | [[File:Vol4 page 0851 eq 002.png]] ........................(1b) | + | [[File:Vol4 page 0851 eq 002.png|RTENOTITLE]] ........................(1b) |

− | This rule of thumb accounts for liquid production, can be used for wells with higher liquid production that require slug sizes of more than 1 to 2 bbl/cycle, and is regarded as a conservative estimate of minimum pressure requirements. To use Eqs. 1a and 1b, first estimate the total liquid production on plunger lift and number of cycles possible per day. Then, determine the amount of liquid that can be lifted per cycle. Use the well tubing size to convert that volume of liquid per cycle into the slug hydrostatic pressure, and use the equations to estimate required casing pressure to operate the system (see example below). | + | This rule of thumb accounts for liquid production, can be used for wells with higher liquid production that require slug sizes of more than 1 to 2 bbl/cycle, and is regarded as a conservative estimate of minimum pressure requirements. To use Eqs. 1a and 1b, first estimate the total liquid production on plunger lift and number of cycles possible per day. Then, determine the amount of liquid that can be lifted per cycle. Use the well tubing size to convert that volume of liquid per cycle into the slug hydrostatic pressure, and use the equations to estimate required casing pressure to operate the system (see example below). |

− | A well that does not meet minimum GLR and pressure requirements still could be plunger lifted with the addition of an external gas source. At this point, design becomes more a matter of the economics of providing the added gas to the well at desired pressures. Several papers in the literature discuss adding makeup gas to a plunger installation through existing gas lift operations, installing a field gas supply system, or using wellhead compression. <ref name="r2"/><ref name="r3"/><ref name="r4"/><ref name="r5"/><ref name="r6"/><ref name="r7"/><ref name="r8"/><ref name="r9"/> | + | A well that does not meet minimum GLR and pressure requirements still could be plunger lifted with the addition of an external gas source. At this point, design becomes more a matter of the economics of providing the added gas to the well at desired pressures. Several papers in the literature discuss adding makeup gas to a plunger installation through existing gas lift operations, installing a field gas supply system, or using wellhead compression. <ref name="r2">Christian, J., Lea, J.F., and Bishop, R. 1995. Plunger Lift Comes of Age. World Oil (November): 43.</ref><ref name="r3">Beeson, C.M., Knox, D.G., and Stoddard, J.H. 1955. Plunger Lift Correlation Equations And Nomographs. Presented at the Fall Meeting of the Petroleum Branch of AIME, New Orleans, Louisiana, 2-5 October. http://dx.doi.org/10.2118/501-g.</ref><ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref><ref name="r5">Abercrombie, B. 1980. Plunger Lift. In The Technology of Artificial Lift Methods, ed. K.E. Brown, Vol. 2b, 483-518. Tulsa, Oklahoma: PennWell Publishing Co.</ref><ref name="r6">Hall, J.C. and Bell, B. 2001. Plunger Lift By Side String Injection. Proc., Forty-Eighth Annual Southwestern Petroleum Short Course, Lubbock, Texas, 17–18..</ref><ref name="r7">Morrow, S.J. Jr. and Aversante, O.L. 1995. Plunger Lift: Gas Assisted. Proc., Forty-Second Annual Southwestern Petroleum Short Course, Lubbock, Texas, 195–201.</ref><ref name="r8">White, G.W. 1982. Combine Gas Lift, Plungers to Increase Production Rate. World Oil (November): 69.</ref><ref name="r9">Phillips, D.H. and Listiak, S.D. 1996. Plunger Lift With Wellhead Compression Boosts Gas Well Production. World Oil (October) 96.</ref> |

− | ==Estimating production rates== | + | == Estimating production rates == |

− | The simplest and sometimes most accurate method of determining production increases from plunger lift is decline-curve analysis<ref name="r1" /> ('''Fig. 1'''). Gas and oil reservoirs typically have predictable declines, either exponential or hyperbolic. Initial production rates usually are high enough to produce the well above critical rates (unloaded) and establish a decline curve. When liquid loading occurs, a marked decrease and deviation from normal decline can be seen. Unloading the well with plunger lift can re-establish a normal decline. Production increases from plunger lift will be somewhere between the rates of the well when it started loading and the rate of an extended decline curve to the present time. Ideally, decline curves would be used with critical-velocity curves to predetermine when plunger lift should be installed. This would enable plunger lift to maintain production on a steady decline and to never allow the well to begin loading. | + | The simplest and sometimes most accurate method of determining production increases from plunger lift is decline-curve analysis<ref name="r1">Ferguson, P.L. and Beauregard, E. 1983. Will Plunger Lift Work In My Well? Proc., Thirtieth Annual Southwestern Petroleum Short Course, Lubbock, Texas, 301–311.</ref> ('''Fig. 1'''). Gas and oil reservoirs typically have predictable declines, either exponential or hyperbolic. Initial production rates usually are high enough to produce the well above critical rates (unloaded) and establish a decline curve. When liquid loading occurs, a marked decrease and deviation from normal decline can be seen. Unloading the well with plunger lift can re-establish a normal decline. Production increases from plunger lift will be somewhere between the rates of the well when it started loading and the rate of an extended decline curve to the present time. Ideally, decline curves would be used with critical-velocity curves to predetermine when plunger lift should be installed. This would enable plunger lift to maintain production on a steady decline and to never allow the well to begin loading. |

− | <gallery widths=300px heights=200px> | + | <gallery widths="300px" heights="200px"> |

File:Vol4 Page 851 Image 0001.png|'''Fig. 1—Effects of plunger lift on a typical gas-well production decline. (Modified from Ferguson and Beauregard.)'''<ref name="r1" /> | File:Vol4 Page 851 Image 0001.png|'''Fig. 1—Effects of plunger lift on a typical gas-well production decline. (Modified from Ferguson and Beauregard.)'''<ref name="r1" /> | ||

</gallery> | </gallery> | ||

− | Another method for estimating production is to build an [[ | + | Another method for estimating production is to build an [[Reservoir_inflow_performance|inflow performance]] (IP) curve on the basis of the backpressure equation ('''Fig. 2''').<ref name="r10">Lea Jr., J.F. and Tighe, R.E. 1983. Gas Well Operation With Liquid Production. Presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 27 February-1 March 1983. SPE-11583-MS. http://dx.doi.org/10.2118/11583-MS.</ref><ref name="r11">Phillips, D.H. and Listiak, S.D. 1998. How to Optimize Production from Plunger Lift Systems. World Oil (May): 110.</ref><ref name="r12">Vogel, J.V. 1968. Inflow Performance Relationships for Solution-Gas Drive Wells. J Pet Technol 20 (1): 83-92. http://dx.doi.org/10.2118/1476-PA.</ref><ref name="r13">Mishra, S. and Caudle, B.H. 1984. A Simplified Procedure for Gas Deliverability Calculations Using Dimensionless IPR Curves. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 16-19 September 1984. SPE-13231-MS. http://dx.doi.org/10.2118/13231-MS.</ref> This is especially helpful if the well has an open annulus and is flowing up the tubing, and if the casing pressure is known. The casing pressure closely approximates bottomhole pressure. Build the IP curve on the basis of: |

+ | |||

*Estimated reservoir pressure | *Estimated reservoir pressure | ||

*Casing pressure | *Casing pressure | ||

*Current flow rate | *Current flow rate | ||

− | <gallery widths=300px heights=200px> | + | <gallery widths="300px" heights="200px"> |

File:Vol4 Page 852 Image 0001.png|'''Fig. 2—Inflow-performance-relationship analysis for estimating plunger-lift performance. Chart shows production increase resulting from reducing liquid hydrostatic pressure with a plunger-lift system. (After Vogel<ref name="r12" /> and Mishra and Caudle<ref name="r13" />.)''' | File:Vol4 Page 852 Image 0001.png|'''Fig. 2—Inflow-performance-relationship analysis for estimating plunger-lift performance. Chart shows production increase resulting from reducing liquid hydrostatic pressure with a plunger-lift system. (After Vogel<ref name="r12" /> and Mishra and Caudle<ref name="r13" />.)''' | ||

</gallery> | </gallery> | ||

Line 42: | Line 44: | ||

Because the job of the plunger lift is to lower the bottomhole pressure by removing liquids, estimate the bottomhole pressure with no liquids. Use this new pressure to estimate a production rate with lower bottomhole pressures. | Because the job of the plunger lift is to lower the bottomhole pressure by removing liquids, estimate the bottomhole pressure with no liquids. Use this new pressure to estimate a production rate with lower bottomhole pressures. | ||

− | ==Models== | + | == Models == |

− | Plunger lift models are based on the sum of forces acting on the plunger while it lifts a liquid slug up the tubing ('''Fig. 3'''). These forces at any given point in the tubing are: | + | Plunger lift models are based on the sum of forces acting on the plunger while it lifts a liquid slug up the tubing ('''Fig. 3'''). These forces at any given point in the tubing are: |

− | <gallery widths=300px heights=200px> | + | <gallery widths="300px" heights="200px"> |

File:Vol4 Page 853 Image 0001.png|'''Fig. 3—Plunger force balance. (Based on Lea.)'''<ref name="r14" /> | File:Vol4 Page 853 Image 0001.png|'''Fig. 3—Plunger force balance. (Based on Lea.)'''<ref name="r14" /> | ||

</gallery> | </gallery> | ||

− | Stored casing pressure freely acting on the cross section of the plunger. | + | Stored casing pressure freely acting on the cross section of the plunger. |

Stored reservoir pressure acting on the cross section of the plunger, based on inflow performance. | Stored reservoir pressure acting on the cross section of the plunger, based on inflow performance. | ||

− | *Weight of the fluid. | + | |

− | *Weight of the plunger. | + | *Weight of the fluid. |

− | *Friction of the fluid with the tubing. | + | *Weight of the plunger. |

− | *Friction of the plunger with the tubing. | + | *Friction of the fluid with the tubing. |

− | *Gas friction in the tubing. | + | *Friction of the plunger with the tubing. |

− | *Gas slippage upward past the plunger. | + | *Gas friction in the tubing. |

− | *Liquid slippage downward past the plunger. | + | *Gas slippage upward past the plunger. |

+ | *Liquid slippage downward past the plunger. | ||

*Surface pressure (line pressure and restrictions) acting against the plunger travel. | *Surface pressure (line pressure and restrictions) acting against the plunger travel. | ||

− | Several publications have dealt with this approach. Beeson et al.<ref name=" | + | Several publications have dealt with this approach. Beeson et al.<ref name="r3">Beeson, C.M., Knox, D.G., and Stoddard, J.H. 1955. Plunger Lift Correlation Equations And Nomographs. Presented at the Fall Meeting of the Petroleum Branch of AIME, New Orleans, Louisiana, 2-5 October. http://dx.doi.org/10.2118/501-g.</ref> first presented equations for high-GLR wells in 1955, on the basis of an empirically derived analysis. Foss and Gaul<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref> derived a force-balance equation for use on oil wells in the Ventura Avenue field in 1965. Lea<ref name="r14">Lea, J.F. 1982. Dynamic Analysis of Plunger Lift Operations. J Pet Technol 34 (11): 2617-2629. SPE-10253-PA. http://dx.doi.org/10.2118/10253-PA.</ref> presented a dynamic analysis of plunger lift that added gas slippage and reservoir inflow, and mathematically described the entire cycle (not just plunger ascent) for tight-gas/very high-GLR wells. |

+ | |||

+ | Foss and Gaul’s methodology<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref> was to calculate (p<sub>c</sub>)min, the casing pressure required to move the plunger and liquid slug just before it reaches the surface. Because (p<sub>c</sub>)min is at the end of the plunger cycle, the energy of the expanding gas from the casing to the tubing is at its minimum. Adjusting (p<sub>c</sub>)min for gas expansion from the casing to the tubing during the full plunger cycle yields (p<sub>c</sub>)<sub>max</sub> , the pressure required to start the plunger at the beginning of the plunger cycle. The pressure must build to (p<sub>c</sub>)<sub>max</sub> to operate successfully. | ||

− | + | The average casing pressure p¯c, maximum cycles C<sub>max</sub>, and gas required per cycle (V<sub>g</sub>) can be calculated from (p<sub>c</sub>)min and (p<sub>c</sub>)max . The equations below are essentially those presented by Foss and Gaul<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref> but are summarized here as presented by Mower et al.<ref name="r15">Mower, L.N., Lea, J.F., E., B. et al. 1985. Defining the Characteristics and Performance of Gas-Lift Plungers. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14344-MS. http://dx.doi.org/10.2118/14344-MS.</ref> The Foss and Gaul model is not rigorous, it: | |

− | |||

*Assumes constant friction associated with plunger rise velocities of 1,000 ft/min | *Assumes constant friction associated with plunger rise velocities of 1,000 ft/min | ||

*Does not calculate reservoir inflow | *Does not calculate reservoir inflow | ||

Line 73: | Line 77: | ||

*Assumes that the user can determine unloaded gas and liquid rates independently of the model | *Assumes that the user can determine unloaded gas and liquid rates independently of the model | ||

− | Also, because this model originally was designed for oilwell operation that assumed the well would be shut in upon plunger arrival, p¯c is only an average during plunger travel. The net result of these assumptions is an overprediction of required casing pressure. If a well meets the Foss and Gaul criteria, it is almost certainly a candidate for plunger lift. For a full description of the Foss and Gaul model and for a description of improved models, see the references.<ref name="r4"/><ref name="r10"/>,<ref name="r15"/><ref name="r16"/><ref name="r17"/> | + | Also, because this model originally was designed for oilwell operation that assumed the well would be shut in upon plunger arrival, p¯c is only an average during plunger travel. The net result of these assumptions is an overprediction of required casing pressure. If a well meets the Foss and Gaul criteria, it is almost certainly a candidate for plunger lift. For a full description of the Foss and Gaul model and for a description of improved models, see the references.<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref><ref name="r10">Lea Jr., J.F. and Tighe, R.E. 1983. Gas Well Operation With Liquid Production. Presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 27 February-1 March 1983. SPE-11583-MS. http://dx.doi.org/10.2118/11583-MS.</ref>,<ref name="r15">Mower, L.N., Lea, J.F., E., B. et al. 1985. Defining the Characteristics and Performance of Gas-Lift Plungers. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14344-MS. http://dx.doi.org/10.2118/14344-MS.</ref><ref name="r16">Rosina, L. 1983. A Study of Plunger Lift Dynamics. MS Thesis, University of Tulsa, Tulsa.</ref><ref name="r17">Lea, J.F. 1999. Plunger Lift vs. Velocity Strings. Paper presented at the 1999 Energy Sources Technology Conference & Exhibition, Houston, 1–2 February.</ref> |

− | ==Basic Foss and Gaul equations== | + | == Basic Foss and Gaul equations == |

− | |||

− | === | + | Basic Foss and Gaul<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref> equations (Modified by Mower et al.<ref name="r15">Mower, L.N., Lea, J.F., E., B. et al. 1985. Defining the Characteristics and Performance of Gas-Lift Plungers. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14344-MS. http://dx.doi.org/10.2118/14344-MS.</ref> and Lea<ref name="r14">Lea, J.F. 1982. Dynamic Analysis of Plunger Lift Operations. J Pet Technol 34 (11): 2617-2629. SPE-10253-PA. http://dx.doi.org/10.2118/10253-PA.</ref>) |

− | + | === Required pressures === | |

− | [[File:Vol4 page 0854 eq | + | [[File:Vol4 page 0854 eq 001.png|RTENOTITLE]] ........................(2) |

− | + | [[File:Vol4 page 0854 eq 002.png|RTENOTITLE]] ........................(3) | |

− | + | and | |

− | + | [[File:Vol4 page 0854 eq 003.png|RTENOTITLE]] ........................(4) | |

− | + | where | |

− | [[File:Vol4 page 0854 eq | + | [[File:Vol4 page 0854 eq 004.png|RTENOTITLE]] ........................(5) |

− | [[File:Vol4 page 0854 eq | + | [[File:Vol4 page 0854 eq 005.png|RTENOTITLE]] ........................(6) |

− | + | [[File:Vol4 page 0854 eq 006.png|RTENOTITLE]] ........................(7) | |

− | + | and | |

− | + | [[File:Vol4 page 0854 eq 007.png|RTENOTITLE]] ........................(8) | |

− | <gallery widths=300px heights=200px> | + | Foss and Gaul suggested an approximation where K and p<sub>lh</sub> + p<sub>lf</sub> are constant for a given tubing size and a plunger velocity of 1,000 ft/min ('''Table 1'''). |

+ | |||

+ | <gallery widths="300px" heights="200px"> | ||

File:Vol4 Page 854 Image 0001.png|'''Table 1''' | File:Vol4 Page 854 Image 0001.png|'''Table 1''' | ||

</gallery> | </gallery> | ||

− | ===Gas (Mscf) required per cycle=== | + | === Gas (Mscf) required per cycle === |

− | [[File:Vol4 page 0855 eq 001.png]] | + | [[File:Vol4 page 0855 eq 001.png|RTENOTITLE]] ........................(9) |

− | where | + | where |

− | [[File:Vol4 page 0855 eq 002.png]] | + | [[File:Vol4 page 0855 eq 002.png|RTENOTITLE]] ........................(10) |

− | ===Maximum cycles=== | + | === Maximum cycles === |

− | [[File:Vol4 page 0855 eq 003.png]] | + | [[File:Vol4 page 0855 eq 003.png|RTENOTITLE]] ........................(11) |

− | ==Examples== | + | == Examples == |

− | ===Rules of thumb and Foss and Gaul calculations=== | + | === Rules of thumb and Foss and Gaul calculations === |

− | Examples are based on the well data given in '''Table 2'''. | + | Examples are based on the well data given in '''Table 2'''. |

− | <gallery widths=300px heights=200px> | + | <gallery widths="300px" heights="200px"> |

File:Vol4 Page 855 Image 0001.png|'''Table 2''' | File:Vol4 Page 855 Image 0001.png|'''Table 2''' | ||

</gallery> | </gallery> | ||

Line 130: | Line 135: | ||

'''Example of rule-of-thumb GLR calculation''' | '''Example of rule-of-thumb GLR calculation''' | ||

− | The minimum GLR (Rgl) = 400 scf/bbl per 1,000 ft of well depth. The well’s GLR is: | + | The minimum GLR (Rgl) = 400 scf/bbl per 1,000 ft of well depth. The well’s GLR is: |

− | [[File:Vol4 page 0856 eq 001.png]] | + | [[File:Vol4 page 0856 eq 001.png|RTENOTITLE]] ........................(12) |

− | [[File:Vol4 page 0856 eq 002.png]] | + | [[File:Vol4 page 0856 eq 002.png|RTENOTITLE]] ........................(13) |

− | where ''q''<sub>''g''</sub> is given in scf. The well GLR is >400 scf/bbl per 1,000 ft and is adequate for plunger lift. | + | where ''q''<sub>''g''</sub> is given in scf. The well GLR is >400 scf/bbl per 1,000 ft and is adequate for plunger lift. |

'''Example of rule of thumb for casing pressure requirement to plunger lift (simple)''' | '''Example of rule of thumb for casing pressure requirement to plunger lift (simple)''' | ||

− | The rule of thumb for calculating the minimum shut-in casing pressure for plunger lift, in psia, is: | + | The rule of thumb for calculating the minimum shut-in casing pressure for plunger lift, in psia, is: |

− | [[File:Vol4 page 0856 eq 003.png]] | + | [[File:Vol4 page 0856 eq 003.png|RTENOTITLE]] ........................(14) |

− | [[File:Vol4 page 0856 eq 004.png]] | + | [[File:Vol4 page 0856 eq 004.png|RTENOTITLE]] ........................(15) |

− | With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. This is the absolute minimum pressure required for low liquid volumes, intermediate well depths, and low line pressures. | + | With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. This is the absolute minimum pressure required for low liquid volumes, intermediate well depths, and low line pressures. |

− | ===Casing pressure requirement=== | + | === Casing pressure requirement === |

− | For this case, assume 10 cycles/day, equivalent to a plunger trip every 2.4 hours. Any reasonable number of cycles can be assumed to calculate pressures. | + | For this case, assume 10 cycles/day, equivalent to a plunger trip every 2.4 hours. Any reasonable number of cycles can be assumed to calculate pressures. |

− | At 10 cycles/day and 10 bbl of liquid, the plunger will lift 1 bbl/cycle. The slug hydrostatic pressure (phs) of 1 bbl of liquid in 2 3/8-in. tubing with a 0.45-psi/ft liquid gradient is approximately 120 psia. Using Eq. 1b, the required casing pressure, in psia, is calculated as: | + | At 10 cycles/day and 10 bbl of liquid, the plunger will lift 1 bbl/cycle. The slug hydrostatic pressure (phs) of 1 bbl of liquid in 2 3/8-in. tubing with a 0.45-psi/ft liquid gradient is approximately 120 psia. Using Eq. 1b, the required casing pressure, in psia, is calculated as: |

− | [[File:Vol4 page 0856 eq 005.png]] | + | [[File:Vol4 page 0856 eq 005.png|RTENOTITLE]] ........................(16) |

− | [[File:Vol4 page 0856 eq 006.png]] | + | [[File:Vol4 page 0856 eq 006.png|RTENOTITLE]] ........................(17) |

− | With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. | + | With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. |

− | ===Method to determine plunger lift operating range=== | + | === Method to determine plunger lift operating range === |

− | In determining plunger-lift operating range, use Foss and Gaul K and plh + plf values for 2 3/8-in. tubing and average rise velocities of 1,000 ft/min. Calculate new friction factors if velocities are more or less than 1,000 ft/min. | + | In determining plunger-lift operating range, use Foss and Gaul K and plh + plf values for 2 3/8-in. tubing and average rise velocities of 1,000 ft/min. Calculate new friction factors if velocities are more or less than 1,000 ft/min. |

− | Calculate the constants ''A''<sub>''t''</sub>, ''p''<sub>''p''</sub>, ''A''<sub>''a''</sub>, ''R''<sub>''a''</sub>, ''F''<sub>''gs''</sub>, ''L'', and ''V''<sub>''t''</sub>: | + | Calculate the constants ''A''<sub>''t''</sub>, ''p''<sub>''p''</sub>, ''A''<sub>''a''</sub>, ''R''<sub>''a''</sub>, ''F''<sub>''gs''</sub>, ''L'', and ''V''<sub>''t''</sub>: |

− | Area of tubing, ft<sup>2</sup>: | + | Area of tubing, ft<sup>2</sup>: |

− | [[File:Vol4 page 0856 eq 007.png]] | + | [[File:Vol4 page 0856 eq 007.png|RTENOTITLE]] ........................(18) |

− | [[File:Vol4 page 0857 eq 001.png]] | + | [[File:Vol4 page 0857 eq 001.png|RTENOTITLE]] ........................(19) |

− | Differential pressure required to lift plunger, psi: | + | Differential pressure required to lift plunger, psi: |

− | [[File:Vol4 page 0857 eq 002.png]] | + | [[File:Vol4 page 0857 eq 002.png|RTENOTITLE]] ........................(20) |

− | where At is given as in.<sup>2</sup>. Therefore: | + | where At is given as in.<sup>2</sup>. Therefore: |

− | [[File:Vol4 page 0857 eq 003.png]] | + | [[File:Vol4 page 0857 eq 003.png|RTENOTITLE]] ........................(21) |

− | Area of annulus, ft<sup>2</sup>: | + | Area of annulus, ft<sup>2</sup>: |

− | [[File:Vol4 page 0857 eq 004.png]] | + | [[File:Vol4 page 0857 eq 004.png|RTENOTITLE]] ........................(22) |

− | [[File:Vol4 page 0857 eq 005.png]] | + | [[File:Vol4 page 0857 eq 005.png|RTENOTITLE]] ........................(23) |

− | Ratio of total area to tubing area: | + | Ratio of total area to tubing area: |

− | [[File:Vol4 page 0857 eq 006.png]] | + | [[File:Vol4 page 0857 eq 006.png|RTENOTITLE]] ........................(24) |

− | [[File:Vol4 page 0857 eq 007.png]] | + | [[File:Vol4 page 0857 eq 007.png|RTENOTITLE]] ........................(25) |

− | Lea<ref name="r14"/> -modified Foss and Gaul<ref name="r4"/> slippage factor [Foss and Gaul used a 15% factor (1.15) that could be translated to approximately 2% per 1,000 ft<ref name="r14"/>]: | + | Lea<ref name="r14">Lea, J.F. 1982. Dynamic Analysis of Plunger Lift Operations. J Pet Technol 34 (11): 2617-2629. SPE-10253-PA. http://dx.doi.org/10.2118/10253-PA.</ref> -modified Foss and Gaul<ref name="r4">Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API.</ref> slippage factor [Foss and Gaul used a 15% factor (1.15) that could be translated to approximately 2% per 1,000 ft<ref name="r14">Lea, J.F. 1982. Dynamic Analysis of Plunger Lift Operations. J Pet Technol 34 (11): 2617-2629. SPE-10253-PA. http://dx.doi.org/10.2118/10253-PA.</ref>]: |

− | [[File:Vol4 page 0857 eq 008.png]] | + | [[File:Vol4 page 0857 eq 008.png|RTENOTITLE]] ........................(26) |

− | [[File:Vol4 page 0857 eq 009.png]] | + | [[File:Vol4 page 0857 eq 009.png|RTENOTITLE]] ........................(27) |

− | Length of 1 bbl of fluid in the tubing, ft/bbl (5.615 = scf in 1 bbl): | + | Length of 1 bbl of fluid in the tubing, ft/bbl (5.615 = scf in 1 bbl): |

− | [[File:Vol4 page 0857 eq 010.png]] | + | [[File:Vol4 page 0857 eq 010.png|RTENOTITLE]] ........................(28) |

− | [[File:Vol4 page 0858 eq 001.png]] | + | [[File:Vol4 page 0858 eq 001.png|RTENOTITLE]] ........................(29) |

− | Volume of tubing above the slug (use for various slug sizes) (Eq. 16.10, but here in Mscf): | + | Volume of tubing above the slug (use for various slug sizes) (Eq. 16.10, but here in Mscf): |

− | [[File:Vol4 page 0858 eq 002.png]] | + | [[File:Vol4 page 0858 eq 002.png|RTENOTITLE]] ........................(30) |

− | Assume some values for S (bbl) and construct '''Table 3'''. | + | Assume some values for S (bbl) and construct '''Table 3'''. |

− | <gallery widths=300px heights=200px> | + | <gallery widths="300px" heights="200px"> |

File:Vol4 Page 858 Image 0001.png|'''Table 3''' | File:Vol4 Page 858 Image 0001.png|'''Table 3''' | ||

</gallery> | </gallery> | ||

Line 216: | Line 221: | ||

It was given that the estimated production when unloaded is 200 Mscf/D with 10 B/D of liquid (GLR = 200/10 = 20 Mscf/bbl), and that the available casing pressure (or the pressure to which the casing will build between plunger cycles) is 800 psia. The available casing pressure, p<sub>c</sub>, is equivalent to the calculated (''p''<sub>''c''</sub>)<sub>max</sub> —or the pressure required to lift the assumed slug sizes. The well GLR is equivalent to the calculated required GLR. The maximum liquid production is a product of the slug size (''S'') and the maximum cycles per day (''C''<sub>max</sub>). Importantly, C<sub>max</sub> is not a required number of plunger trips, but rather the maximum possible on the basis of plunger velocities. In reality, most wells operate below ''C''<sub>max</sub> because well shut-in time is required to build any casing pressure. In Table 16.3, note that the casing pressure (''p''<sub>''c''</sub>)<sub>max</sub> of 810 psia, the GLR of 20 Mscf/bbl, and the production rate of 10 B/D occur at slug sizes between 0.1 and 2.5 bbl. The well will operate on plunger lift. | It was given that the estimated production when unloaded is 200 Mscf/D with 10 B/D of liquid (GLR = 200/10 = 20 Mscf/bbl), and that the available casing pressure (or the pressure to which the casing will build between plunger cycles) is 800 psia. The available casing pressure, p<sub>c</sub>, is equivalent to the calculated (''p''<sub>''c''</sub>)<sub>max</sub> —or the pressure required to lift the assumed slug sizes. The well GLR is equivalent to the calculated required GLR. The maximum liquid production is a product of the slug size (''S'') and the maximum cycles per day (''C''<sub>max</sub>). Importantly, C<sub>max</sub> is not a required number of plunger trips, but rather the maximum possible on the basis of plunger velocities. In reality, most wells operate below ''C''<sub>max</sub> because well shut-in time is required to build any casing pressure. In Table 16.3, note that the casing pressure (''p''<sub>''c''</sub>)<sub>max</sub> of 810 psia, the GLR of 20 Mscf/bbl, and the production rate of 10 B/D occur at slug sizes between 0.1 and 2.5 bbl. The well will operate on plunger lift. | ||

− | ==Nomenclature== | + | == Nomenclature == |

+ | |||

{| | {| | ||

|- | |- | ||

− | |''A''<sub>''a''</sub> | + | | ''A''<sub>''a''</sub> |

− | |= | + | | = |

− | |cross-sectional area of annulus, ft<sup>2</sup> | + | | cross-sectional area of annulus, ft<sup>2</sup> |

|- | |- | ||

− | |''A''<sub>''t''</sub> | + | | ''A''<sub>''t''</sub> |

− | |= | + | | = |

− | |cross-sectional area of tubing, ft<sup>2</sup> or in.<sup>2</sup> | + | | cross-sectional area of tubing, ft<sup>2</sup> or in.<sup>2</sup> |

|- | |- | ||

− | |''C''<sub>max</sub> | + | | ''C''<sub>max</sub> |

− | |= | + | | = |

− | |maximum number of plunger round trips possible per day | + | | maximum number of plunger round trips possible per day |

|- | |- | ||

− | |''d'' | + | | ''d'' |

− | |= | + | | = |

− | |tubing diameter, in. | + | | tubing diameter, in. |

|- | |- | ||

− | |''f''<sub>''g''</sub> | + | | ''f''<sub>''g''</sub> |

− | |= | + | | = |

− | |Darcy-Weisbach friction factor for gas flow through the tubing | + | | Darcy-Weisbach friction factor for gas flow through the tubing |

|- | |- | ||

− | |''F''<sub>''gs''</sub> | + | | ''F''<sub>''gs''</sub> |

− | |= | + | | = |

− | |Foss and Gaul slippage factor of gas lost past plunger on rise cycle | + | | Foss and Gaul slippage factor of gas lost past plunger on rise cycle [approximately 2% per 1,000-ft depth ( = 1 + D/1,000 × 0.02); Foss and Gaul used 1.15 factor on 8,000-ft wells.] |

|- | |- | ||

− | |''f''<sub>''l''</sub> | + | | ''f''<sub>''l''</sub> |

− | |= | + | | = |

− | |Darcy-Weisbach friction factor for the liquid slug | + | | Darcy-Weisbach friction factor for the liquid slug |

|- | |- | ||

− | |''g''<sub>''g''</sub> | + | | ''g''<sub>''g''</sub> |

− | |= | + | | = |

− | |gas specific gravity | + | | gas specific gravity |

|- | |- | ||

− | |''K'' | + | | ''K'' |

− | |= | + | | = |

− | |gas friction in tubing | + | | gas friction in tubing |

|- | |- | ||

− | |''p''<sub>''c''</sub> | + | | ''p''<sub>''c''</sub> |

− | |= | + | | = |

− | |casing pressure, psia | + | | casing pressure, psia |

|- | |- | ||

− | |[[File:Vol4 page 0883 inline 001.png]] | + | | [[File:Vol4 page 0883 inline 001.png|RTENOTITLE]] |

− | |= | + | | = |

− | |average casing pressure during operation, psia | + | | average casing pressure during operation, psia |

|- | |- | ||

− | |(''p''<sub>''c''</sub>)<sub>max</sub> | + | | (''p''<sub>''c''</sub>)<sub>max</sub> |

− | |= | + | | = |

− | |the pressure required to start the plunger at the beginning of the plunger cycle, psia | + | | the pressure required to start the plunger at the beginning of the plunger cycle, psia |

|- | |- | ||

− | |(''p''<sub>''c''</sub>)<sub>min</sub> | + | | (''p''<sub>''c''</sub>)<sub>min</sub> |

− | |= | + | | = |

− | |the casing pressure required to move the plunger and liquid slug just before it reaches the surface, psia | + | | the casing pressure required to move the plunger and liquid slug just before it reaches the surface, psia |

|- | |- | ||

− | |''p''<sub>''cs''</sub> | + | | ''p''<sub>''cs''</sub> |

− | |= | + | | = |

− | |casing pressure at shut-in, psia | + | | casing pressure at shut-in, psia |

|- | |- | ||

− | |''p''<sub>''hs''</sub> | + | | ''p''<sub>''hs''</sub> |

− | |= | + | | = |

− | |slug differential hydrostatic pressure, psi | + | | slug differential hydrostatic pressure, psi |

|- | |- | ||

− | |''p''<sub>''l''</sub> | + | | ''p''<sub>''l''</sub> |

− | |= | + | | = |

− | |line pressure, psia | + | | line pressure, psia |

|- | |- | ||

− | |''p''<sub>''lf''</sub> | + | | ''p''<sub>''lf''</sub> |

− | |= | + | | = |

− | |differential pressure required to overcome liquid friction per barrel, psi/bbl | + | | differential pressure required to overcome liquid friction per barrel, psi/bbl |

|- | |- | ||

− | |''p''<sub>''lh''</sub> | + | | ''p''<sub>''lh''</sub> |

− | |= | + | | = |

− | |differential pressure required to lift liquid weight per barrel, psi/bbl | + | | differential pressure required to lift liquid weight per barrel, psi/bbl |

|- | |- | ||

− | |''p''<sub>''p''</sub> | + | | ''p''<sub>''p''</sub> |

− | |= | + | | = |

− | |differential pressure required to lift plunger weight, psi | + | | differential pressure required to lift plunger weight, psi |

|- | |- | ||

− | |''p''<sub>''R''</sub> | + | | ''p''<sub>''R''</sub> |

− | |= | + | | = |

− | |reservoir pressure, psia | + | | reservoir pressure, psia |

|- | |- | ||

− | |''p''<sub>''t''</sub> | + | | ''p''<sub>''t''</sub> |

− | |= | + | | = |

− | |tubing pressure, psia | + | | tubing pressure, psia |

|- | |- | ||

− | |''q''<sub>''g''</sub> | + | | ''q''<sub>''g''</sub> |

− | |= | + | | = |

− | |gas flow rate, Mscf/D | + | | gas flow rate, Mscf/D |

|- | |- | ||

− | |''q''<sub>''l''</sub> | + | | ''q''<sub>''l''</sub> |

− | |= | + | | = |

− | |liquid flow rate, B/D | + | | liquid flow rate, B/D |

|- | |- | ||

− | |''R'' | + | | ''R'' |

− | |= | + | | = |

− | |specific gas constant (air), 53.3 lbf-ft/(°R-lbm) | + | | specific gas constant (air), 53.3 lbf-ft/(°R-lbm) |

|- | |- | ||

− | |''R''<sub>''a''</sub> | + | | ''R''<sub>''a''</sub> |

− | |= | + | | = |

− | |ratio of annulus + tubing cross-sectional area to the annulus cross-sectional area | + | | ratio of annulus + tubing cross-sectional area to the annulus cross-sectional area |

|- | |- | ||

− | |''v'' | + | | ''v'' |

− | |= | + | | = |

− | |velocity, ft/sec | + | | velocity, ft/sec |

|- | |- | ||

− | |[[File:Vol4 page 0884 inline 002.png]] | + | | [[File:Vol4 page 0884 inline 002.png|RTENOTITLE]] |

− | |= | + | | = |

− | |average velocity of plunger falling through gas, ft/min (typically 200 to 1,200 ft/min) | + | | average velocity of plunger falling through gas, ft/min (typically 200 to 1,200 ft/min) |

|- | |- | ||

− | |[[File:Vol4 page 0884 inline 003.png]] | + | | [[File:Vol4 page 0884 inline 003.png|RTENOTITLE]] |

− | |= | + | | = |

− | |average velocity of plunger falling through liquid, ft/min (typically 50 to 250 ft/min) | + | | average velocity of plunger falling through liquid, ft/min (typically 50 to 250 ft/min) |

|- | |- | ||

− | |[[File:Vol4 page 0884 inline 004.png]] | + | | [[File:Vol4 page 0884 inline 004.png|RTENOTITLE]] |

− | |= | + | | = |

− | |average rise velocity of plunger, ft/min (typically 400 to 1,200 ft/min) | + | | average rise velocity of plunger, ft/min (typically 400 to 1,200 ft/min) |

|- | |- | ||

− | |''V''<sub>''g''</sub> | + | | ''V''<sub>''g''</sub> |

− | |= | + | | = |

− | |volume of gas required per cycle, Mscf | + | | volume of gas required per cycle, Mscf |

|- | |- | ||

− | |''V''<sub>''t''</sub> | + | | ''V''<sub>''t''</sub> |

− | |= | + | | = |

− | |volume of the tubing above the liquid load, Mscf | + | | volume of the tubing above the liquid load, Mscf |

|- | |- | ||

− | |''Z'' | + | | ''Z'' |

− | |= | + | | = |

− | |gas factor | + | | gas factor |

|- | |- | ||

− | |''γ''<sub>''l''</sub> | + | | ''γ''<sub>''l''</sub> |

− | |= | + | | = |

− | |liquid gradient, psi/ft | + | | liquid gradient, psi/ft |

|} | |} | ||

− | ==References== | + | == References == |

− | <references | + | |

− | + | <references /> | |

− | + | ||

− | + | == Noteworthy papers in OnePetro == | |

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

− | |||

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read | ||

− | ==External links== | + | == External links == |

+ | |||

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro | ||

− | ==See also== | + | == See also == |

− | [[Plunger lift]] | + | |

+ | [[Plunger_lift|Plunger lift]] | ||

+ | |||

+ | [[Plunger_lift_applications|Plunger lift applications]] | ||

+ | |||

+ | [[Plunger_design_considerations_and_selection|Plunger design considerations and selection]] | ||

− | [[Plunger lift | + | [[Plunger_lift_installation_and_maintenance|Plunger lift installation and maintenance]] |

− | [[ | + | [[PEH:Plunger_Lift]] |

− | + | ==Category== | |

− | [[ | + | [[Category:3.1.5 Plunger lift]] [[Category:YR]] |

## Latest revision as of 14:53, 30 June 2015

Plunger lift systems can be evaluated using rules of thumb in conjunction with historic well production, or with a mathematical plunger model. Because plunger lift systems typically are inexpensive and easy to install and test, most are evaluated by rules of thumb.

## GLR and buildup pressure requirements

The two minimum requirements for plunger lift operation are:

- Minimum gas-liquid ratio (GLR)
- Well buildup pressure

Plunger lift operation requires available gas to provide the lifting force, in sufficient quantity per barrel of liquid for a given well depth. The minimum GLR requirement is approximately 400 scf/bbl per 1,000 ft of well depth and is based on the energy stored in a compressed volume of 400 scf of gas expanding under the hydrostatic head of 1 bbl of liquid.^{[1]} One drawback to this rule of thumb is that it does not consider line pressures. Excessively high line pressures relative to buildup pressure might increase the requirement. The rule of thumb also assumes that the gas expansion can be applied from a large open annulus without restriction, but slimhole wells and wells with packers that require gas to travel through the reservoir or through small perforations in the tubing will cause a greater restriction and energy loss, which increase the minimum GLR requirement to as much as 800 to 1,200 scf/bbl per 1,000 ft.

Well buildup pressure is the bottomhole pressure just before the plunger begins its ascent (equivalent to surface casing pressure in a well with an open annulus). In practice, the minimum shut-in pressure requirement for plunger lift is equivalent to one and a half times the maximum sales-line pressure, although the actual requirement might be higher. This rule of thumb works well in intermediate-depth wells (2,000 to 8,000 ft) with slug sizes of 0.1 to 0.5 bbl/cycle. It does not apply reliably, however, to higher liquid volumes, deeper wells (because of increasing friction), and excessive pressure restrictions at the surface or in the wellbore.

An improved rule of thumb for minimum pressure is that a well can lift a slug of liquid when the slug hydrostatic pressure (phs) equals 50 to 60% of the difference between shut-in casing pressure (pcs) and maximum sales-line pressure:

or

This rule of thumb accounts for liquid production, can be used for wells with higher liquid production that require slug sizes of more than 1 to 2 bbl/cycle, and is regarded as a conservative estimate of minimum pressure requirements. To use Eqs. 1a and 1b, first estimate the total liquid production on plunger lift and number of cycles possible per day. Then, determine the amount of liquid that can be lifted per cycle. Use the well tubing size to convert that volume of liquid per cycle into the slug hydrostatic pressure, and use the equations to estimate required casing pressure to operate the system (see example below).

A well that does not meet minimum GLR and pressure requirements still could be plunger lifted with the addition of an external gas source. At this point, design becomes more a matter of the economics of providing the added gas to the well at desired pressures. Several papers in the literature discuss adding makeup gas to a plunger installation through existing gas lift operations, installing a field gas supply system, or using wellhead compression. ^{[2]}^{[3]}^{[4]}^{[5]}^{[6]}^{[7]}^{[8]}^{[9]}

## Estimating production rates

The simplest and sometimes most accurate method of determining production increases from plunger lift is decline-curve analysis^{[1]} (**Fig. 1**). Gas and oil reservoirs typically have predictable declines, either exponential or hyperbolic. Initial production rates usually are high enough to produce the well above critical rates (unloaded) and establish a decline curve. When liquid loading occurs, a marked decrease and deviation from normal decline can be seen. Unloading the well with plunger lift can re-establish a normal decline. Production increases from plunger lift will be somewhere between the rates of the well when it started loading and the rate of an extended decline curve to the present time. Ideally, decline curves would be used with critical-velocity curves to predetermine when plunger lift should be installed. This would enable plunger lift to maintain production on a steady decline and to never allow the well to begin loading.

Another method for estimating production is to build an inflow performance (IP) curve on the basis of the backpressure equation (**Fig. 2**).^{[10]}^{[11]}^{[12]}^{[13]} This is especially helpful if the well has an open annulus and is flowing up the tubing, and if the casing pressure is known. The casing pressure closely approximates bottomhole pressure. Build the IP curve on the basis of:

- Estimated reservoir pressure
- Casing pressure
- Current flow rate

Because the job of the plunger lift is to lower the bottomhole pressure by removing liquids, estimate the bottomhole pressure with no liquids. Use this new pressure to estimate a production rate with lower bottomhole pressures.

## Models

Plunger lift models are based on the sum of forces acting on the plunger while it lifts a liquid slug up the tubing (**Fig. 3**). These forces at any given point in the tubing are:

Stored casing pressure freely acting on the cross section of the plunger.

Stored reservoir pressure acting on the cross section of the plunger, based on inflow performance.

- Weight of the fluid.
- Weight of the plunger.
- Friction of the fluid with the tubing.
- Friction of the plunger with the tubing.
- Gas friction in the tubing.
- Gas slippage upward past the plunger.
- Liquid slippage downward past the plunger.
- Surface pressure (line pressure and restrictions) acting against the plunger travel.

Several publications have dealt with this approach. Beeson et al.^{[3]} first presented equations for high-GLR wells in 1955, on the basis of an empirically derived analysis. Foss and Gaul^{[4]} derived a force-balance equation for use on oil wells in the Ventura Avenue field in 1965. Lea^{[14]} presented a dynamic analysis of plunger lift that added gas slippage and reservoir inflow, and mathematically described the entire cycle (not just plunger ascent) for tight-gas/very high-GLR wells.

Foss and Gaul’s methodology^{[4]} was to calculate (p_{c})min, the casing pressure required to move the plunger and liquid slug just before it reaches the surface. Because (p_{c})min is at the end of the plunger cycle, the energy of the expanding gas from the casing to the tubing is at its minimum. Adjusting (p_{c})min for gas expansion from the casing to the tubing during the full plunger cycle yields (p_{c})_{max} , the pressure required to start the plunger at the beginning of the plunger cycle. The pressure must build to (p_{c})_{max} to operate successfully.

The average casing pressure p¯c, maximum cycles C_{max}, and gas required per cycle (V_{g}) can be calculated from (p_{c})min and (p_{c})max . The equations below are essentially those presented by Foss and Gaul^{[4]} but are summarized here as presented by Mower et al.^{[15]} The Foss and Gaul model is not rigorous, it:

- Assumes constant friction associated with plunger rise velocities of 1,000 ft/min
- Does not calculate reservoir inflow
- Assumes a value for gas slippage past the plunger
- Assumes an open, unrestricted annulus
- Assumes that the user can determine unloaded gas and liquid rates independently of the model

Also, because this model originally was designed for oilwell operation that assumed the well would be shut in upon plunger arrival, p¯c is only an average during plunger travel. The net result of these assumptions is an overprediction of required casing pressure. If a well meets the Foss and Gaul criteria, it is almost certainly a candidate for plunger lift. For a full description of the Foss and Gaul model and for a description of improved models, see the references.^{[4]}^{[10]},^{[15]}^{[16]}^{[17]}

## Basic Foss and Gaul equations

Basic Foss and Gaul^{[4]} equations (Modified by Mower et al.^{[15]} and Lea^{[14]})

### Required pressures

and

where

and

Foss and Gaul suggested an approximation where K and p_{lh} + p_{lf} are constant for a given tubing size and a plunger velocity of 1,000 ft/min (**Table 1**).

### Gas (Mscf) required per cycle

where

### Maximum cycles

## Examples

### Rules of thumb and Foss and Gaul calculations

Examples are based on the well data given in **Table 2**.

**Example of rule-of-thumb GLR calculation**

The minimum GLR (Rgl) = 400 scf/bbl per 1,000 ft of well depth. The well’s GLR is:

where *q*_{g} is given in scf. The well GLR is >400 scf/bbl per 1,000 ft and is adequate for plunger lift.

**Example of rule of thumb for casing pressure requirement to plunger lift (simple)**

The rule of thumb for calculating the minimum shut-in casing pressure for plunger lift, in psia, is:

With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift. This is the absolute minimum pressure required for low liquid volumes, intermediate well depths, and low line pressures.

### Casing pressure requirement

For this case, assume 10 cycles/day, equivalent to a plunger trip every 2.4 hours. Any reasonable number of cycles can be assumed to calculate pressures.

At 10 cycles/day and 10 bbl of liquid, the plunger will lift 1 bbl/cycle. The slug hydrostatic pressure (phs) of 1 bbl of liquid in 2 3/8-in. tubing with a 0.45-psi/ft liquid gradient is approximately 120 psia. Using Eq. 1b, the required casing pressure, in psia, is calculated as:

With 800 psia of available casing pressure, the well meets the pressure requirements for plunger lift.

### Method to determine plunger lift operating range

In determining plunger-lift operating range, use Foss and Gaul K and plh + plf values for 2 3/8-in. tubing and average rise velocities of 1,000 ft/min. Calculate new friction factors if velocities are more or less than 1,000 ft/min.

Calculate the constants *A*_{t}, *p*_{p}, *A*_{a}, *R*_{a}, *F*_{gs}, *L*, and *V*_{t}:

Area of tubing, ft^{2}:

Differential pressure required to lift plunger, psi:

where At is given as in.^{2}. Therefore:

Area of annulus, ft^{2}:

Ratio of total area to tubing area:

Lea^{[14]} -modified Foss and Gaul^{[4]} slippage factor [Foss and Gaul used a 15% factor (1.15) that could be translated to approximately 2% per 1,000 ft^{[14]}]:

Length of 1 bbl of fluid in the tubing, ft/bbl (5.615 = scf in 1 bbl):

Volume of tubing above the slug (use for various slug sizes) (Eq. 16.10, but here in Mscf):

Assume some values for S (bbl) and construct **Table 3**.

It was given that the estimated production when unloaded is 200 Mscf/D with 10 B/D of liquid (GLR = 200/10 = 20 Mscf/bbl), and that the available casing pressure (or the pressure to which the casing will build between plunger cycles) is 800 psia. The available casing pressure, p_{c}, is equivalent to the calculated (*p*_{c})_{max} —or the pressure required to lift the assumed slug sizes. The well GLR is equivalent to the calculated required GLR. The maximum liquid production is a product of the slug size (*S*) and the maximum cycles per day (*C*_{max}). Importantly, C_{max} is not a required number of plunger trips, but rather the maximum possible on the basis of plunger velocities. In reality, most wells operate below *C*_{max} because well shut-in time is required to build any casing pressure. In Table 16.3, note that the casing pressure (*p*_{c})_{max} of 810 psia, the GLR of 20 Mscf/bbl, and the production rate of 10 B/D occur at slug sizes between 0.1 and 2.5 bbl. The well will operate on plunger lift.

## Nomenclature

## References

- ↑
^{1.0}^{1.1}^{1.2}Ferguson, P.L. and Beauregard, E. 1983. Will Plunger Lift Work In My Well? Proc., Thirtieth Annual Southwestern Petroleum Short Course, Lubbock, Texas, 301–311. - ↑ Christian, J., Lea, J.F., and Bishop, R. 1995. Plunger Lift Comes of Age. World Oil (November): 43.
- ↑
^{3.0}^{3.1}Beeson, C.M., Knox, D.G., and Stoddard, J.H. 1955. Plunger Lift Correlation Equations And Nomographs. Presented at the Fall Meeting of the Petroleum Branch of AIME, New Orleans, Louisiana, 2-5 October. http://dx.doi.org/10.2118/501-g. - ↑
^{4.0}^{4.1}^{4.2}^{4.3}^{4.4}^{4.5}^{4.6}Foss, D.L. and Gaul, R.B. 1965. Plunger Lift Performance Criteria with Operating Experience—Ventura Avenue Field. Drilling and Production Practices, 124-140. Dallas, Texas: API. - ↑ Abercrombie, B. 1980. Plunger Lift. In The Technology of Artificial Lift Methods, ed. K.E. Brown, Vol. 2b, 483-518. Tulsa, Oklahoma: PennWell Publishing Co.
- ↑ Hall, J.C. and Bell, B. 2001. Plunger Lift By Side String Injection. Proc., Forty-Eighth Annual Southwestern Petroleum Short Course, Lubbock, Texas, 17–18..
- ↑ Morrow, S.J. Jr. and Aversante, O.L. 1995. Plunger Lift: Gas Assisted. Proc., Forty-Second Annual Southwestern Petroleum Short Course, Lubbock, Texas, 195–201.
- ↑ White, G.W. 1982. Combine Gas Lift, Plungers to Increase Production Rate. World Oil (November): 69.
- ↑ Phillips, D.H. and Listiak, S.D. 1996. Plunger Lift With Wellhead Compression Boosts Gas Well Production. World Oil (October) 96.
- ↑
^{10.0}^{10.1}Lea Jr., J.F. and Tighe, R.E. 1983. Gas Well Operation With Liquid Production. Presented at the SPE Production Operations Symposium, Oklahoma City, Oklahoma, 27 February-1 March 1983. SPE-11583-MS. http://dx.doi.org/10.2118/11583-MS. - ↑ Phillips, D.H. and Listiak, S.D. 1998. How to Optimize Production from Plunger Lift Systems. World Oil (May): 110.
- ↑
^{12.0}^{12.1}Vogel, J.V. 1968. Inflow Performance Relationships for Solution-Gas Drive Wells. J Pet Technol 20 (1): 83-92. http://dx.doi.org/10.2118/1476-PA. - ↑
^{13.0}^{13.1}Mishra, S. and Caudle, B.H. 1984. A Simplified Procedure for Gas Deliverability Calculations Using Dimensionless IPR Curves. Presented at the SPE Annual Technical Conference and Exhibition, Houston, Texas, 16-19 September 1984. SPE-13231-MS. http://dx.doi.org/10.2118/13231-MS. - ↑
^{14.0}^{14.1}^{14.2}^{14.3}^{14.4}Lea, J.F. 1982. Dynamic Analysis of Plunger Lift Operations. J Pet Technol 34 (11): 2617-2629. SPE-10253-PA. http://dx.doi.org/10.2118/10253-PA. - ↑
^{15.0}^{15.1}^{15.2}Mower, L.N., Lea, J.F., E., B. et al. 1985. Defining the Characteristics and Performance of Gas-Lift Plungers. Presented at the SPE Annual Technical Conference and Exhibition, Las Vegas, Nevada, 22-26 September 1985. SPE-14344-MS. http://dx.doi.org/10.2118/14344-MS. - ↑ Rosina, L. 1983. A Study of Plunger Lift Dynamics. MS Thesis, University of Tulsa, Tulsa.
- ↑ Lea, J.F. 1999. Plunger Lift vs. Velocity Strings. Paper presented at the 1999 Energy Sources Technology Conference & Exhibition, Houston, 1–2 February.

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## See also

Plunger design considerations and selection

Plunger lift installation and maintenance