NEW MODELING TECHNIQUES FOR TWO-PIECE PLUNGER LIFT COMPONENTS
by DIVYAKUMAR O. GARG, B.E. A THESIS IN PETROLEUM ENGINEERING Submitted to the Graduate Faculty of Texas Tech University in Partial Fulfillment of the Requirements for the Degree of MASTER OF SCIENCE IN PETROLEUM ENGINEERING Approved
Chairperson of the Committee
Accepted
Uean ot the Graduate School December, 2004
ACKNOWLEDGEMENTS There are many people associated with this thesis deserving recognition. I would like to thank Dr. James F. Lea for his overall direction, support, and training. I would like to thank Mr. Joe Mclnemey for setting up the testing equipment and helping me to take the experimental readings. I would also like to thank Dr. James C. Cox for serving on my conmiittee and for his guidance. 1 would like to express thanks to family members, friends, and colleagues whose understanding and support made schooling relatively easier. Special mention is given to Dr. Akanni Lawal for the support provided by him.
TABLE OF CONTENTS
ACKNOWLEDGEMENTS
i
ABSTRACT
v
LIST OF TABLES
vi
LIST OF FIGURES
vii
NOMENCLATURE
ix
CHAPTER I
II
m
INTRODUCTION
1
1.1
2
Obj ective of the Proj ect
METHODS OF DE-WATERING GAS WELLS
3
2.1
Sucker Rod Pumps
3
2.1.1
Basics of Sucker Rod Pump
3
2.1.2
The Successive Steps in the Pump Operation
5
2.2
Hydraulic Pumping
7
2.3
Foaming
9
2.4
Gas Lift
11
2.5
Electrical Submersible Pump (ESP)
12
2.6
Progressive Cavity Pumps (PCP)
13
2.7
Velocity Strings
15
2.8
Summary
15
CONVENTIONAL AND TWO-PIECE PLUNGER BACKGROUND
16
3.1
Plunger Lift
16
3.2
Standard Plunger Operation
17
3.3
Plunger System Equipment
19
3.3.1
Subsurface Equipment - Plungers
19
3.3.2
Down Hole Equipment - Springs and Stops
19
n
IV
V
3.3.3
Surface Equipment
19
3.3.4
Controllers
20
3.4
Conventional Plunger Cycle Steps
21
3.5
Plunger Lift - Will it Work?
22
3.6
Conventional Plunger Operation
24
3.7
Two-Piece Plunger
25
3.8
Two - Piece Mechanical Components
26
3.8.1
26
Equipment Description:
3.9
Two - Piece Plunger Cycle Steps
27
3.10
Two - Piece Plunger Cycle Concerns
29
TWO-PIECE PLUNGER TESTING FACILITY AND TEST PROCEDURE
30
4.1
32
TestPocedure
RESULTS AND DISCUSSIONS OF TWO-PIECE PLUNGER CASES
33
5.1
Examples: Discussion of Results for Two-Piece Plunger Cases
33
5.1.1
Fall Velocity for Ball
33
5.1.2
Fall Velocity for Hollow Cylinder
35
5.1.3
Discussion for Component Fall Velocities
36
Re-plots for Titanium and Steel Two - Piece Plunger Sets
36
5.2.1
Fall Velocity Re-plots for Ball
36
5.2.2
Fall Velocity Re-plots for Hollow Cylinder
38
5.2.3
Discussion - Titanium and Steel Two-Piece Plunger Sets
39
5.2
5.3
Lifting of Liquid Slugs
40
5.4
Additional Plotted Model Predictions
41
5.4.1
Titanium Plunger and Ball Set, 6 in.
42
5.4.2
Titanium Plunger and Ball Set, 10 in.
43
5.4.3
Steel Plunger and Ball Set, 6 in.
44
5.4..4
Steel Plunger and Ball Set, 8 in.
45
m
VI
5.4.5
Titanium Plunger and Ball Set, 8 in.
46
5.4.6
Steel Plunger and Ball Set, 9 in.
47
5.4.7
Summary
48
SUMMARY: TESTING AND MODELLING FOR THE TWO-PIECE PLUNGER
49
REFERENCES
51
APPENDIX
56
A
B
DEVELOPMENT OF DRAG EQUATIONS
56
A. 1
Suspension Testing - Drag Coefficient Model
56
A.2
Dynamic Testing - Drag Coefficient Model
60
CALCULATION OF DRAG COEFFICIENTS OF TWO-PIECE PLUNGER COMPONENTS
63
B. 1
Drag Coefficient for Ball
63
B.2
Drag Coefficient for Hollow Cylinder
64
B.3
Drag Coefficient for Ball and Cylinder Combined
66
C
CRITICAL RATE EQUATIONS
67
D
COMPUTER PROGRAM
69
D.I
Cylinder Flowrate Code
69
D.2
Fall Velocities Code
70
E
EQUATIONS FOR LIFTING OF SLUGS
73
F
SAMPLE DATA FOR TWO-PIECE PLUNGER CASES
74
F.l Data for Ball
74
F.2 Data for Hollow Cylinder
81
F.3 Data for Ball and Hollow Cylinder Combined
87
IV
ABSTRACT
The two piece plunger (a steel ball below and a hollow cylinder) seals the tubing when the ball is on the bottom of the cylinder. The plunger is designed to carry liquids from a producing gas well to prevent liquid loading. As such it can lift liquids when the components are together with gas pressure providing the lifting energy. When the two combined components reach the surface, the liquid is produced and the ball is pushed away from the cylinder to begin to fall against the flow. The cylinder is retained on the ball push rod until a short shut-in period of the well. Then the cylinder falls against the flow and hopefully combines with the ball at the bottom of the well to collect more liquids in the gas well and carry them to the surface with the combined ball and cylinder. There are many instances where using this plunger results in production increases. However in some cases, it appears to have a lesser effect. Results of testing show that above certain rates, the components will not fall against the flow in the well. Test results, and the result of drag models to fit the test data are extended to show the potential user what the allowable rates are from the well, before the individual components are predicted to fall more slowly or to be unable to fall in the well, thereby making application impossible without a temporary reduction in the flow rate. The results should allow the user to be able to better use the two piece plunger in a wider range of application conditions to remove liquids from a flowing gas well.
LIST OF TABLES F.I.I
Physical Parameters for the titanium ball
74
F. 1.2
Results Extrapolated for titanium ball in Air
74
F. 1.3
Results Extrapolated for titanium ball in Gas (0.65)
77
F.2.1
Physical Parameters for the titanium hollow cylinder
81
F.2.2
Results Extrapolated for titanium hollow cylinder in Air
81
F.2.3
Results Extrapolated for titanium hollow cylinder in Gas (0.65)
84
F.3.1
Physical parameters for the 2 in. titanium set
87
F.3.2.1
Two in. titanium set for 500 fpm fall velocity
88
F.3.2.2
Two in. titanium set for 1000 fpm fall velocity
89
VI
LIST OF FIGURES 2.1 Components of a Sucker Rod pump
4
2.2 Pump Card
5
2.3 Plunger and Ball Valve Details
6
2.4 Jet Pump
8
2.5 Setup for Testing of Foaming Agents
10
2.6 Diagram ofTypical Rotative Gas Lift System
12
2.7 Submersible Pump and Impeller Schematic
13
2.8 Typical PCP Installation
14
3.1 Plunger Lift System
18
3.2 Time Cycle Arrangements
20
3.3 Conventional Plunger Lift Cycle
22
3.4 Feasibihty for a two inch plunger
23
3.5 Two-piece plungers
25
3.6 Mechanical components ofthe Two-piece plunger
27
3.7 Two-piece plunger cycle
28
4.1 Testing Facility at Texas Tech University
31
4.2 Ball suspended in tubing
31
5.1 Critical rates for Titanium Ball
34
5.2 Critical rates for Titanium Cylinder
35
5.3 Titanium Ball Straight Line Plot
37
5.4 Steel Ball Straight Line Plot
37
5.5 Titanium Cylinder Straight Line Plot
38
5.6 Steel Cylinder Straight Line Plot
39
5.7 Titanium Set (Ball and Cylinder) for rise velocity 500 fpm
40
5.8 Titanium Set (Ball and Cylinder) for rise velocity 1000 fpm
41
5.9 Sihca Nitrate Ball, 1^^^ in O.D. and weighs 0.164 lbs
42
5.10 Cylinder 1.9 in O.D and weighs 1.56 lbs
42
5.11 Zircon Ceramic Ball, 1^'^ in O.D. and weighs 0.29 lbs
43
Vll
5.12 Cylinder 1.9 in O.D and weighs 2.63 lbs
43
5.13 Zircon Ceramic Ball, 1^'* in O.D. and weighs 0.29 lbs
44
5.14 Cylinder 1.9 in O.D and weighs 2.75 lbs
44
5.15 Steel Ball, l^^^in O.D. and weighs 0.387 lbs
45
5.16 Cylinder 1.9 in O.D and weighs 3.65 lbs
45
5.17 Titanium Ball, 1 ^'^ in O.D. and weighs 0.23 lbs
46
5.18 Cylinder 1.9 in O.D and weighs 2.125 lbs
46
5.19 Cobah Ball, 1^'^ in O.D. and weighs 0.437 lbs
47
5.20 Cylinder 1.9 in O.D and weighs 4.22 lbs
47
A. 1 Schematic Forces on Ball
57
A.2 Schematic Forces on Hollow Cylinder
58
A.3 Schematic forces for Ball and Cylinder combined
59
B.2 Explanation of Variables
64
vui
NOMENCLATURE a
=
Outside radius of cylinder, ft
A
=
Internal tubing diameter, ft
Acir
=
Clearance area between cylinder and tubing, ft^
A I
=
Internal area of Cylinder, ft
Ao
=
Annular area between cylinder and tubing, ft^
Ap
=
Projected area, ft^
Area
=
Area ofthe object, ft^
Atbg
=
Area ofthe tubing, ft^
B
=
Internal cylinder diameter, ft
Cd
=
Drag coefficient, dimensionless
Cdcaic
-
Calculated drag coefficient, dimensionless
Cdmeas
-
Measured drag coefficient, dimensionless
D
=
Intemaldiameter ofpipe, ft
Dj
=
External diameter of cylinder, ft
Di*
=
Intemaldiameter of cylinder, ft
Do
=
Internal diameter of tubing, ft
EPT
=
Effective plunger travel, dimensionless
ESP
=
Electrical Submersible Pump, dimensionless
f
=
Friction factor, dimensionless
g(.
=
Gravitational constant, Ibm-ft /Ibf-sec
GLR
=
Gas-liquid ratios, scC^Dbl
I.D.
=
Internal diameter, ft
L
=
Length of cylinder, ft
m
=
Mass, lbs
MPT
=
Maximum plunger travel, dimensionless
O.D.
=
Outer diameter, ft
p
=
Pressure, psi
P
=
Pressure, psi
IX
Pc
Casing pressure, psi
PCP
Progressive cavity pump, dimensionless
"friction
Pressure due to friction, psi
"weight
Pressure due to column weight, psi
Qgcond
Flow rate of condensate in gas stream, MMscf/D
Q:
Flow rate through internal diameter, ft^/D
Qm
Flow rate through the cylinder in tubing, ft^/D
Qtbg
Flow rate in tubing, ft^/D
Qtot
Total Flow rate through tubing, ft'^/D
Re
Reynolds Number, dimensionless
^Gijquid
Specific gravity of liquid, dimensionless
Slug
Mass in British gravitational system, -32.17 Ibm
Slugiength
=,ft
t
Time, sec
TbgiD
Internal diameter of tubing, ft
Vfall
Velocity of falling object, ft/sec
Vgas
In-situ velocity of gas, ft/sec
Vgcond
Velocity of condensate in gas stream, ft/sec
Vgwater
Velocity of water in gas stream, ft/sec
'rise
Rise velocity, ft/sec
Vt
Critical velocity by Turner, ft/sec
Vtbg
In-situ velocity in tubing, ft/sec
Wt
Weight, lbs
z
Gas deviation factor, dimensionless Viscosity, Cp
pair
Density of air, Ib/ft^
Pdrag
Density of air around object median, lb/ft
pimp
Density of air at impact on object, lb/ft
a
Interfacial tension, dynes/cm
AP
=
Pressure difference across the object, psi
APcaic
=
Calculated pressure difference across object, psi
iAPmeas
=
Mcasurcd pressure difference across object, psi
XI
CHAPTER 1 INTRODUCTION Forty percent of the wells in the worid are on some kind of artificial lift. For gas wells, as they deplete liquids often accumulate in the wellbore and the need for artificial lift arises to lift the hquids from the well. Accumulafion of the liquids in the wellbore is known as liquid loading, hi mature gas wells, the accumulation of fluids in the well can impede and sometimes haft gas production. Gas flow is maintained by removing accumulated fluids using the following most common methods of de-watering of gas wells: 1) Plunger hft 2) Beam pump 3) Swabbing 4) Soaping 5) Venting the well to atmospheric pressure (blowing down the well) 6) Small tubing (velocity strings or Siphon string) 7) Intermittent gas lift; chamber lift 8) Hydraulic jet or reciprocating hydraulic pump 9) Surfactants Plunger lift systems have benefits of increasing production, being a cost effective alternative usually requiring no outside source of energy, which work to reduce the fallback of liquids slugs as they rise with gas pressure underneath. Continuous removal of liquids results in higher daily gas production rates than those compared prior to plunger lift installation The literature " provides background information on conventional plunger lift operations. In fact, the plunger systems^ also eluninate or reduce frequency of well treatments required for scale and paraffin removal'^ and remedial treatments such as swabbing'^ and chemicals. The industry consensuses that plunger lift is one ofthe most cost effective methods to de-water a gas well.
This research project focuses on a new plunger introduced to the industry. The plunger constitutes of two separate components (a ball and a hollow cylinder above) called a two-piece plunger . Combined together the components form a seal of sorts in the tubing and can allow gas pressure to lift the liquids and the plunger components out of the well. The components (ball on bottom and cylinder on top) are then controlled to fall back independently to rejoin at the bottom of the well. The report provides details as to the equipment used for the testing and the points of caution and concern when using a two-piece plunger. Drag models to predict the rise and fall of the two individual components of the new two-piece plunger were developed based upon experimentally obtained data. Details of the equations used and models developed are provided in the Appendix A and Appendix B. The results section deals with the cases run and their discussion. This research project results provide information needed to better, in general, operate the two-piece plunger systems
1.1 Objective ofthe Project This research project provides test data and mathematical models to improve applications of the two-piece plunger. Data was collected on the gas rate required to suspend the individual components ofthe two-piece plunger; i.e. the ball and the hollow cylinder both separately and also combined. From this data, by calculating drag coefficients, models were developed to determine the rise and fall velocities of the ball and the cylinder as a function of gas rate and pressure. The models developed from suspension tests were verified by spot checking measured fall velocities with some gas production taking place. The tests were made using compressed air, but the models developed allow the calculation of performance in natural gas. The model and charts developed predict the fall rates for the individual components against a given flow rate for a given pressure.
CHAPTER 2 METHODS OF DE-WATERING GAS WELLS This section discusses the most prevalent options in artificial lift methods for solving the problems of liquid loading as used by the petroleum industry. It provides briefly a discussion of their method of operation, important features and tables of the advantages, disadvantages and conditions of applicability of each method.
2.1 Sucker Rod Pumps 2.1.1 Basics of Sucker Rod Pump Sucker rod pump systems are designed to lift fluids to the surface and are perhaps the most common methods to remove liquids from gas wells. These systems are applied when wells do not have enough pressure and gas liquid ratio to allow use of other methods. The liquid is usually pumped up the tubing and the gas production takes place from the casing. Beam pump installations have higher installation and operatmg costs as opposed to other methods such as plunger lift, foaming, or velocity strings. Beam pumps can work well to remove liquids from a gas well and are hence used in spite of their comparative high initial and operational costs. Initial costs can be as high as $20,000 $60,000 US for placing a typical gas well on rod pump. In addition one can expect to spend approximately $20,000 US per unit to replace worn downhole pumps and it is common to pull the pump twice per year (to as low as once in perhaps 4 years) on an average'^. Attention to problem areas can significantly reduce operating expense. The components of a sucker rod surface pumping system are illustrated in figure 2.1.
PUMPING UMH \ V
SHEAVES AND BELTS PRIME MOVER,
CLAMP AND CARRIER BAR Yy POUSHED ROD t / ^ STUFfrHG BOX FLOV/ LINE
CASIKQ TUetNG SUCKER RODS
TUBING AKa^OR SINKER BARS PUMP GAS AWCHOR
Figure 2.1: Components of a Sucker Rod pump (Courtesy Harbison Fischer) The pumping unit converts the rotary motion from the prime mover to reciprocating motion. The prime mover is generally an electrical motor. A good installation for a sucker rod pumping unit would have an energy efficiency of about 50 percent with efficiency being defined as the energy used to pump the fluids divided by the energy provided to the installation. The downhole pump is required to handle some free gas; performing the function of a liquid pump plus a gas compressor. The work on the fluid done per cycle may be determined from the area of the pump card which is a plot of the calculated rod loads and position above the pump made each cycle of the pump. An important tool for diagnosing beam pump problems is the surface dynamometer card. A surface dynamometer card is the plot ofthe measured or predicted rod loads at the various positions throughout a complete sfroke. The load is usually
displayed in pounds of force and the position is usually displayed in inches. The pump dynamometer card is a plot of usually calculated loads at various positions of pump stroke and represents the load the pump applies to the bottom of the rod string. Identifying how the pump is performing and analysis of down-hole problems is one ofthe primary uses of the pump dynamometer card. An example pump card is shown in figure 2.2. Since the objective is to pump liquids without gas interference, use of a good downhole gas separator is recommended to prevent gas lock conditions and low volumetric efficiency in the pump. From the pump card problems such as leaky traveling or standing valve, tight stuffing box, tubing anchor slipping, gas locked pumps, and spacing can be diagnosed. Design considerations are available in the literature'^'''* .During the pumping cycle the gas bubbles in the liquid tend to rise to the top of the pump. At slow pumping speeds, this separation of gas and liquid may be complete; or in handling "foamed" fluids, it may be negligible. Often small amounts of liquid must be produced to allow gas to flow. When a beam pump is operated at a rate at a rate beyond the capacity of the reservoir to produce liquids, the liquid level in the well is pumped below the pump intake and the pump is said to pump-off Considerable literature'^'"^ exists concerning beam pump systems on pump off control. 2.1.2 Pump Operation Steps
Figure 2.2: Pump card
In figure 2.2 the maximum plunger travel, MPT, is the maximum length of the plunger movement with respect to the pump barrel during one complete stroke. The fluid load is a force caused by differential pressure acting on the pump plunger. The differential pressure acts across traveling valve on the upstroke and is transferred to the standing valve on the down stroke. The differential pressure is the difference between the pressure due to the tubing fluids and the pressure in the wellbore. The magnitude of the fluid load is equal to the pump discharge pressure minus the pump intake pressure multiplied by the plunger area. From points B to C the rods carry the fluid load, while the traveling valve is closed. From points D to A the tubing carries the fluid load, while the standing valve is closed. The effective plunger travel, EPT, is the length of the plunger travel when the full fluid load is acting on the standing valve. A schematic of plunger and ball valve details are shown in figure 2.3. Sucking Rod Plunger
Well Casing Riding Valv« Inlets
Standing Valve
Figure 2.3: Plunger and ball valve details 14
There are many kinds of surface units, rods, downhole pumps and other components of the beam pumping system. The surface units are rated for torque developed by the gear box, maximum load at the carrier bar, and stroke length. For instance a 456-305-144 unit can develop 456,000 inch-lbs of torque from the gear box, carry a maximum load of
30,500 Ibfs. and has maximum stroke length of 144 inches of stroke. The rods are rated with a minimum tensile value that is used to determine the fatigue loading of the rods. For instance a grade D rod has a minimum tensile rating of 115,000 psi. The main variable for design for the downhole pump is the diameter that determines the amount of fluid lifted on each cycle. The motor must provide the energy to move the unit, and overcome friction in the unit as well as starting torque.
2.2 Hydraulic Pumping Hydrauhcally powered down-hole pumps are powered by a stream of highpressure water or oil (power fluid) supplied by a power-fluid pump at the surface. Hydraulic downhole pumps are of two types. 1) Piston pumps, which are similar to beam pumps. 2) Jet pumps that operate by power fluid passing through a Venturi, exposing the formation to low pressure at the outlet of a nozzle or jet. Pressure is recovered as the jet passes into a throat and then into a diffuser. Then the high pressure fluid is allowed to produce to the surface. The surface power-fluid pump usually is a piston-type or centrifugal highpressure pump. The power fluid transfers the power necessary to lift liquids from the surface to the bottomhole pump. The literature ^'^' discusses the features of hydraulic pumping and how it may be applied to de-watering gas wells. The figure 2.4 shows a typical jet pump with a power fluid being supplied down tubing and production and power fluid commingling and returning to the surface through the casing annulus.
Power fluid
Vlj Co-n'i
HI |HH'j|n Well Rind
2
1 MHHBHBBBK f
Figure 2.4: Jet Pump. (Courtesy Schlumberger) Hydraulic pumps can be used to remove liquids from gas wells and are not limited by depth. They can tolerate a wide range of operating conditions and jet pumps only handle sand laden or abrasive fluids. Fairly high rates of production are possible. Jet pumping does require high power for the production achieved or in other words, they have poor energy efficiency. Jet pumps are capable of handling all forms of fluid production including gas, steam, or liquid. They are usually installed vertically, but can be mounted horizontally as well. Reciprocating pumps can lower the formation to lower values of pressure but can tolerate little solids and less gas than the jet pump. Reciprocating pumps are much more efficient and may have higher efficiencies than a beam pump system.
2.3 Foaming In gas well applications, the liquid/gas/surfactant mixing occurs most commonly dovm-hole. There are various methods of introducing surfactants into the well. The simplest method is to batch or continuously inject chemicals down the annulus of a well with no packer. Also, soap sticks can be dropped down the tubing, manually or with an automatic dispenser. Surfactant injection can be achieved either down the casing tubing annulus or through the tubing. Another injection system is one using a capillary tube lubricated down the tubing to allow injection to depth in flowing wells. Wells are unloaded with surfactants using two techniques namely batch treatment and continuous surfactant treatment. Foaming guidelines include the following. 1) Screen foaming agents with lab tests to be sure they will foam well bore fluids. 2) Water is easiest to foam. Condensates are more difficult and require more expensive chemicals. Water loading is most common problem in the field operations with most liquid loaded wells being (80-90%) being loaded with produced and also very commonly loaded with condensed water. 3) If a packer is present, systems exist that allow the lubrication of a 1/4 in. capillary tube down the tubing to inject chemicals at depth. 4) Soap sticks can be launched down the tubing manually or with various automation schemes. 5) With no packer, agents can be introduced down the atmulus, either batched or injected. Consider automated measurements and confrols to schedule treatments. Foaming is a cheap initial-cost solution for gas-well de-watering, but can be expensive if large volumes of surfactants are required. Soap sticks are inconsistent and generally fail to unload the well fully, and when they do unload the well successfully it may be a shorter term solution. The cost for unloading the well with soap sticks is approximately $100 US per well each month. It has been used successfully in many appUcations. Some operators prefer that foams be tried first for liquid-loading problems because they are inexpensive. The foam produces a less dense mixture by increasing the surface area of the liquid with bubbles. The result is less gas/liquid slippage. The gas can more easily
carry the foamed liquids to the surface. Foaming is usually possible for liquids if the liquids contain high percentage of water. Foaming could assist other lift methods for example plunger lift. The literature^ "^' provides details for foam effect on production of liquids, foam selection, generation, stability, types of surfactants, correlations, and laboratory and field testing procedures. Figure 2.5 shows Bureau of Mines dynamic testing of foaming agents. FOAV - O t
OuttE! CD G L - S S ,
24 cm LOfiG S-r.tHQ BtUCH
HOOKS MARK
:-«-—0 6 i.B. h ..ASTJC. 1 4 0 c « , lOfiZ-
i@3
i_^
•••MED rRlTTEO CiSC
23
Figure 2.5: Setup for Testing of Foaming agents
10
setup for
2.4 Gas Lift Gas lift introduces additional external gas into the tubing to lighten the flowing gradient and can increase the fluid velocity above critical rate for the wellbore''^ Critical rate is a gas rate above which suspended droplets of liquids are predicted to be carried upward by the gas flow and below critical, droplets are predicted to fall and liquids to accumulate in the well. Details ofthe equations used for calculating critical rate are given in Appendix C. A compressor or a high-pressure gas well must supply the lift gas for gaslift. The usual process is to inject gas down the casing and through a gas lift valve into the tubing. The gas in the tubing lightens the gradient, and the well produces at a higher rate. Gas can be injected below the tubing end or injected through only one valve or port if gas pressure is available to unload. A series of unloading valves can be used to help inject near the bottom ofthe well with limited gas pressure. The two primary types of gas lift that are prevalent in the industry are continuous flow and intermittent flow. Gas cycling is another method to flow additional gas down the annulus and into the bottom of the tubing^'^. A typical gas lift setup with a packer can be seen in figure 2-6. Gas lift operational guidelines might include the following: 1) Compare costs with other methods. 2) Be sure that compressors and additional gas are available. 3) Model the wells, and possibly the entire field, with gas lift, comparing with other methods. Gas lift can be used for high GLR wells and can handle higher sand production than conventional pumping systems as it is not prone to erosion. It is adaptable to changes in the reservoir condition and can be used in deviated wells. Changes in the installation can be made from surface without pulling tubing. The cost of installing a continuous gas lift system is approximately $30,000 to $50,000 US per well plus the incremental cost of compression and injection lines.
11
Figure 2.6: Diagram of a typical rotative gas lift system. (Courtesy of McMurry-Macco Lift Systems)
2.5 Electrical Submersible Pumping (ESP) The concept has proved to be an effective and economical means of lifting large volumes of fluid from great depths under a variety of well conditions. Today's ESPs are essentially multistage centrifugal pumps that employ impellers, attached to a long shaft. The shaft is connected to an electrical motor that is submerged in the well. The pump usually is installed in the tubing just below the fluid level, and elecfrical power is supplied through a special heavy-duty armored cable. Systems are available that allow an ESP to pump or dispose of water below a packer if an injection zone is present. Other pumping methods could inject water as well. An injection test should be run on a suitable underlying injection zone before considering this method. Figure 2.6 shows a submersible pump and an impeller.
12
FI^
•ack
Ey«
Sci"s«!tf.ainl»«c
Vart6
£i6etrc
Figure 2.7: Submersible pump and Impeller Schematic34 Electrically submersible pumps are generally used for handling large liquid volumes. They consume more power per barrel than beam pumping systems and their installation is expensive. The efficiency of this pump system is significantly reduced when gas is allowed to enter the pump restricting their use for gas well de-watering operations. The literature^''"^^ refers to the effects of free gas and gas separation and handling devices in the industry.
2.6 Progressive Cavity Pumps (PCP) It is of simple design and can handle solids and viscous fluids required for many operations. They are used for de-watering coal bed methane production, gas wells, and other water and oil wells. These pumps are preferably used for shallow wells having
13
depth less than 6000 ft. and high fluid rates. The elastomeric stator is vulnerable to chemical attack and high temperature and many stator rubbers are limited to perhaps 250 degrees F. The literature^^'"*' provides insight into considerations for the components selection and operational factors, and their troubleshooting. Figure 2.7 shows a typical PCP setup.
Flow Tee (Gas)'
0^_, Drilled Open Hole
o o
o
o
Figure 2.8: Typical PCP Installation40 The rotating rods can wear the tubing so centralizers are used. Some advanced designs employ an ESP motor downhole (ESPPCP). The unit must not pump off as the PCP pumping only gas can generate very high temperatures in a short time.
14
2.7 Velocity Strings The size of the flow conduit through which the gas is being produced determines how long the production tubing will produce the well before production declines and liquid loading begins. The basic concept of tubing design is to have a large enough tubing diameter so that excessive friction will not occur and a small enough tubing diameter so that the velocity is high and liquid loading will not occur. The tubing installation is designed such that these requirements are met for as long as possible in the future. A smaller tubing is installed to increase the velocity for a given rate and effectively remove the liquids from the tubing. However, too small a tubing can cause a larger flowing bottomhole pressure due to excess friction. Also, swabbing and plunger lift operations might not be able to be carried out. Pressure bombs, test tools, and coiled tubing carmot be run in smaller strings. Guidelines for redesigning a tubing string are: 1) Check Nodal analysis for stability. 2) Compare Nodal solution rate to top and bottom ofthe flow string. 3) Ensure appropriate flow correlation used to calculate the Nodal Solution The literature''^"^^ shows work done on tubing strings for design, analysis and economic fife.
2.8 Summary There are many methods and the best solution must be found for gas well dewatering. The parameters that affect this decision apart from the advantages and disadvantages of the individual methods are location, economic considerations, experience, and company policies on their continued use.
15
CHAPTER 3 CONVENTIONAL AND TWO-PIECE PLUNGER - BACKGROUND
3.1 Plunger Lift The need for plunger lift'"^ operations develops when the natural reservoir pressure decreases as gases and liquids are produced from the formation. This creates a condition where the fluids to start collecting in the wellbore, creating a hydrostatic condition that inhibits the flow ofthe fluids and gases out ofthe formation. The objective of plunger lift is to keep the immediate vicinity of the wellbore as dry as possible by lifting liquids on an intermittent basis to the surface. To achieve this when the formation is producing liquids along with the gas as in natural flow or production, the gas flow must be of sufficient velocity to deliver all the liquids to the surface in a cyclical manner. The main reason to remove the liquids from the tubing is so that the pressure on the formation is reduced as a result of which gas can flow at a higher rate. Also, continual removal of all produced liquids allows a drying effect on the production formation. This drjdng effect may actually change in-flow characteristics, giving a well greater capacity for oil and gas production. Plunger lift production systems include a cylindrical plunger which travels from a tubing stop installed as close to the formation as possible to a surface catcher/lubricator. The plunger travels in reaction time/pressure sequence in order to expel accumulated fluids into surface facilities. The plunger is designed to provide the necessary interface between fluid column and the lifting gas. As the plunger is surfacing, gas is leaking or bypassing around the sides of the plunger, and if excessive, too much energy will be lost and the plunger will not surface. This prohibits fluid fallback. The volume of fluid above the plunger should be approximate amount of fluid arriving at the surface although it is no uncommon for some fluids to follow the plunger.
16
In addition to increased productivity there are other advantages of plunger hft versus other types of artificial lift^. One is the relative inexpensive initial investment and operating cost compared to sucker rod pumping. Also the advent of automatic electronic controllers has helped in the removal of much ofthe guesswork associated with a plunger installation. The automatic electronic controller saves the man hours normally applied towards fine tuning a plunger system. Finally the plunger can prevent paraffin and scale buildup from the tubing walls and eliminating costly downtime spent on intermittent paraffin cleaning. Achieving the continual removal of liquids and gases is dependent upon the correct installation and operation of plunger lift system. The plunger system would work well as long as there is sufficient GLR and sufficient pressure along with the hquid slug. One rule of thumb is that plunger lift requires 400 scf7(bbl-1000ft) but this does not address the pressure requirement as reservoir pressure is not considered. The plunger lift systems works satisfactorily with a larger tubing hence there is no need to dov^Tisize the tubing. The plunger lift works better with no packer or requires wells with relatively higher formation pressure for the plunger system to work. There might be more recoverable production with an expensive beam pump system even though the plunger can take the well to depletion. It has been seen that plunger lift operates successfully to depths of 20,000 ft and a minimum installation would cost approximately $4000 US.
3.2 Standard Plunger Operation A typical conventional plunger hft installation^ can be seen in figure 3.1. The plungers and down hole springs and stops constitute the subsurface equipment. The surface equipment consists of the lubricator and catcher, the master valve motorized valve and electronic controllers. The bumper spring and stop cushions the fall of the plunger at the bottom of the well. The lubricator and catcher are installed above the master valve of a well and is a permanent part ofthe wellhead. The lubricator provides an upper Emit for plunger tiravel and acts as a shock absorber when the plunger reaches the top. The catcher is provided to 17
catch the plunger for inspection or exchange. Once the plunger reaches the top it hovers between the bleed valve and master valve, wherein a sensor senses the plunger and sends a magnetic signal to the electronic controller. The electronic controller^ helps to monitor the plunger cycle by operating the motor valve based upon fluctuations in sales line pressure, flow rates, pressure differentials, etc. The electronic controller logic based upon the plunger rise and fall velocities, the casing pressure and possible other form sensor information.
'
LUBRICATOR
ELECTRONIC CONTROLLER
FLOW TEE W/O-ntlG
PLUM GER
BUMPER SPRHG
I'D :2L
Jf^
TUBING STOP
,rr Figure 3.1: Plunger Lift System
18
3.3 Plunger System Equipment 3.3.1 Subsurface Equipment - Plungers There are a variety of plungers available depending upon the set of well conditions for which they are to be required. General types of plungers include turbulent seal brush, wobble washer, expandable blade, multiple turbulent seal, combination turbulent seal, etc. Also the new two-piece plunger is explained in a following section. 3.3.2 DowTi Hole Equipment - Springs and Stops The springs and stops are manufactured in various configurations. They serve as the lower limit to plunger travel and absorb the impact ofthe plunger when it reaches the bottom of the well. The two pieces of equipment could also be combined into one assembly consisting of a bumper spring and a standing valve cage, collar lock or tubing stop. This would make the installation and retrieval easier and less expensive. It also ensures that the spring stays connected to the stop and doesn't try to flow to the surface with the plunger. 3.3.3 Surface Equipment 1) Lubricators and Catchers: These are installed above the master valve of an oil or gas well and become a permanent part of the wellhead. The lubricator serves as the upper limit for the plunger's fravel and acts as a shock absorber. The catcher, mounted below the lubricator, is there to manually catch and hold the plunger for inspection or exchange. 2) Motor Valves: A diaphragm-controlled motor valve is normally included as part of the surface equipment. They are available for a variety of configurations and sizes. This includes high pressure, flanged or screwed ends, and severe service. The motor valve is usually controlled by an electronic controller. 3) Sensors: They detect the arrival of the plunger at the surface, alerting the electronic controller to activate the proper mode, such as after flow or shut in. Sensors could be both magnetic and inductive sensors. Magnetic sensors are
19
normally mounted on the catcher nipple, while the new highly sensitive inductive sensors can be mounted elsewhere 3.3.4 Controllers The biggest drawback to plunger lift operations is time ad expertise required to optimize and maintain that optimization. Cycle selection process is generally a time consuming process that can tie up valuable man hours and require numerous trips to the well. With continuous changes in sales line pressure, the normal decline of a well, changing efficiency due to wear of plunger seals, maintaining correct cycles is important. The electronic controller uses software to create a good window'*^ for most effective plunger usage. The figure 3.2 below is only one form of logic used for plunger lift controllers. This particular logic must be further refined to shorted faster cycles for maximum production. TIME C Y a E OPERATING WINDOWS: TIME,
urns. 0 FAST ARRlVAt WINDOW { LOW TIME ) GOOD ARRIVAL WINDOW { HIGH TIME } SLOW ^ R i V A L WINDOW
NO ARRIVAL WINDOW .48
Figure 3.2: Time Cycle Arrangements
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3.4 Conventional Plunger Cycle Steps The figure 3.3 is a schematic for conventional plunger lift cycle steps. 1) The well is closed in: Pressure builds to needed value to lift the plunger and liquid slug in the casing. The casing pressure will expand into the tubing and lift the plunger and associated liquids when the well is opened. If the amount of liquid present above the plunger is small, then the casing pressure builds to needed value quicker. 2) Plunger rises: As the plunger rises, a good seal is needed between the plunger and the tubing ID to prevent gas from bypassing the plunger. A value of about 750 ft/min average velocity during the rise period is often mentioned in the industry as good practice. Slower results in too much gas slippage and faster results in friction losses and possible damage to hardware. 3) Plunger surfaces: The liquid above the plunger is produced from the well. It is not uncommon to detect some liquids following the plunger. The well pressure and flow hold the plunger at the surface. Gas production commences. 4) Gas produces to lower rates with time: As gas velocity drops with the plunger at the surface, liquids accumulate in the tubing. This is the concept that as liquids drop below a critical velocity, liquids are no longer efficiently carried from the well. The longer the well is allowed to flow at a low rate, the more liquids will accumulate in the well for the next cycle. It is desirable to keep the liquid slug size to a small value to optimize production. 5) Plunger falls: From manual or computer controlled signal, the production valve is closed. For optimum production, the plunger needs to fall fast, collect liquids, and return when pressure builds to a needed value in the casing. Many conventional plungers have mechanical devices that open sealing mechanisms or open a passage though or around the plunger so it will fall faster when the well is closed.
21
t.
•
'•••""-!
1'-'
1 \
I •Bii (1) Well is closed. Casing pressure is building
<3) Gas flows (S) Valve shuts with Plunger & Plunger falls at surface. (2> Valire opens, <4) Liquids accumulate Plunger & »n well as gas velocity liquids rise. slows Figure 3.3: Conventional Plunger Lift Cycle'49
3.5 Plunger Lift - Will it Work? Figure 3.4^" refers to a plot that shows the feasibility of a two inch plunger for a well. This plot is one of the many approximate industry guidelines prevalent in the petroleum industry to check for plunger feasibility. Example: Depth: 8000 ft Casing buildup pressure in 3 hours: 250 psi Separator pressure: 50 psi Net operating pressure: 250 - 50 = 200 psi
22
Result: From chart, about 10,000 scf / bbl for the GLR is needed for plunger operation from the well. If the well has a lower produced GLR, then the well is considered to NOT be a candidate for plunger lift. Again this is only an approximate guideline but it does 40000
36000
1 2" PLL NGEER
32000
28000
1
CQ 24000
m
O CO
Q
20000
»
16000
8000
ll
4000
^
12000
v\^
DEPTH
f >
^•^^^OOOi
0
200
400 600 800 1000 1200 NET OPERATING PRESSURE - PSI
1400
Figure 3.4: Feasibility for a two inch plunger 50 include consideration of gas and liquid flow, well pressure, depth and tubing size. It is not clear from Reference 2 what casing sizes are considered to develop this chart. In general larger casing is preferred for plunger feasibility.
Note: Another guideline is the there should be a produced well GLR of 400 scf/bbi per 1000 ft of lift. This guideline is an approximate one as it does not consider the pressure available from the well.
23
3.6 Conventional Plunger Operation A few important pointers for conventional plunger operation are mentioned below: 1) When a well is flowing at low flow rates it has a tendency to load. This liquid accumulation in the wellbore increases the backpressure and reduces the production inflow rate. Thus it is advisable to keep low rate flow periods to short intervals. 2) To keep the average casing pressure low we should set plunger cycles such that small amounts of liquid loads are lifted rather than larger loads, thus reducing the backpressure on the formation and increasing the overall production. This can be achieved by keeping short build up times. 3) Restiictions in general, such as a choke at the surface reduces plunger and flowing well performance. 4) The lowest the fluids can flow back into the formation from the wellbore is taken to be at the last open perforations. This is at times used to push the fluids back into the reservoir and restart production. If the plunger is below the open perforation there already is fluid load acting on it. It is hence preferred to keep the tubing end above open perforations. 5) The plunger weight does not greatly affect the load to be lifted. It is seen that the plunger weight accoimts up to two percent ofthe total load to be lifted out ofthe wellbore. 6) The height of a liquid column varies with the cross sectional area of the tubing. For larger tubing diameter the height ofthe liquid column is lesser than the height for same amount of liquid tubing with smaller diameter. This helps to reduce the pressure exerted by the liquid column. Hence a plunger lift may work better in larger tubing. 7) Since conventional plunger uses the energy of the trapped casing gas it is best to operate with no packer in the well. When packers are present, higher flowing wells with a larger buildup pressure are required.
24
3.7 Two-Piece Plunger .12,51 consists of a hollow cylindrical piston and a ball below. The The plunger'^'^'
hollow cylindrical piston could be changed in length, material used, thickness, size and number of grooves depending upon usage but is usually a fixed configuration with various materials available. The ball used along with the hollow cylindrical piston could also be varied in size and material used but is usually varied only with materials used for construction. The only consideration is that the ball fits the hollow end of the cylindrical piston suitably, such that together they appear one piece when joined. The figure below shows different sizes of plunger. For this report the hollow cylindrical piston along with the ball would constitute a plunger. Figure 3.5 shows the various types of two-piece plungers currently being used in the industry.
Figure 3.5: Two-piece plungers'^ (Courtesy MGM Well Services) The two-piece plunger usage has the following mentioned important features. These features also suggest why it could be used instead ofthe conventional plunger. 1) The two-piece plunger cycle typically requires only 5 - 1 0 seconds of shut-in time.
25
2) The ball and the cylindrical piston both fall against a flow rate. This means that the well is producing, even when the objects are falling to the bottom of the tubing. This results in more production being obtained from the well. 3) There is a longer flow time as the well is shut-in only for a small time to allow the cylinder to fall. This leads to the well producing at near about a constant rate. 4) The two-piece plunger does not depend upon the expansion energy of the gas that is trapped in the casing and tubing annulus but more on velocity and pressure in the tubing. So even if a there is a packer in the well the two-piece plunger should function as, it is not dependent on the trapped gas expansion energy. Thus it can be used with a packer in the hole. In fact, recent field tests show that the twopiece plunger has been successfiilly used in the field with low flow rate wells having packers installed from Reference 12.
3.8 Two - Piece Mechanical Components View figure 3.6 for the mechanical components that are used in the two-piece plunger. On left is the bottomhole bumper spring. On the right is the spring to cushion arrival and the shifting rod which holds the cylinder at surface when flow is taking place. 3.8.1 Equipment Description: The Shifting rod is a downward facing metallic rod. It generally has a taper to it with a larger diameter towards the bottom ofthe rods. The other mechanical components have been explained in the system equipment for the conventional plunger.
26
Piston
Lubricator
Ball
Surface Springs
Anvil Bottom Hole Spring Shifting Rod
Figure 3.6: Mechanical components ofthe Two-piece plunger'^
3.9 Two - Piece Plunger Cycle Steps Figure 3.6 shows the various stages involved in the two-piece plunger cycle. The working ofthe two-piece plunger cycle can be explained by the following points. 1) The figure 3.6 begins with the tubing production automated valve open and the two-piece plunger sealed with the ball on the bottom of the cylinder bringing up a slug of liquid. 2) WTien the surface is reached, the cylinder comes over a downward facing rod and the rod pushes the ball from the bottom of the cylinder and the ball falls (if the production is not too much). The cylinder remains on the rod while production flows up between the rod and the I.D. ofthe cylinder. The flow time-period when the cylinder is at the surface has to be long enough to allow the ball a head start, or the cylinder will catch it before it reaches bottom. 27
3) Typically when flow becomes lower, the well is shut in for approximately 10 seconds which is presumed long enough for the cylinder to fall off the rod and then begin to fall to the bottom to re-join with the ball which is presumed to already be at the bottom of the tubing on a bumper spring. 4) The cylinder rejoins the ball at the bottom on the bumper spring. There may be accumulated slug on bottom or the plunger may just collect some liquids on the way up. 5) The ball seals the bottom of the cylinder and the ball and cylinder travel upward again carrying accumulated liquids to the surface similar to what a conventional plunger would do.
T
T
h-OSSIDK
/
liquid
'
load
^
t f
Gas
Gas
Gas-
t
1^
Ball and cylinder rise together
Cylinder slides over rod - ball falls
Ball reaches bottom
Cylinder released with 10 sec shut-in. Falls to ball
Figure 3.7: Two-piece plunger cycle
28
12
Ball and cylinder rise again
3.10 Two - Piece Plunger: Summary of Concerns 1) If the cylinder is released too soon then it could catch the ball before it hits the bottom. As a result the components would combine above the tubing bottom and come back up the tubing leaving the liquids below. When the ball and the cylinder join they act as one body, offering more surface area for flow resistance and sealing between the liquid and the gas below. This enables the fluid flow to lift the ball and cylindrical plunger to the surface together. 2) Flow period with the plunger at the surface: If the gas velocity in the tubing has not dropped to a level below which liquids accumulate in the tubing i.e. below the critical velocity, the well can be continued to flow with the plunger at the surface till liquid begins to fall back in the tubing. Even if the gas velocity in the tubing is above critical velocity the plunger can used. Since the plunger collects droplets and liquid film up on the way up, it can still cycle effectively as long it collects a slug on the way up to cushion the arrival. The liquids when lifted to the surface also help to keep the tubing closer to a dry condition and result in a lower pressure drop down the tubing and less pressure on the formation, which the goal. 3) Some wells show less response - This could be due to the flow rates not allowing the components to rejoin near the bottom ofthe well in a reasonable time. 4) Testing was done to determine the fall rates for the components under different conditions.
29
CHAPTER 4 PLUNGER TESTING FACILITY AND TEST PROCEDURE The testing to obtain date were conducted at the Texas Tech University, Petroleum Engineering Department. The equipment used consisted of a horizontal pressure vessel, a gas compressor with a rating of 125 psig, pipe connections with valve provisions for fluid inlet at the bottom ofthe tubing, a transparent hardened plastic tubing of 30 feet in height and a 2 inch tubing diameter according to industry acceptance, and also pressure gauges at relevant locations. There was also a support structure to facilitate access to various parts of the tubing. A titanium ball and cylindrical piston set were initially used. It was an 8 inch titanium plunger and ball set. The titanium ball used was of 1 3/8* in diameter and weighed 0.218 lbs. The titanium cylindrical piston was of 1.85 inch O.D. and weighed 2.095 lbs. Figure 4.1 shows the testing facility with other equipment used and figure 4.2 shows the ball suspended in the tubing at the testing facility.
30
Figure 4.1: Testing Facility at Texas Tech University
Figure 4.2: Ball suspended in tubing
31
4.1 Test Procedure The air was compressed and stored in the horizontal pressure vessel to provide a steady source of flow of air through the tubing. By opening the valve the air was introduced into the tubing. The flow was measured using a flow meter to measure the amount of gas being flown on a per day basis. At the bottom ofthe tubing the component of the two-piece plunger was positioned (ball or cylinder) that was to be suspended with the flow. Once the air was introduced into the tubing, the object was suspended such that it achieved a steady position, with the object neither rising nor falling in the tubing. The pressure was read of the respective gauges and the temperature was recorded. The experiments were repeated until a satisfactory degree of repeatability was obtained. The object here implies that test runs were made independently for the ball, the cylindrical piston and the ball and the piston together. Thus in this maimer the weight was equated to the drag diuing the suspension tests. The drag model was developed for all the three cases ofthe plunger, firstly for the ball, secondly for the cylinder and lastly for both the ball and the cylinder together. The drag model equations are given in details in the Appendix A for all the three cases. The reason why the three cases needed to be considered was the ball and the hollow cylinder would fall separately in the hibing, but would rise together as one body while lifting the fluids out of the tubing. This model was based upon data with specific temperature and pressure conditions present for air flowing through tubing, was very easily then extrapolated to different pressures and temperatures using gas of different densities. The change in the density from air to methane as shown in the results was achieved by simply using the equation of state. Thus predicted results could be plotted for a gas, as seen in field conditions, ft is also noteworthy that the drag model for the ball and that for the ball together with the cylinder were relatively easy to develop. For the hollow cylindrical piston there were two drag terms to be considered as flow took place through the inside and as well as the outside of the hollow cylinder. In fact, to account for the flow rate that took place through the inside and around the cylinder there is a program code written which has been supplied in the Appendix D.
32
CHAPTER 5 RESULTS AND DISCUSSION OF TWO-PIECE PLUNGER CASES The results of a few example cases have been shown to better explain the working of a two-piece plunger. These cases show the fall rate of the component for a given flow rate and specific pressure. Data was obtained for components falling against a measured air flow rate as described in the test procedure. The model then extends this data, to predict the fall velocity of the components, to a gas flow rate natural gas using gas law relationships. The specific gravity of gas that was used in the calculations was 0.65 and has been mentioned in the plotted results. The range of fall speed for the components covers the entire practical and industry preferred velocities. These results show the operational points for the two-piece plunger. The tabulated data values for the results which give the pressure, flow rate and component fall speed can be seen in Appendix F.
5.1 Examples: Discussion of Results for Two-Piece Plunger Cases 5.1.1 Fall Velocity for Ball 1) Data: 400 MscfTD production and 200 psi. Reading the figure 5.1, the ball is predicted to fall at about 1000 Q)m, which is in accordance with the field observation and hence acceptable. Figure 5.1 gives the predicted fall rate ofthe ball for a known flow rate and specific pressure. Critical rate according to Turner's"*^ is also plotted to show minimum flow rate to avoid liquid loading. If the well has this given pressure and is flowing at mentioned rate, then the ball when pushed from then end of the cylinder falls to the bottom of the well with the predicted velocity. This happens as the flow takes place around the falling ball and the flow rate is insufficient to support the weight ofthe ball. However, at the well surface the cylinder slides up and over the rod remaining suspended due to the tapered geometry of
33
the rod. This forces more fluid to act on the cross sectional area ofthe cylinder and resists it's fall. As a result, sufficient time is provided for ball to fall all the way to the bumper spring and avoid the cylinder to catch up with it mid way in the tubing enabling the components to rejoin only at the bottom ofthe well and help in removal of accumulated liquids. 2) Data: 1000 Mscf/D and 500 psi. Reading figure 5.1, the ball is estimated to fall at a littie more than 200 fpm. This is fairly slow and it would take 50 minutes to fall in a 10,000' well. If the well is choked the well back to 600 psi and about 500 Mscf D, then it would fall at about 700 fpm. Then it would fall back in a 10,000' well in about 15 minutes. If you allow the well to continue to produce 1 MMscf/D after the ball is dropped, then you must continue to flow with the cylinder at the surface for 50 minutes. This may be too long for a weak well that is loosing sfrength and allowing liquids to accumulate as the well falls below the critical velocity. It might be more desirable to choke the well back to around 600 psi and 500 Mscf/D and then you would only have to flow the well for a minimum of 15 minutes to insure the ball has reached the bottom before releasing the cylinder.
Gas(0.65) - Various Vfaii rates for Ball 1000 , X 800 (S "•
Q
\
\
\ ^^ \
•
\
\
\ 600 -
jj
400 -
D.
^
•
\
V \ \ \
200 n
t
+ +
\ \
" ^ ^
/
/
/
-' /
A, - ( l i y ,•' \-^ / / '"' \ ph / / •'' I -J _/ y^ •'' 4^ yy'^'*
\^/yy^''
-fc^^^^^ 0 (D
250
500
^
/ /
^ rh
\
A i\ ; V
^
—^ —• —® —^ —*
200fiDm 400fi3m eoofjsm SOOfjam lOOOIjDm
.-.•-.- ofpm
^ " ' Critical Rates
750
1000
1250
1500
Flow Rates, Mscf/D Figure 5.1: Critical rates for Titanium ball
34
1750
2000
5.1.2 Fall Velocity for Hollow Cylinder 1) Data: 400 MscCD production and 200 psi. Reading figure 5.2, this shows the cylinder would fall faster than 1000 fpm and this is acceptable for most cases. Only the 10 second shut-in would be required to make sure the cylinder would drop off the downward projecting rod at the surface. It would go to the bottom in 10 minutes or less in a 10,000 ft well. 2) Data: 1000 MscfiD and 500 psi. Reading figure 5.2, this shows the cyhnder would fall about 800 fpm.
The
cylinder would fall to bottom in 12.5 minutes in a 10,000 ft well. This would probably be acceptable. You would probably not have to choke the well back to insure the cylinder would fall at an acceptable rate. The well could continue to flow while the cylinder falls once it is released from the rod at surface with a 10 sec shut-in.
Gas(0.65) -Various Vfan Rates of Cylinder 1000
+
T
^
f
.•
800 Q.
600 -Hi— 200fpm -c,— 400f{3m eOOfpm -^— 800fpm -o—lOOOfpm -•--- Ofpm --H - - Critical Rates
i 400 °- 200 0 300
600
900
1200 1500 1800 2100 2400 2700 3000
Flow Rates, Mscf/D Figure 5.2: Critical rates for Titanium Cylinder
35
5.1.3 Discussion for Component Fall Velocities In conclusion, it is the ball and not the cylinder which may not fall at desired velocity against higher flow rates for a reasonably timed cycle of operation. Therefore considering the above selected data, the well would have to be reduced in flow or choked back with the cylinder at the surface to insure that the ball reaches bottom to complete an effective cycle. Then the well could be shut in for a short time to release the cylinder. If this is not done for higher rates, then the ball will not reach bottom the cylinder will not reach bottom before recombining with the ball and rising again. This would defeat the cycle no liquids would be removed from the well. This would not be knovm by the operator unless careful attention is paid to the well when the cylinder and ball re-surface. If you drop the ball and cylinder against no flow, then they both fall about 2000 ^ m . Another option as seen below is to use a ball make of heavier metal.
5.2 Re-plots for Titanium and Steel Two - Piece Plunger Sets If the plots shown in the above section would be plotted with a change in plot axis as seen below, then we would obtain plots with straight lines. These straight line plots would predict the same resuhs as the cross plots above for the exact same data. In addition to the titanium plunger set in the previous section a straight line plot for the steel plunger set has also been discussed here. 5.2.1 Fall Velocity re-plots for the Ball Read figure 5.3. For a flow rate of 500 MscfOD and 100 psi the titanium ball is falling at a speed of 400 ^ m . Now read from figure 5.4. For the same conditions of 500 Mscf/D flow rate and 100 psi the steel ball is falling at a speed of 1400 fpm. Hence the steel ball falls at a faster rate than compared to the titanium ball.
36
GAS{0,65) - Flow Rate vs Plunger Speed (Ball)
••—lOpsi - • - 25psi -*— 50psi - ^ ^ 75psi -«-100psi -^125psi -t—ISOpsi — 175psi — 200psi 200
400
600
800
1000 1200
1400 1600
1800 2000
Plunger Speed, fpm
Figure 5.3: Titanium Ball Straight Line Plot
GAS(0.65) - Flow Rate vs Plunger Speed (Ball)
0
200
400
600
800
1000
1200
1400
1600
1800 2000
Plunger Speed, fpm
Figure 5.4: Steel Ball Straight Line Plot
37
5.2.2 Fall Velocity Re-plots for Hollow Cylinder For a flow rate of 700 Mscf/D reading from Figure 5.5, and at a pressure of 75 psi the titanium cylinder falls at a speed of 200 fpm. Now examine Figure 5.6. For the same conditions of 700 Mscf/D flow rate and pressure of 75 psi the steel cylinder falls at a speed of 1800 fpm. GAS - Flow Rate vs Plunger Speed (Cylinder)
200
400
600
800
1000
1200
1400
1600
1800
Plunger, fpm
Figure 5.5: Titanium Cylinder Straight Line Plot
38
2000
GAS - Flow Rate vs Plunger Speed (Cylinder)
200
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.6: Steel Cylinder Straight Line Plot
5.2.3 Discussion - Titanium and Steel Two-Piece Plunger Sets Titanium is lighter than steel. The total weight of the steel set is significantly more than that of the titanium set. As seen from the straight line plots above the steel ball and the steel cylinder fall faster than their respective titanium counterparts on account of their weight, for same conditions of flow rate and pressure. So, for a well using lighter equipment (titanium set) we can choke back the well to enable the ball to fall to the bottom. On the other hand, for higher flow rate wells we can consider using the heavier equipment (steel set) as they will fall against a higher flow rate than the titanium components. However, care must be taken not to choke the well below critical for too long as it might lead to liquid loading the well.
39
5.3 Lifting of Liquid Slugs Read figure 5.7 and figure 5.8. These figures are plots for predicted rise velocities of 500 fpm and 1000 fpm ofthe titanium two-piece plunger set for a range of pressures against a producing well flow rate. The ball and cylinder combine together at the bottom of the tubing, and rise to lift the liquid slug above them out of the tubing. It is important to note that the ball and cylinder combine together to rise.. These figures show different hquid slugs to be lifted, from no slugs to 1 bbl slugs in a gas gravity of 0.65, by the titanium set. The equations used are given in Appendix E. Currently these appear to be conservative figures as gas leakage past the plunger greatly aerates the liquid to be lifted and thus lowering the pressure requirement.
Gas (0.65) - Vrise @ 500 fpm, Bali and Cylinder 500 1 400 ca
°:m ^200 a>
100
200
400
600
800
1000
1200
1400
1600
1800
2000
Flow Rate, IViscf/D
Figure 5.7: Titanium Set (ball and cylinder) for rise velocity 500 fpm
The results are plotted from Foss and Gaul^ model. More work in terms of testing with a known liquid slug over the plunger set with a measured flow rate could be performed. The model predicting liquid slug removal could then be developed to agree reasonably with experimental results with a better understanding of the gas interference with the hquid slug.
40
Gas (0.65) - Vrise @ 1000 fpm, Bail and Cylinder
0
200
400
600
800
1000 1200 1400
1600
1800 2000
Flow Rate, IWscf/D
Figure 5.8: Titanium Set (ball and cylinder) for rise velocity 1000 fjpm
5.4 Additional Plotted Model Predictions The physical quantities ofthe two-piece plunger sets, such as the length, diameter and weight, could be changed resulting in different configurations or two-piece plunger sets. The difference in weights for same cylinder lengths is directly dependent on material of construction. Presented below are the results for such different configurations. These configurations or two-piece plunger sets are those that are currently being used by the industry. All ofthe following plots give the falling speed ofthe ball and the cylinder for a given flow rate and operating pressure.
41
5.4.1 Titanium Plunger and Ball Set, 6 in.
GAS(0.65) - Flow Rate vs Plunger Speed (Bal
- ^ 10psi -*- 25psi -*r- 50psi -5<- 75psi -^•^ lOOpsi -*- 125psi -t— 150psi -^175psi — 200psi 200
400
600
800
1000
1200
1400
1600
1800 2000
Plunger Speed, fpm
Figure 5.9: Silica Nitrate Ball, 1-3/8 in. O.D. and weighs 0.164 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
-10psl - 25psi - SOpsi - 75psi -lOOpsI •125psi •1 SOpsi 175psl 200psi 200
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.10: Cylinder 1.9 in. O.D and weighs 1.56 lbs 42
5.4.2 Titanium Plunger and Ball Set, 10 in. GAS(0.65) - Flow Rate vs Plunger Speed (Ball)
200
400
600
800
1000 1200
1400
1600
1800 2000
Plunger Speed, fpm
Figure 5.11: Zircon Ceramic Ball, 1-3/8 in. O.D. and weighs 0.29 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
-•-lOpsi -^
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.12: Cylinder 1.9 in. O.D and weighs 2.63 lbs
43
5.4.3 Steel Plunger and Ball Set, 6 in. GAS(0.65) - Flow Rate vs Plunger Speed (Ball)
-^10psi - * - 25psi -Tk— SOpsi -^<— 75psi -^K— 10Opsi - » - 125psi - I — 1 SOpsi -^175psi — 0
200
400
600
800
1000 1200
1400
1600
1800 2000
Plunger Speed, fpm
Figure 5.13: Zircon Ceramic Ball, 1-3/8 in. O.D. and weighs 0.29 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.14: Cylinder 1.9 in. O.D and weighs 2.75 lbs
44
200psi
5.4.4 Steel Plunger and Ball Set, 8 in. GAS(0.65) - Flow Rate vs Plunger Speed (Ball)
•^lOpsi - • - 25psi -*- SOpsi -K— 7Spsi ^i«— lOOpsi -^125psi -^— ISOpsi —17Spsi — 200psi 200 200
400
600
800
1000 1200
1400 1600
1800 2000
Plunger Speed, fpm
Figure 5.15: Steel Ball, 1-3/8 in. O.D. and weighs 0.387 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
200
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.16: Cylinder 1.9 in. O.D and weighs 3.65 lbs
45
5.4.5 Titanium Plunger and Ball Set, 8 in. GAS(0.65) - Flow Rate vs Plunger Speed (Ball)
-•-lOpsi - • - 25psi -ifc- SOpsi -^<— 7Spsi ^tf-l00psi -^125psi —i— ISOpsi ^—17Spsi - — 200psi 200
400
600
800
1000
1200
1400 1600
1800 2000
Plunger Speed, fpm
Figure 5.17: Titanium Ball, 1-3/8 in. O.D. and weighs 0.23 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
200
400
600
800
1000
1200
1400
1600
1800 2000
Plunger, fpm
Figure 5.18: Cylinder 1.9 in. O.D and weighs 2.125 lbs
46
5.3.6 Steel Plunger and Ball Set, 9 in. GAS(0.65) - Flow Rate vs Plunger Speed (Ball) 800
-^-
-»-
Rate, Mscf
-*—10psi 700
- " - 25psi
600
-*— SOpsi -><— 75psi
500 -
-^1^ lOOpsi
5 400 o
- • - 125psi
-^-
m—
.
-H— ISOpsi
300
— 175psi •
•
—^—
200 200
400
-•—
'
' 600
—•—— • — — • — 1
'
800
1
1
1
' ' 1000 1200 1400 1600
—i>
1
1800 2000
Plunger Speed, fpm
Figure 5.19: Cobalt Ball, 1-3/8 in. O.D. and weighs 0.437 lbs
GAS (0.65) - Flow Rate vs Plunger Speed (Cylinder)
200
400
600
800
1000
1200
1400
1600
1800
2000
Plunger, fpm
Figure 5.20: Cylinder 1.9 in. O.D and weighs 4.22 lbs
47
— 200psi
5.4.7 Summary From the different predicted situations we see: 1) Consider the 6 in. titanium plunger with the 6 in. steel plunger. For a flow rate of 500 Mscf/D and 50 psi the titanium cylinder falls at 200 fpm. For a 5000 ft. well the titanium cylinder would travel for 25 min to reach the bottom. For the same flow rate and pressure the steel plunger falls at a predicted velocity of approximately 1800 fpm. taking a little under 3 min to travel 5000 ft. Hence, a heavier two-piece plunger set falls faster when compared to a lighter two-piece plunger set. Similarly, due to the difference in weights it is seen that the heavier ball is predicted to fall faster than the lighter ball. 2) The operator can choose the cylinder and ball or a configuration set for the twopiece plunger based upon the flow rate and time taken by the components to travel to the bottom. For quicker cycles in a high flow rate well it would do good to use a heavier set and a lighter set for a weak well. 3) For different configurations a predicted set of ready results is available. The results plot provide the freedom to choose a specific cylinder and ball to form a two-piece plunger set to better suit the well conditions and facilitate removal of liquids to improve production.
48
CHAPTER 6 SUMMARY: TESTING AND MODELLING RESULTS FOR THE TWO-PIECE PLUNGER
Tests were made in firll scale using real two-piece plungers. 1) Resuhs show operators possible cycle failure modes not previously considered. 2) The Two-Piece plunger may give more production since no build up time, but components should be allowed to re-join at or near the bottom ofthe well. This also helps to keep the production rate fairly constant and assists to keep low bottom hole flowing pressure. 3) Test data and models predict the fall times for the ball and cylinder separately to help insure operational cycles. 4) If you choke back to allow components to fall, then try to avoid choking back below critical flow, or don't choke back below critical for too long. However, choking back probably may not be necessary if you switch to heavier equipment for higher flow rates. 5) The well continues to produce even when the objects are falling owing to their clearance areas. 6) A shut-in time of only seconds does not create high spikes in wellhead pressures or volumes. Thus for a two-piece plunger it is not necessary to oversize the compressor to accommodate the volume spikes common with the conventional plunger systems. 7) Two-piece plunger will work wherever a conventional plunger can and has mostly shown to improve production rate. 8) Results are immediately applicable but may need some adjustment to field applications
49
9) Companies are now considering longer times to hold the cylinder in place in high rate application to allow ball to fall as shown necessary by this testing. 10) Future work should include a. Testing for the effects of adding some bbls of liquid/ MMscf to see effect of liquids with gas on performance of the two-piece plunger b. With additional testing with liquids, a computer model of the two-piece plunger can be developed to help operators set cycle times for various well conditions for field applications.
50
REFERENCES 1. Lea, J. F.: "Dynamic Analysis of Plunger Lift Operations," Tech. Paper SPE 10253 (November 1982), 2617-2629. 2. Beeson, C. M., Knox, D. G., and Stoddard, J. H.: "Part 1: The Plunger Lift Method of Oil Production", "Part 2: Constructing Nomographs to Simplify Calculations", "Part 3: How to User Nomographs to Estimate Performance", "Part 4: Examples Demonstrate Use of Nomographs", and "Part 5: Well Selection and Apphcations," Pefroleum Engineer (1957). 3. Otis plunger Lift Technical Manual (1991). 4. Ferguson Beauregard Inc Plunger Operation Handbook (1998). 5. Foss, D. L. and Gaul, R. B.: "Plunger Lift Performance Criteria with Operating Experience-Ventura Field," Drilling and Production Practice, API (1965) 124-40. 6. Phillips, Dan, and Listiak, Scott: "How to Optimize Production form plunger Lifted Systems, Pt. 2," Worid Oil (May 1991). 7. McCoy, J., Rowlan, L., and Podio, A. L.: "Plunger hft Optimization by Monitoring and Analyzing Well High Frequency Acoustic Signals, Tubing Pressure and Casing Pressure," SPE 71083 presented at the 2001 SPE Rocky Mountain Petroleum Technology Conference in Keystone, Colorado, U.S.A., May 21-23. 8. Hacksma, J. D.: "Users Guide to Predict Plunger Lift Performance," presented at Southwestern Petroleum Short Course (SWPSC), Lubbock, Texas U.S.A. (1972). 9. Beauregard, E., and Morrow, S.: "New and Unusual Applications for Plunger Lift System," SPE 18868 presented at the 1989 Production Operations Symposium in Oklahoma City, Oklahoma, U.S.A., March 13-14. 10. Wang, B., and Dong L.: "Paraffin Characteristics of Waxy Oils in China and Methods of Paraffin Removal and hihibition," SPE 29954 presented at the 1995 International Meeting on Petroleum Engineering in Beijing, China, November 1417.
51
11. Lestz, R.: "Swabbing under Pressure and Flow through Plungers," presented at the Denver Gas Well De-Watering Workshop (March 2003). 12. Garg, D. et al.: "Two-Piece Plunger Test Results," presented at the SWPSC, Lubbock, Texas, U.S.A.(19-2I April 2004). 13. Stephenson, G. B., Rouen, R. P., and Rosenzweig, M. H.: "Gas Well DeWatering: A Coordinated Approach," SPE 58984 presented at the 2000 International Petroleum Conference and Exhibition in Villahermosa, Mexico, February 1-3. 14. Parker, R.M.: "How to Prevent Gas-Locked Sucker Rod Pumps", World Oil (June 1992), pp. 47-50. 15. Elmer, W., and Gray, A.: "Design Considerations when Rod Pumping Gas Wells," First Conference of Gas Well De-Watering, SWPSC, Denver (March 2003). 16. Neely, A.B.: "Experience with Pump-Off Control in the Permian Basin," SPE 14345 presented at the 1985 Annual Technical Conference and Exhibition ofthe SPE, Las Vegas, Nevada, U.S.A., September 22-25. 17. Lea, J.F.: "New Pump-Off Controls Improve Performance," Petroleum Engineer International (December 1986), pp. 41-44. 18. Clark, K. M.: "Hydraulic Lift Systems for Low Pressure Wells," Petroleum Engineer International (February 1980). 19. Tait, H.: "Hydrauhc Pumping Systems," presented at the SWPSC, Lubbock, Texas, U.S.A. (21-22 April 1993). 20. Martin, J. M., and Coleman, W. P.: "hmovative Jet Pump Design Proves Beneficial in Coalbed Methane De-watering Applications." presented the SWPSC, Lubbock, Texas, U.S.A. (21-22April 1993). 21. Fretwell, J. A., and Blair, E. S.: "Achieving Low Producing Bottomhole Pressure in Deep Wells Using Hydraulic reciprocating Pumps," presented at the SWPSC, Lubbock, Texas, U.S.A. (21-22 April 1999).
52
22. Simpson, D., and Deherrera, W.: "Water Lifting Experiences in the CBM Fairway," Amoco presentation for Gas Well De-Watering Forum, Farmington, New Mexico, U.S.A. (1999). 23. Dunning, H.N. et al.: "Foaming Agents for Removal of Liquids from Gas Wells," Bull. 06-59-1, American Gas Assoc, New York City. 24. Libson, T.N., and Henry, J.R.: "Case Histories: Identification of and Remedial Action for Liquid Loading in Gas Wells Intermediate Shelf Gas Play," paper SPE 7467, JPr(April 1980) 685; Trans., AME, 269. 25. Campbell, S., Ramchandran, S. and Bartrip, K.: " Corrosion Inhibitors/Foamer Combination treatment to Enhance Gas Production," SPE Paper 67325 presented at the SPE Production and Operations Symposium, Oklahoma City, Oklahoma (24-27 March 2001). 26. Blauer, R. E., Mitchell, B. J., and Kohlhaas, C.A.: "Determination of Laminar, Turbulent, and Transitional Foam Flow Losses in Pipes," SPE Paper 4888 presented at the 1974 Annual California Regional Meeting, April 4-5. 27. Jacoby, R. H., NHGPA Phase Equilibrium Project, API Proceedings Division of Refining (1964), p. 288. 28. Hough, E. W. et al.: "Interfacial Tensions at Reservoir Pressures and Temperattires; Apparattrs and the Water-Methane System," JPT (1951);Trans., AIME, 57. 29. Katz, D. L. et al. Handbook of Natural Gas Engineering, McGraw Hill, New York (1959). 30. Vosika, J. L.: "Use of Foaming agents to alleviate liquid Loading in the Greater Green River TFG Wells," SPE/DOE 11644 presented at the SPE/DOE Symposium on Low Permeablity, Denver (14-16 March 1983). 31. Sloan, R., High Plains Wireline, Elk City, Oklahoma. Waggoner, Richard, Foamtech, Woodward Oklahoma (1996). 32. Lestz, R.S.: "Capillary Strings to hiject Surfactants," presented at the SWPSC School on De-Watering Gas Wells, Lubbock, Texas, U.S.A. (24 April 2001).
53
33.Centrilift Submersible Pump Handbook, 6'^ Edition, Centrilift, Claremore, Oklahoma (1997). 34. Turpin, J. L., Lea, J. F., and Bearden J. L.: "Gas Liquid Flow through Centrifiigal Pumps-Correlation of Data," presented at the SWPSC, Lubbock, Texas, U.S.A. (1986). 35. Centrilift Gas Handling Manual. 36. Dunbar, C.E.: "Determination of Proper Type of Gas Separators," REDA Technical Bulletin (1989). 37. Wood Group ESP hic. Bulletin on XGC gas separator. Wood Group ESP, Oklahoma City, Oklahoma (2002). 38. ABB Presentation on World Wide Artificial Lift Statistics by ABB Automation Technology Products (14 December 2001). 39. Klein, S. T.: "Selecting a Progressive Cavity Pumping System," presented at the SWPSC, Lubbock, Texas, U.S.A. (20-21 April 1994). 40. Weatherford ALS Progressive Cavity Pump Manual (2001). 41. Griffin Pumps Operators Manual, 5654 55'*' Street, Calgary, S.E., Alberta, Canada, T2C 3G9. 42. Turner, R.G., Hubbard, M.G., and Dukler, A.E.: "Analysis and Prediction of Minimum Flow Rate for the Continuous Removal of Liquids from Gas Wells," paper SPE 2198, /Fr(November 1969) 1475; Trans., AIME, 246. 43. Coleman, S.B., et al: "A New Look at Predicting Gas Well Liquid Load-Up," JPT, (March 1991). 44. Wesson, H. R.: "Coiled Tubing Velocity/Siphon Struig Design and Installation," the 1993 Annual Conference on Coiled Tubing Operations and Slimhole Drilling Practices, Houston, March 1-4. 45. WIS Solutions on "Coiled Tubing Velocity Strings: A Simple, Yet Effective Tool for the Future Technology," Schlumberger, Dowell. 46. Weeks, S.G.: "Small Diameter Concentric Tubing Extends Economical Life of High Water-Sour Gas Edwards Producers," SPE 10254 presented at the 1961
54
Annual Fall Technical Conference and Exhibition of SPE of AME, San Antonio, Texas, October 5-7. 47. Lea, J. F.: "Plunger Lift versus Velocity Strings," Journal of Energy Resources Technology, Vol. 121 (December 1999), 234-40. 48. Morrow S. J., and Rogers, J. R.: "Increasing Production using Microprocessors and Tracking Plunger-Lift Velocity," SPE 24296 presented at Mid-Continent Gas Symposium in Amarillo, Texas, U.S.A. (13-14 April 1992). 49. Lea, J. F.: "Solving Gas-Well Liquid-Loading Problems," SPE 72092, Distinguished Author Series, JPT (April 2004). 50. Ferguson, P.L., and Beauregard, E.: "How to Tell if Plunger Lift Will Work in Your Well," World Oil (August 1985), pp.33-37. 51,Bizanti, M.S., and Moonesan, A.: "How to Determine Minimum Flowrate for Liquid Removal," World Oil (September 1989), pp. 71-73.
55
APPENDIX - A DEVELOPMENT OF EQUATIONS This Appendix is divided into two sub sections, both dealing with model development for calculation of drag coefficients of the two-piece plunger components. The first section deals with model developed for suspension testing and the second section deals with dynamic testing. The drag coefficients obtained from both these models were in agreement, which served the purpose of verifying the validity of the suspension model and it's results.
A. 1 Suspension Testing - Drag Coefficient Model Presented here schematically are the forces and the force balance equations that were considered to calculate drag coefficients. In suspension testing the force balance is done for the component when it is suspended against a measured flow rate. The component is freely suspended and there is no acceleration or movement of the component in either the upward or downward direction. A. 1.1 Suspended Drag Model for Ball The direction of forces acting on the ball can be seen in figure A. 1 Equating the drag to weight we get the following equation:
2*g^*l44 Solving for Vgas it is possible to plot the results from the following equation nO.5
Vgas =
{Wt/Area)*2*gc*l44
Vfall.
^ " Pimp
56
...(A.2)
Weight
Drag
Figure A. 1: Schematic Forces on Ball
A. 1.2 Suspended Drag Model for Hollow Cylinder The direction of forces acting on falling hollow cylinder can be seen in figure A.2. Drag forces are seen on the inside and outside of the cylinder due to the gas flow and also at the bottom surface of the cylinder due to impact. The equation for cylinder is a bit more complex. For the hollow cylinder equate impact and longitudinal drag to weight. Pressure drop across the cylinder due to flow through the hollow cylinder and outside (annular area between the cylinder and tubing) the cylinder is the same. It was found that the flow through the cylinder accounted for mostly the entire pressure drop. So the overall drag for the cylinder is given by impact term and the longitudinal drag on the inside as seen from the equation below.
2*gc *144
ID, *g,*UA*\AiY^i * Pdrag) Pdrag ...(A.3)
57
Figure A.2: Schematic of Forces on Hollow Cylinder
Let, A
Cd* Pimp ^ „ Pdrag* f'^L*{Atf, * Pi ) ^—; and B = f z :r 2*g^*144 2*Di *g,*144*(4- * Pdrag?
..(A.4)
Rearranging the terms we get, {Vgas + Vfallf *A + {Vgas + Vfallf * B = 1.43411
...(A.5)
Solving for Vgas below, we can plot the results.
Thus, Vgas =
1.43411 A+B
0.5
...(A.6)
- Vfall.
58
Note: The suspension test gave the necessary flow rate required to suspend hollow cylinder in the tubing. Based on the program giyen in Appendix D.l it was established that almost all (99.5 percent) ofthe flow was taking place through the cylinder. Usmg the fact a model for the drag internal to the cylinder was developed. The drag on the inside and the outside ofthe cylinder necessarily has to give identical pressure drops. A. 1.3 Suspended Drag Model for Ball and Cylinder Combined Figure A.3 shows the explanation ofthe various forces that are acting on the ball and cylinder combined. Gas PxA Do
Drag
Tubing
= TiD^i^^
Weight of cylinder &ball Ball/Cylinder Rising PxA Pressure below Ball and Cylinder Rising
Figure A.3: Schematic forces for Ball and Cylinder combined The ball and the cylinder when combined together constitute a single body. When combined gas flow took place around the cylinder through the annular area between the
59
outside ofthe cylinder and the inner tubing diameter. For the force balance equation the impact and the outside drag were equated to the weight. The laminar flow equation was used for the outside drag based upon calculation of Reynolds number showing value of less than 2000. The Reynolds number was calculated based on the drag from the flow rate, outside the ball, required to suspend the combined ball and cylinder. The force balance equation for the ball and cylinder combined is given as, Cd * Pimp* (Vgas +Vfall f ^^^^TTTJ'A
2 * g , *144
, +f
(Vgas+Vfall)*8^*A,i, ; V^
.--6-
('='-''')' ln{a/b)
Cd * Pimp 2*g
= Wt/Area
... (A.7)
*144
8juL * A^i^
*144 a —b
\n{alb)
= 144
and C = Vlij (2\^^ A * Vf^ii +B)+C = 0 fall{A)+ \^'^ F' ^fall " fall^^r^-^
• • • (^-8)
Rearranging the terms and solving for the equation below, results for Vgas were plotted andF|^,(^) + Fg«,(2^*F^,„+5)+C = 0 .
...(A.9)
A.2 Dynamic Testing - Drag Coefficient Model In dynamic testing the acceleration term is infroduced in drag model equations that were used in suspension testing. The component was allowed to fall freely in the tubing against a measured flowrate and for a predetermined distance and the fall was timed. These spot checks were conducted to check the feasibility of the model for dynamic conditions. The tests were conducted for the ball and the hollow cylinder. A.2.1 Dynamic Drag Model for BaU The drag equation that was considered was
60
Cd*pAp *v^ mg = m*a.
...(A 10)
ft has the drag coefficient, Cd. Differentiating the acceleration term twice and integrating it, the equations for time and distance respectively are obtained as Tank t*gc*Vfall =
Cd*pA, 2mg^
-V gas
Cd*pA.
...(All)
2mg^ f
2m and X = -- In Cosh t*gc Cd* pA,
\Cd*pAp
...(A.12)
— Vgas * t. 2mgc
In equation A.12 we give time the value that was obtained from the dynamic tests and fix the distance as the specific distance for which the component fall was measured. The input value for the drag coefficient was varied until the time for the distance input agreed with what was measured for the time. At this point we have the drag coefficient. Compare the fall drag coefficient to the one that was calculated by the suspension tests. Our tests conducted showed the drag coefficients obtained from both tests to be in agreement. Tests were conducted for ball falling through an air and water tubing column. A.2.2 Dynamic Drag Model for Hollow Cylinder The drag equation that was considered was Cd*Pimp * (V,as + Vfallf
2*gc
* ^P , Pdrag *f*L* (Ajbg * Pimpf * ^p , / b + ; ;; T Y gas ^^ fall I 2*Di *gc*(Ai * Pdrag)' - mg = ma. ...(A13)
ft has the drag coefficient, Cd. Differentiating the acceleration term twice and integrating it, the equations for time and distance respectively are obtained as
61
V 2wgc and x = - — — l n C o ^ 4 * ^ c * V c ) - F g a . * /
...(A.15)
where,
2m*^c
'
2m*A**gc*(4*Prf.ag)'
and C = ^-1-5.
...(A.16)
In equation A.16 we give time the value that was obtained from the dynamic tests and fix the distance as the specific distance for which the component fall was measured. The input value for the drag coefficient was varied until the time for the distance input agreed with what was measured for the time. At this point we have the drag coefficient. Compare the fall drag coefficient to the one that was calculated by the suspension tests.
62
APPENDIX B CALCULATION OF DRAG COEFFICIENTS OF TWO-PIECE PLUNGER COMPONENTS Presented here are the force balance equations that were used to calculate the drag coefficient for each of the objects. The values seen are those that were experimentally obtained for those objects at the testing facility. Spot checks were made for the ball and cylinder falling through the tubing for velocities measuring up to 1500 j^jm. The drag coefficients obtained are considered constant for this work report.
B.l Drag Coefficient for Ball Equating drag to pressure drop by the following equation Pimp
' thv
^ 2*g^*144
, ^ ,^
= tJt'
...(B.l)
WTiere,
P^^P
^•^ * (^-3 ^^^-^^^ 0.093613 Ib/ft^ (460 + 88)
_100*24*60*(38.5-fl4.7)*520^^^^3^3Q^^^^^ -^tot 2.42*14.7*548 204345.091*14.7*548^^^^^^^ 3^^3^P ^'^^ (4.3+ 14.7)* 520 V,
- ^ = Atbg ^Hbg
166611.57 ^ 88.83ft/s. ;r* 24* 3600 n • (1.995)^* yi.~ 4* (12) 2
Substituting in equation B.l we get.
63
0.06524 * C ^ = AP
...(B.2)
Cdmeas = 2.51 ...@APn,eas = 0.2. Cdcaic = 1 . 8 3 ...@APcalc = 0.146.
B.2 Drag Coefficient for Hollow Cylinder Figure B.2 explains the variables used in this section upon which the drag coefficient for the hollow cylinder was determined. The figure also provides the acttial physical data ofthe titanium test cylinder.
Do-D, = 0.145/12 = 0.0121 ft Di* = Di-thk = 1.85-(2*6.5/l 0/2.54) =1.3382/12= 0.11152 ft >D;
• ^ — •
Ao = (7c/4) * (Do^ - Di^) = 3.04083* 10-^ ft D,
A*j = (7i/4) * Di* = 9.7678*10"^ ft
•Do
Figure B.2-Explanation of Variables The equation is: '
Qtot-Qo^
{QIA)l Do-Di
...(B.3) Di
64
Substituting the values we get, 94.099^2 _ g 2 ^ +2Qt,tQo -Qlt
=0
... (B.4)
100* 24* 60* (83+ 14.7)* 520 a<" = 2.567M4.7.548 = ^"'^^^ 35378.2*14.7*548 ^ . Qtbs = -? X = 216626.04 ft^/D ^''^ (10.6+ 14.7)* 520
^"^
a i g = 216626.04 ft^/D g<, = 20147.75 ft^/D g,*= 196478.29 ft^/D. The equation used to calculate the drag coefficient for the cylinder is APimpact + AParag=AP Cd*Pimp*Vil, 2*gc*144
^ Pdrag*f*L*Vi' 2*gc*Di*U4
. ^
Where, ^'""P
22:KlO:6±ii:Z) = 0.12465 lb/ft3 (460 + 88) / " i n /: , n o
2.7* Pdrag
1M±M,14.7
K
^ (460 + 88)
^
J = 0.12268 Ib/ft^
.^ - ^ = ^^^^^^Q^ = 115.5ft/s ^''^ ^o ;r* (1.995)^* 24* 3600 4* (12)^ y*-£=. 196478.29 ^ ^32.78 ft/s ' ^* ;r* (0.11152)^* 24* 3600 ^^ ^ p*v*D M
_ v;^D ^ 232.78*0.11152 ^ ^44220.142. V 1.8*10~^...@88°P
The Reynolds number is greater than 2000 so turbulent flow is indicted. Friction Factor, F = 0.0056+ 0.5/^-^-^^ =0.01677 65
... (B.5) ^^.^^
Thus from (B.2) we get, Cdmeas = 3 . 5 . . . @ A P ™ a s = 0 . 7 . C d calc = 7 . 6 . . . @ A P e a l c = 1.43.
B.3 Drag Coefficient for Ball and Cylinder Combined The impact and longitudinal drag term are equated to pressure drop by ^d
Pimp " tbg 2*g^*U4
Qtbg*^*ML
= AP
+
...(B-7)
= 144
a —b ln«/ Where, a = Do/2 = 1.995 / (2*12) = 0.083125 ft b=Di/2 = 1.85 / (2*12) = 0.077083 ft Pimp
= 2-7* (9+ 14.7) ^ 0.11871985 Ib/ft^ (460 + 79) 1 0 0 * 2 4 * 6 0 * ( 9 + 14.7)*520 ^ ^^^^^_^^
^^"^ ^'^^
Vtbg =
^^^
6.2666*14.7*539 35741.77*14.7*539 - = 35138.95 ft^/D (0.8+ 14.7)* 520 Qtb9
35135.57
Ao
;r* (1.995)^* 24* 3600
: 18.74 ft/s.
4 * (12)^ Substituting in equation (B.3) we get, 4.495874283*10'^ C j +0.247224983 = AP. Thus from (B.8) we get, C d n.eas= 1 2 2 . 9 7 . . . @ Apneas = 0 . 8 .
Cd calc = 136.324 .. .@ APcaic = 0.86.
66
...(B.8)
APPENDIX - C CRITICAL RATE EQUATIONS 42
Turner et al. developed two mechanistic models to estimate critical velocity. 1) A film of liquid on the wall of the tubing. 2) A droplet suspended in the flowing gas. The model that best fit their well data was the droplet model. Figure 3.9 shows the models considered. Gas rates exceeding critical velocity are predicted to lift liquid droplets that are present in the gas stream upward. Lower rates, lower than critical, allow droplets to fall £ind accumulate. Coleman et al.''^ later correlated to well data with lower average surface flowing pressures than did Turner.
Figure 3.9-Tumer's droplet model
Turner's''^ analysis gives the following for critical velocity y =
—^
Pg
1/2
51
...(C.l)
ft/s.
The above equation 3.1 can be expressed as a fiinction of pressure as, 4.02(45-0.0031;?)^^^
"'''""'
(f).m\pf^
...(C.2)
-ft/s
and
67
Vgwater =
5.34(67-0.0031w)^^^ , ^ TJ^ ft/s . (0.003 Ip)*^ 2
.. .(C.3)
When water and condensate both present, use the water equation. The corresponding critical gas rate, Qgcond, is Qscond=
3.06*P^*v„^o„^ ^^^^MMscf/D.
...(C.4)
Typically evaluated at the wellhead, the equations are valid at any well depth if the in-situ pressure and temperature are known. The distance between the tubing end and the perforations should be minimized because casing flow is usually liquid loaded. The critical rate in this report uses the Turner Equation. Critical rate equations^' other than Turner's are also in use by the industry. This creates a spread for critical rate predications leading to uncertainty for the user to consider.
68
APPENDIX - D COMPUTER PROGRAMS hi this section is presented the program code that was used to generate results in this Report. D.l Cylinder Flowrate Code Flow rate calculation from measured data. This code is written in Java. It was used to calculate the amount of flow that was taking place from within and outside the hollow cylinder. This was used to aid in the calculation of the drag coefficient for the hollow cylinder.
public class a{ public static void main(String[] args){ long lowerlimit = 0; long upperlimit = 0; double Cd = 7.626239019; double rho_imp = 2.718945051; double diameter = 0.16625; double areajbg = Math.PI * diameter * diameter / 4; double mu = 0.0183; double L = 8.1; double D = 1.85; double C = 0.145; double gc = 32.2; double Frac = 0.0; double A = Cd * rhojmp / (2 * gc * areajbg * areajbg * 144 * 24 * 3600 * 24 * 3600); double B = mu * L / (4885.05 * D * Math.pow(C, 1.52)); double weight_oyer_area = 1.43411; 69
for(long Q_tot=lowerJimit; Qjot<=upper_limit; Qjot+=10000){ Frac = (weight_over_area / (Q_tot * B) - (Q tot * A) / B); if(Frac < 0.001 || Frac > 0.95) { continue; } System.out.println("Q_tot = " + Q_tot + " Frac = "+ Frac + " LHS = 0"); }
D.2 Fall Velocities Code This is a visual basic code. It is used in conjunction with excel to generate results for given fall velocities. This code changes the values to be inputted in specific excel spreadsheet cells, which the go ahead and calculate values based on a series of interlinked formulae. Provided is the general code for generating output for different fall velocities of the ball and the cylinder. Following is the routine: Sub copypaste2()
copypaste2 Macro Macro recorded 10/03/2004 by Divyakumar Garg
Keyboard Shortcut: Ctrl+n
Dim columnnamestart Dim columnnameend Dim row start 70
Dim numberofrows Dim rowend Dim cellstart Dim cellend Dim rangevarfixed Dim gap Dim I Dim velocitycell Dim velocity_startvalue Dim velocityvalue Dim velocity incr velocityJncr = 200 velocity_start_value = -200 velocity_value = velocitystartvalue velocity_cell = "Q52" gap = l column_name_start = "M" column_name_end = "R" row_start = 54 numberofrows =10 cell_start = column_namestart + CStr(row_start) row_end = row_start + numberofrows cellend = column_name_end + CStr(row_end) range_yar_fixed = cell_start + ":" + cellend For I = 1 To 12 'velocity_value = velocityvalue + velocity incr
Range(velocity_cell). S elect ActiveCell.FormulaRlCl = velocityvalue
71
Range(range_var_fixed). S elect Selection.Copy Range(column_name_start + CStr(row_end + 2 * gap)).Select ActiveCell.FonnulaRlCl = "Output for Velocity = " + CStr(velocity_value) + " fpm" Range(column_name_start + CStr(row_end + 3 * gap)).Select Selection.PasteSpecial
Paste:=xlPasteValues,
SkipBlanks:=False, Transpose:=False cellstart = columnnamestart + CStr(row_start) row_end = row_start + number_ofjows cell_end = column_name_end + CStr(row_end) row_start = row_end + 3 * gap velocityvalue = velocity_value + velocity incr Next I End Sub
72
Operation :=xlNone,
APPENDDC E EQUATIONS FOR LIFTING OF LIQUID SLUGS The ball and cylinder combined are used to lift the liquid slug out of the tubing. The set of equations to predict lifting of hquid slugs in Chapter 5 are given below. These are the plunger lift equations from Foss and Gaul^. Foss and Gaul predicted the maximum and minimum casing pressure for the begirming ofthe cycle and when the plunger arrived to surface to improve on production with maximum cycles ofthe plunger per day. _ 62.4*5G/,-g^,Vj * hquid* Slugiength *Vrise^ "friction ~ frh /\ ' [^i^SlD/ 1*2*32.2*144*3600
I
. .-.(.li-ij
/12,
Where various terms in equation E. 1 could be determined by, Pv^eight = Slugiength * 0-433 * SGuq^id
• • -(6.2)
Pc * Slug = (Freight + Pfrinction ) * Slug
• • i^-V
^^"^/e«...*^^^^--'^^^^*5.615 Pc,min = (14.7 + Pp+ P^h + Pc^ Slug){l + Depth IK) p
-cpjj^p
•• .(E.5) ...(E.6)
where, CPR =
...(E.4)
[Aann+Athg)l^ann-
73
APPENDIX F SAMPLE DATA FOR TWO-PIECE PLUNGER CASES Presented here are the physical parameters ofthe objects used in the experiments and the result data exfrapolated from models developed based on calculated drag coefficients.
F.l Data for Ball Table F. 1.1. Physical Parameters for the titanium ball Parameter Diameter Weight c/s Area Pressure Drop (measured) Pressure Drop (calculated)
Value 0.1148 0.2176 0.010357 0.2 0.146
Units Ft Lbs Ft^ Psi Psi
Table F.1.2. Results Extrapolated for titanium ball in Air Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 0 fpm pair (lb/ft') Vgas (ft/s) Qtbg (Mcf/D) 230.4850 0.0493 122.8739 77.7122 145.7715 0.1232 103.0760 0.2464 54.9509 84.1612 44.8672 0.3695 72.8858 38.8561 0.4927 65.1910 34.7540 0.6159 59.5110 31.7259 0.7391 55.0965 29.3725 0.8622 51.5380 27.4754 0.9854
Qtbg (Mscf/D) 148.7812 235.2438 332.6850 407.4542 470.4876 526.0211 576.2273 622.3966 665.3699
Pressure (psia) 10 25 50 75 100
Output for Velocity = 200 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 224.2324 119.5405 0.0493 139.5189 74.3789 0.1232 96.8234 51.6175 0.2464 77.9086 41.5339 0.3695 66.6331 35.5228 0.4927
Qtbg (Mscf/D) 144.7451 225.1534 312.5042 377.1831 430.1261
74
Table F.1.2. Continued. Pressure (psia) 125 150 175 200
pair (Ib/ft^) 0.6159 0.7391 0.8622 0.9854
Qtbg (Mcf/D) 58.9384 53.2584 48.8438 45.2854
Qtbg (Mscf/D) 475.5692 515.6850 551.7639 584.6469
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 400 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0493 116.2072 217.9798 0.1232 71.0456 133.2663 0.2464 48.2842 90.5708 0.3695 38.2005 71.6560 0.4927 32.1895 60.3805 0.6159 28.0873 52.6858 0.7391 25.0592 47.0057 0.8622 22.7058 42.5912 0.9854 20.8088 39.0328
Qtbg (Mscf/D) 140.7089 215.0630 292.3235 346.9119 389.7646 425.1173 455.1427 481.1313 503.9239
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 600 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0493 112.8739 211.7272 0.1232 67.7122 127.0137 0.2464 44.9509 84.3182 0.3695 34.8672 65.4034 0.4927 28.8561 54.1279 46.4332 0.6159 24.7540 40.7531 0.7391 21.7259 36.3386 0.8622 19.3725 32.7802 17.4754 0.9854
Qtbg (Mscf/D) 136.6728 204.9727 272.1427 316.6408 349.4031 374.6654 394.6005 410.4986 423.2009
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 800 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 205.4746 109.5405 0.0493 120.7611 64.3789 0.1232 78.0656 41.6175 0.2464 59.1508 31.5339 0.3695 47.8753 25.5228 0.4927 40.1805 21.4206 0.6159 34.5005 18.3926 0.7391 30.0860 16.0391 0.8622 26.5275 14.1421 0.9854
Qtbg (Mscf/D) 132.6366 194.8823 251.9619 286.3697 309.0415 324.2136 334.0582 339.8660 342.4778
Vgas (ft/s) 31.4206 28.3926 26.0391 24.1421
75
Table F.1.2. Continued. Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 1000 fom pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0493 106.2072 199.2219 0.1232 61.0456 114.5084 0.2464 38.2842 71.8129 0.3695 28.2005 52.8981 0.4927 22.1895 41.6227 0.6159 18.0873 33.9279 0.7391 15.0592 28.2479 0.8622 12.7058 23.8334 0.9854 10.8088 20.2749
Qtbg (Mscf/D) 128.6005 184.7919 231.7812 256.0985 268.6800 273.7617 273.5159 269.2333 261.7548
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 1200 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0493 102.8739 192.9693 0.1232 57.7122 108.2558 0.2464 34.9509 65.5603 0.3695 24.8672 46.6455 0.4927 18.8561 35.3701 14.7540 0.6159 27.6753 0.7391 11.7259 21.9953 9.3725 17.5807 0.8622 14.0223 0.9854 7.4754
Qtbg (Mscf/D) 124.5643 174.7015 211.6004 225.8274 228.3185 223.3098 212.9737 198.6007 181.0318
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 14 00 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (Ib/ft^) 186.7167 99.5405 0.0493 102.0032 54.3789 0.1232 59.3077 31.6175 0.2464 40.3929 21.5339 0.3695 29.1174 15.5228 0.4927 21.4227 11.4206 0.6159 15.7426 8.3926 0.7391 11.3281 6.0391 0.8622 7.7697 4.1421 0.9854
Qtbg (Mscf/D) 120.5282 164.6111 191.4197 195.5563 187.9570 172.8579 152.4314 127.9681 100.3088
Pressure (psia) 10 25 50 75 100
Output for Velocity = 16 00 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 180.4641 96.2072 0.0493 95.7506 51.0456 0.1232 53.0551 28.2842 0.2464 34.1403 18.2005 0.3695 22.8648 12.1895 0.4927
Qtbg (Mscf/D) 116.4920 154.5208 171.2389 165.2851 147.5955
76
Table F.1.2. Continued. Pressure (psia) 125 150 175 200
pair (Ib/ft^) 0.6159 0.7391 0.8622 0.9854
Qtbg (Mcf/D) 15.1701 9.4900 5.0755 1.5171
Qtbg (Mscf/D) 122.4060 91.8891 57.3354 19.5857
Pressure (psia) 10 25 50 75 100 125 150 175 200 J
Output for Velocity = 1800 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0493 92.8739 174.2115 0.1232 47.7122 89.4980 0.2464 24.9509 46.8025 0.3695 14.8672 27.8877 0.4927 8.8561 16.6122 0.6159 4.7540 8.9174 0.7391 1.7259 3.2374 0.8622 -0.6275 -1.1771 0.9854 -2.5246 -4.7356
Qtbg (Mscf/D) 112.4559 144.4304 151.0582 135.0140 107.2340 71.9541 31.3468 -13.2972 -61.1373
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 2000 fpm Vgas (ft/s) Qtbg (Mcf/D) pair (Ib/ft^) 167.9588 89.5405 0.0493 44.3789 83.2453 0.1232 21.6175 40.5498 0.2464 21.6350 11.5339 0.3695 10.3596 5.5228 0.4927 2.6648 1.4206 0.6159 -3.0152 -1.6074 0.7391 -7.4297 -3.9609 0.8622 -10.9882 -5.8579 0.9854
Qtbg (Mscf/D) 108.4197 134.3400 130.8774 104.7429 66.8725 21.5022 -29.1954 -83.9299 -141.8603
Vgas (ft/s) 8.0873 5.0592 2.7058 0.8088
Table F.l.3. Results Extrapolated for titanium ball in Gas (0.65) Pressure (psia) 10 25 50 75 100 125 150 175
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720
Output for Velocity = 0 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 285.6527 152.2843 0.0321 180.4544 96.2020 0.0804 127.3505 67.8918 0.1614 103.7767 55.3244 0.2430 89.6957 47.8177 0.3253 80.0672 42.6846 0.4083 72.9455 38.8880 0.4919 67.3752 35.9184 0.5766
77
Qtbg (Mscf/D) 184.3927 291.2145 411.0325 502.4195 578.9983 646.0562 706.3102 761.1034
Table F.1.3. Continued. Pressure (psia) 200
Z Factor 0.9688
pair (lb/ft') 0.6611
Qtbq (Mcf/D) 62.9199
Qtbq (Mscf/D) 812.3133
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 200 fom Pair (Ib/ft3) Vgas (ft/s) Qtbg (Mcf/D) 0.0321 148.9510 279.4001 0.0804 92.8687 174.2018 0.1614 64.5585 121.0979 0.2430 51.9910 97.5241 0.3253 44.4844 83.4431 0.4083 39.3513 73.8146 0.4919 35.5547 66.6929 0.5766 32.5851 61.1226 0.6611 30.2099 56.6673
Qtbg (Mscf/D) 180.3566 281.1241 390.8517 472.1484 538.6368 595.6043 645.7679 690.4707 731.5903
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 400 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0321 145.6176 273.1475 0.0804 89.5354 167.9492 0.1614 61.2251 114.8453 0.2430 48.6577 91.2715 0.3253 41.1510 77.1905 36.0180 0.4083 67.5620 32.2213 60.4403 0.4919 29.2517 54.8700 0.5766 50.4147 26.8766 0.6611
Qtbg (Mscf/D) 176.3204 271.0337 370.6709 441.8773 498.2753 545.1524 585.2257 619.8381 650.8672
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 600 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (Ib/ft^) 266.8948 142.2843 0.0321 161.6966 86.2020 0.0804 108.5926 57.8918 0.1614 85.0188 45.3244 0.2430 70.9379 37.8177 0.3253 61.3094 32.6846 0.4083 54.1877 28.8880 0.4919 48.6174 25.9184 0.5766 44.1621 23.5432 0.6611
Qtbg (Mscf/D) 172.2843 260.9433 350.4902 411.6061 457.9138 494.7005 524.6834 549.2054 570.1442
Z Factor 0.9984 0.9961
Output for Velocity = 800 fpm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 260.6422 138.9510 0.0321 155.4439 82.8687 0.0804
Qtbg (Mscf/D) 168.2481 250.8530
Pressure (psia) 10 25
Vgas (ft/s) 33.5432
78
Table F.1.3. Continued. Pressure (psia) 50 75 100 125 150 175 200
Z Factor 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
pair (Ib/ft^) 0.1614 0.2430 0.3253 0.4083 0.4919 0.5766 0.6611
Qtbg (Mcf/D) 102.3400 78.7662 64.6853 55.0568 47.9351 42.3647 37.9094
Qtbg (Mscf/D) 330.3094 381.3350 417.5523 444.2486 464.1411 478.5728 489.4212
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1000 ff )m Qtbg (Mcf/D) Vgas (ft/s) pair (Ib/ft^) 254.3896 135.6176 0.0321 149.1913 79.5354 0.0804 96.0874 51.2251 0.1614 72.5136 38.6577 0.2430 58.4327 31.1510 0.3253 48.8041 26.0180 0.4083 41.6824 22.2213 0.4919 36.1121 19.2517 0.5766 31.6568 16.8766 0.6611
Qtbg (Mscf/D) 164.2120 240.7626 310.1287 351.0639 377.1908 393.7968 403.5989 407.9402 408.6982
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1200 f pm Qtbg (Mcf/D) Vgas (ft/s) pair (lb/ft') 248.1370 132.2843 0.0321 142.9387 76.2020 0.0804 89.8348 47.8918 0.1614 66.2610 35.3244 0.2430 52.1800 27.8177 0.3253 42.5515 22.6846 0.4083 35.4298 18.8880 0.4919 29.8595 15.9184 0.5766 25.4042 13.5432 0.6611
Qtbq (Mscf/D) 160.1758 230.6722 289.9479 320.7927 336.8292 343.3449 343.0566 337.3075 327.9751
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720
Output for V<3ocity=1400 fpm Qtbq (Mcf/D) Vgas (ft/s) pair (lb/ft') 241.8844 128.9510 0.0321 136.6861 72.8687 0.0804 83.5822 44.5585 0.1614 60.0084 31.9910 0.2430 45.9274 244844 0.3253 36.2989 19.3513 0.4083 29.1772 15.5547 0.4919 23.6069 12.5851 0.5766
Pressure (psia) 10 25 50 75 100 125 150 175 200
Pressure (psia) 10 25 50 75 100 125 150 175
Vgas (ft/s) 54.5585 41.9910 34.4844 29.3513 25.5547 22.5851 20.2099
79
Qtbg (Mscf/D) 156.1397 220.5818 269.7672 290.5216 296.4677 292.8930 282.5143 266.6749
Table F. 1.3. Continued. Pressure (psia)
200
Pressure (psia)
10 25 50 75 100 125 150 175 200
Pressure (psia)
10 25 50 75 100 125 150 175 200
Pressure (psia)
10 25 50 75 100 125 150 175 200
Z Factor 0.9688
pair (Ib/ft^) 0.6611
Vgas (ft/s) 10.2099
Qtbg (Mcf/D) 19.1516
Qtbo (Mscf/D^ 247 2521
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1600 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 0.0321 125.6176 235.6317 0.0804 69.5354 130.4335 0.1614 41.2251 77.3295 0.2430 28.6577 53.7557 0.3253 21.1510 39.6748 0.4083 16.0180 30.0463 0.4919 12.2213 22.9246 0.5766 9.2517 17.3543 0.6611 6.8766 12.8990
Qtbq (Mscf/D) 152.1035 210.4915 249.5864 260.2505 256.1062 242.4411 221.9721 196.0422 166.5291
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1800 fpm pair (\blff) Vgas (ft/s) Qtbg (Mcf/D) 0.0321 122.2843 229.3791 0.0804 66.2020 124.1808 0.1614 37.8918 71.0769 0.2430 25.3244 47.5031 0.3253 17.8177 33.4222 0.4083 12.6846 23.7937 0.4919 8.8880 16.6720 0.5766 5.9184 11.1016 0.6611 3.5432 6.6463
Qtbg (Mscf/D) 148.0674 200.4011 229.4056 229.9793 215.7447 191.9892 161.4298 125.4096 85.8061
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 2000 fpm pair (Ib/ft^) Vgas (ft/s) Qtbg (Mcf/D) 223.1265 0.0321 118.9510 117.9282 62.8687 0.0804 64.8243 34.5585 0.1614 41.2505 21.9910 0.2430 27.1696 14.4844 0.3253 17.5410 9.3513 0.4083 10.4194 5.5547 0.4919 4.8490 2.5851 0.5766 0.3937 0.2099 0.6611
Qtbg (Mscf/D) 144.0312 190.3107 209.2249 199.7082 175.3832 141.5373 100.8875 54.7769 5.0830
80
F.2 Data for Hollow Cylinder Table F.2.1. Physical Parameters for the titanium hollow cylinder Parameter Outer Diameter Inner Diameter Thickness Length Weight Pressure Drop (measured) Pressure Drop (calculated)
Value 1.85 1.338 0.512 8.1 2.0953 0.7 1.43
Units Inch Inch Inch Inch Lbs Psi Psi
Table F.2.2. Results Exfrapolated for titanium hollow cylinder in Air Output for Velocity = 0 fpm Pressure (psia) 10 25 50 75 100 125 150 175 200
Pimp (lb/ft")
Pdrag (lb/ft')
0.0493 0.1232 0.2464 0.3695 0.4927 0.6159 0.7391 0.8622 0.9854
0.0457 0.1196 0.2428 0.3660 0.4892 0.6123 0.7355 0.8587 0.9819
Vgas (ft/s) 179.5463 113.7801 80.5048 65.7453 56.9429 50.9343 46.4984 43.0503 40.2708
Qtbg (Mscf/D)
336.7468 213.3994 150.9902 123.3081 106.7988 95.5295 87.2096 80.7428 75.5296
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 200 fpm Q,bg (Mscf/D) Vgas (ft/s) Pimp (Ib/ft^) Pdrag (lb/ft') 330.4949 176.2130 0.0457 0.0493 207.1476 110.4468 0.1196 0.1232 144.7384 77.1715 0.2428 0.2464 117.0563 62.4120 0.3660 0.3695 100.5470 53.6095 0.4892 0.4927 89.2777 47.6010 0.6123 0.6159 80.9578 43.1650 0.7355 0.7391 39.7170 74.4909 0.8587 0.8622 36.9374 69.2777 0.9819 0.9854
Pressure (psia) 10 25 50
Output for Velocity = 400 fpm Qtbg (Mscf/D) Pimp (lb/ft') Pdrag (lb/ft') Vgas (ft/s) 172.8796 324.2431 0.0457 0.0493 107.1134 200.8958 0.1196 0.1232 73.8382 138.4866 0.2428 0.2464
81
Q (Mscf/D) 217.3746 344.3806 487.3313 596.9782 689.4008 770.8202 844.4252 912.1097 975.1072
Q (Mscf/D) 213.3390 334.2915 467.1532 566.7110 649.0446 720.3749 783.8908 841.4862 894.3947
Q (Mscf/D) 209.3034 324.2025 446.9750
Table F.2.2. Continued. Pressure (psia)
Pimp (lb/ft')
Pdrag (lb/ft')
75 100 125 150 175 200
0.3695 0.4927 0.6159 0.7391 0.8622 0.9854
0.3660 0.4892 0.6123 0.7355 0.8587 0.9819
Vgas (ft/s) 59.0787 50.2762 44.2677 39.8317 36.3837 33.6041
Q,bg (Mscf/D)
110.8045 94.2952 83.0259 74.7060 68.2391 63.0259
Q (Mscf/D) 536.4438 608.6883 669.9295 723.3564 770.8627 813.6821
10 25 50 75 100 125 150 175 200
Output for Velocity = 600 fpm Pimp (lb/ft') Pdrag (lb/ft') Vgas (ft/s) Qtbg (Mscf/D) 0.0493 0.0457 169.5463 317.9913 0.1232 0.1196 103.7801 194.6440 0.2464 0.2428 70.5048 132.2348 0.3695 0.3660 55.7453 104.5527 0.4927 0.4892 46.9429 88.0434 0.6159 0.6123 40.9343 76.7741 0.7391 0.7355 36.4984 68.4542 0.8622 0.8587 33.0503 61.9873 0.9854 0.9819 30.2708 56.7741
Q (Mscf/D) 205.2678 314.1134 426.7969 506.1766 568.3320 619.4842 662.8220 700.2392 732.9696
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 800 fpm Vgas (ft/s) Qtbg (Mscf/D) Pimp (lb/ft') Pdrag (lb/ft') 0.0457 166.2130 0.0493 311.7395 0.1196 100.4468 188.3922 0.1232 125.9830 0.2428 67.1715 0.2464 0.3660 52.4120 98.3009 0.3695 81.7916 0.4892 43.6095 0.4927 37.6010 70.5223 0.6123 0.6159 62.2024 0.7355 33.1650 0.7391 55.7355 29.7170 0.8587 0.8622 26.9374 50.5223 0.9819 0.9854
Q (Mscf/D) 201.2321 304.0243 406.6187 475.9094 527.9757 569.0388 602.2876 629.6157 652.2570
Pressure (psia) 10 25 50 75 100 125 150 175
Output for Velocity = 1000 fpm Qtbg (Mscf/D) Vgas (ft/s) Pimp (Ib/ft^) Pdrag (lb/ft') 305.4877 162.8796 0.0457 0.0493 97.1134 182.1404 0.1196 0.1232 119.7312 63.8382 0.2428 0.2464 92.0491 49.0787 0.3660 0.3695 75.5398 40.2762 0.4892 0.4927 34.2677 64.2705 0.6123 0.6159 29.8317 55.9506 0.7355 0.7391 26.3837 49.4837 0.8587 0.8622
Pressure (psia)
82
Q (Mscf/D) 197.1965 293.9353 386.4406 445.6422 487.6194 518.5935 541.7531 558.9922
Table F.2.2. Continued. Pressure (psia)
Pimp
Pdrag (lb/ft')
Vgas (ft/s)
Qtbg (Mscf/D)
Q (Mscf/D)
0.9819
23.6041
44.2705
571.5444
Q,bg (Mscf/D)
Q (Mscf/D) 193.1609 283.8462 366.2625 415.3750 447.2632 468.1481 481.2187 488.3687 490.8319
200
(Ib/ft^) 0.9854
Pressure (psia)
Pimp (lb/ft')
Pdrag (lb/ft')
10 25 50 75 100 125 150 175 200
0.0493 0.1232 0.2464 0.3695 0.4927 0.6159 0.7391 0.8622 0.9854
0.0457 0.1196 0.2428 0.3660 0.4892 0.6123 0.7355 0.8587 0.9819
Output for Velocity = 1200 fpm Vgas (ft/s) 159.5463 93.7801 60.5048 45.7453 36.9429 30.9343 26.4984 23.0503 20.2708
299.2359 175.8886 113.4794 85.7973 69.2879 58.0187 49.6988 43.2319 38.0187
Output for Velocity = 1400 fpm Vgas (ft/s) Q,bg (Mscf/D) Pimp (Ib/ft^) J Pdrag (lb/ft') 0.0493 0.0457 156.2130 292.9841 0.1196 0.1232 90.4468 169.6368 0.2464 0.2428 57.1715 107.2276 0.3660 42.4120 79.5455 0.3695 0.4892 33.6095 63.0361 0.4927 27.6010 51.7669 0.6123 0.6159 43.4470 0.7355 23.1650 0.7391 36.9801 19.7170 0.8587 0.8622 31.7669 16.9374 0.9819 0.9854
Q (Mscf/D) 189.1252 273.7571 346.0843 385.1077 406.9069 417.7028 420.6843 417.7452 410.1193
10 25 50 75 100 125 150 175 200
Output for Velocity = 1600 fpm Qtbg (Mscf/D) Vgas (ft/s) Pimp (lb/ft') Pdrag (Ib/ft^) 286.7323 152.8796 0.0457 0.0493 163.3849 87.1134 0.1196 0.1232 100.9758 53.8382 0.2428 0.2464 73.2937 39.0787 0.3660 0.3695 56.7843 30.2762 0.4892 0.4927 45.5151 24.2677 0.6123 0.6159 37.1952 19.8317 0.7355 0.7391 30.7283 16.3837 0.8587 0.8622 25.5151 13.6041 0.9819 0.9854
Q (Mscf/D) 185.0896 263.6680 325.9062 354.8405 366.5506 367.2574 360.1499 347.1218 329.4068
Pressure (psia)
Oiitpiit for Velocity = 1800 fpm Qtbg (Mscf/D) Pimp (lb/ft') Pdraq (Ib/ft^) Vgas (ft/s)
Q (Mscf/D)
Pressure (psia) 10 25 50 75 100 125 150 175 200
Pressure (psia)
83
Table F.2.2. Continued. Pressure (psia)
Pimp (lb/ft')
Pdrag (ib/ft')
Vgas (ft/s)
Qtbg (Mscf/D)
10 25 50 75 100 125 150 175 200
0.0493 0.1232 0.2464 0.3695 0.4927 0.6159 0.7391 0.8622 0.9854
0.0457 0.1196 0.2428 0.3660 0.4892 0.6123 0.7355 0.8587 0.9819
149.5463 83.7801 50.5048 35.7453 26.9429 20.9343 16.4984 13.0503 10.2708
280.4805 157.1331 94.7240 67.0419 50.5325 39.2633 30.9434 24.4765 19.2633
Pressure (psia) 10 25 50 75 100 125 150 175 200
Output for Velocity = 2000 fpm Vgas (ft/s) Pimp (lb/ft') Q,bg (Mscf/D) Pdrag (lb/ft') 0.0493 0.0457 146.2130 274.2287 0.1232 0.1196 80.4468 150.8813 0.2464 0.2428 47.1715 88.4721 0.3695 0.3660 32.4120 60.7901 0.4927 0.4892 23.6095 44.2807 0.6123 17.6010 33.0114 0.6159 0.7355 13.1650 24.6916 0.7391 0.8587 9.7170 18.2247 0.8622 6.9374 13.0115 0.9819 0.9854
Q (Mscf/D) 181.0540 253.5790 305.7280 324.5733 326.1943 316.8121 299.6155 276.4983 248.6942
Q (Mscf/D) 177.0184 243.4899 285.5499 294.3061 285.8380 266.3667 239.0810 205.8748 167.9816
Table F.2.3. Results Extrapolated for titanium hollow cylinder in Gas (0.65) Output for Velocity = 0 fpm Z Factor Pressure (psia) 0.9984 10 0.9961 25 0.9922 50 0.9883 75 0.9844 100 0.9805 125 0.9766 150 0.9720 175 0.9688 200
Pressure (psia) 10 25 50 75
Z Factor 0.9984 0.9961 0.9922 0.9883
rimp (Ib/ft^)
rdrag (Ib/ft^)
0.0321 0.0804 0.1614 0.2430 0.3253 0.4083 0.4919 0.5766 0.6611
0.0298 0.0781 0.1591 0.2407 0.3230 0.4059 0.4895 0.5742 0.6588
Vgas (ft/s) 222.5216 140.8514 99.4638 81.0686 70.0759 62.5573 56.9953 52.6445 49.1644
Output for Velocity = 200 tpm Vgas (ft/s) 0.0298 219.1882 0.0321 0.0781 137.5180 0.0804 0.1591 96.1304 0.1614 0.2407 77.7352 0.2430
Timp (Ib/ft^) Tdrag (ib/ft1
84
Q,bg (Mscf/D) Q (Mscf/D)
417.3487 264.1727 186.5485 152.0476 131.4303 117.3288 106.8972 98.7370 92.2099
269.4043 426.3178 602.0981 736.1159 848.4005 946.7171 1035.0537 1115.3817 1190.4544
Q,bg (Mscf/D) Q (Msct/U)
411.0968 257.9209 180.2967 145.7958
265.3686 416.2287 581.9199 705.8487
Table F.2.3. Continued. Pressure (psia)
Z Factor
100 125 150 175 200
Pressure (psia)
10 25 50 75 100 125 150 175 200
Pressure (psia)
10 25 50 75 100 125 150 175 200
Pressure (psia)
10 25 50 75 100 125 150 175 200
0.9844 0.9805 0.9766 0.9720 0.9688
rimp (Ib/ft-^) Tdrag (lb/ft") V g a s (ft/s) Qtbg (Mscf/D) 0.3253 0.3230 66.7425 125.1785 0.4083 0.4059 59.2239 111.0770 0.4919 0.4895 53.6620 100.6454 0.5766 0.5742 49.3112 92.4852 0.6611 0.6588 45.8310 85.9580
Q (Mscf/D) 808.0443 896.2717 974.5193 1044.7582 1109.7418
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 4 0 0 fpm Hmp (Ib/fty Tdrag (Ib/ft^ V g a s (ft/s) Qtbg (Mscf/D) 0.0321 0.0298 215.8549 404.8450 0.0804 0.0781 134.1847 251.6691 0.1614 0.1591 92.7971 174.0449 0.2430 0.2407 74.4019 139.5440 0.3253 0.3230 63.4092 118.9267 0.4083 0.4059 55.8906 104.8252 0.4919 0.4895 50.3287 94.3935 0.5766 0.5742 86.2334 45.9778 0.6611 0.6588 42.4977 79.7062
Q (Mscf/D) 261.3330 406.1397 561.7418 675.5815 767.6880 845.8264 913.9849 974.1347 1029.0293
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 6 0 0 fpm Hmp (lb/ft') rdrag (Ib/ft^) Vgas (ft/s) Q,bg (Mscf/D) 398.5932 0.0321 0.0298 212.5216 130.8514 245.4173 0.0804 0.0781 167.7931 0.1614 0.1591 89.4638 133.2921 0.2407 71.0686 0.2430 112.6749 60.0759 0.3230 0.3253 0.4059 52.5573 98.5734 0.4083 88.1417 46.9953 0.4895 0.4919 79.9816 42.6445 0.5742 0.5766 73.4544 39.1644 0.6588 0.6611
Q (Mscf/D) 257.2974 396.0506 541.5637 645.3143 727.3317 795.3810 853.4504 903.5112 948.3167
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 8 0 0 fpm rimp (Ib/ft^) rdrag {Mf) Vgas (ft/s) Q,bg (Mscf/D) 209.1882 392.3414 0.0298 0.0321 127.5180 239.1655 0.0781 0.0804 86.1304 161.5413 0.1591 0.1614 67.7352 127.0403 0.2407 0.2430 56.7425 106.4231 0.3230 0.3253 49.2239 92.3216 0.4059 0.4083 43.6620 81.8899 0.4895 0.4919 39.3112 73.7298 0.5742 0.5766 35.8310 67.2026 0.6588 0.6611
Q (Mscf/D) 253.2618 385.9615 521.3855 615.0471 686.9754 744.9357 792.9160 832.8878 867.6042
85
Table F.2.3. Continued. Output for Velocity = 1000 fpm Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1200 fpm Hmp (Ib/ftT rdrag (lb/ft') Vgas (ft/s) 0.0321 0.0298 202.5216 0.0804 0.0781 120.8514 0.1614 0.1591 79.4638 0.2430 0.2407 61.0686 0.3253 0.3230 50.0759 0.4083 0.4059 42.5573 0.4919 0.4895 36.9953 0.5766 0.5742 32.6445 0.6611 0.6588 29.1644
Pressure (psia) 10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 14(DO fpm rimp ( I b / f f ) rdrag (Ib/ft^) Vgas (ft/s) 0.0321 0.0298 199.1882 0.0804 117.5180 0.0781 76.1304 0.1591 _j 0.1614 0.2430 0.2407 57.7352 0.3253 0.3230 46.7425 0.4083 0.4059 39.2239 0.4919 0.4895 33.6620 0.5766 0.5742 29.3112 0.6588 25.8310 0.6611
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720
Output for Velocity = 16 DO fpm rimp (Ib/ft^) rdrag (Ib/ft^) Vgas (ft/s) 0.0298 195.8549 0.0321 0.0781 114.1847 0.0804 0.1591 72.7971 0.1614 0.2407 54.4019 0.2430 0.3230 43.4092 0.3253 0.4059 35.8906 0.4083 0.4895 30.3287 0.4919 0.5742 25.9778 0.5766
Pressure (psia) 10 25 50 75 100 125 150 175
rimp (lb/ft")
rdrag (Ib/ff^)
0.0321 0.0804 0.1614 0.2430 0.3253 0.4083 0.4919 0.5766 0.6611
0.0298 0.0781 0.1591 0.2407 0.3230 0.4059 0.4895 0.5742 0.6588
86
Vgas (ft/s) 205.8549 124.1847 82.7971 64.4019 534092 45.8906 40.3287 35.9778 324977
Q.bg (Mscf/D)
386.0896 232.9137 155.2895 120.7885 100.1713 86.0698 75.6381 67.4780 60.9508
Qtbg (Mscf/D)
379.8378 226.6619 149.0377 114.5367 93.9194 79.8180 69.3863 61.2262 54.6990
Qtbg (Mscf/D)
373.5860 220.4101 142.7859 108.2849 87.6676 73.5662 63.1345 54.9744 48.4472
Q,bg (Mscf/D)
367.3342 214.1583 136.5340 102.0331 81.4158 67.3144 56.8827 48.7226
Q (Mscf/D) 249.2261 375.8725 501.2074 584.7799 646.6191 694.4903 732.3816 762.2643 786.8916
Q (Mscf/D) 245.1905 365.7834 481.0292 554.5126 606.2629 644.0450 671.8472 691.6408 706.1790
Q (Mscf/D) 241.1549 355.6943 460.8511 524.2454 565.9066 593.5996 611.3128 621.0173 625.4665
Q (Mscf/D) 237.1192 345.6052 440.6730 493.9782 525.5503 543.1543 550.7783 550.3938
Table F.2.3. Continued. Pressure (psia)
10 25 50 75 100 125 150 175 200
J
Pressure (psia)
10 25 50 75 100 125 150 175 200
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 1800 fpm Timp mn rdrag (IWft^) Vgas (ft/s) Qtbg (Mscf/D) 0.0321 0.0298 192.5216 361.0824 0.0804 0.0781 110.8514 207.9065 0.1614 0.1591 69.4638 130.2822 0.2430 0.2407 51.0686 95.7813 0.3253 0.3230 40.0759 75.1640 0.4083 0.4059 32.5573 61.0626 0.4919 0.4895 26.9953 50.6309 0.5766 0.5742 22.6445 42.4707 0.6611 0.6588 19.1644 35.9436
Q (Mscf/D) 233.0836 335.5162 420.4948 463.7110 485.1940 492.7089 490.2439 479.7703 464.0414
Z Factor 0.9984 0.9961 0.9922 0.9883 0.9844 0.9805 0.9766 0.9720 0.9688
Output for Velocity = 2000 fpm rimp (Ib/ft1 rdrag (Ib/ft^ Vgas (ft/s) Qtbg (Mscf/D) 0.0321 0.0298 189.1882 354.8306 0.0804 0.0781 107.5180 201.6547 0.1614 124.0304 0.1591 66.1304 0.2430 0.2407 47.7352 89.5295 0.3230 0.3253 36.7425 68.9122 0.4059 54.8107 0.4083 29.2239 44.3791 0.4895 23.6620 0.4919 19.3112 36.2189 0.5742 0.5766 29.6918 0.6588 15.8310 0.6611
Q (Mscf/D) 229.0480 325.4271 400.3167 433.4438 444.8377 442.2636 429.7095 409.1468 383.3288
F.3 Data for Ball and Hollow Cylinder Combined Table F.3.1. Physical parameters for the 2 in. titanium set Parameter Clearance (Plunger-Tubing) Cylinder Outer Diameter Weight Pressure Drop (measured) Pressure Drop (calculated)
Value 0.145 1.85 2.3129 0.8
0.86
87
Units Inch Inch Lbs Psi Psi
Table F.3.2.1. Two in. titanium set for 500 fpm fall velocity Pressure (psia) 23.7 50 100 250 500 750 1000 Pressure (psia) 23.7 50 100 250 500 750 1000 Pressure (psia) 23.7 50 100 250 500 750 1000 Pressure (psia) 23.7 50 100 250 500 750
0.25 bbl of water and 64.33 ft Slug length) Z Factor Pimp (lb/ft') Vgas (ft/s) Qtbg (Mcf/D) 0.9962 0.07746 91.314 171.285 0.995 0.16362 65.422 122.718 0.9944 0.32744 48.686 91.325 0.9572 0.85040 33.371 62.597 0.9156 1.77809 25.648 48.110 0.8761 2.78738 22.162 41.572 0.8371 3.88965 20.040 37.590 0.5 bbl of water and 128.66 ft Slug lenqth Z Factor Pimp (lb/ft') Vgas (ft/s) Qtbg (Mcf/D) 0.9962 0.07746 167.276 313.774 0.995 0.16362 117.689 220.760 0.9944 0.32744 85.633 160.630 0.9572 0.85040 56.297 105.602 0.9156 1.77809 41.503 77.851 0.8761 2.78738 34.826 65.325 0.8371 3.88965 30.760 57.699 0.75 bbl of water and 193.0 ft Slug length Z Factor Qtbg (Mcf/D) Pimp (lb/ft') Vgas (ft/s) 0.9962 0.07746 244.740 459.081 0.995 0.16362 170.989 320.740 0.9944 0.32744 123.311 231.305 0.85040 79.677 149.456 0.9572 57.672 108.180 1.77809 0.9156 47.739 2.78738 89.548 0.8761 78.204 41.691 3.88965 0.8371 1 bbl of water and 257.33 ft Slug length Qtbg (Mcf/D) Z Factor Vgas (ft/s) Pimp (Ib/ft^) 322.598 605.124 0.07746 0.9962 421.227 224.560 0.16362 0.995 302.338 161.180 0.32744 0.9944 103.175 193.534 0.85040 0.9572 138.662 73.922 1.77809 0.9156 113.895 60.718 2.78738 0.8761
1000
0.8371
Pressure (psia)
Z Factor
23.7 50
0.9962 0.995
52.679 3.88965 0.0 bbl of water Pimp (lb/ft') 0.07746 0,16362
88
Vgas (ft/s) 35.8690 27.2730
Q (Mscf/D) 266.419 402.696 599.358 1027.049 1578.724 2046.238 2467.032 Q (Mscf/D) 488.049 724.415 1054.201 1732.638 2554.653 3215.435 3786.713 Q (Mscf/D) 714.060 1052.494 1518.035 2452.176 3549.876 4407.747 5132.484 Q (Mscf/D) 941.218 1382.238 1984.223 3175.365 4550.149 5606.109
98.814
6485.084
Qtbg (Mcf/D)
Q (Mscf/D)
67.2825
104.6520
51.1582
167.8738
Table F.3.2.1 Continued. Pressure (psia)
Z Factor
Pimp(lb/ft^)
Vgas (ft/s)
Q,bg (Mcf/D)
100
0.9944
250 500 750 1000
0.9572 0.9156 0.8761 0.8371
0.32744 0.85040
21.7186 16.6374 14.0756 12.9194 12.2155
40.7395 31.2082 26.4028 24.2340 22.9136
1.77809 2.78738 3.88965
Q (Mscf/D) 267.3702 512.0417 866.3960 1192.8439 1503.8002
Table F.3.2.2. Two in. titanium set for 1000 ^ m fall velocity Pressure (psia) 23.7 50 100 250 500 750 1000 Pressure (psia) 23.7 50 100 250 500 750 1000
0.25 bbl of water and 64.33 ft Slug lenqth Z Factor Pimp (lb/ft') Vgas (ft/s) Qtbg (Mcf/D) 0.9962 0.07746 99.802 187.208 0.16362 0.995 73.863 138.550 0.32744 57.095 107.098 0.9944 0.85040 0.9572 41.751 78.316 1.77809 34.014 0.9156 63.803 2.78738 0.8761 30.521 57.252 3.88965 0.8371 28.395 53.263 0.5 bbl of water and 128.66 ft Slug length Z Factor Qtbg (Mcf/D) Pimp (lb/ft') Vgas (ft/s) 0.9962 0.07746 175.924 329.996 0.995 0.16362 126.239 236.797 0.9944 0.32744 94.120 176.548 0.85040 64.725 121.411 0.9572 49.902 93.606 1.77809 0.9156 81.055 2.78738 43.211 0.8761 73.413 39.137 3.88965 0.8371 0.75 bbl of water and 193.0 ft Slug length Pimp (lb/ft')
Vgas (ft/s)
Qtbg (Mcf/D)
0.07746 0.16362 0.32744
253.547 179.648 131.874
475.599 336.981 247.368
Pressure (psia) 23.7 50
Z Factor 0.9962 0.995
100
0.9944
250
88.153 0.85040 66.104 1.77809 0.9156 56.151 2.78738 0.8761 50.092 3.88965 0.8371 1 bbl of water and 257.33 ft Slug length
500 750 1000 Pressure (psia) 23.7 50
0.9572
Z Factor 0.9962 0.995
Q (Mscf/D) 291.185 454.647 702.876 1284.962 2093.661 2818.042 3495.615 Q (Mscf/D) 513.279 777.041 1158.672 1992.030 3071.636 3989.689 4818.062 Q (Mscf/D) 739.753 1105.791 1623.455
165.356 123.996 105.328 93.961
2713.040 4068.894 5184.440 6166.585
Pimp (lb/ft')
Vgas (ft/s)
Qtbg (Mcf/D)
Q (Mscf/D)
0.07746 0.16362
331.562 233.328
621.939 437.673
967.372 1436.206
89
Table F.3.2.2 Continued. Pressure (psia)
Z Factor 0.9944 0.9572 0.9156
Pimp (lb/ft')
Vgas (ft/s)
Q,bg (Mcf/D)
0.32744 0.85040 1.77809
169.820 111.698 82.387
0.8761
2.78738
69.157
318.546 209.522 154.541 129.723
Q (Mscf/D) 2090.591 3437.699 5071.200 6385.238
1000
0.8371
3.88965 61.101 0.0 bbl of water
114.613
7521.934
Pressure (psia)
Z Factor
Pimp (lb/ft')
Vgas (ft/s)
Qtbg (Mcf/D)
23.7
0.9962 0.995 0.9944 0.9572 0.9156 0.8761 0.8371
0.07746 0.16362 0.32744 0.85040 1.77809 2.78738 3.88965
44.22086 35.61907 30.06099 24.97631 22.41278 21.25581 20.55141
82.9488593 66.8137479 56.3879814 46.8502076 42.0415681 39.8713528 38.5500381
Q (Mscf/D) 129.01969 219.24671 370.06992 768.68565 1379.5777 1962.5443 2530.0089
100 250 500 750
50 100 250 500 750 1000
90
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