C H A P T E R
3
CRITICAL VELOCITY
3.1 INTRODUCTION To effectively plan and design for gas well liquid loading problems, it is essential to be able to accurately predict when a particular well might begin to experience excessive liquid loading. In the next chapter, Nodal Analysis (Macco-SchlumbergerTM) techniques are presented that can be used to predict when liquid loading problems and well flow stability occur. In this chapter, the relatively simple “critical velocity” method is presented to predict the onset of liquid loading. This technique was developed from a substantial accumulation of well data and has been shown to be reasonably accurate for vertical wells. The method of calculating a critical velocity will be shown to be applicable at any point in the well. It should be used in conjunction with methods of Nodal Analysis if possible.
3.2 CRITICAL FLOW CONCEPTS The transport of liquids in near vertical wells is governed primarily by two complementing physical processes before liquid loading becomes more predominate and other flow regimes such as slug flow and then bubble flow begin. 3.2.1 Turner Droplet Model
It is generally believed that the liquids are both lifted in the gas flow as individual particles and transported as a liquid film along the tubing wall by the shear stress at the interface between the gas and the liquid
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Gas Well Deliquification
before the onset of severe liquid loading. These mechanisms were first investigated by Turner et al. [1], who evaluated two correlations developed on the basis of the two transport mechanisms using a large experimental database as illustrated here. Turner discovered that liquid loading could best be predicted by a droplet model that showed when droplets move up (gas flow above critical velocity) or down (gas flow below critical velocity). Turner et al. [1] developed a simple correlation to predict the so-called critical velocity in near vertical gas wells assuming the droplet model. In this model, the droplet weight acts downward and the drag force from the gas acts upward (Figure 3-1). When the drag is equal to the weight, the gas velocity is at “critical”. Theoretically, at the critical velocity the droplet would be suspended in the gas stream, moving neither upward nor downward. Below the critical velocity, the droplet falls and liquids accumulate in the wellbore. In practice, the critical velocity is generally defined as the minimum gas velocity in the production tubing required to move liquid droplets upward. A “velocity string” is often used to reduce the tubing size until the critical velocity is obtained. Lowering the surface pressure (e.g., by compression) also increases velocity. Turner’s correlation was tested against a large number of real well data having surface flowing pressures mostly higher than 1000 psi. Examination of Turner’s data, however, indicates that the range of applicability for his correlation might be for surface pressures as low as 5 to 800 psi. Two variations of the correlation were developed, one for the transport of water and the other for condensate. The fundamental equations derived by Turner were found to underpredict the critical velocity from the database of well data. To better match the collection of measured
Figure 3-1: Illustrations of Concepts Investigated for Defining Critical Velocity
Critical Velocity
33
field data, Turner adjusted the theoretical equations for required velocity upward by 20 percent. From Turner’s [1] original paper, after the 20 percent empirical adjustment, the critical velocity for condensate and water were presented as vgcond =
4.02(45 − 0.0031 p)1/ 4 ft/sec (0.0031 p)1/ 2
(3-1)
vgwater =
5.62(67 − 0.0031 p)1/ 4 ft/sec (0.0031 p)1/ 2
(3-2)
where p = psi. The theoretical equation from Ref. 1 for critical velocity Vt to lift a liquid (see Appendix A) is Vt =
1.593σ 1/ 4(ρl − ρg )1/ 4 ft/sec ρg1/ 2
(3-3)
where s = surface tension, dynes/cm, r = density, lbm/ft3. Inserting typical values of: Surface Tension Density Gas Z factor Vt ,condensate =
Vt ,water =
20 and 60 dyne/cm for condensate and water, respectively 45 and 67 lbm/ft3 for condensate and water, respectively 0.9
1.593(20)1/ 4(45 − .00279P/Z )1/ 4 3.368(45 − .00279P/Z )1/ 4 = (.00279P/Z )1/ 2 (.00279P/Z )1/ 2
1.593(60)1/ 4(67 − .00279P/Z )1/ 4 4.43(67 − .00279P/Z )1/ 4 = (.00279P/Z )1/ 2 (.00279P/Z )1/ 2
Inserting Z = 0.9 and multiplying by 1.2 to adjust to Turner’s data gives: Vt ,condensate =
4.043(45 − .0031P )1/ 4 (.0031P )1/ 2
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Gas Well Deliquification
Vt ,water =
5.321(67 − .0031P )1/ 4 (.0031P )1/ 2
Turner [1] gives 4.02 and 5.62 in his paper for these equations. These equations predict the minimum critical velocity required to transport liquids in a vertical wellbore. They are used most frequently at the wellhead with P being the flowing wellhead pressure. When both water and condensate are produced by the well, Turner recommends using the correlation developed for water because water is heavier and requires a higher critical velocity. Gas wells having production velocities below that predicted by the preceding equations would then be less than required to prevent the well from loading with liquids. Note that the actual volume of liquids produced does not appear in this correlation and the predicted terminal velocity is not a function of the rate of liquid production. 3.2.2 Critical Rate
Although critical velocity is the controlling factor, one usually thinks of gas wells in terms of production rate in SCF/d rather than velocity in the wellbore. These equations are easily converted into a more useful form by computing a critical well flow rate. From the critical velocity Vg, the critical gas flow rate qg, may be computed from: qg =
3.067PVg A MMscf/D (T + 460)Z
(3-4)
where A= T P A dt
(π )dti2 2 ft 4 × 144
= surface temperature, ºF = surface pressure, psi = tubing cross-sectional area = tubing ID, inches
Introducing the preceding into Turner’s [1] equations gives the following:
Critical Velocity
qt ,condensate(MMscf/D) = qt ,water(MMscf/D) =
35
.0676Pdti2 (45 − .0031P )1/ 4 (T + 460)Z (.0031P)1/ 2
.0890 Pdti2 (67 − .0031P )1/ 4 (T + 460)Z (.0031P )1/ 2
These equations can be used to compute the critical gas flow rate required to transport either water or condensate. Again, when both liquid phases are present, the water correlation is recommended. If the actual flow rate of the well is greater than the critical rate computed by the preceding equation, then liquid loading would not be expected. 3.2.3 Critical Tubing Diameter
It is also useful to rearrange the preceding expression, solving for the maximum tubing diameter that a well of a given flow rate can withstand without loading with liquids. This maximum tubing is termed the critical tubing diameter, corresponding to the minimum critical velocity. The critical tubing diameter for water or condensate is shown here as long as the critical velocity of gas, Vg, is for either condensate or water. dti, inches =
59.94qg(T + 460)Z PVg
3.2.4 Critical Rate for Low Pressure Wells—Coleman Model
Recall that these relations were developed from data for surface tubing pressures mostly greater than 1000 psi. For lower surface tubing pressures, Coleman et al. [2] has developed similar relationships for the minimum critical flow rate for both water and liquid. In essence the Coleman et al. formulas (to fit their new lower wellhead pressure data, typically less than 1000 psi) are identical to Turner’s equations but without the Turner [1] 1.2 adjustment to fit his data. With the same data defaults given above to develop Turner’s equations, the Coleman et al.2 equations for minimum critical velocity and flow rate would appear as: Vt ,condensate =
3.369(45 − .0031P )1/ 4 (.0031P )1/ 2
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Gas Well Deliquification
Vt ,water =
4.434(67 − .0031P )1/ 4 (.0031P )1/ 2
qt ,condensate(MMscf/D) =
qt ,water(MMscf/D) =
.0563Pdti2 (45 − .0031P )1/ 4 (T + 460)Z (.0031P)1/ 2
.0742 Pdti2 (67 − .0031P )1/ 4 (T + 460)Z (.0031P )1/ 2
However, if the original equations of Turner were used, the coefficients would be 4.02 and 5.62 both divided by 1.2 to get the Coleman equations, so there can be some confusion. The concern is that even if some slight errors in the Turner development are present, the equations with the coefficients have been used with success, and the question is “are the original coefficients better than if they are corrected”?
Example 3-1: Calculate the Critical Rate Using Turner et al. and Coleman et al. Well surface pressure = 400 psia Well surface flowing temperature = 120º F Water is the produced liquid Water density = 67 lbm/ft3 Water surface tension = 60 dyne/cm Gas gravity = 0.6 Gas compressibility factor for simplicity = 0.9 Production string = 2-3/8 inch tubing with 1.995 in ID, A = .0217 ft2 Production = .6 MMscf/D
Critical Rate by Coleman et al. [2] Calculate the gas density:
ρg =
28.97γ g P Mairγ g P 0.6 × 400 = 1.24 lbm/ft 3 = = 2.7 580 × .9 R(T + 460)Z 10.73(T + 460)Z
Vg =
1.593σ 1/ 4 (ρl − ρg )1/ 4 1.593601/ 4(67 − 1.24)1/ 4 = = 11.30 ft/sec 1.241/ 2 ρg1/ 2
Critical Velocity
qt ,water =
37
3.067PAVg 3.067 × 400 × .0217 × 11.30 = .575 MMscf/d = (T + 460)Z (120 + 460) × 0.9
Critical Rate by Turner et al. [1] Since the Turner and Coleman variations of the critical rate equation differ only in the 20 percent adjustment factor applied by Turner for his high pressure data, then Vg = 1.2 × 11.30 = 13.56 ft/sec qt,water = 1.2 × 0.575 = 0.690 MMscf/d For this example, the well is above critical considering Coleman (.6 > .575 MMscf/D) but below critical (.6 < .69 MMscf/D) according to Turner. We would say it is above critical since the more recent lower wellhead pressure correlation of Coleman et al. [2] says it is flowing above critical. This example illustrates that the more recent Coleman et al. [2] relationships require less flow to be above critical when analyzing data with lower wellhead pressures. Also the example shows that the relationships require surface tension, gas density at a particular temperature, and pressure including use of a correct compressibility factor and gas gravity. If these factors are not taken into account for each individual calculation, then the approximate equation may be used. For this example, the approximate Coleman equation gives .0742 Pdti2 (67 − .0031P )1/ 4 (T + 460)Z (.0031P )1/ 2 .0742 × 400 × 1.9952 (67 − .0031 × 400)1/ 4 = = .579 MMscf/d (120 + 460) × 0.9 (.0031 × 400)1/ 2
qt ,water =
and is very close to the previously calculated 0.575 MMscf/D. 3.2.5 Critical Flow Nomographs
To simplify the process for field use, the following simplified chart from Trammel [6] can be used for both water and condensate production. To use the chart, enter with the flowing surface tubing pressure (see the dotted line) at the bottom x-axis for water and top axis for
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Gas Well Deliquification
condensate. Move upward to the correct tubing size then either left for water or right for condensate to the required minimum critical flow rate.
Example 3-2: Critical Velocity from Figure 3-2 [6] 200 psi well head pressure 2-3/8 inch tubing, 1.995 inch ID What is minimum production according to the Turner equations? The example indicated by the dotted line shows that for a well having a well head pressure of 200 psi and 2-3/8 inch tubing, the flow rate must be at least ≈586 Mscf/D (actually 577 calculated) or liquid loading will likely occur. A similar chart was developed by Coleman et al. [2] using the Turner correlation for flowing well head pressures below about 800 psi. Note only one set of curves are represented on this chart to be used for both
100
10
10,000
4 1/2
r
ate
9.0
lw /ga
3 1/2 2 7/8 2 3/8 2 1/16 1 1/2 1 1/4
lb
1,000 586 MCF/Day
100
10,000 10,000 ate
ens
45°
I
AP
nd Co
1,000
4 1/2 3 1/2 2 7/8 2 3/8 2 1/16 1 1/2 1 1/4
Normal API Tubing 10 10
1,000
100 200 psi 1,000
Minimum gas flow rate in MCF/Day to remove liquids from a well bore. After Turner. Hubbard & Dukler, p 1475 Transaction of SPE Nov. 1969. SPE 2198
100
10
Flow Rate to Remove Liquids, MCF/Day
Flow Rate to Remove Liquids, MCF/Day
Surface Tubing Pressure, psia, Condensate
10,000
Surface Tubing Pressure, psia, Water
Figure 3-2: Nomograph for Critical Rate for Water or Condensate (after [6]) for a Constant Z = 0.8, Temperature of 60º F, and the Original Turner Assumptions of Surface Tension of s = 20 dynes/cm for Condensate, and 60 dynes/cm for Water, r = 45 lbm/ft3 for Condensate and 67 lbm/ft3 for Water, and Gas Gravity = 0.6
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Critical Velocity
water and condensate. The chart is used in the same manner as the above chart with no distinction between water and condensate. If water and condensate are present, the more conservative water coefficients are used anyway. The Coleman et al. [5] correlation would then be applicable for flowing surface tubing pressures below about 800 psi and the Turner chart (or Turner correlation) for surface tubing pressures above about 800 psi. The dividing line between using Turner or Coleman might best be obtained from experience or even a blend of the two from 500 to 1000 psi. The chart of Figure 3-4 is another way of looking at critical velocity. It was prepared using a routine calculating actual Z factor (gas compressibility) at each point but still depends on fluid properties and temperatures. For this 60 dyne/cm for surface tension, 67 lbm/ft3, gas gravity of 0.6 and 120º F were used.
Example 3-3: Critical Velocity with Water: Use Turner’s [1] Equations with Figure 3-4 100 psi wellhead pressure 2-3/8 inch tubing, 1.995 inch ID Read from Figure 3-4 a required rate of about 355 Mscf/D. Compare to the simplified Turner equations using Z = 0.9 for simplicity.
Minimum Gas Rate, Mscf/D
Critical Gas Rate 10000 2 3/8
2 7/8
3 1/2˝ tubing
1000
100
1.66
1.315
10 10
100
1000
10000
Flowing Wellhead Pressure, PSIA
Figure 3-3: The Exxon Nomograph for Critical Rate [2] (for lower surface tubing pressures)
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Gas Well Deliquification Turner Unloading Rate for Well Producing Water 3000 4-1/2 OD 3.958 ID 3-1/2 2.992 2-7/8 2.441 2-3/8 1.995 2-1/16 1.751
Rate (Mcfd)
2500 2000 1500 1000 500 0 0
50
100
150
200
250
300
350
400
450
500
Flowing Pressure (psi)
Figure 3-4: Simplified Turner Critical Rate Chart
5.32(67 − .0031P )1/ 4 (.0031P )1/ 2 5.32(67 − .0031 × 100)1/ 4 5.32 × 2.86 = = = 27.22 ft/ sec (.0031 × 100)1/ 2 .557
Vt ,water =
qg =
3.067PVg A 3.067 × 100 × 27.22 × .0217 = 0.346 MMscf/D = (T + 460)Z 580 × .9
In this case the difference between the calculations and reading from chart can be attributed to that fact that the chart was calculated using actual Z factors and not an assumed value of 0.9. Using one of the critical velocity relationships, the critical rate for a given tubing size vs. tubing diameter can be generated as in Figure 3-5 where a surface pressure of 200 psi and surface temperature of 80º F is used. (In this case, specific liquid and gas properties were used in the critical flow equations rather than the typical values given above.) This type of a presentation provides a ready reference for maximum tubing size given a particular well flow rate. A large tubing size may exhibit below critical flow and a smaller tubing size may indicate that the velocity will increase to be above critical. Tubing sizes approaching and less than 1 inch, however, are not
Critical Velocity
41
Figure 3-5: Critical Rate vs. Tubing Size (200 psi and 80º F) from Maurer Engineering, PROMOD program. Use this type of presentation with critical velocity model desired
generally recommended as they can be difficult to initially unload due to the high hydrostatic pressures exerted on the formation with small amounts of liquid. It is difficult to remove a slug of liquid in a small conduit. See also Bizanti [4] for pressure, temperature, diameter relationships for unloading and Nosseir et al. [5] for consideration of flow conditions leading to different flow regimes for critical velocity considerations.
3.3 CRITICAL VELOCITY AT DEPTH Although the preceding formulas are developed using the surface pressure and temperature, their theoretical basis allows them to be applied anywhere in the wellbore if pressure and temperature are known. The formulas are also intended to be applied to sections of the wellbore having a constant tubing diameter. Gas wells can be designed with tapered tubing strings, or with the tubing hung off in the well far above the perforations. In such cases, it is important to analyze gas well liquid loading tendencies at locations in the wellbore where the production velocities are lowest. For example, in wells equipped with tapered strings, the bottom of each taper size would exhibit the lowest production velocity and thereby be first to load with liquids. Similarly, for wells having the tubing string hung well above the perforations, the analysis must be performed using
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Gas Well Deliquification Liquid Transport in a Vertical Gas Well Pressure and temperature may vary significantly along the tubing string. This means that the gas velocity changes from point to point in the tubing even though the gas rate (e.g., Mscf/d) is constant. Check the gas velocity at all depths in the tubing to be sure that the critical velocity is attained throughout the tubing string.
Tubing set above perforations may allow liquid buildup in the casing below the tubing because of the low gas velocity in the larger casing.
Figure 3-6: Completions Effects on Critical Velocity
the casing diameter near the bottom of the well since this would be the most likely location of the initial liquid buildup. In practice, it is recommended that liquid loading calculations be performed at all sections of the tubing where diameter changes occur. In general for a constant diameter string, if the critical velocity is acceptable at the bottom of the string, then it will be acceptable everywhere in the tubing string. In addition, when calculating critical velocities in downhole sections of the tubing or casing, downhole pressures and temperatures must be used. Minimum critical velocity calculations are less sensitive to temperature, which can be estimated using linear gradients. Downhole pressures, on the other hand, must be calculated by using flowing gradient routines (perhaps with Nodal Analysis, Macco SclumbergerTM) or perhaps a gradient curve. Bear in mind that the accuracy of the critical velocity prediction depends on the accuracy of the predicted flowing gradient.
43
Critical Velocity Critical Flow Rate - Pressure with Gray (Mod) Depth (1000 ft MD) 0 1 2 3
Pfwh 100 Formation Gas Rate 444 Condensate 7.7 Water 307.0 Tubing String 1
psig Mscfd bbl/MMscf bbl/MMscf
4 5 6 7 8 9 10 11 0
400 800 1200 1600 2000 2400 2800 3200 3600 4000 4400 4800 5200 5600 Gas Rate (Mscfd)
Figure 3-7: Critical Velocity with Depth
Figure 3-7 shows critical rate calculated using the Gray correlation. The vertical line is the actual rate. The blue line is the required critical rate for the tubing and the casing on the bottom. Note the well is predicted to be just above critical rate at the surface but the rest of the tubing is below critical and as usual, well below critical for the casing flow. Normally the required rate is maximum at the bottom of the tubing but for high pressure, high temperature (unusual for most loaded gas wells) the critical may be calculated to be maximum at surface conditions. Guo et al. [7] present a kinetic energy model and show critical rate and velocity at downhole conditions. They mention that Turner underpredicts the critical rate. They mention the controlling conditions are downhole.
3.4 CRITICAL VELOCITY IN HORIZONTAL WELL FLOW In inclined or horizontal wells the preceding correlations for critical velocity cannot be used. In deviated wellbores, the liquid droplets have very short distances to fall before contacting the flow conduit rendering the mist flow analysis ineffective. Due to this phenomenon, calculating gas rates to keep liquid droplets suspended and maintain mist flow in
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Gas Well Deliquification
horizontal sections is a different situation than for tubing. Fortunately, hydrostatic pressure losses are minimal along the lateral section of the well and only begin to come into play as the well turns vertical where critical flow analysis again becomes applicable. Another, less understood effect that liquids could have on the performance of a horizontal well has to do with the geometry of the lateral section of the wellbore. Horizontal laterals are rarely straight. Typically, the wellbores “undulate” up and down throughout the entire lateral section. These undulations tend to trap liquid, causing restrictions that add pressure drop within the lateral. A number of two phase flow correlations that calculate the flow characteristics within undulating pipe have been developed over the years and, in general, have been met with good acceptance. Once such correlation is the Beggs and Brill method [6]. These correlations have the ability to account for elevation changes, pipe roughness and dimensions, liquid holdup, and fluid properties. Several commercially available nodal analysis programs now have this ability. A rule of thumb developed from gas distribution studies suggests that when the superficial gas velocity (superficial gas velocity = total in-situ gas rate/total flow area) is in excess of ≈14 fps, then liquids are swept from low lying sections as illustrated in Figure 3-8. Upon examination, this is a conservative condition and requires a fairly high flow rate. Bear in mind, however, when performing such calculations that the velocity at the toe of the horizontal section can be substantially less than that at the heel.
Figure 3-8: Effects of Critical Velocity in Horizontal/Inclined Flow
Critical Velocity
45
3.5 REFERENCES 1. 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,” Journal of Petroleum Technology, Nov. 1969. pp. 1475–1482. 2. Coleman, S. B., Clay, H. B., McCurdy, D. G., and Norris, H. L. III. “A New Look at Predicting Gas-Well Load Up,” Journal of Petroleum Technology, March 1991, pp. 329–333. 3. Trammel, P. and Praisnar, A. “Continuous Removal of Liquids from Gas Wells by use of Gas Lift,” SWPSC, Lubbock, Texas, 1976, 139. 4. Bizanti, M. S. and Moonesan, A. “How to Determine Minimum Flowrate for Liquid Removal,” World Oil, September 1989, pp. 71–73. 5. Nosseir, M. A. et al. “A New Approach for Accurate Predication of Loading in Gas Wells Under Different Flowing Conditions,” SPE 37408, presented at the 1997 Middle East Oil Show in Bahrain, March 15–18, 1997. 6. Beggs, H. D. and Brill, J. P. “A Study of Two-Phase Flow in Inclined Pipes,” Journal of Petroleum Technology, May 1973, 607. 7. Guo, B., Ghalambor, A., and Xu, C. “A Systematic Approach to Predicting Liquid Loading in Gas Wells,” SPE 94081, presented at the 2995 SPE Production and Operations Symposium, Oklahoma City, Ok., 17–19, April 2005.