Variable Tubing Temperature
Fluid temperature may vary considerably with depth as the hot water or superheated steam flows down the tubing. The pressure of the steam vapor also changes as a result of energy losses due to friction and pressure increase with depth as a result of the static pressure gradient. For injection rates typically encountered in the oilfield, the pressure loss due to friction exceeds the pressure increase resulting from the static pressure gradient. Consequently, the pressure and temperature of the steam decrease with depth. In this case, the depth step methods, suggested by Satter (1965), Earlongher (1969), Pacheco et al. (1972), and Sugiura et al. (1979), can be used to determine the tubing temperature at each depth of the well. The following equations (after Sugiara et ah, 1979 and Goetzen, 1987) can be used to predict the pressure drop, the change in quality of the steam, and the related temperature at different depths of the well:
Pressure drop:
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dp U |
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pv dv 9c dl |
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1 144 |
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(4.126) |
Heat loss rate to surroundings:
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dQ |
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h + |
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(4.127) |
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m |
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dl |
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v2 _ 9_J_ ^9c^c 9c dc |
where:
dp/dl = pressure gradient, psi/ft.
p = density of the two-phase mixture, lbm/ft3. 1
.(?s(Fst + (1 — qst)Vw g = acceleration due to gravity, ft/s2.
gc = gravitational constant, 32.17 ft-lbm/lbf-s2.
v = velocity of the two-phase mixture, ft/s.
7/ _
/ = friction factor. dQ/dl = radial heat flow gradient. Btu/sec-ft.
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See Text |
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TUBING 1 1 : 2 3/8* х 4.83 mm 2 : 2 7/8" х 5.St mm 3 : 3 1/2" x 6.4S mm |
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и — i. o — 0.9 — £ 0.8 — г * 0.7 — •O’l — ‘°’тз 0.6 — 0.5 — 0.4 — 0.3 — |
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111 See Text |
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IV |
Fig. 4.37: Radial heat flow as a function of completion techniques, Emsland. Northern Germany. (After Goetzen, 1987; courtesy of ITE-TU Clausthal.)
m = mass flow rate of the fluids (steam and water), lbm/s.
H = h(qst, p) = qstHst + (1 — qsi)hw, Btu/lbm.
Hst = enthalpy of steam, Btu/lbm.
hw = enthalpy of water, Btu/lbm.
qst = steam quality, fraction.
Vst — volume of steam, ft3.
Vw = volume of water, ft3.
Jc — mechanical equivalent of heat. 778 ft-lbm/Btu.
A = flow cross-section, ft2.
The solution of the wellbore model involves several successive iterative solutions, because both tubing and casing temperatures depend on the overall heat transfer coefficient. As a result, wellbore heat loss and casing temperature for steam injection wells are often calculated by assuming that the temperature of the flowing fluid at the internal surface of the tubing and at the outer surface of the tubing are equal to the injection temperature. A single value of Vto1 is calculated based on the injection temperature and the average formation temperature.
The temperatures and heat losses experienced in steam injection wells were presented against injection time and rate, depth, and completion systems by Willhite (1967) and Pacheco et al. (1972). In addition to these studies, Goetzen (1986) developed a more rigorous computer program to include simultaneous calculation of steam quality, pressure and temperature as the steam flows down the tubing, and radial heat losses and casing temperatures for different completion systems. The results predicted by the computer program were compared with the field data obtained from a steam injection project in Emsland in northern Germany. Some of these results are presented in Figs. 4.34 through 4.38.
Fig. 4.38: Radial heat flow as a function of completion techniques. Emsland. Northern Germany. (After Goetzen. 1987; courtesy of ITE-TU Clausthal.)
Figures 4.34 and 4.36 show that at a given depth the steam pressure and heat loss decrease, whereas the steam quality increases with increasing injection rate. From these results it may be concluded that for a given depth there is a certain rate above which an increase in injection rate leads to an insignificant increase in steam quality but a large drop in pressure. The pressure determines the temperature of the saturated steam and is. therefore, directly related to the rate of heat loss. Various authors have noted that after a certain time the relative increase in casing temperature becomes very small with time. Field results have confirmed the theoretical investigations (Fig. 4.36).
Figure 4.35 shows that casing temperature and the rate of heat loss increase as the tubing size increases. It is also evident that the types of completion and the tubing insulation are major factors controlling the rate of heat loss. Wellbore heat loss can be reduced considerably by applying tubing insulation and thereby lowering the surface immisivity. Results of the investigation also show that the heat loss can be reduced by 60% by lowering the tubing immisivity.
Figures 4.37 and 4.38 present radial heat flow as a function of completion technique for nine completion systems with variable insulation. The key to the figures is given below.
The casing and hole diameter variables are:
I Casing: 7 in. x 9.19 mm; hole diameter (= bit diameter): 9| in. II Casing: 9| in. x 10.03 mm; hole diameter: 12 j in.
III Outer casing: 10| in. x 10.16 mm; inner casing: 7 in. x 9.19 mm; hole diameter: 14^ in.
IV Outer casing: 131 in. x 12.19 mm; inner casing: 7 in. x 9.19 mm; hole diameter: 17 ■1 in.
V Outer casing: 13| in. x 12.19 mm; inner casing: 9| in. x 10.03 mm; hole diameter: 17|-in.
The completions are listed below:
1. Tubing is bare and casing is exposed to steam.
2. Tubing is bare, annulus is packed-off. tubing is filled with nitrogen gas, and annular pressure is equal to injection pressure.
3. Same as (2), but immisivity of the tubing is reduced to 0.3 by insulating at the external surface.
4. Tubing is bare, annulus is packed off. and annular space is filled with nitrogen gas under atmospheric pressure.
5. Same as (4) but the immisivity of the tubing is reduced to 0.3 by insulating the external surface.
6. Tubing is partially insulated (85%). annulus is packed-off. annulus is filled with nitrogen, and annular pressure is equal to the injection pressure.
7. Same as (6), but the annulus is at atmospheric pressure.
8. Tubing is completely insulated, annulus is packed-off and filled with nitrogen gas and the annular pressure is equal to the injection pressure.
9. Same as (8), but pressure in the annulus is at atmospheric pressure.
From the results obtained, it is evident that minimal heat loss can be achieved for the completion described in (9): insulated tubing, annulus filled with X2 at atmospheric pressure and annulus sealed with a packer.