Program predicts altered zone heat loss in steam injector

Nov. 18, 1996
I.M. Kutasov MultiSpectrum Technologies Santa Monica, Calif. Computer Program "SWHL" (FORTRAN) [.pdf file] A Fortran computer program was written for determining heat loss for a steam-injection well with an altered reservoir zone. The heat-loss calculations allow one to estimate the effect of thermal insulation on the rate of heat loss from a steam-injection well, determine the dry zone radius, and to calculate the casing temperatures.
I.M. Kutasov
MultiSpectrum Technologies
Santa Monica, Calif.
A Fortran computer program was written for determining heat loss for a steam-injection well with an altered reservoir zone.

The heat-loss calculations allow one to estimate the effect of thermal insulation on the rate of heat loss from a steam-injection well, determine the dry zone radius, and to calculate the casing temperatures.

Steam injection is widely used for recovering viscous crudes. Thermal insulated tubing can reduce heat losses from the well bore and thereby save fuel and costs. In most heat-loss calculations, the water vaporization near the well bore is not accounted for.1-3

Based on physical considerations, formation of a dry zone increases the heat losses from the well bore. As the dry zone radius slowly changes with time, the radial temperature gradient at the well bore dry formation interface will increase.

Knowing the casing temperatures is important for evaluating thermal stresses and thermal elongation in the casing.

The Fortran program "SWHL," given in the accompanying listing, simplifies the calculations. The input file is shown at the end of the article.

Analysis

If it is assumed that the temperatures in the well bore will remain practically constant, the temperature change due to the well heat-loss will be compensated for by condensation and reduction of steam quality. Also, there will be a slight change in temperature caused by a change in pressure with increased depth.4

A computer program obtained a numerical solution of a system of differential equations of heat conductivity (for insulation, dry, and wet zones) and the Stefan equation. The results of these calculations were combined with the results of the hydrodynamical modeling5 to develop an empirical expression for the ratio of heat flows at the dry zone/wet zone interface.

Introducing this relationship into the Stefan equation, and assuming a steady-state temperature distribution in the insulation and in the thawed zone, leads to a semitheoretical equation for the radius of drying. The results of computer calculations have also shown that the rate of heat flow from the well bore can be approximated by Equation 1 (see Equation box [39684 bytes]).

Equation 2 determines the effective thermal conductivity of the insulation, Kef.

The overall coefficient of heat loss is the sum of all thermal resistances. Although for a steam injection well the thermal resistances across films, deposits, and metals can be neglected, the estimation of the resistance to radiation and free convection in the annulus is a laborious procedure.1-3

Reference 1 shows the method for calculating Rh.

Equation 3 is obtained by assuming a steady-state radial temperature distribution in the well bore and in the dry zone for the time-dependent casing temperature, Tc.

Example

A modification from Reference 1, p. 130, illustrates the calculations.

Steam at 600° F. is injected down 3.5-in. tubing with a packer in 95/8-in., 53.5-lb/ft, N-80 casing. The annulus contains a stagnant gas at zero gauge pressure at the wellhead, and the casing is cemented to surface in a 12-in. hole.

The tubing is insulated with 1 in. of calcium silicate, the insulation being held in place and sealed from accidental entry of liquids in the annulus by a very thin sheath of aluminum. Emissivity at the surface of insulation (eins) is equal to the emissivity at inner radius of the casing (eci).

A temperature survey in the well indicates a mean subsurface temperature of 100° F. over the 1,000-ft depth, zh.

To estimate the rate of heat loss 21 days after steam injection is started, as well as the casing temperature, one can assume that an altered zone (due to water vaporization) near the well bore exists and:

The undisturbed formation temperature Tf = To + Gz, where To = surface temperature of 70° F., G = geo thermal gradient of 0.060° F./ft, and z = depth. Therefore the mean subsurface temperature is 100° F.
  • Water content W = 20.0 lbm/cu ft
  • Latent heat of vaporization qv = 960.0 BTU/lbm
  • Vaporization temperature Tev = 212° F.

Thus the following data apply: r1 = 1.75 in. = 0.1458 ft, rins = 2.75 in. = 0.2292 ft, rci = 4.27 in. = 0.3556 ft, rco = 4.81 in. = 0.4010 ft, rw = 6.00 in. = 0.5000 ft, t = 21 days, ad = 0.96 sq ft/day, eins = eci = 0.9, Kd = 24 BTU/ ft-day-°F., Rh = 0.108 (BTU/ ft-day-°F.)-1, zh = 1,000 ft, tD = 80.6, f(80.6) = 2.60, Ts = 600 °F., To = 70° F, Tev = 212° F., G = 0.060° F./ft, W = 20.0 lbm/ cu ft, qv = 960.0 BTU/lbm.

Thermal conductivities of the cement and insulation are: Kcem = 12 BTU/ft-day-°F., Kins = 0.96 BTU/ ft-day-°F.

Equation 2 obtains the value of the effective thermal conductivity of insulation: Kef = ln(6.00/1.75)/(2 x 3.1416 x 0.108 - 2.60/24) = 2.16 (BTU/ft-day-°F.).

Table 1 [80418 bytes] presents the output files for this example and Table 2 [107317 bytes] shows the efficiency of the thermal insulation.

References

1. Prats, M., Thermal Recovery, SPE Monograph Series, Dallas, 1982, pp. 128-33.

2. Willhite, G.P., "Over-all Heat Transfer Coefficients in Steam and Hot Water-injection Wells", JPT, May 1967, pp. 607-15.

3. White, R.D., and Moss, J.T., Thermal Recovery Methods, PennWell Publishing Co., Tulsa, 1983, pp. 92-98

4. Ramey, H.J. Jr., "Well bore heat transmission," JPT, April 1962, pp. 427-35

5. Kutasov, I.M., "Thermal Parameters of Wells Drilled in Permafrost Regions," Nedra, Moscow, 1976.

Input file

2.,0.00001,1.00000001

0.96, 24.0, 1.49

600.0, 70.0, 0.060, 20.

1000.0,1.75,6.00

212.,960.

7,10.,21.,50.,100.,150.,200.,250.,300.,350.,400.,450.,500.

10,100.,200.,300.,400.,500.,600.,700.,800.,900.,1000.

The Author

I.M. Kutasov is senior research engineer with MultiSpectrum Technologies Inc., Santa Monica, Calif. He was a graduate faculty member in the petroleum engineering and geosciences department at Louisiana Tech University and worked for Shell Development Co., Houston, as a senior research physicist.
Kutasov's research interests include the temperature regime of deep wells, transient pressure flow analysis, and drilling in permafrost areas. He holds an MS in physics from Yakutsk State University and a PhD in physics from O. Schmidt Earth Physics Institute in Moscow. Kutasov is a member of SPE.

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