I.M. KutasovMultiSpectrum Technologies Inc.

Santa Monica, Calif.

Sodium chloride added to drilling mud left in the annulus helps lower the fluid's freeze point, eliminating the chance of casing collapse from thaw/refreeze cycles in the permafrost around the well.

Arctic drilling experience has shown that extensive washouts occur in the permafrost interval. Thus, the drilling mud cannot be properly displaced prior to setting of the surface casing.

When a well is shut in during or after drilling or after a short production period, thawed permafrost and water-based fluids outside the casing wilt refreeze and generate inward radial loads around the well bore. The ability of the outer frozen permafrost to compress and accommodate the phase change expansion (about 9% volume increase at the water/ice transition) determines the magnitude of the load around the well bore.

Freeze-back pressures will build up continuously during the refreeze process. Complete refreeze is not required for pressures to reach significant levels.

Thus, in some cases large compressive loading can lead to casing buckling. As the pressure increases, the temperature of freezing (Tf) of the water-based mud decreases according to the empirical Bridgman-Tamman equation. In this case, when the difference between Tf and the static temperature of permafrost (Tp) vanishes, the freezing process of water is terminated. Thus, the maximum pressures upon the casing depend on the permafrost temperature. If the collapse resistance of casing is known, the corresponding critical temperature of casing (Tcr) can be estimated. For 13 3/8-in. casing, which is usually used to protect the permafrost interval, the values of Tcr can be calculated.

### EQUATIONS

To avoid casing collapse, it is suggested to lower the mud freezing temperatures by introduction of a salt solution.

The following method can be used to calculate the concentration of sodium chloride in the mud to prevent the buckling of casing.

The empirical Bridgman-Tamman formula can be used to calculate values of Tf at various freeze-back pressures.

P = 1-127Tf-1.519Tf2 (1)

In Equation 1, pressure (P) is in kgf/sq cm and temperature is in C. Equation 1 can be conveniently rewritten in the following form:

Tf = -41.80 + [1,747.24 -0.6583(P - 1)]1/2 (2)

For small quantities of sodium chloride in the solution, the freezing temperature/pressure/salt relationship may be approximated by Equation 3.1

T(C,P) = TWO + T(O,P) (3)

In this equation, C is the quantity of sodium chloride in kg/1,000 1. of water. T(C,0) = the freezing temperature of the salt solution at atmospheric pressure, in C. T(C,0) = MC. T(C,O) -10 C. T(0,P) = Tf(P), which is the freezing temperature according to the Bridgman-Tamman equation.

M = -1,000 l.C./17 kg (4)

To determine the salt concentration C for which buckling of casing is impossible, it is assumed that T(C,P) = TP and T(O,P) = Tcr.

The critical temperatures (Tcr) for the 13 3/8-in. OD casing were calculated from Equation 2 by assuming that the pressure G kgf/sq cm = 14.22 psi) is equal to the collapse resistance of the casing (Table 1)(14683 bytes).

From Equations 3 and 4, one obtains the following:

C = (Tp -Tcr)/M (5)

For slow freezing, the formed ice represents pure frozen water, while the salt ions remain in the unfrozen zone of the washouts. As the transition of the quantity of water into ice increases, the concentration of salt in the unfrozen portion of the washouts increases. But, for practical purposes, it is impossible to attain values of the collapse resistance (pressure) if the original concentration of the solution is calculated from Equation 5.

Also, the collapse rating of permafrost casing must be greater than the difference between external freeze-back pressure and internal packer fluid pressure. This margin provides an additional safety factor against freeze-back collapse. In the calculations, the internal fluid pressure is neglected.

Table 1 (14683 bytes) lists the critical temperatures for 13 3/8-in. OD American Petroleum Institute standard casing.2

### EXAMPLE

Assume that grade N-80 13 3/8-in. casing is used to protect the permafrost interval (Table 1)(14683 bytes). From caliper log data, it was determined that the drilling mud at some depth was not completely displaced prior to setting of the surface casing, and the static temperature of permafrost at this depth is -4.0 C. (24.8 F.).

The sodium chloride concentration is obtained from Equation 5:

C = (-4.0 C. + 1.50 C.) x (-17 kg)/(1,000 1. C.)

C = 0.0425 kg/l. = 0.355 ppg sodium chloride

Thus, the drilling fluid behind the casing should have a sodium chloride concentration of 0.355 ppg.

### REFERENCES

- Kutasov, I.M., "Critical Temperature Governing the buckling of casing pipes in boreholes," Kolyma, No 8, 1977, pp 23 25.
- Halliburton Cementing Tables, Duncan, Okla, 1979, p. 24.

*Copyright 1995 Oil & Gas Journal. All Rights Reserved.*