Practical Application of Wellbore Heat Transfer Model
The transient heat conduction function, /(f), >s introduced into the above equation because the heat flow into the surrounding formation varies with time. Heat losses to the formation are initially large but decrease with time as the thermal resistance to the flow of heat builds up in the formation. Ramey (1962) provided the following approximate3 method for evaluating /(f):
where:
cij — thermal diffusivity of the formation.
Equating Eqs. 4.121 and 4.123, the expression for the temperature at the cement formation interface, TCTrto, is obtained:
Tcmo = lrst /(f) + — А — Te) X (7(0 + -7-) (4.125)
V TtboUtot / V ^ib0k tot /
Examination of Eqs. 4.122 and 4.125 shows that, the casing temperature is a
function of overall heat transfer coefficient, L’tot. Inasmuch as casing temperature
“Reasonable for injection periods greater than 7 days. For shorter periods see Jessop (1966).
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Fig. 4.35: Radial heat and temperature distribution as a function of steam injection rate, Emsland, Northern Germany. (After Goetzen. 1987: courtesy of ITE-TU Clausthal.) |
TOC o "1-5" h z PRESSURE, bar TEMPERATURE, X
INJECTION RATE STEAM QUALITY
• rii — 1.2 t/h X — 0.00
o m — 2.4 t/h X — 0.42
■ m — 2.1 t/h X — 0.37
Fig. 4.36: Pressure and temperature distributions in a typical steam injection well Rolermohr steam injection project. Emsland. Northern Germany. (After Goetzen, 1987; courtesy of ITE-TU Clausthal.)
at the internal surface is used to determine natural convection and radiation heat transfer coefficients, it is necessary to use an iterative solution to obtain the correct combination of Uiot and TCt.