Often we are forced out of ignorance to use valve and wellhead seals which are over designed or overly expensive for a given environment, particularly in an environment of hot production fluids. A common industry approach has been to use the seals Which will withstand the worst thermal conditions possible in both the inside and outside environment. A combined program of testing and mathematical modeling has been designed to predict system thermal response and permit seal optimization based on environment, geometry and conductivity.
Tests were run on several designs of 2-1/16 " 5000 PSI alloy steel gate valves in an attempt to find means of calculating internal temperatures for equipment in steam injection or other hot production fluid service. Valves tested are designated valve A, valve B, and valve C, each having (of course) the same flange and bore size, but different geometry. The valves were set in an enclosed still air environment with thermocouples attached, and connected to a hot oil circulation tank. (See Figure 1)
The valves were equipped with thermocouples as shown in Figure 2. Information was collected and recorded by a computer system capable of sampling, recording, and displaying each data point at two second intervals. Tests were run for a minimum of three and a half hours to establish steady-state conditions. Two tests were run on valve A; one test each was run on valves B and C. Results are shown graphically in Figures 3-6. The results are as expected, with all temperatures in the valve bodies cooler than the flow temperature. The worst possible case for heat removal from a valve in such service; i.e., the case in which the internal temperatures are the highest, is the case in which it is sitting in totally still air. Thus in any other conceivable instance the internal temperatures at any location would be lower relative to the flow.
Concurrently with the valve testing, additional tests were done on a wellhead body for API fire resistance modeling. The wellhead tests differed from the valve tests in that the transient response of the system in fire conditions was modeled, but the basic equations (without the time dependency) can still be considered accurate. This work, as shown in OTC Paper 90-6479 (1), demonstrated that despite irregularities on the surface, the exterior convection coefficient on a wellhead body can be treated as a constant over the surface. It also showed that the hollow wellhead body can be reasonably approximated as a solid cylinder for computational purposes.
In order to predict the temperature of any point in a body, knowledge of various physical parameters is required. These parameters include geometry, conductivity of the materials, boundary temperatures, and the convection coefficients. Geometry and materials, being functions of design and API requirements, may be taken as "given" for any particular valve. Similarly, the external and internal temperatures are "given" for any particular problem. The convection coefficient must be determined.