ABSTRACT
In his classical paper H. Ramey (1962) had drawn the attention of petroleum engineers to the fact that the three solutions: for a cylinder losing heat at constant temperature, for a constant heat fl ow line source, and for a cylinder losing heat under the convection boundary, practically converge after some time. The simple solution for a constant fl uid fl ow (or heat fl ow) line source is expressed through the exponential integral , and is widely used in reservoir engineering. To use this solution for any value of circulation time, we introduce below the adjusted circulation time. For the fi rst time the concept of adjusted dimensionless production time was suggested by Ehlig-Economides and Ramey (1981). Let us assume that during time 0 ≤ t ≤ tp the wellbore is producing at a constant bottom-hole pressure . In this case the radial pressure distribution and the time dependent fl ow rate are expressed by complex integrals. By using the material balance condition the adjusted dimensionless production time can be obtained from Ehlig-Economides and Ramey (1981):
Nt q
= The actual adjusted circulation time is
, 2*
η wD
c rt
t = where ND is the dimensionless cumulative production and qLD is the dimensionless fl ow rate at t = tp and η is the hydraulic diffusivity. Thus we replaced the fl uid production at a constant bottom-hole pressure by a fl uid production at a constant fl ow rate . And exponential integral solution for the pressure distribution and the fl ow rate can be utilized. Now let us assume that during the time period 0 < t ≤ tp the temperature of the drilling fl uid at a given depth can be considered as a constant. In this case by using the heat energy balance condition the adjusted dimensionless heating time can be obtained from
Qt =* .
