@happy12688 Wellbore heat transfer can be computed either numerically or analytically (Ramey's equation) in T2Well. Looking at T2Well-ECO2N (2011) user's guide:

*The heat exchanges between wellbore and the surrounding formation will either be calculated as*

the "normal" heat flow terms in standard TOUGH2 if the surrounding formation is explicitly

represented in the numerical grid or they will be calculated (optionally) semi-analytically if no

grid blocks of surrounding formation exist.

Thus, if the wellbore grid is connected to the "reservoir" grid, as typically happens inside the reservoir or if the "reservoir" grid is extended up to the surface, the analytical option is not used and there is no need to assign the formation temperature T(z) in eq. 31.

If the "reservoir" grid is not extended up to the surface, then the analytical heat exchange option can be used above the "reservoir" grid up to the surface. In this case the formation temperature T(z) must be supplied to be used in eq. (31). Eq. (31) is a simplified form of Ramey's equation, in which the effects of well completion are not considered.

Ramey's time function f(t) is given by eq. (32). Both Kwi (formation thermal conductivity) and alfa (formation thermal diffusivity) need to be specified in the input file using thermal conductivity, rock density and rock specific heat for the rock domains assigned to wellbore cells.

As far as the assignment of T(z), the user's guide states:

*The temperature in the surrounding formation (T∞(z) in Eq. 31) equals the initial temperature in each wellbore cell. In the case of a re-start run, the ambient temperatures are obtained from the section after "+++" of the INCON block. Note that the surrounding formation cells must not exist in the grid if the semi-analytical calculation is turned on. Otherwise, the thermal exchange between wellbore cells and the surrounding formation would be overestimated because of the heat flow would be calculated by both semi-analytical and normal Fourier Law conduction*.

The above applies to T2Well-ECO2N (2011).

Regards,

Alfredo