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# How to set up semi-analytical method to calculate heat transfer in t2well?

Dear TOUGH community users,

Could you please advise on configuring the semi-analytical method for computing heat transfer in t2well-eco2m? As far as I understand, the thermal conductivity has been assigned a negative value, and the AHTX value of the unit responsible for heat transfer with the surrounding rock at ELEME is non-zero. Any assistance you can provide would be greatly appreciated!

## 4replies

• kenny
• 1 mth ago
• Reported - view

The negative thermal conductivity will evoke semi-analytical method for computing heat transfer. AHTX is not required. The heat transfer interface area will be calculated using the diameter of the wellbore and the well element length.

• happy12688
• 1 mth ago
• Reported - view

Thank you for your reply! Besides the negative thermal conductivity, is there any other special setting that needs to be set? Does MOP(15) need to be set to 1? If the temperature and pressure of the surrounding rock are distributed with the geothermal gradient and hydrostatic pressure, what should be set to transfer the heat capacity?

• kenny
• 1 mth ago
• Reported - view

MOP(15) does not need to be set to 1.  T2well uses Ramey's formula (Eq.7 in Kanev et al. 1997, Geothermics Vol. 26, No. 3, pp. 329-349) for the heat loss calculation. The input of temperature and pressure of the surrounding rock is not required. The heat exchange rate is a function of temperature history at the well element.

• Reservoir Engineer
• Alfredo_b
• 1 mth ago
• Reported - view

@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

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