The first step of the calculation was to obtain the temperature profile because temperature is the first initial value use for determination of exploration geothermal gradient mapping. There are several methods available for precisely  predicting temperature gradient along the production well. 

With a one-dimensional steady state, Carslaw and Jaeger (1959) was proposed to use the thermal conduction equation.

with the boundary conditions (z=0) are

T(0) = T0

The temperature profile can be determined by direct integration of the temperature gradient with the determination of other parameters.


The details of the parameters were used for calculating the temperature shown in Table 1.
Table 1 the initial measured of Bouillante 3 
The predicted temperature gradient of the BO-3 production well is shown in figure 3. The graph indicates the relation wall temperature from the surface down to the bottom hole of the reservoirs. The temperature range at 500 m depth is around 260 C.
Figure 3. The predicted wall temperature of the BO-3 
Figure 4 The comparison temperature profile with depth in each Bouillante