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5.6 Bad Urach  273


                            150
                                                                        430
                            100
                           Y
                                                                 410
                             50                  390
                                      430
                                                   350
                                                                     370                430
                                                         U3     330
                                              370
                             0
                              −400         −300        −200         −100          0           100
                         (a)                                   X

                            150

                                                        1.0
                            100
                           Y
                                                  3.0
                             50
                                                       3.0
                                                                           5.0
                                                         U3
                                             5.0                         7.0
                             0
                              −400         −300        −200         −100          0           100
                         (b)                                   X
                         Figure 5.18  Monte Carlo analysis: average [K] (a) and stan-
                         dard deviation (b) of temperature in a horizontal cross
                         section after 15 years.


                         center after 15 years of operation. The largest variances appear at places where
                         temperature gradients are highest, that is, around the cooling fronts. Maximum
                         standard deviation is large, that is, about 8. Figure 5.19 depicts temperature
                         ‘‘frequencies’’ in the observation point at different operation times (1, 2, 5, 10,
                         and 15 years). The frequency plot represents the number of calculated temperature
                         values. The frequency range is time dependent: it is narrow in the early (one year)
                         and late (15 years) stages (i.e., almost undisturbed or cooled reservoir), and it is
                         widely distributed in the middle of the reservoir ‘‘lifetime’’ (5–10 years). During
                         this time, a prediction of reservoir temperature is most uncertain. This finding
                         corresponds to Figure 5.18 that the uncertainty is largest around the propagating
                         cooling front due to the dominating advective heat transport. Figure 5.20 illustrates
                         the 20, 80, and 100% uncertainty zones of the 100 temperature profiles between the
                         boreholes after 15 years. The 20% zone covers 20% of 100 obtained temperatures
                         around the median. The 100% zone provides an envelope to all 100 realizations
                         with a maximum temperature difference of about 40 K.
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