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Table 8 Comparison of real observations and conditions with calculation results of scenarios 1–4. The critical flow velocity \({U_{critical = min.}}\) and the washout flow velocity \({U_{washout = max.}}\) were calculated by Eq. 12 considering also the parameter ranges. The ripple height and ripple length were calculated by Eqs. 4 and 5 considering also the parameter ranges. In the lower part of the table, ripple length and height predictions by the simple Eqs. 13 are indicated for comparison. Empty fields: unknown parameters, n.v. = equations not valid for the given input parameters (out of calibration)

From: Rippled scales in a geothermal facility in the Bavarian Molasse Basin: a key to understand the calcite scaling process

  Observed ripple geometries Observed conditions during production Observed conditions during maintenance Scenario 1 (production \(22\, \mu \hbox {m}\) calcite) Scenario 2 (production \(150\, \mu \hbox {m}\) flocc. calcite) Scenario 3 (maintenance \(22 \, \mu \hbox {m}\) calcite) Scenario 4 (maintenance \(92 \, \mu \hbox {m}\) coated oil)
T, \(^\circ \hbox {C}\)   139 20 139 139 20 20
\({\dot{V}}\)   110 \(5\, \pm \,2\) 110 110 \(5\, \pm \,2\) \(5\, \pm \,2\)
\(\nu\), \(10^{-7}\cdot \, {\hbox {m}}^2/\hbox {s}\)   2.19 9.81 2.19 2.19 9.81 9.81
\(\rho _p\), \({\hbox {kg/m}}^3\)   \(2710\, \pm \,0.14\) \(2710\, \pm \,0.14\) \(2710\, \pm \,0.14\) \(2710\, \pm \,0.14\) \(2710\, \pm \,0.14\) \(1073\,\pm \,28\)
\(\rho _l\), \({\hbox {kg/m}}^3\)   927   927 927 \(1020\, \pm \,10\) \(1020\, \pm \,10\)
\({\hbox {d}}_{50}\), \(\hbox {m} \cdot 10^{-6}\) 22 (Q1: 18, Q3: 28)    22 (Q1: 18, Q3: 28) 150 22 (Q1: 18, Q3: 28) 92 (Q1: 71, Q3: 117)
D*     1.35 – 2.00 11.00 0.44 – 0.73 0.38 - 1.4
\(\Theta _c\)     0.09 - 12 0.03 0.16 - 0.20 0.12 - 0.21
\({U_{critical = min.}}\), m/s   1.2 0 0.18 0.22 0.21 0.04
\({U_{washout = max.}}\), m/s   2.2 0.08 0.52 0.33 0.58 0.23
\(\eta _{max}\), \(\hbox {m} \cdot 10^{-3}\) 1.2    3.1 - 3.9 8 n.v. n.v.
\(\lambda _{max}\), \(\hbox {m} \cdot 10^{-3}\) 9.7    31 - 33 83 n.v. n.v.
\(\eta _{max-flem.}\), \(\hbox {m} \cdot 10^{-3}\) 1.2    1.2 - 1.9 10 1.2 - 1.9 4.8 - 7.9
\(\lambda _{max-colem.}\), \(\hbox {m} \cdot 10^{-3}\) 9.7    8.6 - 12.0 42 8.6 - 12.0 24 - 35
\(\lambda _{max-yalin}\), \(\hbox {m} \cdot 10^{-3}\) 9.7    18 - 28 150 18 - 28 71 - 117