Do tracer tests enable model-independent predictions of georeservoir output? two examples from Southern Germany, involving thermal drawdown and solute co-production
Authors: Ghergut Horst Behrens Julia , Wiegand Bettina , Wagner Bianca , Sauter Martin 
Published: March 2022

&lt;p&gt;For geothermal reservoirs operated by production/re-injection wells, thermal lifetime is usually defined in terms of a temperature drop threshold, and estimated as a function of fluid turnover time and heat exchange surface-area-per-volume,&lt;/p&gt;&lt;p&gt;T&lt;sub&gt;heat&lt;/sub&gt;&amp;#160; =&amp;#160; R &amp;#183; T&lt;sub&gt;fluid&lt;/sub&gt;&amp;#160; +&amp;#160; D &amp;#183; &amp;#963;&lt;sup&gt;2&lt;/sup&gt; &amp;#183; T&lt;sub&gt;fluid&lt;/sub&gt;&lt;sup&gt;2&lt;/sup&gt;&amp;#160; ,&lt;/p&gt;&lt;p&gt;with T&lt;sub&gt;fluid&lt;/sub&gt; supposed to be measurable by means of a tracer test;&amp;#160;&lt;br&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; &amp;#963; is rather difficult to infer from tracer signals alone.&lt;/p&gt;&lt;p&gt;For &amp;#8216;aquifer&amp;#8217;-like reservoirs, the linear term prevails:&lt;/p&gt;&lt;p&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; R &gt; (&gt;&gt;) 1 ,&amp;#160;&amp;#160;&amp;#160; D &amp;#183; &amp;#963;&lt;sup&gt;2&lt;/sup&gt; &amp;#183; T&lt;sub&gt;fluid&lt;/sub&gt; &lt;&lt; 1&lt;/p&gt;&lt;p&gt;For fracture-dominated (&amp;#8216;petrothermal&amp;#8217;) reservoirs, the quadratic term prevails:&lt;/p&gt;&lt;p&gt;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160;&amp;#160; R &amp;#8776; 1 ,&amp;#160; &amp;#160; &amp;#160; &amp;#160; &amp;#160;&amp;#160; D &amp;#183; &amp;#963;&lt;sup&gt;2&lt;/sup&gt; &amp;#183; T&lt;sub&gt;fluid&lt;/sub&gt; &gt;&gt; 1&lt;/p&gt;&lt;p&gt;Deriving T&lt;sub&gt;fluid&lt;/sub&gt; from artificial-tracer signals looks 'model-independent', but is subject to large-time extrapolation uncertainty (which 'restores' model-dependence).&lt;/p&gt;&lt;p&gt;Unlike thermal forecasting, tracer-based prognosis of solute co-production (more precisely, of its lower-bound level, assuming conservative transport by fluid turnover only, non-'replenished' from adjacent rocks) isn't impeded by large-time extrapolation uncertainty, nor by reservoir model/parameter ambiguity, since mass output prediction as a function of time,&lt;em&gt;&lt;br&gt;&lt;/em&gt;&lt;/p&gt;&lt;p&gt;M&lt;sub&gt;out&lt;/sub&gt; (t)&amp;#160;&amp;#160; = &amp;#160; (C&lt;sub&gt;ini&lt;/sub&gt; &amp;#8211; C&lt;sub&gt;resid&lt;/sub&gt;)&amp;#160; [ VOL&lt;sub&gt;out&lt;/sub&gt;(t) &amp;#8211; &amp;#8747;&lt;sub&gt;o&lt;/sub&gt;&lt;sup&gt;t&lt;/sup&gt; &amp;#8747;&lt;sub&gt;o&lt;/sub&gt;&lt;sup&gt;t'&lt;/sup&gt; Q(t&amp;#8217;) Q(t&amp;#8217;&amp;#8217;) g(t&amp;#8217;&amp;#8217;) dt&amp;#8217;&amp;#8217; dt&amp;#8217;&amp;#160; ]&lt;/p&gt;&lt;p&gt;requires just knowledge of conservative-tracer fluxes within the forecasting time horizon.&lt;/p&gt;&lt;p&gt;Once a tracer test was conducted in accordance with the rules of the art [usually including observance of flux-type B.C. for tracer input and fluid sampling, cf. &lt;strong&gt;Kreft_and_Zuber_1978&lt;/strong&gt;], the reservoir can be treated like a 'black box' with 'response function' (Green&amp;#8217;s kernel surrogate) g.&lt;/p&gt;&lt;p&gt;This approach is adequate for (conservative) solute co-production, but not for heat transport.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;Tracer test results from a particular Upper-Jurassic (Malm) carbonate aquifer near Munich illustrate the issue with T&lt;sub&gt;heat&lt;/sub&gt;&amp;#160; as a 'function' of T&lt;sub&gt;fluid&lt;/sub&gt;. Tracer signals available to date yield T&lt;sub&gt;fluid&lt;/sub&gt; in the range of months (still subject to extrapolation uncertainty), and are compatible with both fracture-dominated and &amp;#8216;aquifer&amp;#8217;-like representations of reservoir structure; &amp;#8216;compatible&amp;#8217; &amp;#963; values span four(!) magnitude orders.&lt;/p&gt;&lt;p&gt;By contrast, tracer signals from a fractured-porous reservoir, Eastern side of the Upper Rhine rift could be used to predict 'geothermal lithium' output (and its gradual depletion in reservoir fluid turnover), irrespective of reservoir model availability/parametrization. The non-trivial challenge, however, is to foresee and quantify overall WRI effects of &amp;#8216;spent fluid&amp;#8217; re-injection, the latter being depleted of its particular micro-constituent (albeit at trace levels only), but likely acidized / 'unreliably' buffered at major-ion levels. WRI cannot be told from conservative-tracer signals; hydrogeochemical modeling (&lt;strong&gt;K&amp;#246;lbel_et_al._2020&lt;/strong&gt;, &lt;strong&gt;Maier_et_al._2021&lt;/strong&gt;) becomes indispensable.&lt;/p&gt;&lt;p&gt;We gratefully acknowledge long-term support from Germany&amp;#8217;s Federal Ministry for Economic Affairs and Energy (&lt;strong&gt;BMWi&lt;/strong&gt;) within applied research projects &amp;#8220;&lt;strong&gt;LOGRO&lt;/strong&gt;&amp;#8221;, &amp;#8220;&lt;strong&gt;TRENDS&lt;/strong&gt;&amp;#8221;, &amp;#8220;&lt;strong&gt;UnLimiteD&lt;/strong&gt;&amp;#8221;, funded under grant nos.&amp;#160; &lt;strong&gt;0325111B&lt;/strong&gt;, &lt;strong&gt;0325515&lt;/strong&gt;, &lt;strong&gt;03EE4023E&lt;/strong&gt; (www.geothermal-lithium.org, https://sites.google.com/site/goetracerhydro/researchprojects, https://sites.google.com/view/bmwi-0325515-trends).&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;&lt;p&gt;K&amp;#246;lbel L, K&amp;#246;lbel T, Maier U, Sauter M, Sch&amp;#228;fer T, Wiegand B (2020) Water-rock interactions in the Bruchsal geothermal system by U-Th series radionuclides. GeoThermalEnergy, 8:24&lt;/p&gt;&lt;p&gt;Kreft A, Zuber A (1978) On the physical meaning of the dispersion equation and its solutions for different IBC. Chem Eng Sci, 33:1471&amp;#8211;1480&lt;/p&gt;&lt;p&gt;Maier U, Tatomir A, Sauter M (2021) Hydrogeochemical modeling of mineral alterations following CO&lt;sub&gt;2&lt;/sub&gt; injection. Appl Geochem, 136:10515&lt;/p&gt;