Do tracer tests enable model-independent predictions of georeservoir output? two examples from Southern Germany, involving thermal drawdown and solute co-production

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,

T_heat  =  R · T_fluid  +  D · σ² · T_fluid²  ,

with T_fluid supposed to be measurable by means of a tracer test; 
         σ is rather difficult to infer from tracer signals alone.

For ‘aquifer’-like reservoirs, the linear term prevails:

       R > (>>) 1 ,    D · σ² · T_fluid << 1

For fracture-dominated (‘petrothermal’) reservoirs, the quadratic term prevails:

       R ≈ 1 ,           D · σ² · T_fluid >> 1

Deriving T_fluid from artificial-tracer signals looks 'model-independent', but is subject to large-time extrapolation uncertainty (which 'restores' model-dependence).

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,

M_out (t)   =   (C_ini – C_resid)  [ VOL_out(t) – ∫_o^t ∫_o^t' Q(t’) Q(t’’) g(t’’) dt’’ dt’  ]

requires just knowledge of conservative-tracer fluxes within the forecasting time horizon.

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. Kreft_and_Zuber_1978], the reservoir can be treated like a 'black box' with 'response function' (Green’s kernel surrogate) g.

This approach is adequate for (conservative) solute co-production, but not for heat transport.

 

 

Tracer test results from a particular Upper-Jurassic (Malm) carbonate aquifer near Munich illustrate the issue with T_heat  as a 'function' of T_fluid. Tracer signals available to date yield T_fluid in the range of months (still subject to extrapolation uncertainty), and are compatible with both fracture-dominated and ‘aquifer’-like representations of reservoir structure; ‘compatible’ σ values span four(!) magnitude orders.

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 ‘spent fluid’ 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 (Kölbel_et_al._2020, Maier_et_al._2021) becomes indispensable.

We gratefully acknowledge long-term support from Germany’s Federal Ministry for Economic Affairs and Energy (BMWi) within applied research projects “LOGRO”, “TRENDS”, “UnLimiteD”, funded under grant nos.  0325111B, 0325515, 03EE4023E (www.geothermal-lithium.org, https://sites.google.com/site/goetracerhydro/researchprojects, https://sites.google.com/view/bmwi-0325515-trends).

 

Kölbel L, Kölbel T, Maier U, Sauter M, Schäfer T, Wiegand B (2020) Water-rock interactions in the Bruchsal geothermal system by U-Th series radionuclides. GeoThermalEnergy, 8:24

Kreft A, Zuber A (1978) On the physical meaning of the dispersion equation and its solutions for different IBC. Chem Eng Sci, 33:1471–1480

Maier U, Tatomir A, Sauter M (2021) Hydrogeochemical modeling of mineral alterations following CO₂ injection. Appl Geochem, 136:10515