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Titel |
Stochastic Estimates of the Permeability Field of the Soultz-sous-Forêts Geothermal Reservoir - Comparison of Bayesian Inversion, MC Geostatistics, and EnKF Assimilation |
VerfasserIn |
Christian Kosack, Christian Vogt, Volker Rath, Gabriele Marquart |
Konferenz |
EGU General Assembly 2010
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 12 (2010) |
Datensatznummer |
250035362
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Zusammenfassung |
The knowledge of the permeability distribution at depth is of primary concern for any
geothermal reservoir engineering. However, permeability might change over orders of
magnitude even for a single rock type and is additionally controlled by tectonic or engineered
fracturing of the rocks. During reservoir exploration pumping tests are regularly performed
where tracer marked water is pumped in one borehole and retrieved at one or a few others. At
the European Enhanced Geothermal System (EGS) test site at Soultz-sous-Forêts
three wells had been drilled in the granitic bedrock down to 4 to 5 km and were
hydraulically stimulated to enhance the hydraulic connectivity between the wells. In
July 2005, a tracer circulation test was carried out in order to estimate the changes
of the hydraulic properties. Therefore a tracer was injected into the well GPK3
for 19 hours at a rate of 0.015Â m3 s-1 and a concentration of 0.389Â mol m-3.
Tracer concentration was measured in the production wells over the following 5
months, while the produced water was re-injected into GPK3. This experiment
demonstrated a good hydraulic connection between GPK3 and one of the production
wells, GPK2, while a very low connectivity was observed in the other one, GPK4.
We tested three different approaches simulating the pumping experiment with the
numerical simulator shemat_suite in a simplified 3D model of the site in order to
study their respective potential to estimate a reliable permeability distribution for
the Soultz reservoir: A full-physics gradient-based Bayesian inversion, a massive
Monte Carlo approach with geostatistic analysis, and an Ensemble-Kalman-Filter
(EnKF) assimilation. A common feature in all models is a high permeability zone
which acts as main flow area and transports most of the tracer. It is assumed to be
associated with the fault zone cutting through the boreholes GPK2 and GPK3. With the
Bayesian Inversion we were able to estimate a parameter set consisting of porosity,
permeability, and dispersivity which produces a nearly perfect fit to the measured
tracer data. The models used for the inversion are simplified to the main geologic
elements of the geothermal reservoir and consist of only 2 to 4 regions of constant
properties. Optimal a-posteriori parameter estimates will be complemented by an
analysis of parameter dependencies and uncertainties as a by-product of the nonlinear
inversion. With both ensemble methods a cell-wise discrete spatial distribution of the
permeability can be retrieved. For MC approach we produced a large number of
system realizations with permeability distributions randomly picked from a bimodal
histogram of the enhanced zone and the surrounding. The main fracture area is
modelled by assuming a high permeability and an anisotropic correlation length. After
forward simulation of the tracer experiment, the successful realizations are selected
and further grouped to study principal features of the permeability distribution.
Similar to the MC approach, the EnKF is based on a forward propagation of an
ensemble of realizations. At successive instants in time, different kinds of data as tracer
concentration, bottom hole pressure, and permeability in various drill holes are
collected in one data vector and used to update (assimilate) the system variables to
improve the match between observation and simulation leading to a convergence
of the ensemble. We studied the performance and spatial resolution of the EnKF
procedure for a 3D test model which is based on the borehole locations and tracer
experiment of the Soultz geothermal reservoir. We used all available information to
condition the pressure field and to estimate the permeability. Already after a few
assimilation steps the ensemble average permeability shows coarse features of the
expected permeability field. However, any estimates of smaller scale permeability
variations turn out to be very sensitive to the (potentially unknown) correlation lengths. |
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