Reducing temperature uncertainties by stochastic geothermal reservoir modelling

Abstract

S U M M A R YQuantifying and minimizing uncertainty is vital for simulating technically and economically successful geothermal reservoirs. To this end, we apply a stochastic modelling sequence, a Monte Carlo study, based on (i) creating an ensemble of possible realizations of a reservoir model, (ii) forward simulation of fluid flow and heat transport, and (iii) constraining postprocessing using observed state variables. To generate the ensemble, we use the stochastic algorithm of Sequential Gaussian Simulation and test its potential fitting rock properties, such as thermal conductivity and permeability, of a synthetic reference model and-performing a corresponding forward simulation-state variables such as temperature. The ensemble yields probability distributions of rock properties and state variables at any location inside the reservoir. In addition, we perform a constraining post-processing in order to minimize the uncertainty of the obtained distributions by conditioning the ensemble to observed state variables, in this case temperature. This constraining post-processing works particularly well on systems dominated by fluid flow. The stochastic modelling sequence is applied to a large, steady-state 3-D heat flow model of a reservoir in The Hague, Netherlands. The spatial thermal conductivity distribution is simulated stochastically based on available logging data. Errors of bottom-hole temperatures provide thresholds for the constraining technique performed afterwards. This reduce the temperature uncertainty for the proposed target location significantly from 25 to 12 K (full distribution width) in a depth of 2300 m. Assuming a Gaussian shape of the temperature distribution, the standard deviation is 1.8 K. To allow a more comprehensive approach to quantify uncertainty, we also implement the stochastic simulation of boundary conditions and demonstrate this for the basal specific heat flow in the reservoir of The Hague. As expected, this results in a larger distribution width and hence, a larger, but more realistic uncertainty estimate. However, applying the constraining post-processing the uncertainty is again reduced to the level of the post-processing without stochastic boundary simulation. Thus, constraining post-processing is a suitable tool for reducing uncertainty estimates by observed state variables.

Improving the temperature predictions of subsurface thermal models by using high-quality input data. Part 2: A case study from the Danish-German border region

“…Norden and Förster, 2006;Schütz et al, 2012a,b;Homuth et al, 2014). In that respect, our results are generally consistent with results from Vogt et al (2010) and Mottaghy et al (2011). They showed that considering the spatial distribution of TC (using a stochastic modelling approach with realizations of TC probability distributions) combined with a constraining post-processing procedure (calibration on temperatures) helps to significantly reduce temperature uncertainties (more than 50%) compared with the use of homogeneous layer values.…”

Hydraulic and hydrochemical properties of deep sedimentary reservoirs of the Upper Rhine Graben, Europe

“…Due to a mostly relatively short standstill period, the measured BHT values had to be corrected using the method of Leblanc et al (1982), Horner (1951), Lachenbruch & Brewer (1959) or Middleton (1982) dependent as well on additional information like number of temperature measurements, borehole diameter and duration of drilling fluid circulation (e.g. Hermanrud et al 1990;Vogt et al 2010).…”

Effective thermal conductivity of heterogeneous rocks from laboratory experiments and numerical modeling

“…Such experiments will provide information on possible larger scale heat flow anisotropy caused by anisotropy and heterogeneity of thermal conductivity at a scale smaller than numerical grid scale size and larger than sample size which cannot be observed by measurements on small samples. Characteristic lengths of the thermal conductivity variations inside a larger scale reservoir can be determined from correlation lengths obtained from variogram analysis of spatial data (e.g., Deutsch and Journel [1998] and applied by Vogt et al [2010]). …”