# Inversion of geothermal parameters using borehole and core data

Hartmann, Andreas (Author); Clauser, Christoph (Thesis advisor)

*Aachen / Publikationsserver der RWTH Aachen University (2008)* [Dissertation / PhD Thesis]

*Page(s): 120 S. : Ill., graph. Darst., Kt.*

Abstract

This thesis analyses the inversion of petrophysical and temperature measurements for the study of geothermal problems. The inversion of temperature data and the inversion of petrophysical measurements are first considered separately, then jointly by introducing a new algorithm for the combined inversion. Heat conduction is studied with emphasis on the transient effect of a variable ground surface temperature caused by past climate changes. Here, the focus is on uncertainties and sensitivity of the results when using insufficient data. Inversions are subdivided into two types based on the length of the computed time-series: (1) Analyses of the last ice-age (100000} years length) and (2) studies of the last 1000 years. A very good knowledge of thermal conductivity is required for both types of inversion. This implies that an inversion of ground surface temperature histories can greatly benefit from a continuous profile of thermal properties. Thermal diffusivity has a secondary effect on the inversion results but thermal conductivity directly influences the inference of ground surface temperatures. This is particularly true for boreholes in sedimentary basins where petrophysical properties can vary continuously with depth. The combined inversion requires to study the feasibility of calculating thermal conductivity from other petrophysical properties. Core data from the Southern German Molasse Basin are used for this purpose. A regression analysis of thermal conductivity, sonic velocity, bulk density, and porosity yields an accuracy of 0.2 W/(m K) for the prediction of thermal conductivity. This type of direct correlation is suitable for predicting thermal conductivity from a single petrophysical property. For the study of wireline data, a mixing law approach is used. The computation of thermal conductivity from wireline data is performed for a borehole from the Southern German Molasse Basin. Two inverse algorithms of varying complexity are used and the results are tested against core data from the same borehole. The accuracy of the prediction is 0.3 W/(m K). The uncertainty is larger than for the computation of thermal conductivity from core measurements under controlled laboratory conditions. This is due to problems of core-log matching, different spatial resolution of measurements, and changes in sample properties during the coring process. However, the large number of data points compensates this disadvantage. The analysis shows the feasibility of the inversion of wireline measurements for the computation of thermophysical data. To this end an algorithm is proposed to achieve the joint inversion. Requirements are different from conventional algorithms for the petrophysical problem because the differential equation for transient heat conduction needs to be solved, resulting in a more complex forward problem. The inverse problem is solved by a Quasi-Newton iterative scheme with a Bayesian type regularisation. To make the implementation most efficient the techniques of automatic differentiation and matrix compression are considered. In this particular application automatic differentiation does not improve efficiency. Matrix compression can drastically improve the computational speed of the algorithm for certain classes of inverse problems. A comparison of results of the new algorithm with the programs used before for the paleoclimate and petrophysical inversion shows that these problems can be treated as special cases of the new algorithm. A borehole in Southern Germany serves as a case study for the algorithm. An inversion is performed using wireline and temperature data. The algorithm is able to match both wireline and temperature data with good accuracy and in a consistent manner. The ground surface temperature history cannot be reconstructed without ambiguity because of two reasons: (1) The log terminates at 2000 m depth, too shallow for a full reconstruction of the temperatures of the last glacial; (2) In the inversion results, the transient temperature perturbation is not entirely independent of the petrophysical properties. In particular this is the case for the shale petrophysical properties that are not well constrained. The petrophysical inversion is demonstrated in a second case study on a core sample that is extensively analysed using continuous core scanning methods. The sample consists of low-porosity chemical sediments. Several petrophysical models are tested to provide the optimum match to the measured data. Wyllie's travel time average and the geometric mixing law fail to explain the measured values of sonic velocity and thermal conductivity. Therefore, a mixing law using an additional structural parameter is introduced in the inversion and the mineral thermal conductivities are considered as inversion parameters. This allows a detailed analysis yielding a value of the structural parameter and values for mineral thermal conductivities suitable for this type of sediment.

### Identifier

- URN: urn:nbn:de:hbz:82-opus-23728
- REPORT NUMBER: RWTH-CONV-112703