Characterizing the Spatial Variability of Thermodynamic Properties for Heterogeneous Soft Rock Using Random Field Theory and Copula Statistical Method

Studying the thermodynamic properties of soft rocks is critical for geothermal energy extraction, as it elucidates their temperature-dependent mechanical behaviors and heat transfer mechanisms, thereby optimizing reservoir stimulation, enhancing extraction efficiency, and ensuring long-term operational stability. Owing to the intricate geothermal settings and interconnected physicochemical processes, the thermodynamic properties exhibit pronounced spatial heterogeneity and interdependencies. Concurrently, constraints imposed by technical and economic limitations result in scarce practical field survey and experimental data on these properties, severely hampering comprehensive assessments of geothermal energy potential and exploitation feasibility. To evaluate the spatial variability of thermodynamic properties for heterogeneous soft rock using limited data, the thermal conductivity (TC), heat capacity (HC), and thermal diffusivity (TD) were measured. A new Copula statistical method is used to analyze thermodynamic properties under limited measurement data. Spatial variability in heterogeneous soft rocks is quantified using random field theory. The methodology’s reliability is confirmed through cross-validation against theoretical predictions, empirical measurements, and simulation outputs. The analysis framework of thermodynamic variability characteristics has been presented by stability point analysis and linear regression analysis processes. The variance reduction function, scale of fluctuation, autocorrelation distances, and autocorrelation structure of thermodynamic properties for heterogeneous soft rock are analyzed and discussed. This study can provide scientific data for thermal energy analysis and geothermal reservoir modification specifically applicable to soft rock formations with diagenetic and tectonic histories similar to those investigated in the Weishan Lake area.