Heat-capacity measurements of sandstone at high temperatures

Abstract

To evaluate geothermal energy generation systems, we must predict the amount of heat present and the rate at which it can be extracted. These two factors—amount of heat and recovery rate—in turn depend on the basic physical properties of the reservoir rocks. The amount of heat present in a reservoir depends on the heat capacity C_P of the rocks. The heat capacity of the rocks is needed to evaluate energy storage, Q = (1 − ϕ)ρC_P(T)T, where ϕ is the porosity, ρ is the density, C_P is the heat capacity, and T is the temperature. For global heat balances, the mean specific heat between two extreme temperatures T₁ and T₂, can be defined as $Q = \frac{1}{{T_{2} - T_{1} }}\int\nolimits_{{T_{1} }}^{{T_{2} }} {C_{P} \left( T \right)dT}$, where C_P(T) is the temperature-dependence of the heat capacity. For dynamic processes, the value of heat-capacity at each given temperature is needed. The area under a C_P(T) curve between any two temperature limits yields an enthalpy change as $\Delta H = \int\nolimits_{{T_{1} }}^{{T_{2} }} {C_{P} \left( T \right)dT}$. In the present work we have detailed study of the temperature dependence of the heat capacity (C_P) of sandstone over the temperature range from 308 to 763 K using a differential scanning calorimeter model of 204 F1. The combined expanded uncertainty of the heat capacity measurements at the 95% confidence level with a coverage factor of k = 2 is estimated to be 1%. A rapid increase (from 1.06 to 1.85 kJ kg⁻¹ K⁻¹) of the measured heat capacities above the classical value (3R) in the high-temperature range above 575 K was observed. This increase at high temperatures can be explained as being due to microstructural changes during heating of the sample (the microstructural effect), which was confirmed by thermal expansion coefficient measurements. The effect of microstructural changes (“thermal cracking”) on the temperature behavior of heat-capacity of sandstone was studied. Theoretically-based correlations for the heat capacity were adopted to accurately represent the measured data. The measured C_P(T) data for sandstone were used to check the accuracy, predictive capability, and applicability of various correlation models proposed in the literature. The proposed correlation equations for the heat capacity are based on the present experimental data that have been critically assessed for consistency with other measured properties and for agreement with theory whenever possible.