Retrieving electrical and structural carbonate formation properties from measurements on crushed rock using a multidata inversion approach
Authors: Börner Jana H , Herdegen Volker , Repke Jens-Uwe , Spitzer Klaus 
Published: March 2022

Quantification understanding, and prediction of physical rock properties rely so far predominantly on laboratory analyses of cores and plugs. Based on such data, petrophysical models are found that relate both microstructural properties and environmental conditions to geophysically accessible quantities. When considering reactive rock–fluid–gas systems, for example in geothermal energy, enhanced oil recovery or carbon dioxide sequestration, especially with carbonatic rock matrix, this approach is costly and time-consuming at best, or impossible to implement at worst. This is based on the two following reasons: First, porosity, permeability and accessible internal surface area in solid rock plugs are often so low that experimental time duration of many months or even years would be required to achieve chemical equilibrium. Secondly, plugs are single specimens of their — generally heterogeneous — original rock formation, which strongly questions the representativeness of single-plug data. To overcome these shortcomings, we present a new methodology based on the combination of systematic crushing, multimethod laboratory measurements and model-based computational evaluation with solving an inverse problem. As a first step, a large amount of undisturbed rock is intentionally crushed and divided in several particle size classes. Then, petrophysical laboratory measurements are carried out on all particle size classes. The resulting data set is finally inverted for the intended properties of the undisturbed rock. This inverse problem entails a three-level forward model, which parametrizes the undisturbed rock properties, particle characteristics and particle packings, but can also be freely adapted to other tasks by any suitable model representation. The three-level model is designed to enforce the petrophysical correlation of all properties at all levels while using a minimal set of model parameters, thus keeping the inverse problem overdetermined. For the inversion, we have developed a publicly available software tool (AnyPetro) based on a Gauss–Newton inversion scheme to minimize a damped least-squares objective function. To demonstrate and validate the proposed methodology, we present a study using five rock types — four carbonates and one sandstone as a reference. Laboratory measurements of complex electrical conductivity (from spectral induced polarization), specific surface (from nitrogen adsorption) and intraparticle porosity (from mercury intrusion) have been carried out on eight particle size classes and on plugs of each rock for comparison. Supportive and complementary analyses include, for example particle geometry, nuclear magnetic resonance, scanning electron microscopy, computer tomography, uniaxial compression strength and mineralogical composition. We show that our new methodology is highly capable of robustly recovering the complex electrical conductivity, specific surface and porosity of the undisturbed rocks from the measured data. The resulting sets of model parameters are petrophysically reasonable and verifiable. The presented methodology can further be applied to the use of drill cuttings as sample material, which is often the only available rock material from deep wells. Our findings also represent a methodological advance for laboratory experiments on reactive systems and both the interpretation and prediction of petrophysical rock properties in such systems.