Development of a Modelling Framework for Core Data Integration using XRF Scanning

Abstract

Sedimentary deposits are important archives of the Earth’s history. In addition, they are of key economical and societal importance because they contain natural resources (e.g., hydrocarbons and drinking water). Hence, it is of utmost importance that we understand the mechanisms controlling the heterogeneity, morphology and spatial distribution of sedimentary deposits. Tools for characterisation of sediment bodies in the subsurface include seismic data, well-log data and core data. Since cores reflect the only continuous physical sample of the rock body under investigation, they provide the input necessary to construct detailed reservoir models. Despite their high information content, financial constraints, time constraints and the desire to keep cores intact limit the amount and resolution of quantitative data that can be retrieved from cores. In an attempt to overcome these problems, spectroscopic core scanners have been developed which facilitate fast, inexpensive, high resolution and non-destructive acquisition of quantitative core data in situ. This research is centered around one such method, which is X-ray fluorescence core scanning (XRF-CS). The first goal of this study is to build a mathematical-statistical framework for the construction of so-called integrated core descriptions using XRF-CS. We define an integrated core description as a collection of lithofacies, chemical and petrophysical records on the same, high (1 cm) resolution, and with quantifed uncertainties. The interpretation of these descriptions, possibly in combination with other data sets, is referred to as integrated integrated core analysis. Developing methods which facilitate integrated core analysis is the second goal of this study. To reach these goals, six objectives have been defined: (1) to characterise statistically the relevant data types, (2) to formalise interpretation of bulk chemical data, to improve (3) and extend (4) the existing state-of-the-art calibration framework, (5) to evaluate the performance of the new modelling frameworks for diferent sediment properties and diferent cores, and (6) to explore the added value of XRF-CS in the core analysis framework. Prior to this study, the state-of-the-art calibration method for XRF-CS was a bivariate method based on logratios (i.e., the BLC method). In an attempt to improve and extend this method, a multivariate alternative (i.e., the MLC method) is proposed which uses Partial Least Squares (PLS) (Chapt. 2). The MLC is an extension of the BLC because it facilitates prediction of "absolute" concentrations. The quality of the MLC method is compared to that of a variety of alternative models, including the BLC method. Results show that (1) the commonly used direct linear calibration (DLC) methods, which are based on the questionable assumption of a unique linear relation between intensities and concentrations and do not acknowledge the compositional nature of the calibration problem, give poor results; (2) the univariate log-ratio calibration (ULC) method, which is consistent with the com- positional nature of the calibration problem but does not fully incorporate absorption and enhancement effects on intensities nor does it permit estimation of "relative" concentrations, is markedly better, and (3) the MLC model which incorporates measurement uncertainties, accommodates absorption and enhancement effects on intensities, and exploits the covariance between and among intensities and concentrations, is the best by far. The improved predictive capabilities of the MLC method compared to the other methods are fully exploited by employing automatic sample selection based on the multivariate geometry of intensity measurements in log-ratio space. In Chapter 3, PLS is used to formalise interpretation of geochemical data (Chapter 3). The rationale behind PLS is decomposition of two data sets into unique signals, and sig- nals that are shared among the two data sets. When applied to geochemical composition and grain size, these two types of signals have geological signifcance: whereas the unique chemical signals are likely to be the response of provenance, the shared signal mainly reflects the conditions under which the sediment was deposited. Applying this methodology to three marine soft-sediment cores yields that employing "textbook" proxies for grain size, such as Al/Ti, can be risky: for the three analysed cores, Ti concentrations once showed no correlation, once positive correlation and once negative correlation with grain size. As for XRF-CS data, chemical proxies therefore require "calibration" for which the PLS-based model provides a framework. Uncertainty estimates are indispensable for statistically rigorous inference, and for quantifcation of the predictive performance of XRF-CS. In an attempt to characterise statistically spectroscopic and compositional data, Chapters 4 and 5 deal with theoretical and empirical error models associated with these data. We propose that, given their counting or similar statistical nature, all spectroscopic and compositional data are prone to errors caused by counting a fnite-sized sample (i.e. counting errors). Given that it removes the effect of scale and transforms the data to a suitable metric space, analysing these count data in terms of centered logratios is a potentially powerful approach. Error propagation shows that in this space, the error-correlation structure of multinomial (e.g., point counts) and Poisson-distributed (e.g., element intensities) data become identical (Chapt. 4). Furthermore, counting errors in clr space are generally not i.i.d.: in clr-space, the errors are correlated among the variables and the error associated with low counts is higher than that associated with high counts. To construct reduced-rank approximations to count data in clr space in a maximum likelihood manner, an algorithm is proposed, which is referred to as Optimal Scale-invariant Reduced-Rank Approximation (OSIRA). In Chapter 5 we review the structure of widely-used functions for predicting the uncertainty of chemical analyses. The structure of these functions suggests that counting is not the dominant mechanism controlling chemical uncertainty. Moreover, their structure is inconsistent with the defnition of concentrations as mass fractions. This inconsistency reflected by the asymmetric nature of these UFs (i.e., f(c) 6= f(1-c) where c ? [0,1]). Derivations using physical-spectroscopic theory yield that for strictly univariate calibration without matrix corrections, the analytical uncertainty may indeed behave in a fully asym- metrical manner. Ideally, matrix corrections or appropriate multivariate calibration compensate for this faw, making the concentration estimates indistinguishable from proper concentrations. In practical applications, however, the analytical uncertainty can behave anywhere between fully asymmetric and fully symmetric. Irrespective of its behaviour, however, statistical theory prescribes that UFs used for inference must be symmetric. A new modelling framework is developed to cope with this inconsistency and a fundamentally diferent defnition of the well-known Horwitz function (i.e., the Binomial Horwitz Function (BHF)) and the associated performance criterion ’HorRat’ is proposed. In Chapter 6 we investigate the ability to predict lithofacies (i.e. categorical data) from XRF-CSdata. Given that the associated mean prediction error turned out to be 16%, we conclude that XRF-CS can be of great value for automatic lithofacies prediction. Next, we tried to further improve the prediction of chemical composition and petrophysical properties. An extension of the modelling framework presented in Chapter 2 is proposed in Chapter 7, which is tested on two cores: one unconsolidated- and one consolidated-sediment core, both comprising a large compositional and sedimentological variability. The quality of the XRF-CS predictions is found to be signifcantly lower than conventional geochemical and petrophysical analysis. Only for the geochemical composition of relatively homogeneous sediments, the core scanner performs as good as destructive analysis. Evaluation of the results yields a set of guidelines for the expected ratio between prediction uncertainty associated with XRF-CS data and the uncertainty of conventional destructive analysis (i.e., the PPR): homogeneous soft-sediment cores (PPR chem ? 2), heterogeneous soft-sediment cores (1 ? PPR chem ? 3), heterogeneous cores of sedimentary rock (3 ? PPR chem ? 4). Chapter 8 explores the added value of integrated core analysis. We show that incorporating XRF-CS predictions in the workfow can yield diferent average facies properties which, in turn, can have important consequences for reservoir models. Secondly, by com- plementing standard petrophysical analysis with XRF-CS data, it is shown how a core may be described in terms of its reservoir quality in a fully automated manner. Thirdly, the use of high-resolution predictions of reservoir quality in combination with petrographical analyses facilitate detailed identifcation of the control on reservoir quality in a detailed manner: in addition to grain size and dolomite cement, it turns out that also calcite cement controlled reservoir quality. Furthermore, dolomite cement plays a larger role for reservoir quality than suggested by the petrographical analyses. This illustrates the importance of high resolution geochemistry-controlled extrapolation of thin-section analysis. Future improvements to calibration and processing of XRF-CS data may be achieved by establishing separate calibration models for diferent lithologies (i.e., stratifed calibration). Exploitation of the core images will also contribute to more detailed descriptions. Complementing the XRF data with other data sets such as hyperspectral images, in-situ microscopic images and minipermeametry will further support integrated core analysis. Hyperspectral imaging hopefully leads to a better understanding of the relation between chemical and mineralogical composition, which is important to make the connection with sediment-transport equations, whereas microscopic image analysis potentially facilitates direct estimation of grain size. Another subject of future research is the application of XRF-CS in a project involving numerous cores (e.g., re-evaluation of the structure of a mature gas field).