The importance of perceiving heterogeneity at multiple scales in a natural resource context

Abstract

To analyze, compare and draw conclusions within a resource assessment context based upon parameter values that represent a large range of variability or evaluate their interaction is far from being straight forward. One of the difficulties stems from the nonuniqueness of the process-response system. Quantitative results are interpreted according to the processes that controls inherent heterogeneity within multiple scales. To prove or reject correlations between input parameters and observed responses requires knowledge in each step of the analysis. Obtaining such knowledge has been the motivation of this thesis with a three-folded purpose: (1) To assess how resource parameters are measured, recorded, analyzed and interpreted relative to resource assessment objectives at given scales, (2) to assess parameter variability at multiple scales as part of a process-response system that may include not only the geosciences per se, but can also be enlarged to encompass the societal consequences of natural resource issues, and (3) to use the representative elementary volume (REV) and area (REA) concepts as a backcloth for interpreting the significance of variability at multiple scales. The REV/REA concept has allowed for an explicit evaluation of the behavior of the study parameter within a given volume or area. To produce a representative value, the volume or area must be large enough for the initial random behavior to become continuous. The examples aborded during this thesis cover the interaction of parameter variability and the corresponding REV/REA in a comprehensive fashion only at the reservoir scale. The other examples at the play, basin and national level have only explored the REV/REA properties in a descriptive fashion due to lack of in-depth data.

Different methods have been applied for each of the nine individual case studies presented. For the first case study, at the lithofacies level, a multivariate statistical analysis has been used to decompose heterogeneous populations (e.g grains of a fluvial deposit) into their underlying populations (e.g sand, shale and coal) that can explain both withinand cross lithological effects. A structured principal component (PCA) methodology that only use records selected from separate lithological units has been used to obtain a more precise definition of variability sources than is possible by an unstructured approach that use all the records from the well logged interval. New synthetic variables representing the combination of the original wireline log variables can by this methodology be interpreted relative to underlying geological processes. The second case study using an inverse procedure (the Eckart-Young theorem) permitted the back-calculation of new wireline log responses that now correspond to the specific underlying geological process previously identified. Results from the use of this methodology on a sandstone interval has permitted to separate global sandstone porosity values into individual porosity contributions from different underlying and independent sedimentological processes. In the subsequent third reservoir case study a process oriented numerical modeling tool (SBED) was used for upscaling lithological heterogeneity at mm-scale to lithofacies heterogeneity (cm-scale). A further upscaling to seismic (10m-scale) permitted to include multilayer sub-seismic heterogeneity in the generation of synthetic seismic traces. The resulting workflow shows that very detailed layering can be modelled and synthetic seismic traces can be generated that takes into account the inter-bedded seismic multiples which may be of great importance in thin-layered reservoirs. In the fourth reservoir study a sequential re-burial methodology to compute high-resolution re-burial porosity-depth values was used that allows for stratigraphic interwell correlation. The results show that this methodology can lead to alternative inter-well correlation scenarios based on differentially compacted sediments in the subsurface.

A different operational scale was chosen for the fifth case study where characteristic analysis (CA) was re-implemented in a GIS environment that permitted the disaggregation of a regional fault map and the construction of fault signatures within 1 × 1km2 related to the accumulation of hydrocarbons. A sixth study focusing on the regional downscaling of fault data was achieved by pre-processing the fault attributes into a cell based ternary coding expressing either favorable or unfavorable conditions or a situation where the controlling effect of an attribute is either unknown or unevaluated. By using a weighted linear combination of these ternary coded attributes, favorability was computed using a probability significance metric for selecting cells and variables to outline favorable cells where further exploration should be conducted. In addition to the CA-GIS hydrocarbon assessment examples, a seventh probabilistic assessment at the sedimentary basin scale was undertaken to show how intra-country (meso-scale) hydrocarbon volumes can be estimated. This assessment used the U. S. Geological Survey (USGS) world petroleum assessment approach to estimate the prospective oil resources of Chad within three types of sedimentary basins. Input parameters derived from published literature and oral contributions from Chad officials were used in this assessment.

An eighth case study at the same operational scale as the previous one was undertaken to investigate the resource management policy options of Chad relative to prospectivity, exploration effort and the endemic risk for conflict from post-colonial to the present time. The result shows that exploration (and later production) and severe conflicts in Chad have co-existed in a symbiotic way, where the government and the extractive industry has sought to increase their reserve base and maintain production volumes, whereas those opposing the government has tried to get a just share of the revenue derived from these activities. The revenue management plan crafted by the World Bank in relation to oil revenues intended to distribute that wealth justly but failed. A ninth case study this time on a multi-national scale (Sub-Saharan region) and addressing renewable resources was undertaken to investigate the utility of using a newly developed non-state conflict database for a large-N study of non-state conflicts versus the annual variations in the access to renewable resources, such as food with precipitation as a proxy. A standard regression analysis was carried out using the spatial proxy data for testing non-state conflicts and their relation to various theoretical hypothesis of lack of access to renewable resources and the origin of such conflicts. The result of the analysis showed no statistically significant correlations as could be expected from the REA evaluation that indicated only partly to inadequate spatial and temporal representativity of the input parameters. More efforts need to be conducted e.g. regarding the homogeneity of the sub-types of non-state conflicts and the spatial and temporal categorizations of the input data used. This thesis with operational focus ranging from lamina scale to multi-national scale, has shown that the interpretation of a given phenomenon depends on the required scale appropriate for the quantification of this phenomenon.

The thesis further attempts to show that there is an unredeemed potential for using the REV/REA concept in all studies that have a spatial or temporal operational scale for problem solving. In the non-reservoir examples, still more work has to be carried out in order to prove the utility of the REV/REA concept outside its established proven domain within reservoir characterization.