Quantifying geological uncertainty in metamorphic phase equilibria modelling;a Monte Carlo assessment and implications for tectonic interpretations

Pseudosection modelling is rapidly becoming an essential part of a petrologist＇s toolkit and often forms the basis of interpreting the tectonothermal evolution of a rock sample, outcrop, or geological region. Of the several factors that can affect the accuracy and precision of such calculated phase diagrams, ＂geological＂ uncertainty related to natural petrographic variation at the hand sample- and/or thin section-scale is rarely considered. Such uncertainty influences the sample＇s bulk composition, which is the primary control on its equilibrium phase relationships and thus the interpreted pressure-temper- ature （P-T） conditions of formation. Two case study examples--a garnet-cordierite granofels and a garnet-staurolite-kyanite schist--are used to compare the relative importance that geological uncer- tainty has on bulk compositions determined via （1） X-ray fluorescence （XRF） or （2） point counting techniques. We show that only minor mineralogical variation at the thin-section scale propagates through the phase equilibria modelling procedure and affects the absolute P-T conditions at which key assemblages are stable. Absolute displacements of equilibria can approach ＋l kbar for only a moderate degree of modal proportion uncertainty, thus being essentially similar to the magnitudes reported for analytical uncertainties in conventional thermobarometry. Bulk compositions determined from multiple thin sections of a heterogeneous garnet-staurolite-kyanite schist show a wide range in major-element oxides, owing to notable variation in mineral proportions. Pseudosections constructed for individual point count-derived bulks accurately reproduce this variability on a case-by-case basis, though averaged proportions do not correlate with those calculated at equivalent peak P-T conditions for a whole-rock XRF-derived bulk composition. The main discrepancies relate to varying proportions of matrix phases （primarily mica） relative to porphyroblasts （primarily staurolite and kyanite）, indicating that point counting preserves small-scale petrographic features that are otherwise averaged out in XRF analysis of a larger sample. Careful consideration of the size of the equilibration volume, the constituents that comprise the effective bulk composition, and the best technique to employ for its determination based on rock type and petrographic character, offer the best chance to produce trustworthy data from pseudosection analysis.

The impact of geological uncertainty on primary production from a fluvial reservoir

Deposition of fluvial sandbodies is controlled mainly by characteristics of the system, such as the rate of avulsion and aggradation of the fluvial channels and their geometry. The impact and the interaction of these parameters have not received adequate attention. In this paper, the impact of geological uncertainty resulting from the interpretation of the fluvial geometry, maximum depth of channels, and their avulsion rates on primary production is studied for fluvial reservoirs. Several meandering reservoirs were generated using a process-mimicking package by varying several con- trolling factors. Simulation results indicate that geometrical parameters of the fluvial channels impact cumulative pro- duction during primary production more significantly than their avulsion rate. The most significant factor appears to be the maximum depth of fluvial channels. The overall net-to-gross ratio is closely correlated with the cumulative oil production of the field, but cumulative production values for individual wells do not appear to be correlated with the local net-to-gross ratio calculated in the vicinity of each well. Connectedness of the sandbodies to each well, defined based on the minimum time-of-flight from each block to the well, appears to be a more reliable indicator of well-scale production.

Assessing geological uncertainty of a cement raw material deposit,southern Vietnam,based on hierarchical simulation

Resource modeling plays a crucial role in raw material quality management for cement manufacturing.Research has shown that geological uncertainty in resource modeling is inevitable and results in risk to future extraction planning and operations of the cement plant.This study aims to assess the geological uncertainty and associated risk in modeling a cement raw material deposit in southern Vietnam.For this deposit,soil,clay,laterite,and limestone are the four primary rock types,controlling the occurrence and spatial distribution of chemical grades.In this study,hierarchical simulation method was used to evaluate the uncertainty.Rock types were first simulated,and the chemical grades conditioning to the rock types were then generated.The results demonstrated the capability of the hierarchical simulation approach to incorporate the uncertainty of rock types in resource modeling and to allow evaluating the risks in providing the desired raw material for the cement plant in the form of grade-tonnage curves.

A new generic open pit mine planning process with risk assessment ability

Conventionally, mining industry relies on a deterministic view, where a unique mine plan is determined based on a single resource model. A major shortfall of this approach is the inability to assess the risk caused by the well-known geological uncertainty, i.e. the in situ grade and tonnage variability of the mineral deposit. Despite some recent attempts in developing stochastic mine planning models which have demonstrated promising results, the industry still remains sceptical about this innovative idea. With respect to unbiased linear estimation, kriging is the most popular and reliable deterministic interpolation technique for resource estimation and it appears to remain its popularity in the near future. This paper presents a new systematic framework to quantify the risk of kriging-based mining projects due to the geological uncertainties. Firstly, conditional simulation is implemented to generate a series of equally-probable orebody realisations and these realisations are then compared with the kriged resource model to analyse its geological uncertainty. Secondly, a production schedule over the life of mine is determined based on the kriged resource model. Finally, risk profiles of that production schedule, namely ore and waste tonnage production, blending grade and Net Present Value （NPV）, are constructed using the orebody realisations. The proposed model was applied on a multi-element deposit and the result demonstrates that that the kriging-based mine plan is unlikely to meet the production targets. Especially, the kriging-based mine plan overestimated the expected NPV at a magnitude of 6.70% to 7.34% （135 M$ to 151 M$）. A new multivariate conditional simulation framework was also introduced in this paper to cope with the multivariate nature of the deposit. Although an iron ore deposit is used to prove the concepts, the method can easily be adapted to other kinds of mineral deposits, including surface coal mine.

Optimal Feedback Control of Oil Reservoir Waterflooding Processes

Waterfiooding is a process where water is injected into an oil reservoir to supplement its natural pressure for increment in productivity. The reservoir properties are highly heterogeneous, its states change as production progresses which require varying injection and production settings for economic recovery. As water is injected into the reservoir, more oil is expected to be produced. There is also likelihood that water is produced in association with the oil. The worst case is when the injected water meanders through the reservoir, it bypasses pools of oil and gets produced, Therefore, any effort geared toward finding the optimal settings to maximize the value of this venture can never be over emphasized. Waterflooding can be formulated as an optimal control problem. However, traditional optimal control is an open-loop solution, hence cannot cope with various uncertainties inevitably existing in any practical systems. Reservoir models are highly uncertain. Its properties are known with some degrees of certainty near the well-bore region only. In this work, a novel data-driven approach for control variable （CV） selection was proposed and applied to reservoir waterflooding process for a feedback strategy resulting in optimal or near optimal operation. The results indicated that the feedback control method was close to optimal in the absence of uncertainty. The loss recorded in the value of performance index, net present value （NPV） was only 0.26%. Furthermore, the new strategy performs better than the open-loop optimal control solution when system/model mismatch was considered. The performance depends on the scale of the uncertainty introduced. A gain in NPV as high as 30.04% was obtained.