Optimizing Drillhole Spacing for Enhanced Value of Information

Drillhole Spacing Determination with Value of Information Ben Harding

Problem Motivation Geologic uncertainty is related to data availability Geologic uncertainty due to sparse data presents economic risks How much data should be collected? Is the reduction in uncertainty worth the cost? Which configuration is optimal? Go beyond geologic uncertainty alone VOI allows a decision-maker to quantify the future value data could provide before collecting it Remove subjectivity from drillhole spacing decisions 2

Value of Information Concepts VOI can help us decide what decision alternative maximizes value How does reducing uncertainty generate value in our scenario? Improved technical design Interaction of geologic and engineering scales Economic parameters Project and deposit specific What is the optimal drillhole spacing? 3

Value of Information Concepts Value generated through some form of transfer function Mine plan, stope sequence Decision framework is often two-fold in mining: First is to determine the optimal technical design to mine a volume Second is to collect more information or not to improve the design Considering the technical constraints of the problem: Evaluate many future configurations over a range of data spacings Determine if additional information improves the proposed alternative 4

Numerical Approaches to the Value of Information We need access to future information Data driven approach Resample and resimulate High resolution realizations of the true distribution provide access to future data which honour histogram and variogram Evaluate the impact of many data collection schemes May require decimating existing data or adding synthetic drillholes Need to consider multiple true models Need to consider a sufficient number of realizations 5

Numerical Approaches to the Value of Information Consider T=10 and L=100 1. Simulate set of true reference models 2. Sample true models at future data configurations 3. Re-simulate L realizations conditional to each new data set 4. Formulate objective function 5. Optimize (heuristic) an engineering design which maximizes value across all L realizations 6. Calculate value of design against reference model 7. Repeat for all future data configurations 8. Take expected VOI for all future data configurations ? ? ???(?) =1 ????(?) ? = 1, ,? ? = 1, ,? ? ?=1 6

Key Results Variogram range has a non-linear influence on value generation The scale of engineering design controls how geologic detail is captured influencing value generation The interaction between geologic and engineering scales is non-linear The cost structure influences the choice of optimal drillhole spacing Decision-maker risk preferences change the value of information 7

Key Results Numerical VOI framework can be practically applied to determine optimal drillhole spacing A point of diminishing returns is present Depends on geologic and decision scales Multiple scales of geologic heterogeneity may be present Decision alternative which maximizes net value of information is the correct decision Maximum value for least amount of data collected Consider site and project-specific cost structures 8

Implementation Details VOI is sensitive to the choice of both T and L T = 10 true models and L = 100 realizations provide stable results Too few true models could introduce bias in resampled data Too few realizations may lead to imprecise uncertainty in response Potential for computationally expensive workflow 9

Conclusions and Future Work VOI is a tool that allows a decision-maker to optimize the collection of information given site-specific constraints VOI response is a response to the interaction of geologic continuity, engineering parameters, cost structure, decision-maker risk preferences and economic factors VOI is particularly useful for advanced mining projects with an established basis to calculate value Numerical approach to VOI is conceptually clear, easily adapted to different scenarios, can be implemented in practice Future Work Consider time cost of information Consider imperfect information Consider multiple sources of information Develop approximations of value 10