Uncertainty analysis is crucial in geothermal systems engineering, helping quantify the reliability of predictions and assessments. By understanding different types of uncertainty, engineers can make informed decisions about resource potential and project feasibility, leading to more effective risk management strategies.

The chapter covers various aspects of uncertainty, including types, sources, quantification methods, and reduction strategies. It also explores how uncertainty affects decision-making, resource assessment, and project phases, as well as the tools and regulatory implications involved in managing uncertainty in geothermal projects.

Types of uncertainty

• Uncertainty analysis plays a crucial role in geothermal systems engineering by quantifying the reliability of predictions and assessments
• Understanding different types of uncertainty helps engineers make informed decisions about resource potential and project feasibility
• Proper classification of uncertainties enables more effective risk management strategies in geothermal exploration and development

Aleatory vs epistemic uncertainty

• Aleatory uncertainty stems from inherent randomness or variability in natural systems
• Epistemic uncertainty arises from lack of knowledge or incomplete information about the geothermal system
• Aleatory uncertainty cannot be reduced through additional data collection (reservoir heterogeneity)
• Epistemic uncertainty can be decreased with more measurements or improved modeling techniques (subsurface temperature distribution)

Measurement vs modeling uncertainty

• Measurement uncertainty relates to errors in data collection and instrument limitations
• Modeling uncertainty involves simplifications and assumptions made in representing complex geothermal systems
• Measurement uncertainties include well logging tool accuracy and sampling frequency
• Modeling uncertainties encompass numerical approximations and boundary condition assumptions in reservoir simulations

Parametric vs structural uncertainty

• Parametric uncertainty focuses on uncertainties in specific input variables or parameters
• Structural uncertainty addresses the overall form and equations used in geothermal models
• Parametric uncertainties include variations in rock permeability or fluid chemistry
• Structural uncertainties involve choices between different conceptual models (single-porosity vs dual-porosity reservoirs)

Sources of uncertainty

Geological data limitations

• Sparse well data in geothermal exploration leads to interpolation uncertainties
• Limited core samples result in incomplete characterization of reservoir properties
• Geophysical survey resolution affects the accuracy of subsurface structure mapping
• Uncertainties in fault and fracture network characterization impact fluid flow predictions

Reservoir property variability

• Spatial heterogeneity in porosity and permeability creates uncertainty in flow patterns
• Temporal changes in reservoir pressure and temperature introduce dynamic uncertainties
• Variations in fluid composition and phase behavior affect production forecasts
• Uncertainties in heat transfer coefficients impact thermal breakthrough predictions

Well testing inaccuracies

• Pressure transient analysis interpretation errors lead to uncertain reservoir parameters
• Wellbore storage effects mask early-time data in pressure buildup tests
• Temperature log uncertainties affect estimates of formation temperature profiles
• Tracer test analysis uncertainties impact predictions of reservoir connectivity

Numerical model assumptions

• Grid resolution and discretization choices introduce numerical uncertainties
• Simplifications in multiphase flow physics lead to model structural uncertainties
• Boundary condition assumptions affect long-term production simulations
• Upscaling of fine-scale heterogeneities creates uncertainties in reservoir-scale models

Uncertainty quantification methods

Monte Carlo simulation

• Generates multiple realizations of uncertain parameters to assess output variability
• Allows for incorporation of complex parameter distributions and correlations
• Provides probabilistic estimates of geothermal resource potential and production forecasts
• Computationally intensive for large-scale geothermal reservoir models

Sensitivity analysis

• Identifies key parameters that have the greatest impact on model outputs
• Local sensitivity analysis examines parameter impacts around a base case
• Global sensitivity analysis explores the entire parameter space
• Helps prioritize data acquisition efforts to reduce critical uncertainties

Bayesian inference

• Updates prior parameter distributions with new data to obtain posterior distributions
• Incorporates expert knowledge and historical information into uncertainty quantification
• Allows for sequential updating of geothermal models as new measurements become available
• Provides a framework for data assimilation in reservoir characterization

Fuzzy logic approaches

• Handles uncertainties in linguistic variables and expert judgments
• Useful for integrating qualitative geological information into quantitative models
• Applies membership functions to represent degrees of uncertainty in parameter values
• Enables reasoning with imprecise or vague concepts in geothermal system characterization

Probabilistic resource assessment

P10, P50, P90 estimates

• P10 represents the optimistic scenario with a 10% chance of being exceeded
• P50 indicates the median estimate with equal chances of being higher or lower
• P90 denotes the conservative scenario with a 90% chance of being exceeded
• Used to communicate the range of possible outcomes in geothermal resource assessments

Cumulative probability curves

• Display the full range of possible outcomes for key performance indicators
• X-axis represents the parameter of interest (power output)
• Y-axis shows the probability of exceeding a given value
• Useful for visualizing the uncertainty in geothermal resource estimates

Expected monetary value

• Combines probabilistic resource estimates with economic factors
• Calculates the weighted average of potential outcomes based on their probabilities
• Helps in decision-making by quantifying the financial risk and reward of geothermal projects
• Incorporates uncertainties in both technical and economic parameters

Decision-making under uncertainty

Risk-based decision analysis

• Evaluates potential outcomes considering both probability and consequences
• Applies decision trees to map out possible scenarios and their associated uncertainties
• Incorporates risk tolerance levels of stakeholders in geothermal project planning
• Helps optimize resource allocation and investment strategies under uncertainty

Value of information concept

• Quantifies the potential benefit of acquiring additional data before making decisions
• Compares the cost of data acquisition to the expected improvement in decision outcomes
• Guides the prioritization of exploration activities in geothermal prospect evaluation
• Helps determine when to proceed with development based on existing information

Scenario planning techniques

• Develops multiple plausible future scenarios to account for key uncertainties
• Identifies robust strategies that perform well across various potential outcomes
• Incorporates both quantitative and qualitative factors in geothermal project planning
• Enhances adaptability to changing conditions in long-term geothermal field management

Uncertainty reduction strategies

Data acquisition programs

• Design optimal well placement strategies to maximize information gain
• Implement continuous monitoring systems for real-time data collection
• Conduct targeted geophysical surveys to reduce subsurface structural uncertainties
• Perform laboratory experiments on core samples to constrain rock property distributions

Reservoir surveillance methods

• Deploy distributed temperature sensing for detailed wellbore temperature profiling
• Utilize microseismic monitoring to track reservoir deformation and fluid migration
• Implement tracer testing programs to characterize reservoir connectivity
• Conduct periodic well tests to update reservoir property estimates over time

History matching techniques

• Adjust model parameters to match observed production data and pressure trends
• Apply automated history matching algorithms to efficiently explore parameter space
• Incorporate multiple objective functions to balance different types of observations
• Use ensemble-based methods to maintain geological realism in matched models

Ensemble modeling approaches

• Generate multiple reservoir model realizations to capture structural uncertainties
• Implement statistical ranking and weighting of ensemble members based on performance
• Apply model averaging techniques to combine predictions from different realizations
• Update ensemble predictions using data assimilation methods as new information becomes available

Reporting and communicating uncertainty

Confidence intervals

• Provide a range of values likely to contain the true parameter with a specified probability
• Express uncertainty in key geothermal resource parameters (reservoir temperature)
• Help stakeholders understand the reliability of estimates and potential variability
• Can be derived from statistical analysis of measurement data or model outputs

Error bars and ranges

• Graphically represent the uncertainty associated with data points or model predictions
• Show the potential variation in geothermal resource estimates on charts and graphs
• Can indicate different levels of uncertainty (1σ, 2σ) for more comprehensive understanding
• Useful for comparing uncertainties across different parameters or scenarios

Tornado diagrams

• Visualize the relative impact of different uncertain parameters on a specific output
• Rank uncertainties based on their influence on geothermal project performance metrics
• Help prioritize uncertainty reduction efforts by identifying key drivers of variability
• Useful for communicating sensitivity analysis results to decision-makers

Probability distribution plots

• Display the full range of possible values for uncertain parameters or outcomes
• Show the likelihood of different scenarios in geothermal resource assessments
• Can be used to compare uncertainties before and after data acquisition programs
• Help stakeholders understand the shape and spread of uncertainty in key variables

Uncertainty in geothermal project phases

Exploration stage uncertainties

• Limited subsurface data leads to high uncertainty in resource extent and quality
• Geophysical survey interpretation uncertainties affect conceptual model development
• Uncertainties in heat source characteristics impact long-term resource sustainability estimates
• Exploration well results may have limited representativeness for the entire reservoir

Development stage uncertainties

• Well productivity variations create uncertainty in overall field capacity
• Reservoir connectivity uncertainties affect optimal well placement strategies
• Scaling and corrosion potential uncertainties impact facility design decisions
• Uncertainties in reservoir pressure support influence reinjection strategy planning

Production stage uncertainties

• Thermal breakthrough timing uncertainties affect long-term power generation forecasts
• Reservoir pressure decline uncertainties impact sustainable production rates
• Chemical evolution of geothermal fluids introduces uncertainties in plant performance
• Induced seismicity potential creates uncertainty in regulatory and social acceptance

Software tools for uncertainty analysis

@RISK and Crystal Ball

• Add-ins for Microsoft Excel that facilitate Monte Carlo simulation and risk analysis
• Provide user-friendly interfaces for defining parameter distributions and correlations
• Generate probabilistic forecasts and sensitivity analyses for geothermal project metrics
• Useful for quick assessments and communication of uncertainties to non-technical stakeholders

PEST and PEST++

• Parameter estimation and uncertainty analysis tools for environmental models
• Support various methods including Markov Chain Monte Carlo and Null-Space Monte Carlo
• Enable automated calibration and uncertainty quantification of geothermal reservoir models
• Provide advanced features for handling highly parameterized models and complex observations

OpenCOSSAN framework

• Open-source toolbox for uncertainty quantification and reliability analysis
• Implements various sampling methods and sensitivity analysis techniques
• Supports parallel computing for efficient analysis of computationally intensive models
• Provides flexibility for integration with custom geothermal simulation codes

Uncertainty Quantification Toolbox

• MATLAB-based package for uncertainty propagation and sensitivity analysis
• Implements both local and global sensitivity analysis methods
• Supports various probability distributions and sampling techniques
• Useful for academic research and prototype development in geothermal uncertainty analysis

Regulatory and financial implications

Resource classification standards

• Incorporate uncertainty assessments in geothermal resource reporting guidelines
• Define criteria for classifying resources based on confidence levels and uncertainties
• Harmonize uncertainty reporting across different jurisdictions and regulatory frameworks
• Impact how geothermal resources are valued and reported in financial statements

Investor confidence considerations

• Transparent communication of uncertainties affects investor perception of project risks
• Probabilistic resource assessments influence investment decisions and financing terms
• Uncertainty reduction strategies may be required to secure funding for project advancement
• Regular updates on uncertainty quantification efforts demonstrate project due diligence

Insurance and risk mitigation

• Uncertainty analysis informs the development of geothermal resource insurance products
• Risk transfer mechanisms may be designed based on probabilistic performance guarantees
• Detailed uncertainty quantification can lead to more favorable insurance premiums
• Comprehensive risk assessment supports the structuring of project finance agreements