[Paper Review] Closed-loop geothermal systems: Modeling and predictions

K. Adhikari, M. K. Mudunuru+1 more|arXiv (Cornell University)|Jun 12, 2024

Geothermal Energy Systems and ApplicationsEnergy3 citations

TL;DR

This paper presents a reduced-order modeling (ROM) framework for closed-loop geothermal systems that accurately predicts temperature fields and outlet temperatures by incorporating jump conditions across narrow vasculature channels. The model enables fast, reliable predictions of thermal efficiency and power output, showing that comb-shaped layouts outperform U-shaped layouts at high mass flow rates, while U-shaped designs are more efficient at low flow rates.

ABSTRACT

Geothermal energy is a sustainable baseload source recognized for its ability to provide clean energy on a large scale. Advanced Geothermal Systems (AGS) -- offer promising prototypes -- employ a closed-loop vascular layout that runs deep beneath the Earth's surface. A working fluid (e.g., water or supercritical carbon dioxide (sCO2)) circulates through the vasculature, entering the subsurface at the inlet and exiting at the outlet with an elevated temperature. For designing and performing cost-benefit analysis before deploying large-scale projects and maintaining efficiency while enabling real-time monitoring during the operational phase, modeling offers cost-effective solutions; often, it is the only available option for performance assessment. A knowledge gap exists due to the lack of a fast predictive modeling framework that considers the vascular intricacies, particularly the jumps in the solution fields across the channel. Noting that the channel diameter is considerably smaller in scale compared to the surrounding geological domain, we develop a reduced-order modeling (ROM) framework for closed-loop geothermal systems. This ROM incorporates the jump conditions and provides a quick and accurate prediction of the temperature field, including the outlet temperature, which directly correlates with the power production capacity and thermal draw-down. We demonstrate the predictive capabilities of the framework by establishing the uniqueness of the solutions and reporting representative numerical solutions. The modeling framework and the predictions reported in this paper benefit the closed-loop geothermal community, enabling them to determine the system's performance and optimal capacity.

Motivation & Objective

• Address the lack of fast, accurate predictive models for closed-loop geothermal systems with complex vascular layouts.
• Overcome the computational burden of full-scale simulations by developing a reduced-order model (ROM) that captures jump conditions across narrow channels.
• Enable reliable long-term performance forecasting for design optimization and cost-benefit analysis of Advanced Geothermal Systems (AGS).
• Provide a mathematically robust framework with proven solution uniqueness and predictive capability for real-world deployment.
• Support real-time monitoring and operational decision-making through fast, accurate temperature and power output predictions.

Proposed method

• Model the vasculature as a 1D curve embedded in a 3D domain, reducing computational complexity while preserving thermal physics.
• Incorporate jump conditions across the channel interface to accurately represent heat transfer discontinuities due to high thermal gradients.
• Use a finite element method (FEM) formulation to solve the initial boundary value problem (IBVP) with weak enforcement of jump conditions.
• Leverage mathematical foundations from microvascular composite thermal regulation to ensure solution uniqueness and stability.
• Validate the model’s predictive power through numerical solutions and convergence analysis across varying domain sizes and flow rates.
• Extend the framework to analyze transient thermal responses and surface temperature impacts over time.

Experimental results

Research questions

• RQ1 How can a reduced-order model accurately predict the transient temperature field and outlet temperature in closed-loop geothermal systems with complex vascular layouts?
• RQ2 What is the optimal combination of vascular layout (U-shaped vs. comb-shaped) and mass flow rate for maximizing thermal efficiency and power output?
• RQ3 How do domain size and boundary conditions affect the accuracy and convergence of the ROM in predicting system performance?
• RQ4 To what extent does the system’s thermal drawdown impact surface temperature, and does this pose environmental risks to surrounding land?
• RQ5 Can the proposed ROM serve as a reliable predictive tool for long-term performance assessment and real-time operational monitoring?

Key findings

• The ROM framework ensures solution uniqueness and provides fast, accurate predictions of the temperature field and outlet temperature, which directly correlate with thermal efficiency and power production.
• At low mass flow rates (5 kg/s and 10 kg/s), the U-shaped layout produces higher average thermal power than the comb-shaped layout due to better heat extraction efficiency.
• At high mass flow rates (e.g., 60 kg/s), the comb-shaped layout significantly outperforms the U-shaped layout in power output due to enhanced fluid distribution and heat transfer capacity.
• The time to reach peak power output depends on the mass flow rate, with higher flow rates accelerating system response and thermal equilibrium.
• For a square domain of 100 m side length, the mean surface temperature increases by about 2 K over time, but for larger domains (≥200 m), the rise is marginal (<1 K), indicating minimal surface impact.
• The study confirms that geothermal systems do not cause significant thermal pollution to surrounding land, as surface temperature increases are negligible beyond a few kilometers from the system.