[Paper Review] Large-scale Ocean-based or Geothermal Power Plants by Thermoelectric Effects

Liping Liu|arXiv (Cornell University)|May 8, 2012

Advanced Thermoelectric Materials and Devices14 references3 citations

TL;DR

This paper proposes large-scale thermoelectric power plants using oceanic or geothermal heat sources with small temperature differences, leveraging laminated thermoelectric materials to dramatically enhance power factor. It demonstrates that such plants are economically viable and scalable, with ocean wave energy potentially powering fluid circulation at no net cost, enabling continuous, green electricity generation at tropical sites.

ABSTRACT

Heat resources of small temperature difference are easily accessible, free and unlimited on earth. Thermoelectric effects provide the technology for converting these heat resources directly into electricity. We present designs of electricity generators based on thermoelectric effects and using heat resources of small temperature difference, e.g., ocean water at different depths and geothermal sources, and conclude that large-scale power plants based on thermoelectric effects are feasible and economically competitive. The key observation is that the power factor of thermoelectric materials, unlike the figure of merit, can be improved by orders of magnitude upon laminating good conductors and good thermoelectric materials. The predicted large-scale power plants based on thermoelectric effects, if validated, will have a global economic and social impact for its scalability, and the renewability, free and unlimited supply of heat resources of small temperature difference on earth.

Motivation & Objective

• To demonstrate the feasibility of large-scale thermoelectric power plants using low-temperature-difference heat sources such as ocean thermoclines and geothermal reservoirs.
• To address the economic and scalability limitations of conventional thermoelectric systems by shifting focus from figure of merit to power factor enhancement through material engineering.
• To design a system where ocean wave energy drives fluid circulation without net energy cost, enabling continuous, maintenance-free power generation.
• To show that thermoelectric generators can achieve competitive power output and cost-effectiveness when heat sources are free and unlimited, even with low conversion efficiency.

Proposed method

• Utilizes thermoelectric (TE) materials laminated with good conductors to enhance the power factor by orders of magnitude, bypassing the efficiency limitations of traditional figure of merit optimization.
• Designs a thermoelectric generator where cold deep-seawater is pumped through TE tubes exposed to warmer surface water, creating a temperature gradient across the tube walls to generate electricity.
• Employs a segmented TE tube model with constant electric current density across segments, optimizing for maximum power per unit volume under fixed temperature difference.
• Applies the Navier-Stokes equation to model laminar flow in cylindrical tubes, deriving volumetric flow rate and viscous power dissipation as functions of pressure gradient, radius, and length.
• Uses energy and heat balance equations to model temperature variation along the tube, accounting for heat flux through the tube wall and fluid cooling, with analytical solution for outlet temperature.
• Derives total electrical power output as a function of temperature difference, material properties, tube geometry, and flow parameters, incorporating the exponential decay of temperature along the tube.

Experimental results

Research questions

• RQ1 Can large-scale thermoelectric power plants be economically viable when powered by free, unlimited heat sources like ocean thermoclines or geothermal reservoirs?
• RQ2 To what extent can the power factor of thermoelectric materials be enhanced through structural engineering, such as lamination with conductors, to offset low conversion efficiency?
• RQ3 Can ocean wave energy be harnessed to drive fluid circulation in thermoelectric generators without incurring net energy costs?
• RQ4 How does the temperature profile along a thermoelectric tube affect overall power output, and what is the optimal segment length for maximum power generation?
• RQ5 What is the theoretical power output of a large-scale ocean-based thermoelectric plant under realistic flow and material parameters?

Key findings

• The power factor of thermoelectric materials can be enhanced by orders of magnitude through lamination of good conductors and thermoelectric materials, making large-scale applications feasible despite low figure of merit.
• The total electrical power output is approximated by $ P_{ m out} = rac{P_f heta^2 l_{ m tb} L_{ m tb}}{4t_{ m tb}} rac{1 - ext{exp}(- heta)}{ heta} $, where $ heta = rac{2 heta_{ m tb}}{L_*} $, showing dependence on material properties, geometry, and temperature difference.
• The outlet temperature of the fluid is given by $ T(L_0) = T_{ m ex} + e^{- heta/2}(T^0 - T_{ m ex}) $, indicating exponential cooling along the tube, which limits maximum power output unless flow or geometry is optimized.
• Viscous power dissipation is modeled as $ P^d = rac{8 heta L Q^2}{ heta R^4} $, showing that pumping losses scale with flow rate squared and can be minimized through optimal pipe design.
• The system can be powered by ocean waves via a wave-activated valve system that maintains water height in the cold reservoir without external energy input, enabling zero-net-energy fluid circulation.
• The proposed design achieves continuous, reliable, and green electricity generation with no moving parts, low maintenance, and scalability in three dimensions, particularly suitable for tropical oceanic regions.