Binan Gu

Project: reactive transport and geothermal networks

Reactive Transport and Geothermal Networks

Nonlinear pore-scale dynamics and reduced network models for thermal-carbonaceous reactions in aquifer thermal energy storage.

The problem is practical and mathematical: carbonate aquifers can store thermal energy, but thermal-carbonaceous reactions may alter pore geometry and permeability over operational time scales. My work asks when those microscopic changes matter, and develops reduced models that connect pore-scale reaction physics to network-scale transport.

Published paper Single pore model Spectral extension

Project overview

Aquifer thermal energy storage (ATES) stores heat in underground aquifers and later recovers it for heating demand. In carbonate formations, injected thermal fluids can shift the local chemical equilibrium and drive calcite dissolution or precipitation. These reactions may open or close pores, alter permeability, and create interfracture communication through matrix layers that are often treated as impermeable in larger-scale models.

The problem is difficult because the subsurface interior is largely inaccessible. In practice, data are sparse and are usually recovered only at boreholes, drilling sites, or other boundary-accessible locations. This makes mechanistic numerical modeling especially valuable: it provides a controlled way to infer what may be happening deep underground, away from direct measurements.

The published work addresses this question at the level of a single reactive pore by coupling pressure-driven flow, heat transport, calcium transport, calcite reaction kinetics, and pore-radius evolution. The next stage asks how to propagate the same pore-scale physics through fracture networks, where each edge carries reactive transport dynamics and each vertex enforces continuity and conservation laws.

Published model

Single reactive pore in a calcite matrix

The published paper studies a single axisymmetric pore embedded in a low-permeability calcite matrix between neighboring aquifer strata. The model resolves the quantities that matter for interfracture communication: pressure-driven flow, temperature, calcium concentration, and pore radius.

The full paper derives the following coupled nonlinear PDE system.

\begin{aligned} \frac{\partial h}{\partial t} &= v_1^{(2)}\,\mathrm{Da}\,\mathcal{R}_1(\theta,c), \\[0.4em] \frac{\partial}{\partial z} \left( \frac{h^4}{16}\frac{\partial p}{\partial z} \right) &= h\,v_1^{(2)}\,\mathrm{Da}\,\mathcal{R}_1(\theta,c), \\[0.4em] \frac{\partial \theta}{\partial t} - \frac{h^2}{8}\frac{\partial p}{\partial z} \frac{\partial \theta}{\partial z} &= \mathrm{Le} \left[ \frac{1}{h^2} \frac{\partial}{\partial z} \left( h^2\frac{\partial \theta}{\partial z} \right) - \frac{2\mathrm{Bi}\left(\theta-\theta^{(M)}\right)}{h} \right], \\[0.4em] \frac{\partial c}{\partial t} - \frac{h^2}{8}\frac{\partial p}{\partial z} \frac{\partial c}{\partial z} &= \frac{1}{h^2} \frac{\partial}{\partial z} \left( h^2\frac{\partial c}{\partial z} \right) + \frac{2\mathrm{Da}\,\mathcal{R}_1(\theta,c)}{h}\,v_1^{(2)}c, \end{aligned}

where \(\mathcal R_1(\theta,c)\) is the calcite reaction rate. Positive reaction rate corresponds to dissolution and pore opening; negative reaction rate corresponds to precipitation and pore closure. Temperature shifts the local chemical equilibrium, wall heat exchange controls how quickly the pore feels the matrix forcing, and reaction kinetics control how quickly chemistry becomes geometry change.

The main conclusion is that, in the ATES regimes tested using fracture-scale forcing, reaction-driven pore evolution remains below experimentally reported permeability thresholds. This identifies a regime in which the impermeable-matrix assumption remains defensible.

Read the published paper

Problem

ATES operation changes temperature and chemistry in carbonate media, so pore-scale reactions may alter permeability.

Method

A lubrication reduction produces a one-dimensional reactive pore model coupling flow, heat, species, reaction, and radius evolution.

Result

Thermal forcing selects dissolution versus precipitation; Biot and Damköhler effects control the transient rate.

Ongoing extension

From one reactive pore to a fracture network

The spectral network model is not yet a publication or preprint, so this page records only the modeling plan and a visual placeholder. The detailed derivation can be added once the manuscript is public.

Work in progress

Spectral reduced-order network model

The goal is to turn the published single-pore equations into a fast network solver. Each edge carries near-equilibrium pore dynamics; each vertex supplies the unknown thermal, chemical, and pressure states needed to close the graph problem.

  1. Linearize the single-pore equations about chemical equilibrium.
  2. Construct a spectral decomposition for the temperature and species equations.
  3. Project the vector-valued eigenvalue problem using forward and adjoint modes.
  4. Recover the radius through time evolution, and recover pressure using a Green's-function formula written explicitly in terms of \(H\), \(\Theta\), and \(C\).
  5. Close the network formulation by using vertex conditions for the Dirichlet-type unknowns \(\Theta\), \(C\), and pressure at graph junctions, leading to a large but tractable system of Differential Algebraic Equations.

Spectral convergence

Convergence of the spectral reconstruction as the number of vector-valued modes increases.

Publication