The Long-Term Impact of Direct Capture Approaches to Carbon Dioxide Removal

TL;DR

This paper applies Chemical Reaction Network Theory to analyze Direct Ocean Capture (DOC) as a carbon dioxide removal strategy, modeling the DOC system with power-law kinetics in a five-species, six-complex, seven-reaction network that is weakly reversible with deficiency 0. Using independent subnetworks and CRNT criteria, it proves the existence of at least one positive steady state for all DOC classes and delineates conditions for multistationarity, absolute concentration robustness (ACR), and carbon-reduction potential in oceanic pools. The study contrasts DOC with the established Direct Air Capture (DAC) model, showing that both share key structural properties (deficiency zero, weak reversibility, etc.) and exhibit similar qualitative dynamic behaviors, while also examining an integrated DOC–DAC framework whose properties are the union of the two subsystems. The results provide a parameter-free qualitative lens to assess long-term carbon dynamics, tipping points, and robustness, with implications for evaluating and combining CDR technologies in climate mitigation strategies.

Abstract

Understanding the similarities and differences of the long term impact of different carbon dioxide removal (CDR) techniques is essential in determining the most effective and sustainable strategies to mitigate climate change. In particular, direct ocean capture (DOC) has emerged as a promising approach. In contrast to direct air capture (DAC) which separates carbon dioxide from the atmosphere, DOC performs the separation directly from seawater before storing it in geological reservoirs. In this study, we construct and analyze a kinetic system for CDR via DOC using chemical reaction network theory. Our analysis reveals the necessary conditions for the existence of positive steady states and highlights the potential for multistationarity, where the carbon cycle may admit multiple positive steady states, emphasizing the critical importance of addressing tipping points, thresholds beyond which the system could undergo irreversible changes. Furthermore, we examine conditions under which certain carbon pools exhibit absolute concentration robustness, remaining resistant to change regardless of initial conditions. We also determine the conditions for the carbon reduction capability of the model with the DOC intervention. Importantly, a comparative analysis is then presented, where we compare the DOC model with the well-established DAC model by Fortun et al., and explore an integrated DOC-DAC approach for CDR. This comparison is important given that DAC is already being implemented in large-scale projects, while DOC remains in its early stages with limited trials and is geographically constrained to oceanic vicinity. Our comparative modeling framework provides valuable insights into the long-term impacts and complementary roles of DOC, DAC, and their integration into broader CDR strategies for climate mitigation.

Figures (7)

• Figure 1: A biochemical map of the Earth's carbon cycle with direct ocean capture (DOC). The nodes represent the carbon pools. Furthermore, the solid arrows indicate carbon transfer, while the dashed arrows represent regulatory influences.
• Figure 2: Side-by-side comparison of the biochemical maps of the underlying networks of DAC and DOC systems, placed on the left and right panels, respectively. The differences between the two networks are highlighted in red.
• Figure 3: Biochemical map of the underlying networks of the integrated DAC and DOC systems.
• Figure 4: Plots of the the functions $y(\tau) = C_1 \tau^{q_2 - q_1} + C_2 \tau^{p_1 - p_2} - T$ for non-P-null systems (positive, negative, and Q-null DOC systems), and $z(\tau) = \tau^{q_2 - q_1} + C_2 C_3 \tau^{p_1 - p_2} - T$ for P-null systems, where $T$ is the total concentration from the conservation equation. These expressions result from substituting the steady state parametrizations into the conservation equation. Figure \ref{['fig:MultistationaritySimulation']} shows plots of the functions with four sets of kinetic orders $(p_1, q_1, p_2, q_2)$ correspond to various DOC types: 1. $(1.5, 1.0, 2.5, 3.0)$ corresponds to a positive DOC, 2. $(-1.0, 1.5, 1.0, -1.5)$ corresponds to a negative DOC, 3. $(1.0, 0.5, 1.0, 2.5)$ is for a P-null DOC and uses the function $z(\tau)$, and 4. $(3.0, 1.5, 1.0, 1.5)$ corresponds to a Q-null DOC. Asterisks on the plot mark the $\tau$ values where the functions cross the x-axis, indicating monostationarity (with one solution) or multistationarity (with two solutions) of the DOC systems.
• Figure 5: Time evolution of species concentrations in a P-null DOC system simulated under three different sets of initial conditions. In this system, $p_1 = p_2$. Parameters for the rate constants: $k_1 = 0.5$, $k_2 = 0.8$, $k_3 = 0.5$, $k_4 = 0.7$, $k_5 = 0.4$, $k_6 = 0.6$, and $k_7 = 0.2$, and kinetic orders: $p_1 = 1.0$, $q_1 = 1.5$, $p_2 = 1.0$, and $q_2 = 0.5$ were used. The upper, middle, and lower subplots represent the system behavior under the following initial concentrations for $[A_1,\ A_2,\ A_3,\ A_4,\ A_{17}]$: (upper) $[1.0,\ 0.8,\ 0.3,\ 0.9,\ 0.6]$, (middle) $[0.5,\ 1.0,\ 0.5,\ 1.0,\ 1.0]$, and (lower) $[0.9,\ 0.9,\ 0.9,\ 0.9,\ 0.9]$, respectively. The resulting steady-state concentrations verify that indeed the system exhibits absolute concentration robustness in all species except $A_1$.

Theorems & Definitions (14)

• Theorem 2.1
• Definition 3.1
• Definition 3.2
• Remark 3.3
• Proposition 3.4
• proof
• Theorem C.1
• Theorem C.2
• Theorem C.3
• proof