Optimal Sequestration Regime

• Optimal sequestration regime is a defined set of operational, environmental, and economic conditions that optimize carbon storage efficiency, permanence, and cost-effectiveness in applications like geological storage and afforestation.
• It employs constrained optimization and sensitivity analysis to balance trade-offs among reservoir characteristics, system uncertainties, and market/policy frameworks.
• Practical regimes span deep saline CO₂ storage, soil carbon management, and catalyst applications, with each system using tailored cost functions and performance metrics.

An optimal sequestration regime is a parameterized set of operational, environmental, and economic conditions that maximize the efficiency, permanence, and cost-effectiveness of carbon, greenhouse gas, or other species sequestration, subject to the physics, engineering, and policy constraints of the system. The concept emerges in diverse domains—from deep geological CO₂ storage to soil/forest carbon cycling, industrial catalysis, and more—each with its own regime-defining variables and performance metrics. Explicitly, the regime is “optimal” if it delivers the minimum cost (per tonne or unit sequestered), maximum security and permanence, or the best trade-off among these, typically computed via constrained optimization over the relevant parameter space.

1. Mathematical Structure and Definition

The optimal sequestration regime is usually characterized by an explicit objective function and constraints over the regime-defining parameters. In engineered systems such as CO₂ storage, the problem reduces to

$$\min_{\Theta} C(\Theta) \;\;\text{subject to}\; M_{\text{stored}}(\Theta)\geq M_{\text{target}},\, \text{and safety, operational, and physical constraints}$$

where $\Theta$ is the vector of geologic, operational, or economic parameters, $C$ is the cost metric, and $M_{\text{stored}}$ is the total mass stored given regime $\Theta$.

In SCO₂T (Middleton et al., 2020), $\Theta$ includes reservoir depth $d$, permeability $k$, porosity $\phi$, formation thickness $h$, and geothermal gradient $G$. The cost function $C_{\text{tot}}$ and storage capacity $M_{\text{site}}$ are explicit in closed form, allowing for sensitivity and uncertainty analysis to determine the “sweet spot” for storage cost.

For natural systems (e.g., afforestation (Qubaja et al., 2022), soil carbon (Pagendam et al., 9 Nov 2024)), the objective may focus on maximum net CO₂ sink or net negative annual flux, with parameters spanning species, soil, climate, and management.

In market/policy frameworks, the optimal regime is defined by market-clearing prices and contract structures that jointly minimize the total discounted cost to achieve a warming trajectory or carbon constraint across all future periods (Raffensperger, 2020).

2. Regime Parameters Across Sequestration Domains

Geological CO₂ Storage

• Reservoir parameters: Depth ($d$), permeability ($k$), porosity ($\phi$), thickness ($h$), geothermal gradient ($G$)
• Operational parameters: Injection rate per well, number and placement of injection/extraction wells, pressure management protocols
• Economic parameters: Capital and O&M costs, brine handling, monitoring, cost of capital

Soil/Forest Carbon Sequestration

• Biophysical parameters: Plant species, root depth, soil calcium content, organic/inorganic carbon pool partitioning
• Management parameters: Tillage regime, crop rotation, cover cropping, pasture permanence, fertilization
• Climatic parameters: Annual precipitation, temperature, aridity index

Enzyme/Ion Sequestration (Molecular Scale)

• Thermodynamic parameters: Binding free energies of intermediates $(\Delta G_{ES}, \Delta G_{EP})$, available driving force $\Delta\mu$
• Kinetic/Environmental parameters: System energy/temperature, initial state distribution, path through state space as defined by steepest-entropy-ascent

Market/Policy Sequestration

• Contract parameters: Duration, performance guarantee schedule $W_{p,u,t}$, enforcement, payment schedule
• Market parameters: Dynamic prices $T_{p,u}$, cap trajectory $\mathrm{Cap}_t$, agent bids $B_{a,p,u}$, clearing mechanism

3. Characterization and Solution Methodologies

Physical and Engineering Models

• Reduced-order models (ROMs): SCO₂T employs six local ROMs, trained on full-physics FEHM simulations, for injection rate and plume modeling, enabling rapid parameter sweeps and Monte Carlo uncertainty quantification (Middleton et al., 2020).
• Analytical solutions: For constant-rate radial flow, plume radius as a function of time is given by $r(t) = \sqrt{\frac{4k\Delta p t}{\phi \mu}}$, and reservoir storage scales with $k, d, h, \phi$.
• Surrogate-model-based RL: Embed-to-Control-and-Observe (E2CO) approach enables efficient exploration and closed-loop adaptation of optimal pressure management, incorporating real-world constraints through constrained RL objectives (Chen et al., 12 Mar 2024).

Economic and Policy Frameworks

• Double-sided auction LP: Market-clearing linear program ranks and selects emissions/sequestration activities to maximize surplus while strictly enforcing future warming caps, with the principle that the optimal regime dynamically co-optimizes abatement and sequestration on both timing and scale (Raffensperger, 2020).
• Dynamic pricing: Dual variables $T_{p,u}$ and $\omega_t$ evolve according to the system’s structural and policy constraints, yielding non-monotonic “hot-front, cool-back” price trajectories.

Soil/Forest Dynamics

• Stochastic state-space Bayesian models: The CQUESST model extends the RothC framework, fitting a six-pool, monthly time-stepping stochastic state-space system by Hamiltonian Monte Carlo for all experimental treatments (Pagendam et al., 9 Nov 2024).
• Empirical/Process modeling: Measured sequestration rates in semi-arid afforestation, e.g. 550 g CO₂ m⁻² yr⁻¹ or 22 mg CO₂ yr⁻¹ L⁻¹ in inorganic carbonate, are directly upscaled to infer global sink potential given coverage fractions and site parameters (Qubaja et al., 2022).

Molecular Systems

• Steepest-entropy-ascent QTF: Evolution along entropy gradients in the system’s discrete energy state space, unique for each initial/target condition set, provides a model-free but physically rigorous route to the optimal sequestration curve—i.e. maximum uptake in minimum time at fixed system energy and temperature (McDonald et al., 2023).

4. Regime Sensitivity, Trade-offs, and Uncertainty

Extensive sensitivity analysis is central in quantifying which parameters are high-leverage for the objective. For instance, in deep saline CO₂ storage, permeability ($|e_C^k|\approx1.1$) and depth ($|e_C^d|\approx0.9$) offer the largest elasticity with respect to cost, while porosity ($|e_C^\phi| \approx 0.8$) controls second-order storage and cost through volume effects (Middleton et al., 2020).

In semi-arid afforestation, sequestration is most sensitive to coverage fraction ($f$), root-depth ($d$), and hydrogeology variability, with policy recommendation to prioritize marginal lands and species with favorable hydrologic and flammability profiles (Qubaja et al., 2022).

For molecular sequestration, the tradeoff between binding strength and sequestration/turnover—quantified precisely by the optimality condition $\Delta G_{EP}^*- \Delta G_{ES}^* = \Delta\mu$—illustrates the system’s constraint surface: too weakly bound, flux collapses; too strongly bound, enzyme is sequestered with little catalytic throughput (Deshpande et al., 2019).

Stochastic/Bayesian state-space models for soil carbon allow for full quantification of posterior parameter and flux uncertainty, directly enabling regime ranking with credible intervals (Pagendam et al., 9 Nov 2024).

5. Practical Regimes and Policy Implications

Empirically optimized regimes from state-of-the-art studies can be summarized as follows:

Domain	Optimal Regime (Empirical)	Reference
Deep Saline CO₂ Storage	$d\approx 3000\,\mathrm{m}$, $k\approx 30\,\mathrm{mD}$, $\phi\approx0.35$–$0.40$; $h\approx 60$–$100\,\mathrm{m}$; minimized $C_\text{tot}\sim\$3.8$–$4.0$$/t</td> <td>(<a href="/papers/2005.13688" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Middleton et al., 2020</a>)</td> </tr> <tr> <td>Semi-Arid Afforestation</td> <td>Aleppo pine,$$r_\text{total}\sim4$$Pg CO₂/yr @ 20<td>(<a href="/papers/2205.10641" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Qubaja et al., 2022</a>)</td> </tr> <tr> <td>Soil C Sequestration</td> <td>Permanent pasture (PP), or intensive spring tillage plus winter cover;$$A^\text{(PP)}\sim -0.78$$Mg C ha⁻¹ yr⁻¹</td> <td>(<a href="/papers/2411.06073" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Pagendam et al., 9 Nov 2024</a>)</td> </tr> <tr> <td>Geological RL Management</td> <td>Pressure managed via high early injector 2 input, sustained brine draw, bounded BHP: NPV gain</td> <td>(<a href="/papers/2403.07360" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Chen et al., 12 Mar 2024</a>)</td> </tr> <tr> <td>Enzyme Catalysis</td> <td>$$\Delta G_{EP}^* - \Delta G_{ES}^* = \Delta\mu$$; both free energies moderate, at binding threshold</td> <td>(<a href="/papers/1905.00555" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Deshpande et al., 2019</a>)</td> </tr> <tr> <td>Policy/Market</td> <td>Double-sided, dynamic auction, contract schedules co-select minimum cost and compliance for entire time horizon</td> <td>(<a href="/papers/2003.05114" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">Raffensperger, 2020</a>)</td> </tr> </tbody></table></div> <p>Emergent policy recommendations include: prioritize high-permeability, deep, porous reservoirs for <a href="https://www.emergentmind.com/topics/collaborative-causal-sensemaking-ccs" title="" rel="nofollow" data-turbo="false" class="assistant-link" x-data x-tooltip.raw="">CCS</a>; select native, fire-resistant, deep-rooted species in semi-arid afforestation; adopt land management (e.g., continuous pasture) or tillage and cover cropping with demonstrated negative net fluxes; and—most importantly for global-scale deployments—ensure market and regulatory systems assign explicit value to sequestration contracts that deliver real, durable$$\Delta T$ mitigation. 6. Theoretical Insights and Generalizations The optimal sequestration regime is, in all contexts, a global solution to a dynamic, multi-objective problem under biophysical, operational, and policy constraints. The following theoretical unifications are directly established by primary literature: Non-static optimum: Neither maximal rate nor maximal sequestration alone, but a (potentially time-dependent) profile that balances risk, permanence, and cost—e.g., “front-loaded” abatement followed by “back-loaded” sequestration (Raffensperger, 2020). Elasticity-driven prioritization: Parameters with highest elasticity in cost/sink size must be the focus of site selection and operational optimization (Middleton et al., 2020). Quantifiable risk and uncertainty: Full uncertainty propagation (Monte Carlo or Bayesian) is imperative; optimality is defined with credible intervals, not point values (Pagendam et al., 9 Nov 2024). Contractual and temporal logic: For policy regimes, contract architecture (duration, performance schedule) and dynamic payment are as important as biophysical feasibility (Raffensperger, 2020). Fundamental trade-off in sequestration-reactor kinetics: Biophysical or chemical sequestration systems saturate at a non-extreme point in free energy/affinity space (Deshpande et al., 2019). All optimal sequestration regimes ultimately reflect this rigorous alignment of physics, engineering, and economics, subject to risk, ethical, and policy imperatives. 7. Cross-Domain Implications and Limitations While the regime-defining variables are inherently context-dependent, several cross-cutting principles are validated: No universal parameter set: The optimal regime for deep CCS (high $d$, $k$, $\phi$) differs inherently from that for soil or forest C sequestration (management and species selection), or for market-policied systems (dynamic contract allocation). Permanence and leakage: Regimes providing long-term stability (e.g., inorganic pedogenic CaCO₃, inert soil organic C, sealed geological formations) are prioritized in economic and climate impact terms (Qubaja et al., 2022, Middleton et al., 2020). Scalability requires marginal land utilization: Semi-arid afforestation and improved cropland management offer scalable solutions without displacing agriculture, under appropriate species and water management (Qubaja et al., 2022, Pagendam et al., 9 Nov 2024). Regulatory frameworks must dynamically balance abatement and removal: Static carbon prices, or fixed global warming potentials, yield suboptimal cost and risk profiles—dynamic, futures-regulated auctions outperform (Raffensperger, 2020). Uncertainty is inherent: Optimal regimes must be robust to parameter uncertainty, system shocks, and non-stationary climate/market/payment landscapes (Middleton et al., 2020, Pagendam et al., 9 Nov 2024). Overall, the optimal sequestration regime is a composite solution of biophysical, engineering, and economic design, rigorously derived and empirically validated in each domain. Its construction, deployment, and adaptation are essential to the feasibility and cost-effectiveness of achieving planetary-scale climate stabilization. Sponsor Organize your preprints, BibTeX, and PDFs with Paperpile. Get 30 days free Whiteboard Generate a whiteboard explanation of this topic. Follow Topic Get notified by email when new papers are published related to Optimal Sequestration Regime. Continue Learning How do physical and economic parameters interact to determine the optimal sequestration regime? What role does sensitivity analysis play in refining sequestration strategies across different domains? How can surrogate models and analytical solutions be combined to enhance regime design? In what ways do market and policy frameworks influence the operational parameters of sequestration? 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