AqueousCO2HydrationTrajectory propagates the reversible neutral molecular pair

\[\mathrm{CO_2(aq) + H_2O \rightleftharpoons H_2CO_3}\]

through an ordered set of piecewise-isothermal segments. Each segment uses the exact analytical AqueousCO2HydrationKinetics.advance(...) solution with the Soli and Byrne (2002) correlations, doi:10.1016/S0304-4203(02)00010-5. No kinetic parameter is fitted or tuned by the trajectory helper.

Ordered analytical propagation

For segment $i$ with duration $\Delta t_i$ and temperature $T_i$, the local rates are $k_H(T_i)$ and $k_D(T_i)$. The exact affine update is applied to the result of the preceding segment. This preserves

\[c_{\mathrm{CO_2(aq)}} + c_{\mathrm{H_2CO_3}}\]

without a numerical timestep approximation. The result reports final pair concentrations, elapsed time, segment count, temperature bounds, and the carbon-balance residual.

It also reports the dimensionless cumulative relaxation exposure

\[\Theta = \sum_i \left(k_H(T_i) + k_D(T_i)\right)\Delta t_i.\]

For repeated segments at one temperature, splitting a duration leaves the exact final state unchanged and $\Theta$ equals the ordinary pair Damköhler number. For changing temperatures, the pair equilibrium target also changes. Therefore $\exp(-\Theta)$ is not reported as one global remaining-deviation fraction, and segment order must be preserved.

Java and Python use

double[] durationsSeconds = {0.04, 0.02};
double[] temperaturesK = {288.15, 305.65};

AqueousCO2HydrationTrajectory.TrajectoryResult result =
    AqueousCO2HydrationTrajectory.advance(
        1000.0, 0.0, durationsSeconds, temperaturesK);

The two concentration inputs and outputs use mol/m3. The duration and temperature arrays must be non-null, non-empty, equal in length, and ordered consistently. A zero-duration segment is a valid qualified no-op. Invalid or non-finite input fails closed. Python users call the same Java API through JPype; no separate numerical implementation exists.

Evidence and applicability boundary

The entire trajectory must remain within the published Soli-Byrne range of 288.15–305.65 K at 0.65 molal NaCl. A single out-of-range segment rejects the calculation. The primary source did not qualify dense-phase CO2 pressure or other salinities.

This helper does not apply the van Eldik-Palmer pressure multipliers, combine datasets, select an aqueous phase, calculate gas-to-water transfer or water dropout, run bicarbonate/carbonate speciation or pH, reflash a fluid, integrate a transient pipeline, or calculate corrosion and scale. It is a bounded neutral-pair trajectory diagnostic, not Northern Lights facility calibration or a pipeline reaction source term.

See the CO2 transport reaction-kinetics guide for provenance, the electrolyte handoff, pressure-response limits, and the wider transport-coupling roadmap.