Hybrid Energy-Powered Electrochemical Direct Ocean Capture Model

Abstract

Offshore synthetic fuel production and marine carbon dioxide removal can be enabled by direct ocean capture, which extracts carbon dioxide from the ocean that then can be used as a feedstock for fuel production or sequestered underground. To maximize carbon capture, plants require a variety of low-carbon energy sources to operate, such as variable renewable energy. However, the impacts of variable power on direct ocean capture have not yet been thoroughly investigated. To facilitate future deployments, a generalizable model for electrodialysis-based direct ocean capture plants is created to evaluate plant performance and electricity costs under intermittent power availability. This open-source Python-based model captures key aspects of the electrochemistry, ocean chemistry, post-processing, and operation scenarios under various conditions. To incorporate realistic energy supply dynamics and cost estimates, the model is coupled with the National Renewable Energy Laboratory’s H2Integrate tool, which simulates hybrid energy system performance profiles and costs. This integrated framework is designed to provide system-level insights while maintaining computational efficiency and flexibility for scenario exploration. Initial evaluations show similar results to those predicted by the industry, and demonstrate how a given plant could function with variable power in different deployment locations, such as with wind energy off the coast of Texas and with wind and wave energy off the coast of Oregon. The results suggest that electrochemical systems with greater tolerances for power variability and low minimum power requirements may offer operational advantages in variable-energy contexts. However, further research is needed to quantify these benefits and evaluate their implications across different deployment scenarios.

1. Introduction

Despite advancements in battery technology, carbon-based liquid fuels will likely remain critical energy storage media for the foreseeable future [1]. These fuels can be generated synthetically using carbon dioxide (${\mathrm{CO}}_2$) as a feedstock, which can be extracted offshore using direct ocean capture (DOC) [1,2]. The ${\mathrm{CO}}_2$ captured in this process can then be combined with hydrogen gas via catalytic hydrogenation to produce liquid methanol, which can subsequently be used as a feedstock for most petrochemical products [1]. DOC can also be coupled with geological storage to permanently sequester ${\mathrm{CO}}_2$, and has therefore also been referred to as a form of electrochemical marine carbon dioxide removal (mCDR) [2]. Amongst the variety of mCDR strategies, DOC has high potential scalability and could reach gigaton yearly scales of CDR when powered by the United States’ (U.S.-based) marine and offshore wind energy [2]. Note that, if DOC is not coupled with geological storage, but is instead used for fuel production, then the process could be used to produce gigatons of synthetic fuels and therefore offer a promising avenue for strengthening domestic energy security.

DOC produces acid and base from seawater using electrochemical technologies such as electrodialysis (ED), and uses both solutions to extract ${\mathrm{CO}}_2$ from the ocean (see Figure 1). First, seawater is brought into a container, where it is acidified, thereby converting the dissolved inorganic carbon (DIC) into ${\mathrm{CO}}_2$, which is then vacuumed from the solution. The alkaline solution is then added to the acidified seawater to neutralize it before it is released back into the ocean [2,3,4,5,6]. The resulting effluent has a lower DIC concentration and a higher pH, which enables it to absorb more atmospheric ${\mathrm{CO}}_2$ [2,6]. The vacuumed ${\mathrm{CO}}_2$ can then be converted into products such as synthetic fuels or injected underground into subseafloor sediments or mineral reservoirs to sequester it for thousands of years [2].

DOC pilot plants are currently being deployed at the scale of hundreds to thousands of tons of ${\mathrm{CO}}_2$ capture per year and companies in this space are planning on scaling to commercial plants that can capture tens of thousands to millions of tons of ${\mathrm{CO}}_2$ per year [7,8]. Since these plants will likely use low-carbon energy that can be sourced nearby to scale (such as marine, wind, and other forms of renewable energy), modeling tools are necessary to help developers better understand the energy availability in their potential deployment sites and how this can impact overall yearly ${\mathrm{CO}}_2$ capture rates and costs. Additionally, using models of DOC plants powered with renewable energy sources can highlight how the plants can be adapted to take advantage of variable power profiles. For instance, in DOC operations, the energy requirements for the electrochemical systems are generally higher than those of the pumps, which, according to the literature, have corresponding median energy requirements of 1540 kWh/t${\mathrm{CO}}_2$ and 567 kWh/t${\mathrm{CO}}_2$, respectively [1,2,5,6]. This means that, when power is readily available, DOC plants can prioritize generating the acidic and basic solutions from seawater and storing them for later use in large tanks. That way, ${\mathrm{CO}}_2$ capture can continue when there is only enough energy for the pumps to be used to mix seawater with the chemical solutions. This strategy could therefore increase the overall yearly rate of DOC, though larger tanks could increase capital costs.

This model focuses on DOC plants that rely on ED for their electrochemical system. ED has already been shown to successfully enable desalination under intermittent power availability from renewable energy sources and can do the same for DOC [9,10,11]. While multiple studies on electrochemical mCDR have suggested that renewable energy could power such systems, few have examined the impact of the time-dependent variability of these energy sources on electrochemical mCDR operation [1,2,12]. Moreover, to the authors’ knowledge, none of these studies has investigated the impacts of hybrid renewable energy on these operations nor made their corresponding models open-source for developers in both electrochemical mCDR and renewable energy to use freely. The goal of this work is to develop an open-source model of ED-based DOC plants that can be powered with variable renewable energy. This model is then run using power profiles from hybrid energy systems simulated in the H2Integrate tool (H2I) [13], created by the National Renewable Energy Laboratory (NREL), to simulate how a DOC plant could operate with realistic power profiles in a particular deployment location.

2. Materials and Methods

The overall DOC model accounts for (1) pumping large volumes of seawater, (2) using a fraction of that volume to electrochemically produce acidic and basic solutions via the ED system, (3) adding the acid solution into the remaining seawater to acidify it, (4) vacuuming out the extracted ${\mathrm{CO}}_2$, (5) post-processing the gas to enable it to be purified and stored for future sequestration or conversion into commercial products, (6) adding the basic solution back to the acidified seawater to neutralize it, and (7) storing some of the produced acid and base for later use in storage tanks. See Figure 2 for a diagram of the full system. Note that the time-step for the model, $t_{step}$, is set to one hour and the example DOC plant modeled in this study is sized to capture about 1 Mt${\mathrm{CO}}_2$/yr under constant power, which is about the potential size of a large commercial-scale DOC plant, though the model can be used to model smaller or larger plants [7,8].

The hourly output of the Python-based model depends on the input energy and the volume of acid and base in the chemical storage tanks at a given time-step. Based on these values, the model determines (1) what operational scenario to use (for instance, determining if either conducting DOC or filling the tanks needs to be prioritized) and (2) the outputs of the plant (tons of ${\mathrm{CO}}_2$ captured, volumes of acid and base stored in or taken from the tanks, excess energy remaining, and the chemical characteristics of the effluent seawater). The outputs vary depending on the energy available since ED systems can flexibly operate with variable power, producing more acid and base when energy is plentiful and less when less power is available. Such systems have been described in the literature for ED-based desalination [9,10,11]. This is approximated in the model by splitting the ED system into discrete “units” with constant power and flow rate needs where the number of ED units represents a given ED system’s ability to handle direct power inputs (see Figure 3). Note that these “units” are a simplified representation of how flexible ED systems can operate and future comparisons with operational DOC plants can further validate this approximation (see Section 2.6 for more details).

These discrete units enable the overall DOC system to handle variable power since the units can turn on and off depending on how much power is available. For instance, if there is only enough power available to power half of these units, then half as much seawater will be pumped into them and half as much acid and base will be generated. As a result, the number, flow rate, and energy need of the ED units determine the amount of seawater that is pumped, the ${\mathrm{CO}}_2$ that is captured, and therefore the power needed to pump the seawater and to vacuum and post-process the ${\mathrm{CO}}_2$. Therefore, the number and power needs of the individual ED units set discrete ranges of output values which are determined by the model prior to the time-dependent analysis for each operation scenario. Once the time-dependent analysis begins, the model simply looks up the output values that can be produced at each time-step given the power available and the model’s operation scenario.

The model employs a set of four heuristic operation scenarios to explore how acid and base from the ED system are allocated for DOC. In scenario 1, all of the acid and base produced by the ED system is used for DOC. Scenario 2 assumes partial use for DOC, with the remainder stored in product tanks. Scenario 3 represents a power-limited case, where the ED system cannot operate and stored acid and base are used instead. Scenario 4 considers the reverse: sufficient power is available for ED operation, but not enough to pump seawater for DOC, resulting in tank storage. These scenarios offer a structured approach to capture key system-level behaviors under variable power conditions. Additional details are provided in Section 2.5.

This model uses information from the literature about DOC and its associated processes and its development has been aided by advisement from a company in the industry. As mentioned in Section 1, the DOC model is operated in conjunction with the H2I tool to examine its performance with realistic hybrid renewable energy systems.

This section describes the key components of the DOC model, including the electrochemical processes, ocean chemistry, pump and vacuum systems, ${\mathrm{CO}}_2$ purification and compression, and the defined operation scenarios (see Section 2.1, Section 2.2, Section 2.3, Section 2.4 and Section 2.5). It also describes the core modeling assumptions (Section 2.6) and the integration of the hybrid energy system model used to simulate variable renewable power supply (Section 2.7).

The parameters used for the example DOC plant in this study are generic and not based on any specific systems known to the authors, see

Table 1. Input parameters of example DOC model.

Parameter	Value	Parameter	Value
$N_{ED,max}$	10	$\Delta p_{ED,min}$	0.1 bar
$N_{ED,min}$	1	$\Delta p_{ED,max}$	0.5 bar
$Q_{ED,1}$	0.6 m3/s	$\Delta p_{ED4,min}$	0.1 bar
$P_{ED,1}$	24 MW	$\Delta p_{ED4,max}$	0.5 bar
${ϵ}_{HCl}$	0.05 Wh/molHCl	$\Delta p_{a,min}$	0.1 bar
${ϵ}_{NaOH}$	0.05 Wh/molNaOH	$\Delta p_{a,max}$	0.5 bar
${\gamma }_{sw}$	0.01	$\Delta p_{b,min}$	0.1 bar
$p{H}_i$	8.1	$\Delta p_{b,max}$	0.5 bar
$DI{C}_i$	2.2 mM	${\gamma }_{ext}$	0.9
T	25 °C	${\gamma }_{vac}$	0.6
S	35 ppt	$\Delta p_{vac,min}$	0.4 bar
${\gamma }_{pump}$	0.9	$\Delta p_{vac,max}$	0.8 bar
$\Delta p_{o,min}$	0.1 bar	$y_{pur}$	0.2
$\Delta p_{o,max}$	0.5 bar

for the inputs used in the example DOC model. While the model has been applied to a real-world system in collaboration with an industry partner, the results from that analysis cannot be shared publicly due to the proprietary nature of the data. As such, the validation presented in this work is limited to the comparative error metrics disclosed in Section 2.8, and no further public validation was possible. Simulations of the example DOC plant are detailed in Section 2.9, including evaluation of the impacts of seawater conditions, variable power, differing levels of ED discretization, and renewable energy at potential deployment locations on plant performance.

2.1. Electrochemical Model

The concentrations of acid and base generated by a single ED unit (in mol/m³), $C_{a,1}$ and $C_{b,1}$, are determined by the flow rate of seawater into the unit (in m³/s), $Q_{ED,1}$, the initial concentrations of acid and base in the seawater (in mol/m³), $C_{HCl,In}$ and $C_{NaOH,In}$, the power required by each unit (in watts), $P_{ED,1}$, and the ED unit’s efficiency in producing acid and base (in watt-hours per mole of acid and base, respectively), ${ϵ}_{HCl}$ and ${ϵ}_{NaOH}$ [14].

$$C_{a,1}={\displaystyle \frac{1}{Q_{a,1}}}({\displaystyle \frac{P_{ED,1}}{3600{ϵ}_{HCl}}}-Q_{ED,1}{C}_{HCl,In})$$

(1)

$$C_{b,1}={\displaystyle \frac{1}{Q_{b,1}}}({\displaystyle \frac{P_{ED,1}}{3600{ϵ}_{NaOH}}}-Q_{ED,1}{C}_{NaOH,In})$$

(2)

Note that the flow rates of acid and base are equivalent and depend on the flow rate of seawater into the ED unit.

$$Q_{a,1}=Q_{b,1}={\displaystyle \frac{Q_{ED,1}}{2}}$$

(3)

Meanwhile, the initial concentrations of acid and base (in mol/m³), $C_{HCl,In}$ and $C_{NaOH,In}$, are determined by the pH of seawater, $p{H}_{sw}$, which is commonly around 8.1, and the water dissociation constant of seawater, $K_w$, which is ${10}^{-13.22}$ at 25 °C and 35 g/kg or parts per thousand (ppt) salinity (see Appendix A.1 for more details on how this constant’s value varies with seawater temperature and salinity [6]).

$$C_{HCl,In}=1000\ast {10}^{-p{H}_{sw}}$$

(4)

$$C_{NaOH,In}=1000\ast {\displaystyle \frac{K_w}{{10}^{-p{H}_{sw}}}}$$

(5)

Although the overall power need, $P_{ED}$, and the flow rates of seawater, $Q_{ED}$, acid, $Q_a$, and base, $Q_b$, for the ED system vary linearly with the number of active ED units, $N_x$, the concentration of acid and base generated remains the same.

$$P_{ED}=N_x{P}_{ED,1}$$

(6)

$$Q_{ED}=N_x{Q}_{ED,1}$$

(7)

$$Q_a=N_x{Q}_{a,1}$$

(8)

$$Q_b=N_x{Q}_{b,1}$$

(9)

As mentioned previously, the overall intake of seawater for the DOC system is determined by the number of active ED units. This is because the ED system is set to consistently take a fraction, ${\gamma }_{sw}$, of the intake flow rate, $Q_o$. For instance, if 1% of the intake flow is required by the ED system, then the intake has 100x the flow rate required by the electrochemical system [8]. Therefore,

$$Q_o={\displaystyle \frac{Q_{ED}}{{\gamma }_{sw}}}.$$

(10)

The parameters or inputs set for the electrochemical model in this case are shown in Table 1, which shows all of the inputs used in the example DOC model. Note that $N_{ED,max}$ and $N_{ED,min}$ refer to the maximum and minimum number of ED units that can be used by the electrochemical system and act as the range of values for $N_x$.

2.2. Ocean Chemistry Model

In this model, the chemistry of the seawater being used by the DOC system is treated as that of a carbonate buffer solution with the same pH and DIC concentration, $\left[DIC\right]$, as seawater. Note that the DIC is the sum of the dissolved ${\mathrm{CO}}_2$, $\left[C{O}_2\right]$, bicarbonate, $\left[HC{O}_3^{-}\right]$, and carbonate concentrations, $\left[C{O}_3^{2-}\right]$.

$$\left[DIC\right]=\left[C{O}_2\right]+\left[HC{O}_3^{-}\right]+\left[C{O}_3^{2-}\right]$$

(11)

These carbonate species can be related to one another using the concentration of acid $\left[H^{+}\right]$ and stoichiometric equilibrium constants, where $K_1$ is ${10}^{-5.86}$ and $K_2$ is ${10}^{-8.92}$ at 25 °C and 35 ppt salinity (see Appendix A.1 for more details on these values at different temperatures and salinities) [6].

$$K_1={\displaystyle \frac{\left[HC{O}_3^{-}\right]\left[H^{+}\right]}{\left[C{O}_2\right]}},$$

(12)

$$K_2={\displaystyle \frac{\left[C{O}_3^{2-}\right]\left[H^{+}\right]}{\left[HC{O}_3^{-}\right]}}.$$

(13)

Meanwhile, the total alkalinity, $\left[TA\right]$, of seawater consists not only of the concentrations of the alkaline carbonate species but also the alkalinity of the water ($\left[O{H}^{-}\right]-\left[H^{+}\right]$) [6]:

$$\left[TA\right]=\left[HC{O}_3^{-}\right]+2\left[C{O}_3^{2-}\right]+\left[O{H}^{-}\right]-\left[H^{+}\right]$$

(14)

The ocean chemistry model primarily relies on the inputs of average seawater pH, DIC, temperature, and salinity, which will vary depending on the location of interest for the simulated DOC plant. These parameters are listed in Table 1 and details on the assumptions of this model are included in Section 2.6.

2.2.1. Acid Addition and ${\mathrm{CO}}_2$ Extraction

As discussed previously, the acid addition to seawater is what enables the extraction of ${\mathrm{CO}}_2$. The equations needed to model the acid addition differ depending on if the moles of the acid are greater than the moles of total alkalinity, where the mole rate of acid added (in mol/s), $n_a$, is as follows:

$$n_a=C_a{Q}_a.$$

(15)

Meanwhile, the mole rate of the total alkalinity from the seawater initially (in mol/s), $n_{TA,i}$, is dependent on the flow rate of the seawater remaining after a portion of the flow is used for the ED system, $Q_i$:

$$n_{TA,i}={\left[TA\right]}_i{Q}_i.$$

(16)

If the mole rate of the acid is greater than or equal to the mole rate of total alkalinity, then the second equivalence point is reached, which results in a pH of about 4.3 at 25 °C and 35 ppt salinity, and a corresponding acid concentration of ${\left[H^{+}\right]}_{eqiv}$[6]. After this point, the solution can no longer buffer any additional acid and the remaining moles of acid left over after consuming the moles of total alkalinity rapidly increase the acidity of the solution. Therefore, the moles of acid can be split among the amount needed to consume the moles of total alkalinity and the moles remaining afterwards, where $Q_{a,x}$ is the flow rate of acid needed to consume the moles of total alkalinity, $Q_{a,y}$ is the flow rate of the remaining acid, and ${\left[H^{+}\right]}_{a,f}$ is the concentration of acid in the seawater after the acid addition:

$$Q_a=Q_{a,x}+Q_{a,y}$$

(17)

$$Q_{a,x}={\displaystyle \frac{n_{TA,i}}{C_a}}$$

(18)

$${\left[H^{+}\right]}_{a,f}={\displaystyle \frac{{\left[H^{+}\right]}_{eqiv}(Q_i+Q_{a,x})+C_a{Q}_{a,y}}{Q_a+Q_i}}.$$

(19)

However, if there are not enough moles of acid to consume all of the moles of total alkalinity, then the definition for total alkalinity, Equation (14), can be rewritten in terms of the initial concentration of DIC, ${\left[DIC\right]}_i$, the final concentration of acid in the solution, ${\left[H^{+}\right]}_{a,f}$, and the stoichiometric and dissociation constants by incorporating Equations (11)–(13). For the remaining mole rate and concentration of total alkalinity after the acid addition, $n_{TA,af}$ and ${\left[TA\right]}_{af}$ are as follows:

$$n_{TA,af}=n_{TA,i}-n_a,$$

(20)

$${\left[TA\right]}_{af}={\displaystyle \frac{n_{TA,af}}{Q_i+Q_a}},$$

(21)

$${\left[TA\right]}_{af}={\displaystyle \frac{{\left[DIC\right]}_i}{1+\frac{{\left[H^{+}\right]}_{a,f}}{K_1}+\frac{K_2}{{\left[H^{+}\right]}_{a,f}}}}+{\displaystyle \frac{2{\left[DIC\right]}_i}{1+\frac{{\left[H^{+}\right]}_{a,f}}{K_2}+\frac{{\left({\left[H^{+}\right]}_{a,f}\right)}^2}{K_1{K}_2}}}+{\displaystyle \frac{K_w}{{\left[H^{+}\right]}_{a,f}}}-{\left[H^{+}\right]}_{a,f}.$$

(22)

Note that finding the acid concentration after acid addition ${\left[H^{+}\right]}_{a,f}$ in this case requires an iterative method between Equations (21) and (22), where, for a given pH range, the model will compare the ${\left[TA\right]}_{af}$ values from Equation (22) with that of (21) until it finds the acid concentration with the lowest difference between the two values. The pH range in this case is set to be between the pH at the second equivalence point and that of pre-acidified seawater with a pH step size of 0.01.

The amount of ${\mathrm{CO}}_2$ dissolved in seawater after the acid addition, ${\left[C{O}_2\right]}_{a,f}$, is then determined given the new acid concentration and by combining Equations (11)–(13):

$${\left[C{O}_2\right]}_{a,f}={\displaystyle \frac{{\left[DIC\right]}_i}{1+\frac{K_1}{{\left[H^{+}\right]}_{a,f}}+\frac{K_1{K}_2}{{\left({\left[H^{+}\right]}_{a,f}\right)}^2}}}.$$

(23)

Therefore, the mole rate of ${\mathrm{CO}}_2$ dissolved in seawater, $n_{CO2,sw}$, within the flow of the acidified seawater, $Q_{asw}$, is as follows:

$$n_{CO2,sw}={\left[C{O}_2\right]}_{a,f}(Q_a+Q_i)={\left[C{O}_2\right]}_{a,f}{Q}_{asw}.$$

(24)

The mole rate of ${\mathrm{CO}}_2$ extracted from the seawater, $n_{CO2,Cap}$, is then determined by a user input for extraction efficiency, ${\gamma }_{ext}$, which, in this case, is assumed to be about 90% and is typical for the industry [15]:

$$n_{CO2,Cap}=n_{CO2,sw}{\gamma }_{ext}.$$

(25)

Following unit conversions and applying the molar mass of ${\mathrm{CO}}_2$ and the length of the time-step for the model, which is set to one hour, the tons of ${\mathrm{CO}}_2$ captured per hour can be determined as $m_{CO2,Cap}$.

2.2.2. Base Addition and Seawater Neutralization

Since dissolved ${\mathrm{CO}}_2$ acts as a weak acid, extracting it reduces the acidity and concentration of DIC in the seawater. The acid concentration post ${\mathrm{CO}}_2$ extraction and prior to base addition, ${\left[H^{+}\right]}_{b,i}$, can be found by determining the remaining concentration of dissolved ${\mathrm{CO}}_2$, ${\left[C{O}_2\right]}_{b,i}$, and the remaining concentration of DIC, ${\left[DIC\right]}_f$:

$${\left[C{O}_2\right]}_{b,i}=(1-{\gamma }_{ext}){\left[C{O}_2\right]}_{a,f},$$

(26)

$${\left[DIC\right]}_f={\left[DIC\right]}_i-{\gamma }_{ext}{\left[C{O}_2\right]}_{a,f},$$

(27)

$${\left[C{O}_2\right]}_{b,i}={\displaystyle \frac{{\left[DIC\right]}_f}{1+\frac{K_1}{{\left[H^{+}\right]}_{b,i}}+\frac{K_1{K}_2}{{\left({\left[H^{+}\right]}_{b,i}\right)}^2}}}.$$

(28)

Similar to the methodology used to determine ${\left[H^{+}\right]}_{a,f}$ in Section 2.2.1, an iterative method is used to determine ${\left[H^{+}\right]}_{b,i}$. In this case, for a given pH range, the resulting values for ${\left[C{O}_2\right]}_{b,i}$ determined by Equation (28) are compared with that determined by Equation (26). The value with the lowest difference is then used to find ${\left[H^{+}\right]}_{b,i}$. The pH range is from the pH of ${\left[H^{+}\right]}_{a,f}$ to the initial pH of seawater, 8.1, and has a pH step size of 0.01. The resulting total alkalinity, ${\left[TA\right]}_{bi}$, at this pH and DIC concentration is determined using a similar equation to Equation (22):

$${\left[TA\right]}_{bi}={\displaystyle \frac{{\left[DIC\right]}_f}{1+\frac{{\left[H^{+}\right]}_{b,i}}{K_1}+\frac{K_2}{{\left[H^{+}\right]}_{b,i}}}}+{\displaystyle \frac{2{\left[DIC\right]}_f}{1+\frac{{\left[H^{+}\right]}_{b,i}}{K_2}+\frac{{\left({\left[H^{+}\right]}_{b,i}\right)}^2}{K_1{K}_2}}}+{\displaystyle \frac{K_w}{{\left[H^{+}\right]}_{b,i}}}-{\left[H^{+}\right]}_{b,i}.$$

(29)

Once the alkaline solution produced by the ED system is added to the acidified seawater, the total alkalinity, ${\left[TA\right]}_{bf}$, increases by the number of moles of base added:

$${\left[TA\right]}_{bf}={\displaystyle \frac{{\left[TA\right]}_{bi}{Q}_{asw}+C_b{Q}_b}{Q_{asw}+Q_b}}$$

(30)

The resulting acidity after the base addition, ${\left[H^{+}\right]}_{b,f}$, can then be determined via applying the iterative method used to compare Equations (21) and (22) to Equations (30) and (31), with pH bounds from the pH of ${\left[H^{+}\right]}_{b,i}$ to about 13.22, or the logarithmic form of the water dissociation constant, $K_w$, and a step size of 0.01.

$${\left[TA\right]}_{bf}={\displaystyle \frac{{\left[DIC\right]}_f}{1+\frac{{\left[H^{+}\right]}_{b,f}}{K_1}+\frac{K_2}{{\left[H^{+}\right]}_{b,f}}}}+{\displaystyle \frac{2{\left[DIC\right]}_f}{1+\frac{{\left[H^{+}\right]}_{b,f}}{K_2}+\frac{{\left({\left[H^{+}\right]}_{b,f}\right)}^2}{K_1{K}_2}}}+{\displaystyle \frac{K_w}{{\left[H^{+}\right]}_{b,f}}}-{\left[H^{+}\right]}_{b,f}.$$

(31)

The resulting pH after the DOC process, $p{H}_{bf}$, can then be determined from this acid concentration. As mentioned previously, the pH of seawater increases overall due to the extraction of the weakly acidic dissolved ${\mathrm{CO}}_2$. However, once this neutralized seawater is released back into the ocean, the increase in alkalinity and reduction in DIC will likely drive more atmospheric ${\mathrm{CO}}_2$ to enter the water and replace what was extracted, enabling the effluent to reach equilibrium with its surrounding environment [4,5]. Despite this equalization, overly alkaline or very low DIC concentrations could still be potentially harmful to the local environment, especially to autotrophic organisms, and effluent water from DOC systems needs to abide by the limits set by existing permits for wastewater treatment or desalination plants, which is why the values of ${\left[DIC\right]}_f$ and $p{H}_{bf}$ are recorded by the model [2,3,15]. Note that additional research is necessary to fully understand the environmental impacts of this effluent.

2.3. Pumps and Vacuum

The pumps and vacuum modeled are displayed in Figure 4 and all use a similar power equation, Equation (32), where the power P of each pump and vacuum depends on flow rate Q, pressure drop $\Delta p$, and efficiency $\gamma$:

$$P={\displaystyle \frac{Q\Delta p}{\gamma }}$$

(32)

Section 2.3.1 details how to determine the pressure drop from the seawater flow rates, which can then be used to find the power requirements for the liquid pumps, while Section 2.3.2 describes how to determine the gas vacuum power requirement from the flow rate and pressure drop based on the mole rate of captured ${\mathrm{CO}}_2$. Assumptions for modeling the pumps and vacuum are included in Section 2.6.

2.3.1. Liquid Pump Equations

For this model, it is assumed that the pressure drops of the pumps vary linearly with flow rate, as shown by the Hagen–Poiseuille equation for pressure drops in a pipe (Equation (33)), where $\mu$ is the dynamic viscosity of the fluid, L is the length of the pipe, and r is the pipe radius, all of which are assumed to be constant and not dependent on the pressure drop or flow rate. For simplicity, it is assumed that the fluid flow through the system is laminar so that the pressure drop is as follows:

$$\Delta p={\displaystyle \frac{8\mu LQ}{\pi r^4}}.$$

(33)

Since the seawater pump flow rate varies with power availability, the pressure drop needed to determine the power requirements for the pumps and vacuum can be determined by a linear fit given the pressure drop and flow rate ranges, as shown in Equation (34):

$$\Delta p=\Delta p_{min}+(\Delta p_{max}-\Delta p_{min}){\displaystyle \frac{Q-Q_{min}}{Q_{max}-Q_{min}}}.$$

(34)

In this model, each pump, as shown in Figure 4, has the same input efficiency, ${\gamma }_{pump}$, but they differ in terms of their minimum and maximum pressure drop and flow rate range, as shown in Table 1. Note that the flow rates of each pump depend on the power availability and the operation scenario, as described in Section 2.5. Note that, for the example DOC plant described in this paper, only pumps “O”, “ED”, “a”, “b”, and “ED4” have nonzero pressure or non-atmospheric pressure drops, meaning the other pumps have a zero power requirement as fluid flows due to gravity in these cases. Note that these pressure values are examples of those that can be expected for a DOC plant and were discussed with our industry partner to ensure that the values are reasonable.

2.3.2. Gas Vacuum Equations

The gas vacuum’s power requirements largely vary depending on the mole rate of ${\mathrm{CO}}_2$ captured, $n_{CO2,Cap}$, which can also be considered as the moles of ${\mathrm{CO}}_2$ vacuumed per hourly time-step. Note that the vacuum will pull in air as well as the captured gas. The overall mole rate of the gas mixture moving through the vacuum $n_{vac}$ can be determined by comparing the purity or mole fraction of ${\mathrm{CO}}_2$ in the mixture $y_{pur}$ with the mole rate of ${\mathrm{CO}}_2$ via Equation (35):

$$n_{vac}={\displaystyle \frac{n_{CO2,Cap}}{y_{pur}}}.$$

(35)

Unlike in the liquid pump case, the gas moving through the vacuum is compressible, meaning that, as the pressure it experiences decreases through the vacuum, the gas’s density decreases, causing its volume and flow rate to increase. Therefore, Equation (32) cannot be used to determine the power needs of the vacuum. However, a modified version of the equation can be used instead with the average flow rate through the vacuum, where the absolute pressure the gas experiences at a given point within the vacuum $p_{vac,i}$ is determined by comparing the pressure drop in Pa at that point, $\Delta p_{vac,i}$, with the atmospheric pressure in Pa, $p_{atm}$, which is about 100 kPa (see Equation (36)). Note that, on account of this, the maximum pressure drop of the vacuum must be less than the atmospheric pressure.

$$p_{vac,i}=p_{atm}-\Delta p_{vac,i}$$

(36)

The flow rate of vacuumed gas at a given point in the vacuum $Q_{vac,i}$ is determined via the ideal gas law, as shown in Equation (37), where R is the universal gas constant or 8.314 J/molK, and $T_{k,air}$ is the air temperature in Kelvin, which is held constant at 298 K.

$$Q_{vac,i}={\displaystyle \frac{n_{vac}R{T}_{k,air}}{p_{vac,i}}}$$

(37)

Note that this model assumes that the pressure decreases consistently through the vacuum so that the average flow rate, $Q_{vac,AVG}$, can be determined by averaging the values of Equations (36) and (37) for a range of pressure drop values, $\Delta p_{vac,i}$, from 0 at the start of the vacuum to $\Delta p_{vac}$, the total pressure drop the gas experiences. The model determines and averages the flow rates at 25 pressure drop values to find $Q_{vac,AVG}$. This average flow rate is then used to approximate the power need for the vacuum, $P_{vac}$, similar to Equation (32):

$$P_{vac}={\displaystyle \frac{Q_{vac,AVG}\Delta p_{vac}}{{\gamma }_{vac}}}.$$

(38)

As for the liquid pump case, it is also assumed that a higher pressure drop is needed to move more fluid. However, since the fluid in this case is compressible, it is assumed that the necessary pressure drop is dependent on the mole rate of ${\mathrm{CO}}_2$ captured at a given hourly time-step. For simplicity, it is assumed that these variables vary linearly. The maximum and minimum mole rates of ${\mathrm{CO}}_2$ that can be extracted, $n_{max}$ and $n_{min}$, are determined using the methodologies described in Section 2.1 and Section 2.2 for the cases where the maximum and minimum numbers of ED units can be powered, respectively. Given this range, the pressure drop for the vacuum, $\Delta p_{vac}$, for a given ${\mathrm{CO}}_2$ mole rate can be determined by Equation (39), which is similar to Equation (34):

$$\Delta p_{vac}=\Delta p_{min}+(\Delta p_{max}-\Delta p_{min}){\displaystyle \frac{n_{CO2,Cap}-n_{min}}{n_{max}-n_{min}}}.$$

(39)

The gas vacuum model requires inputs of efficiency, ${\gamma }_{vac}$, and the pressure drop range; however, the flow rate depends on the mole rate of ${\mathrm{CO}}_2$ captured and the purity of ${\mathrm{CO}}_2$ moving through the vacuum, $y_{pur}$, as described in Equations (35) to (39). Additionally, the fraction of ${\mathrm{CO}}_2$ extracted from seawater in the ocean chemistry model, ${\gamma }_{ext}$, is accounted for in the vacuum model inputs (see Section 2.2). The vacuum parameters used by the example DOC plant described in this study are shown in Table 1. Note that it is assumed that the vacuum does not impact the flow of the acidified seawater and that any water vapor that is also vacuumed up does not significantly impact the gas flow rate.

2.4. Post-Processing ${CO}_2$

As described in Section 2.3, the vacuumed ${\mathrm{CO}}_2$ is not necessarily 100% pure. The gas therefore requires further refinement before it can be compressed into a tank for temporary storage. The model for the ${\mathrm{CO}}_2$ purification process is described in Section 2.4.1 and that of the compression process is described in Section 2.4.2 (see Section 2.6 for details on the assumptions used in these models). The compressed gas is temporarily placed in storage tanks, from where it can later be converted into a commercial product like synthetic fuel or injected into underground or subseafloor geologic reservoirs to be sequestered for long-term storage [2]. Note that this model does not account for ${\mathrm{CO}}_2$ conversion or sequestration, but creating models of these activities is an area of interest for future work.

2.4.1. ${\mathrm{CO}}_2$ Purification

If the extracted ${\mathrm{CO}}_2$ is not 100% pure or $y_{pur}<1$, then additional purification methods are required to refine it prior to compression for tank storage. Such methods can include pressure swing absorption (PSA) and amine-based systems. The thermodynamic minimum energy required per mole of ${\mathrm{CO}}_2$ in J/mol, $w_{sep}^{min}$, to separate ${\mathrm{CO}}_2$ from a mixed gas stream is described in Equation (40) [16,17]:

$$w_{sep}^{min}={\displaystyle \frac{-R{T}_{k,air}}{y_{pur}}}(y_{pur}ln{y}_{pur}+(1-y_{pur})ln(1-y_{pur}))$$

(40)

Equation (40) assumes that none of the captured ${\mathrm{CO}}_2$ is lost in this process and the refined stream of ${\mathrm{CO}}_2$ is 100% pure [16,17]. While achieving lower ${\mathrm{CO}}_2$ purity and losing some of the ${\mathrm{CO}}_2$ in the process is more realistic, assuming no losses and 100% purity results in a higher theoretical energy need, which, in turn, provides a more conservative general estimate [16,17,18]. Future work can further investigate equations that account for lower-purity output streams and ${\mathrm{CO}}_2$ losses. Note that the theoretical minimum energy required for this refinement decreases with a higher ${\mathrm{CO}}_2$ purity or concentration of ${\mathrm{CO}}_2$, as demonstrated in Figure 5, where extracting ${\mathrm{CO}}_2$ from very dilute sources, like ambient air, which has a purity or concentration less than 0.01, requires near exponentially more energy than more concentrated sources [18].

The realistic energy requirements for separation and refinement are determined by accounting for the efficiencies of PSA and amine-based ${\mathrm{CO}}_2$ refinement methods, which, according to the literature, range from 15 to 21% and from 20 to 25%, respectively [17,19,20]. For simplicity, this model assumes a 20% efficiency for ${\mathrm{CO}}_2$ purification, ${\mu }_{CO2}$, which can be used to determine a more realistic energy need per mole of ${\mathrm{CO}}_2$, $w_{sep}^{act}$:

$$w_{sep}^{act}={\displaystyle \frac{w_{sep}^{min}}{{\mu }_{CO2}}}.$$

(41)

2.4.2. ${\mathrm{CO}}_2$ Compression

According to the literature, it is reasonable to assume that about 90 kWh/t${\mathrm{CO}}_2$ is needed to compress 100% pure ${\mathrm{CO}}_2$ to the critical pressure needed for tank storage [21]. Jackson and Brodal investigated a variety of conventional and optimized methods and consistently obtained values close to this value. As a result, the model simply multiplies this value by the amount of ${\mathrm{CO}}_2$ captured per hourly time-step to determine the energy need for compression [21].

2.5. Model Operation Scenarios

The inclusion of chemical storage tanks in the simulated DOC plant enables the use of a heuristic operational strategy to evaluate system behavior under variable power conditions. The tanks store acid and base produced by the electrochemical system, which typically has a higher energy demand than the pumping system [1,2,5,6]. This approach allows the model to simulate scenarios in which stored capture solutions are used during periods of low power availability, while surplus energy during high-power periods is used to replenish the tanks. Additional assumptions underlying this operational framework are detailed in Section 2.6.

Overall, there are four primary scenarios of operation considered by the model. In scenario 1, the tanks are full, so the solutions generated by the ED units are only used for DOC. This scenario is also useful for considering operation without storage tanks (see Section 2.5.1). In scenario 2, the tanks are not full but there is enough energy to enable DOC; therefore, a portion of the chemical solutions generated by the ED system is used to fill the tanks while the rest is used for DOC (see Section 2.5.2 for more details). Meanwhile, in scenario 3, there is only enough power available for the pumps to perform DOC (see Section 2.5.3). Scenario 4 is triggered when there is not a sufficient volume of stored acid and base for DOC but enough power available for the ED system to fill the tanks (see Section 2.5.4). Note that, in the final scenario, scenario 5, there is not enough power or volume, so all of the available power is either excess or needs to be stored for later use in a battery system.

To improve the model’s computational speed, the ranges of ${\mathrm{CO}}_2$ capture rates, flow rates into and out of the tanks, effluent chemistry and flow rates, and power needs for each scenario are initialized prior to simulating the system’s performance at each time-step. This enables the model to look up the relevant values for each time-step of the simulation given the amount of power and tank volumes available.

As mentioned in Section 2.1, these ranges are generally determined by the number of ED units that can be powered. Even for scenario 3, where the ED system is inactive, the flow rates considered are based on the volumes provided to the tanks during scenario 2 or scenario 4, which depend on the number of ED units that can be powered. Therefore, the total number of cases within each scenario, $N_S$, depends on the range of ED units that can be activated (see Equation (42)):

$$N_S=N_{S1}=N_{S3}=N_{S4}=N_{ED,max}-N_{ED,min}+1$$

(42)

For the example DOC plant, $N_{ED,max}$ is 10 while $N_{ED,min}$ is 1, according to Table 1. Therefore, each scenario has at least 10 possible output values depending on how many of those 10 units can be powered, where the number of active ED units that can be powered or the equivalent at a given hourly time-step is $N_x$. Typically, all of these units will be used either solely for DOC or for filling the tanks. The exception to this rule is scenario 2, which has more than 10 output values, since the number of units being used for DOC, $N_y$, versus filling the tanks, $N_z$, can vary (see Section 2.5.2 for more details).

The ranges for the chemical outputs like the ${\mathrm{CO}}_2$ capture rate and the flow rates into and out of the tanks are calculated first for each scenario since these rates are needed to determine the power needs of the vacuum and pumps (see Section 2.3). Afterwards, the power calculations account for the power needs of the number of active ED units, those of the pumps and vacuum given their respective flow rates, and that of the ${\mathrm{CO}}_2$ post-processing to determine the total power required for each case in each scenario. These calculations also determine the minimum power requirement for each scenario, which is essential to determine if there is enough input power to trigger a given scenario. Meanwhile, by determining the flow rate or volume going into and out of the tanks, the outputs of these calculations are essential to determine the overall tank volume for each time-step, which also affects what scenarios can be triggered.

The default maximum volume of the acid and base tanks, $V_{aT,max}$ and $V_{bT,max}$, depend on the total storage time, $t_{store}$, and the flow rates of acid and base provided from a single ED unit (see Equation (43)). This configuration ensures that, if there is very limited power available, then the tanks can at least provide the minimum DOC rates over the duration of the storage time. For the model examined in this work, the storage time is set to 12 h as an example. Future work can investigate optimizing the tank size based on the power availability at a deployment site.

$$V_{aT,max}=V_{bT,max}={\displaystyle \frac{t_{store}{Q}_{ED1}{N}_{ED,min}}{2}}$$

(43)

Additionally, to distinguish the flow rates of acid and base sent to the tanks versus those used for DOC, they are labeled as $Q_{aT}$, $Q_{bT}$, $Q_{aDOC}$, and $Q_{bDOC}$, respectively. These flows are enabled by the acid and base pumps so that $Q_a=Q_{aT}+Q_{aDOC}$ and $Q_b=Q_{bT}+Q_{bDOC}$, except for in scenario 3, where the solutions are coming from the tanks and therefore $Q_a=-Q_{aT}=Q_{aDOC}$ and $Q_b=-Q_{bT}=Q_{bDOC}$ (see Section 2.5.3). Note that pumps “a” and “b” are used to enable these flow rates so $Q_a$ and $Q_b$ must be nonzero if any acid and base is flowing.

2.5.1. Scenario 1: ED Units Used for DOC, Tanks Are Full

Scenario 1 represents DOC operation without filling the storage tanks (see Figure 6). This mode of operation is triggered when the volume at the given time-step is equivalent to the maximum volume of the tanks (or if tanks are not included for the simulated DOC plant) and there is at least enough input energy available to power the system so that the minimum number of ED units is used for DOC. The flow rates in this scenario are described in

Table 2. Flow rates for scenario 1.

Flow Rate	Value
$Q_o$	${\displaystyle \frac{Q_{ED}}{{\gamma }_{sw}}}$
$Q_{ED}$	$Q_{ED,1}{N}_x$
$Q_{ED4}$	0
$Q_a$	${\displaystyle \frac{Q_{ED}}{2}}$
$Q_b$	${\displaystyle \frac{Q_{ED}}{2}}$
$Q_{aDOC}$	$Q_a$
$Q_{bDOC}$	$Q_b$
$Q_{aT}$	0
$Q_{bT}$	0
$Q_i$	$Q_o-Q_{ED}$
$Q_{CO2ex}$	$Q_i+Q_a$
$Q_{asw}$	$Q_{CO2ex}$
$Q_f$	$Q_{asw}+Q_b$

.

2.5.2. Scenario 2: ED Units Used for DOC and Filling Tanks

Scenario 2 represents DOC operation in addition to filling the tanks (see Figure 7). This mode is triggered if the tanks are not filled but there is still enough energy available for DOC with the minimum number of ED units. Note that the minimum power case for this scenario just involves DOC without filling the tank, similar to scenario 1. The rationale for this is that, if the tanks are empty but there is just enough power for minimum DOC, capture should still be performed to maximize yearly DOC. Note that this is the current strategic setup for this case, and future optimization studies could potentially improve this logic.

Unlike the other scenarios, in scenario 2, the ED units can be used for DOC or filling the tanks. The numbers of ED units performing these actions are $N_y$ and $N_z$, respectively. Note Equation (44), where $N_x$ ranges from $N_{ED,min}$ to $N_{ED,max}$ and $N_y$ is nonzero while $N_z$ can be zero:

$$N_x=N_y+N_z$$

(44)

Therefore, to account for a variety of ED units performing DOC or tank filling, while ensuring that Equation (44) is followed, the total number of cases for scenario 2, $N_{S2}$, is determined via Equation (45), which is equal to 55 in this example:

$$N_{S2}=\sum _{k=0}^{N_S}{N}_S-k$$

(45)

Like $N_x$, $N_y$ also ranges from $N_{ED,min}$ to $N_{ED,max}$, while $N_z$ ranges from zero to $N_{ED,max}-N_{ED,min}$, since, for scenario 2 to activate, there must be enough power available for at least the minimum DOC in every case. The respective values of $N_y$ and $N_z$ are determined by the power available and the volume of the tanks. At each time-step, the model first compares the input power available with the power needs of the $N_{S2}$ cases and the additional volume they can provide to the tanks, to identify which cases can be powered while not causing the tanks to overflow. The code then reviews this viable range to identify which of these cases provides the most volume to the tanks. That case’s values for $N_y$ and $N_z$ are then used for the time-step. Note that the current logic prioritizes filling the tanks as quickly as possible while performing minimal DOC. If the tanks are closer to being filled, fewer units will be needed for tank filling, meaning more units can be used for DOC. The flow rates used in this scenario are listed in

Table 3. Flow rates for scenario 2.

Flow Rate	Value
$Q_o$	${\displaystyle \frac{Q_{aDOC}+Q_{bDOC}}{{\gamma }_{sw}}}+Q_{aT}+Q_{bT}$
$Q_{ED}$	$Q_{ED,1}(N_y+N_z)$
$Q_{ED4}$	0
$Q_a$	${\displaystyle \frac{Q_{ED}}{2}}$
$Q_b$	${\displaystyle \frac{Q_{ED}}{2}}$
$Q_{aDOC}$	${\displaystyle \frac{Q_{ED,1}{N}_y}{2}}$
$Q_{bDOC}$	${\displaystyle \frac{Q_{ED,1}{N}_y}{2}}$
$Q_{aT}$	${\displaystyle \frac{Q_{ED,1}{N}_z}{2}}$
$Q_{bT}$	${\displaystyle \frac{Q_{ED,1}{N}_z}{2}}$
$Q_i$	$Q_o-Q_{ED}$
$Q_{CO2ex}$	$Q_i+Q_{aDOC}$
$Q_{asw}$	$Q_{CO2ex}$
$Q_f$	$Q_{asw}+Q_{bDOC}$

.

2.5.3. Scenario 3: Solutions in Tank Used for DOC

Scenario 3 represents the case where the acidic and basic solutions stored in the tanks are used for DOC and is activated when there is not enough power for the ED units to provide additional solutions for capture but there is enough power for the pumps and enough volume in the tanks for the minimum DOC (see Figure 8). Note that, if there is enough energy for scenario 2, then it will be activated in place of scenario 3, as the tanks are currently intended to be used only when there is not enough power for the ED system during periods of low power availability. Note that future optimization work can assess if overall DOC can be increased by altering this strategy. The flow rates used in this scenario are listed in

Table 4. Flow rates for scenario 3.

Flow Rate	Value
$Q_o$	${\displaystyle \frac{Q_{ED}}{{\gamma }_{sw}}}$
$Q_{ED}$	0
$Q_{ED4}$	0
$Q_a$	${\displaystyle \frac{Q_{ED,1}{N}_x}{2}}$
$Q_b$	${\displaystyle \frac{Q_{ED,1}{N}_x}{2}}$
$Q_{aDOC}$	$Q_a$
$Q_{bDOC}$	$Q_b$
$Q_{aT}$	$-Q_a$
$Q_{bT}$	$-Q_b$
$Q_i$	$Q_o$
$Q_{CO2ex}$	$Q_i+Q_{aT}$
$Q_{asw}$	$Q_{CO2ex}$
$Q_f$	$Q_{asw}+Q_{bT}$

.

2.5.4. Scenario 4: ED Units Just Fill Tanks, No DOC Is Performed

In scenario 4, a smaller volume of seawater is directly pumped into the ED system to fill the tanks with acid and base and no DOC is performed (see Figure 9). This scenario is only activated if there is enough power for the ED system but not enough for the pumps to perform DOC and the tanks do not have enough volume to perform DOC. Since the typical ED pump is connected to the much larger “pump O”, which has a minimum flow rate much larger than the ED system can handle, there is a second ED pump, “pump ED4”, that can pull in seawater directly to the ED system. Note that this pump is also assumed to have a filtration unit and therefore has the same pressure drop range as “pump O” (see Table 1). If a pilot plant effectively has the same pump for “ED” and “ED4”, then they can still use this model to simulate their system by giving both pumps the same inputs; if not, they can provide different pressure drop ranges for each of them. The flow rates used in this scenario are listed in

Table 5. Flow rates for scenario 4.

Flow Rate	Value
$Q_o$	0
$Q_{ED}$	0
$Q_{ED4}$	$Q_{ED,1}{N}_x$
$Q_a$	${\displaystyle \frac{Q_{ED4}}{2}}$
$Q_b$	${\displaystyle \frac{Q_{ED4}}{2}}$
$Q_{aDOC}$	0
$Q_{bDOC}$	0
$Q_{aT}$	$Q_a$
$Q_{bT}$	$Q_b$
$Q_i$	0
$Q_{CO2ex}$	0
$Q_{asw}$	0
$Q_f$	0

.

2.6. DOC Model Assumptions

The DOC model presented in this work incorporates a number of assumptions and simplifications to strike a balance between computational efficiency and capturing key system-level behavior. While these assumptions may introduce some limitations in output precision and fully capturing non-linear behaviors, the model offers valuable insights into how variable power can influence DOC plant performance. The rationality of these assumptions is supported by the consistency between model outputs and industry-provided data (see Section 3.1). As more data becomes available from ED-based DOC experiments and real-world deployments powered by variable renewable energy, future work will focus on enhancing model fidelity and expanding its applicability.

As detailed in Section 2 and shown in Figure 3, the ED system is represented as a collection of discrete “units” with fixed efficiencies, flow rates, and power requirements that can switch on and off at hourly time-steps without changes in performance. This simplification supports a plant-level modeling approach focusing on overall system behavior. In practice, ED systems are considerably more dynamic—their efficiency and power demands vary within the hour due to fluctuations in current and voltage driven by factors such as pH, membrane properties, and temperature [5,9,11]. Additionally, long-term performance degradation, particularly from membrane wear, affects system behavior and maintenance needs over time [4]. While these complexities are not captured in the current model, future work will aim to incorporate more detailed component-level dynamics and experimental validation to better reflect real-world ED performance.

As described in Section 2.2, the ocean chemistry model treats the seawater as a carbonate buffer solution. However, seawater also contains other chemical species that can contribute to buffering changes to pH, such as borate and divalent ions [22]. While the model accounts for seawater temperature and salinity effects on DOC plant operation (see Appendix A.1), these parameters are currently represented by average-valued inputs rather than time-varying data. Despite these simplifications, the model outputs were consistent with the expectations of our industry partner (see Section 3.1). Future improvements could incorporate more detailed ocean chemistry models to better capture the full range of buffering interactions [22].

The control strategy for the operation scenarios, as described in Section 2.5, is based on a heuristic approach that prioritizes filling the chemical storage tanks during periods of excess power. The strategy reflects the assumption that the power from variable renewable energy sources will be intermittent, leading to periods of limited availability during which only stored acid and base in the tanks can be used for DOC (see Scenario 3 in Section 2.5.3). The current framework does not include a scenario in which both the tanks and the ED units operate in parallel to provide acid and base for capture, as this could prematurely deplete the tanks and reduce DOC potential during low-power conditions. This control logic is based on the premise that, unless future power availability can be reliably forecasted, simultaneous use would generally result in reduced overall carbon removal. As such, the present strategy serves as an initial operational baseline. Future work can explore more sophisticated control schemes that incorporate forecasts of power availability, battery energy storage, variable electricity prices, or dynamic carbon market incentives. Future optimization studies will be especially important for evaluating whether predictive or hybrid control strategies could improve DOC performance under realistic operating conditions.

In addition to the broader modeling assumptions, the efficiencies of the pumps, vacuum, ${\mathrm{CO}}_2$ extraction from seawater, and post-processing system are treated as constant values. In practice, these efficiencies may vary due to factors such as temperature fluctuations, aging equipment, and operating conditions. To maintain model simplicity, pressure drops in the pumps and vacuum systems are assumed to vary linearly with liquid flow rate and the mole rate of ${\mathrm{CO}}_2$ (modeled as an ideal gas), respectively. The post-processing system is modeled as yielding a fully purified ${\mathrm{CO}}_2$ stream with no loss of the targeted species. Furthermore, the model assumes that switching between operational scenarios requires negligible energy and has no adverse effect on component performance—a reasonable approximation based on findings from flexible ED-based desalination [11]. Additionally, energy consumption for plant monitoring and control is assumed to be minimal and is not explicitly modeled.

2.7. Hybrid Energy Models and Parameters

The hybrid energy systems are modeled using NREL’s H2I [13], an open-source Python tool for designing and analyzing hybrid power plants and hybrid energy systems. H2I includes individual energy generation and storage technologies that can be configured at the component level and then combined into hybrid power plants or energy systems. Figure 10 shows the technologies included in this analysis and the overall interactions between them. Wind turbines and wave energy converters generate electricity, which is then managed through a controller to either directly supply the electricity to the DOC plant or store it in a battery to later supply the DOC plant. The DOC plant uses the variable electricity profile and ocean water to capture ${\mathrm{CO}}_2$. H2I uses the NREL Production Financial Analysis Scenario Tool based on H2FAST [23] to calculate the levelized cost of energy (LCOE) using cash flow analysis.

The wind system is modeled using IEA 15 MW turbines [24] that have a hub height of 150 m and rotor diameter of 242 m in a gridded layout with seven rotor diameters between turbines. The wind energy production is modeled using the Flow Redirection and Induction in Steady State (FLORIS) [25] wake modeling tool that is integrated into H2I and a wind resource profile from the WindTool Kit resource year 2010 [26]. The costs for the wind system are from the 2024 Annual Technology Baseline (ATB) 2030 moderate case [27]. The floating technology costs are from wind resource class 12 and fixed technology wind resource class 6. The wind energy system is sized based on the maximum allowable power to the DOC plant, which is the maximum power for scenarios 1 and 2.

The wave energy system is modeled using the reference model 3 wave energy converter (WEC), the point absorber, from the reference model project [28]. The WECs are also arranged in a gridded layout with 600 m between each plant. The wave energy production is modeled using the PySAM MhkWave model [29] integrated in H2I and a wave resource profile from the Hindcast Data for resource year 2010 [30]. The costs for the wave system are calculated using a PySAM cost model based on the reference model project. If the wave energy system is included, it is sized based on the minimum power threshold for scenarios 1 and 2 of the DOC plant, and the wind energy system is reduced proportionally. The rationale behind this choice is to use the wave energy system to provide enough power for minimum DOC during periods of low wind availability.

The battery is a simplified representation of a battery for dispatch, and the dispatch model controls the state model and dispatches it according to the chosen strategy. The state model is modeled using the PySAM Battery model [29] and includes battery-specific parameters, such as voltage, current, and thermal effects. The battery dispatch uses a look-ahead rolling horizon, 48-h forecasts, and a 24-h solution to enable decision making with foresight of the next day. The battery dispatch strategy is a load-following heuristic that prioritizes meeting load without considering costs. The battery is set to dispatch if the electricity from the renewable energy sources to the DOC plant is below the minimum threshold for capture. The battery costs are also from the 2024 ATB 2030 moderate case [27].

The electricity provided to the DOC plant is limited to the maximum power rating of the DOC plant and any electricity generation above that point is either used to charge the battery or curtailed. The DOC plant is composed of 10 ED units and 12 h of tank storage, the same as the generic DOC model discussed in Section 2.1, Section 2.2, Section 2.3, Section 2.4 and Section 2.5.

2.8. Comparison with Industry Parameters

Confidential input parameters provided by our industry partner were used to validate that the DOC plant model produces reasonable performance results. While these specific inputs cannot be disclosed, the percent errors between the model outputs and the partner’s reported values are presented in Section 3.1. The specific variables that differ from the values in Table 1 include the flow rate, power needs, and efficiencies of the ED system, in addition to the pressure differences of the pumps. All other parameters are the same as they are either publicly available information or common general assumptions [6,8,17,19,20].

2.9. Characteristics of Example Simulations

By accounting for the electrochemistry, ocean chemistry, performance strategies, and electricity costs of DOC plants, this model can be used to assess the impacts of variable power, ED system characteristics, and realistic renewable energy power profiles on their performance (see Section 2.9.1, Section 2.9.2 and Section 2.9.3, respectively). These are a few example simulations that utilize and vary the generic example DOC plant parameters listed in Table 1.

2.9.1. Sine-Wave Power Profile with Periods of Lower Power

To evaluate how the DOC plant can handle variable power, this analysis assesses the example DOC plant, plus tanks with enough storage for 12 h of minimum DOC, under a generic sine-wave power profile over the course of one year. This sine wave has a 24 h period so that zero power is experienced at the first and last hour of each day, in addition to a maximum daily power of 500 MW, which ensures that the plant can power DOC with all ED units at least once per day. To account for periods of low energy, every fifth day, the maximum daily power is temporarily reduced to 50 MW. Note that, in this example, the temperature and salinity are kept constant at 25 °C and 35 ppt. The performance of the example DOC plant under these conditions is detailed in Section 3.2.

2.9.2. Effect of ED Discretization Under Sine-Wave Power Profile

To evaluate the potential benefits of ED systems that have a higher tolerance for variable power, the number of ED units in the example plant are varied while keeping the overall ED power capacity constant at 240 MW. Additionally, the presence of tanks with $N_S$ hours of minimum DOC or one hour of maximum DOC is varied as well. This analysis uses the same power profile and seawater characteristics as those in Section 2.9.1 for plants with 1 to 50 ED units with and without storage tanks. The performance of the DOC plants under these conditions is detailed in Section 3.3.

2.9.3. Case Studies with Hybrid Renewable Energy Systems

To evaluate the model’s performance with realistic renewable energy power profiles, two case studies were performed using the parameters of the generic DOC model in two different deployment locations. The first is off the coast of Texas, shown in Figure 11a, which has a significant amount of oil and gas infrastructure that can be used for injecting the captured ${\mathrm{CO}}_2$ into saline aquifers [2]. This region also has a substantial amount of wind energy, so this resource was selected for the simulated power source [2,31]. The second location is off the coast of Oregon, shown in Figure 11b, which has a significant amount of both wind and wave energy in addition to undersea basalt reservoirs that can be used to permanently sequester the captured ${\mathrm{CO}}_2$ [2,31,32].

The characteristics of each location are shown in

Table 6. Location characteristics.

Parameter	Texas	Oregon
Temperature (°C)	25	12
Salinity (ppt)	36.5	33
Depth (m)	45	482
Average Wind Speed (m/s)	8.06	9.74
Average Omnidirectional Wave Power (kW/m)	N/A	43.75

, and the technology capacities implemented at each location are shown in

Table 7. Technology capacities implemented at each location.

Parameter	Texas	Oregon
Wind Capacity (MW)	345	330
Wave Capacity (MW)	N/A	30.9
Battery Capacity (MW)	50	50
Battery Duration (MWh)	200	200
DOC Capacity (MW)	356.7	362.1

. Note that the wind energy capacity for the Texas case was set to be roughly equivalent to the maximum power need of the DOC plant or the DOC capacity. Meanwhile, in the Oregon case, the wave capacity was set to be enough to enable minimum DOC in scenarios 1 and 2, while the wind capacity was set to provide the approximate remainder of the energy needed to reach the DOC capacity (see Table 7). In both cases, the full DOC capacity could be reached with assistance from power stored in the batteries. Note that the additional power required for the DOC plant in the Oregon location is due to the slightly higher DOC rate enabled by the lower seawater temperature and salinity (see Appendix A.1), which requires a higher volume of ${\mathrm{CO}}_2$ to be vacuumed and therefore more power for the vacuum.

3. Results

This section details the results for the industry comparison described in Section 2.8, and those of the simulations detailed in Section 2.9. The results for the industry comparison are shown in Section 3.1, while those from investigating the impacts of variable power, ED discretization, and realistic hybrid renewable energy systems are shown in Section 3.2, Section 3.3 and Section 3.4.

3.1. Comparison with Industry Parameters

As discussed in Section 2.8, the results of the model with input parameters from our industry partner were compared with their estimates. While the input parameters cannot be shared due to confidentiality, the percent difference in values or the error is shown in

Table 8. Percent difference or error between results from model with industry inputs and estimates reported by industry partner.

Result	Error
Maximum Total Power	<1%
Maximum DOC Rate	<1%
Maximum Total Liquid Pump Power	2%
Maximum Gas Vacuum Power	5%
Maximum Post-Processing ${\mathrm{CO}}_2$ Power (Purification and Compression)	3%

. Note that these maximums were compared since our partner has thus far only made estimates for constant power operation. As additional data from ED-based DOC systems operating under variable power conditions becomes available, the model can be further refined and validated. Nevertheless, the low error values presented here provide preliminary evidence supporting the model’s ability to capture key system dynamics.

3.2. Sine-Wave Power Profile with Periods of Lower Power

As discussed in Section 2.9.1, the example DOC model, using the parameters described thus far, was run under an example sine-wave power profile with periods of low power over the course of one year. The time-dependent results for the example plant with this generic power profile are shown in Figure 12. Note that the blue curve represents the input power from the sine-wave profile in MW, the orange curve shows the excess power remaining in MW every time-step, the green curve shows the rate of DOC in t${\mathrm{CO}}_2$/hr for each time-step, and the black curve shows the volume of solutions stored in the tanks in m³. Additionally, the ranges of power needed for the scenarios are shown, where the dashed red line is the minimum power required to activate scenario 1 or scenario 2, the purple line is the maximum power that can be used by scenarios 1 and 2, the brown line is the minimum power needed for scenario 3, the pink line is the maximum power that can be used by scenario 3, the gray line is the minimum power needed for scenario 4, and the yellow line is the maximum power needed for scenario 4, all in MW.

The first two and the final “days” or wavelengths from trough to trough of the power profile in Figure 12 start with minimal power availability. Once the power availability becomes nonzero, scenario 3 is triggered to enable some capture while reducing the volume of the tanks. Shortly after, the power availability increases enough so that scenario 2 can be triggered, which maintains the same rate of DOC as that of scenario 3 but quickly refills the tank. Once the tank is filled, scenario 1 is activated, enabling higher rates of DOC until the power availability surpasses the maximum for scenario 1. At this point, the DOC rate plateaus at its maximum while the excess power availability peaks. The DOC rate then steadily decreases with the power availability towards the end of the day. Once the power availability is less than the minimum for scenarios 1 and 2, scenario 3 is triggered towards the very end of the day. Note that, since the power profile is consistent, the trend seen in these three “days” is often the norm for this example.

The third “day” has the greatest deviation from this norm since the maximum power available on this “day” is only 10% of the maximum on the other days. This “day” was implemented like this to represent the periods of low power availability that renewable energy powered systems can experience. At the beginning of this day, there is only enough power available to trigger scenario 3’s minimum DOC rate. Shortly after, scenario 3’s DOC rate increases as the volume of acid and base quickly decreases. Towards the middle of the “day”, there is enough power available to trigger scenario 2’s minimum DOC rate. As a result, the rate of DOC decreases but the volume of the tank is conserved until the end of the day, when scenario 3 is once again triggered due to lower power availability, causing the DOC rate to temporarily peak until the volume of acid and base is depleted. However, once the fourth “day” begins, scenario 2 is triggered with its minimum DOC rate. As power availability increases, scenario 2 is used to rapidly fill the tanks. Once the tanks are almost completely full, the increase in tank volume slows as more power is used for DOC, rapidly increasing the DOC rate to about 100 t${\mathrm{CO}}_2$/hr as the tanks are completely filled. After the tanks are full, scenario 1 is activated, causing the DOC rate to plateau, and the rest of the fourth “day” continues the trend that “days” one, two, and five follow.

Overall, the example in Figure 12 demonstrates how a DOC plant could handle general power variability, as shown on the first, second, and fifth “days”; how the tanks could be used to continue capture during days of especially low power availability, as shown on the third “day”; and how these tanks could be quickly refilled in preparation for another low-power period, as shown on the fourth “day”. Note that scenario 3 in this example is only active until the minimum for scenario 2 is reached and, therefore, is never able to operate near its maximum DOC rate. However, as previously mentioned, this switch enables the tanks to conserve their volume in this example. Note that this may not always be the case, and future optimization work can further investigate the ideal conditions to switch between scenarios. Similarly, scenario 4 is not triggered in this case since its minimum power requirement is very close to that of scenario 2 and, given the hour long time-step, the available power is never between these values for this case. One aspect that this simulation does not account for is battery power, which can store up the excess power to increase capture during these periods of lower power availability.

The yearly ${\mathrm{CO}}_2$ capture, power ranges, and other system results for the simulation are shown in

Table 9. System results for example DOC plant under sine-wave power profile.

System Result	Value
Yearly ${\mathrm{CO}}_2$ Capture	720.4 kt${\mathrm{CO}}_2$/yr
DOC Capacity Factor	49.5%
Energy Capacity Factor	41%
Fraction of Time DOC is Performed	90%
Maximum Tank Volume	12,960 m3
Total Plant Power Range	6.5–357 MW
DOC Rate Range	16.6–166 t${\mathrm{CO}}_2$/hr
Intake Pump (“Pump O”) Flow Rate Range	60–600 m3/s
ED Power Range	24–240 MW
Total Pump Power Range	0.68–40 MW
Maximum Vacuum Flow Rate Range	21.6–649.7 m3/s
Vacuum Power Range	1.1–35.6 MW
${\mathrm{CO}}_2$ Purification Power Range	3.2–32.5 MW
${\mathrm{CO}}_2$ Compression Power Range	1.5–15 MW

. The example plant was able to capture about 720 kt${\mathrm{CO}}_2$/yr, which is only about 50% of what it could capture if there was enough power available for it to operate at its maximum rate for the full year. Note that this value is also referred to here as the DOC capacity factor. This DOC capacity factor is lower than those anticipated from the literature, like that from Eisaman’s team, who assumed one of roughly 93% [4]. This is due to the variable nature of the input power. In this example, the energy capacity factor was only 41%. Note that this value compares the total energy produced by this example’s power source to how much it could make if it consistently produced power at its maximum capacity. However, the DOC capacity factor was likely able to be larger than the energy capacity factor due to the ability of the ED units and the tanks to continue DOC despite the lower and variable power. The fraction of time DOC could be performed by the plant was about 90%, which shows that, despite the lower energy availability, the plant could still function almost consistently. Note that the energy capacity factor in this example is high for renewable energy sources, since it typically ranges from about 15 to 30% for solar and wind and from roughly 40 to 50% for hydropower [34].

3.3. Effect of ED Discretization Under Sine-Wave Power Profile

As discussed in Section 2.9.2, to explore the benefits of ED systems with a higher tolerance and with power variability, the number of ED units used by the example DOC plant was varied from 1 to 50 ED units, while the total ED capacity remained at 240 MW, to represent plants with a fixed power need and those that can operate with any amount of power provided. Additionally, the performance of plants with and without storage tanks was assessed to evaluate the benefits of tank storage for the sine-wave power profile detailed in Section 2.9.1. The DOC capacity factor was compared for these cases, and the results are shown in Figure 13.

As shown in Figure 13, the DOC capacity factor rapidly increases between 1 and 5 ED units, but that improvement slows with more units. The tanks also appear to have a greater impact when there are fewer than 10 ED units, after which their benefit significantly decreases and appears to become almost negligible after 30 units or more are used. This is likely because the tanks in these cases are less necessary to continue capture during periods of lower power availability since the minimum power needed for the ED units decreases with more units, as shown in Figure 13. Additionally, as detailed in Section 3.2, DOC via the ED units in scenario 2 is prioritized over DOC via the tanks in scenario 3. This phenomenon can be more clearly seen in Figure 14 and Figure 15, which show portions of the simulations for the 5 and 50 ED unit cases with tanks. Note that these plots have the same format as that in Figure 12.

In the case with five ED units, shown in Figure 14, the tanks are nearly emptied between the beginning and end of the first and last two “days” and completely emptied on the third or low-power “day”. There is only some capture on this day due to scenario 3 activating when there is still some volume remaining and scenarios 3 and 4 triggering when the power availability is high enough for scenario 4 to provide enough volume for scenario 3 at the middle of the day.

Meanwhile, in the case with 50 ED units, shown in Figure 15, the volumes of acid and base in the tanks are barely used, and only at the beginning and end of the third “day”, when the nonzero available power is the lowest. Except for at those moments, the tank volume remains nearly constant at its maximum fill. An additional aspect to note is that the rate of DOC closely follows the power availability in the case with 50 ED units; even on the third “day” shown, the DOC rate follows the sine profile of the power availability. The reason for this disparity in DOC and tank usage is that the difference in minimum power required for scenarios 1, 2, and 3 becomes much smaller for the case with 50 ED units (as indicated in Figure 13, as well as by the lower power needs for the ED system), meaning it is less likely for the power availability to fall between these thresholds and trigger scenario 3. Instead, it is easier to activate scenarios 1 or 2 and continue DOC without using the tanks, which is likely why the benefits of having tanks become negligible beyond 30 ED units.

While the trend observed suggests that lower minimum power requirements and an increased number of ED units—or greater flexibility with handling power inputs—can enhance ${\mathrm{CO}}_2$ capture rates and potentially reduce reliance on storage tanks, these findings are specific to the example power profile and tank sizes used in this study. Further optimization along with experimental validation will be necessary to assess the broader applicability of this trend.

3.4. Case Studies with Hybrid Renewable Energy Systems

The Texas case study utilized wind energy and a battery to power the DOC plant, while the Oregon case study also included wave energy. The Texas case overall produced less energy than the Oregon one, due to a smaller wind resource and insufficient wave resources to incorporate WEC devices. The results of the case studies are shown in

Table 10. Case study results for renewable energy-powered DOC plants.

Parameter	Texas	Oregon
Annual Renewable Energy Production (GWh)	1087.6	1451.7
Wind Capacity Factor (%)	36.0	46.4
Wave Capacity Factor (%)	N/A	40.7
Hybrid Renewable Energy System Capacity Factor (%)	38.2	45.8
LCOE ($/MWh)	148	209
DOC Capacity Factor (%)	34.2	44.4
Yearly ${\mathrm{CO}}_2$ Capture (kt${\mathrm{CO}}_2$/yr)	495.8	685.6

. Note that the “DOC capacity factor” is lower than the renewable energy capacity factors because not all of the renewable energy is fully utilized given the discrete nature of the DOC device. Further optimization of the battery usage could improve the DOC performance. The Texas case had a lower hybrid renewable energy system capacity factor than the Oregon hybrid energy system by 7.6%, meaning the system off the coast of Oregon is able to provide more of the necessary power required to operate its DOC plant than the case off the coast of Texas.

The Oregon case is in deeper water and assumes that floating wind technology is required, leading to higher energy costs than in the Texas case, which assumes fixed-bottom technology is used for the wind system. Thus, despite producing less energy over the year, the Texas plant has a lower LCOE than that of the Oregon system. However, the rate of ${\mathrm{CO}}_2$ captured is higher in the Oregon location (see Table 10).

The time-dependent results for the location off the coast of Texas are shown in Figure 16. Note the high degree of variability in the input power profile and how the tanks almost fully deplete and capture goes briefly to zero due to the low power input between hours 3980 and 4000. This instance in the time-dependent results demonstrates how the tanks can be used to continue capture during the low-power conditions in realistic power profiles.

The time-dependent results for the DOC plant in the Oregon location are shown in Figure 17. During the time range shown, the power remains above the minimum power threshold for operating scenarios 1 and 2, meaning the solutions in the tanks are not utilized and scenario 1 is consistently active. The total percentage of time spent in each scenario is listed in

Table 11. Percentage of time in each scenario at each location.

Parameter	Texas	Oregon
Scenario 1 (%)	59.3	70.4
Scenario 2 (%)	13.8	11
Scenario 3 (%)	7.8	8.3
Scenario 4 (%)	0.7	1.1
Scenario 5 (%)	18.4	9.2

.

The plant in the Oregon location remains in scenario 1 over 70% of the time, while the one off the coast of Texas only remains in it for less than 60% of the time. Despite this, the frequency of using scenarios 2 through 4 is similar between the two cases. However, the DOC plant off the coast of Texas spends more time in scenario 5 or inactive than the other plant. It is possible that the DOC plant off the coast of Oregon has fewer periods of inactivity due to utilizing another form of renewable energy, wave power, which can still produce power when wind availability is limited. However, more research is needed to fully assess the potential benefits of using a diverse array of energy sources for DOC plants.

4. Discussion

The DOC model described in this work combines equations from the literature related to the electrochemistry, ocean chemistry, and thermodynamics of DOC to evaluate the potential performance of these plants under variable renewable energy (see Section 2). The model was developed with advisement from an industry partner in ED-based DOC and validated with their inputs, which are not included in this work due to confidentiality. However, the results of our model with their inputs were similar to those they anticipated for their large-scale system (see Section 3.1). As discussed in Section 2.6, the overall accuracy of this model can later be improved as this technology is deployed more frequently and at larger scales and more information on DOC plant performance is more widely available. As described in Section 3, the overall model can be used to evaluate how DOC can be impacted by power from variable resources, altering system parameters like the number of ED units in the electrochemical system to represent an ED system’s ability to use power more flexibly, and the forms of renewable energy available in potential deployment locations.

The model can account for the impacts of variable power on a DOC plant (see Section 3.2). Prior to evaluating the example DOC plant’s performance with realistic renewable energy power profiles, we first assessed performance with an example sine-like power profile with periods of low power (see Section 2.9.1). The results showed that the scenarios of operation were triggering as expected and the chemical storage tanks were being used to continue DOC during periods of low power availability.

The example DOC plant’s performance with varying levels of ED discretization and with and without tanks was evaluated to examine the benefits of ED systems with a greater tolerance for variable power (see Section 2.9.2 and Section 3.3). The analysis indicated that having a higher number of ED units with the same total ED power need, or an electrochemical system that can better handle power variability and requires a lower minimum power to operate, can have a higher DOC capacity factor and, therefore, a higher total amount of ${\mathrm{CO}}_2$ capture, as shown in Figure 13. This benefit is in part due to the lower energy requirements for enabling minimum DOC, as plants with higher numbers of ED units are better able to use the available power for DOC and minimize excess power than plants with fewer ED units (see Figure 14 and Figure 15). For the power profile used in this analysis, the benefit of having tanks was also reduced as the number of ED units increased, which was also due to the lower minimum power needs for DOC (see Figure 13). This indicates that having an electrochemical system that can better handle variable power with lower power requirements for minimum capture can be generally advantageous, potentially to the point that tanks are rarely necessary except during periods of maintenance of the electrochemical system. Results from the literature for ED-based desalination systems have also shown that ED systems with a greater tolerance for power variability are able to perform better (or, in their case, desalinate more water) than those with fixed power needs, which, in this case, correlates to systems with a high number of ED units and a single ED unit, respectively [11]. Future work can further investigate the accuracy of approximating a variable ED system as a collection of multiple discrete “units” by comparing the model with operational DOC deployments and with results from experiments investigating how variable renewable energy can impact ED-based DOC performance.

Additionally, while this study focuses on ED-based DOC systems, electrolysis can be used in place of ED to generate acid and base in addition to generating valuable hydrogen gas, which can be used directly as a fuel or combined with the captured ${\mathrm{CO}}_2$ to produce synthetic carbon-based fuels [1,2]. Unlike ED, electrolysis requires consistent power and its performance can steadily decrease if the system is repeatedly turned on and off like the ED units are in this model [35]. Electrolysis can therefore be considered to be similar to a single-ED-unit system and, as shown in Figure 13, could greatly benefit from chemical storage tanks. Note that battery storage would still be essential in this case to prevent frequent shutdowns, but, when overall power availability is low, the tanks could be very beneficial for continuing DOC in these alternative systems. Such electrolysis-based DOC systems are another area of interest for future work.

Two case studies were carried out using hybrid energy systems to power DOC, one off the coast of Texas and one off the coast of Oregon. The Texas location has lower wind speeds and smaller wave resources so WECs were not included in the system, resulting in lower annual energy production. Despite lower annual energy production, the costs of the wind–battery hybrid were lower because of the shallower water depths, which allowed for a fixed-bottom turbine substructure to be deployed, which currently has fewer costs than floating structures. However, due to the lower energy input into the DOC plant, there was less ${\mathrm{CO}}_2$ captured overall. Meanwhile, the Oregon location has higher wind speeds and adequate wave resources, so both wind turbines and WECs were included in the system. The wind–wave–battery hybrid produced higher and more consistent energy production over the year. However, the Oregon location is in deeper waters, likely requiring floating turbine substructures, which come at a higher cost. Additionally, current WEC reference models have high costs and have relatively small capacity, adding to the overall hybrid energy system cost. The LCOE of the Oregon location was higher, but the steadier energy profile resulted in higher yearly ${\mathrm{CO}}_2$ capture. Future research can investigate using cost and power performance data for realistic WECs, assess the benefits of using additional power sources, such as solar or tidal energy, and adjust the capacities of renewable energy used in these case studies to minimize costs and maximize capture.

5. Conclusions

This study aimed to develop a model of ED-based DOC to assess how variable power from low-carbon energy sources like renewable energy could impact the amount of ${\mathrm{CO}}_2$ captured by the plants and their electricity costs. DOC utilizes the ocean to separate or capture ${\mathrm{CO}}_2$ from the ambient environment, which can then be converted into a commercial products like synthetic fuels or stored underground for permanent removal [2]. These plants are already being deployed on pilot scales and are planned to reach much more massive scales (hundreds of thousands to millions of tons of yearly capture) [2,7,8,36,37].

The model accounts for the electrochemistry, ocean chemistry, and thermodynamics of DOC and integrates them into the hybrid renewable energy modeling software, H2I. ED-based DOC plants can handle variable power through their electrochemical system, which can directly use variable power from renewable energy sources, and by storing the chemical solutions made by the ED system used for capture, which can be used for DOC during periods of lower power availability [2,9,10]. The modeled DOC plants can leverage the tanks via the operation scenarios described in Section 2.5. The overall model is generalizable and input data for an example nonexistent DOC plant was used to evaluate how seawater conditions, variable power, different plant parameters, and renewable energy at potential deployment locations can impact plant performance. It was found that the plant operated as expected under a generic variable power profile, triggering the relevant operation scenarios given the power and volume available. Further analysis showed that ED systems which can utilize a greater variety of power inputs and have a low minimum power requirement (represented in the model as plants with higher numbers of ED units), and can generally enable more DOC while needing to rely far less on tank storage. Two case studies were conducted off the coasts of Texas and Oregon. The case off the coast of Texas produced less energy and had lower rates of ${\mathrm{CO}}_2$ capture than the one off the coast of Oregon. Further plant optimization including technology capacity sizing and tank capacity in the DOC plant could result in higher rates of ${\mathrm{CO}}_2$ capture. Note that DOC plant cost estimates were not included in this work as current estimates from the literature are sparse and additional research is necessary to build a more up-to-date cost model for current DOC deployments.

The overall motivation behind this work was to develop a tool that encourages and supports collaboration between DOC and renewable energy developers to facilitate larger deployments of renewable-powered DOC plants. Future efforts will explore other processes that can be leveraged by DOC such as technologies that convert ${\mathrm{CO}}_2$ into commercial products like synthetic fuels or subseafloor ${\mathrm{CO}}_2$ storage. Further development could also include optimization studies to refine the control strategy for scenario selection, enhanced validation using experimental and deployment data from ED-based DOC systems under variable power conditions, and expanded capabilities to assess biogeochemical and environmental impacts of DOC and other forms of electrochemical mCDR.