Method of accelerating thermodynamic process parameter computation for carbon capture, utilization, and storage systems

Abstract

Certain aspects of the disclosure provide a method for carbon capture, utilization, and storage (CCUS) process simulation. The method generally includes processing, with a first sub-model of a machine learning (ML) model, input features to generate a first thermodynamic process parameter for a first thermodynamic component, wherein the input features comprise one or more thermodynamic properties; processing, with a second sub-model of the ML model, the input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter when the first thermodynamic process parameter is less than the first threshold; and providing as a first output from the ML model the selected final thermodynamic process parameter.

Description

METHOD OF ACCELERATING THERMODYNAMIC PROCESS PARAMETER COMPUTATION FOR CARBON CAPTURE, UTILIZATION, AND STORAGE SYSTEMSBACKGROUNDField

[0001] Aspects of the present disclosure relate to carbon capture, utilization, and storage process simulation.Description of Related Art

[0002] The stabilization and / or the reduction of atmospheric concentrations of greenhouse gases, particularly carbon dioxide (CO2), represents a key challenge in the attempt to mitigate climate change. In particular, carbon dioxide and other heat-trapping gases have molecular structures that enable them to absorb infrared radiation and re-radiate the infrared waves out in all directions - some into space and some back to Earth. The infrared radiation that is radiated back to Earth causes further warming at the surface and lower atmosphere.

[0003] Concern over environmental effects, including global warming, of carbon dioxide has resulted in significant efforts to reduce overall atmospheric carbon dioxide including, for example, through reforesting, increasing use of renewable energy sources, and the use of carbon capture, utilization, and storage (CCUS) processes. CCUS involves the capture of carbon dioxide prior to release into the atmosphere, generally from large point sources, such as power generation or industrial facilities that use either fossil fuels or biomass as fuel. The captured carbon dioxide is then compressed into a liquid state and transported by pipeline, ship, rail, or road tanker to be injected into deep geological formations, and thus permanently stored in depleted oil and gas reservoirs, coalbeds, or deep saline aquifers, where the geology is suitable for containment. An alternative to permanent storage is to re-use the captured carbon dioxide in industrial processes by converting it into, for example, plastics, concrete, or biofuel, to name a few. This prevents the carbon dioxide from entering the atmosphere, mitigating against carbon emissions from industry and heating and thereby reducing the contribution to global warming, ocean acidification, and other environmental effects. As such, CCUS has emerged as a critical technology in the global effort to combat climate change.

[0004] Modeling and simulation of carbon dioxide storage may be vital to understanding and optimizing CCUS processes. In particular, modeling and simulation involves the use of advanced computational models and simulations to replicate the complex interactions that occur when carbon dioxide is captured, transported, and injected deep underground for long-term storage. Modeling may refer to the collation of subsurface data into a 3-dimensional representation of the subsurface geology and hydrogeology of a carbon dioxide storage site and surrounding area. Simulation may refer to the process of using specialized software to create quantitative predictions of the dynamic effects of carbon dioxide injection, including the migration of carbon dioxide and other formation fluids, pressure and temperature behavior, and the long-term behavior of injected carbon dioxide within the modeled volume. Modeling and simulation of carbon dioxide storage not only enhances understanding of the subsurface behavior but may also play an important role in designing efficient, effective, and safe CCUS systems.

[0005] Simulating the sequestration potential of carbon dioxide and long-term behavior of geologic reservoirs may require calculating the pressure, temperature, and composition properties of carbon dioxide and water (H2O) mixtures at depths typically considered for geological storage. In particular, for temperatures and pressures at such depths (e.g., such as temperatures below 100°C and pressures between 200 and 400 bar), the mixing of carbon dioxide with water may result in two immiscible phases, an HzO-rich liquid phase or a CCh-rich gas or liquid phase. The same two-phase behavior may persist at different temperatures and / or pressures; however, the amount of carbon dioxide present or water present in each phase may vary. In other words, the solubility of carbon dioxide in water and the solubility of water in carbon dioxide may depend on at least the temperature and pressure of where a carbon dioxide and water mixture is situated. The ability to compute the mutual solubilities of carbon dioxide and water in a reliable and efficient manner is thus critical to predicting the flow of carbon dioxide and water in the subsurface using numerical models and simulation software for CCUS process simulation. Further, computing the degree to which carbon dioxide can dissolve in a given aqueous phase is important, not only for estimating the capture of carbon dioxide, but also for optimizing how the carbon dioxide can be injected by dissolving in an aqueous phase, such as brine (e.g., a high-concentration solution of salt in water).SUMMARY

[0006] Certain aspects of the disclosure provide a method of carbon capture, utilization, and storage process simulation, comprising: processing, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component, wherein the plurality of input features comprise one or more thermodynamic properties; processing, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold; and providing as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component.

[0007] Certain aspects of the disclosure provide a method of training an ML model to predict thermodynamic process parameters for carbon capture, utilization, and storage process simulation, comprising: obtaining a first plurality of training data instances, wherein each of the first plurality of training data instances comprises: a first training input comprising one or more thermodynamic properties; and a first training output comprising a thermodynamic process parameter of a first thermodynamic component based on the one or more thermodynamic properties; training a first sub-model of the ML model, to predict a first thermodynamic process parameter for the first thermodynamic component using the first plurality of training data instances; training a second sub-model of the ML model to predict a second thermodynamic process parameter for the first thermodynamic component below a first threshold using a subset of the first plurality of training data instances; and configuring the ML model to select a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is greater than the first threshold; or the second thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold.

[0008] Other aspects provide processing systems configured to perform the aforementioned methods as well as those described herein; non-transitory, computer-readable media comprising instructions that, when executed by a processors of a processing system, cause the processing system to perform the aforementioned methods as well as those described herein; a computer program product embodied on a computer readable storage medium comprising code for performing the aforementioned methods as well as those further described herein; and a processing system comprising means for performing the aforementioned methods as well as those further described herein.

[0009] The following description and the related drawings set forth in detail certain illustrative features of one or more aspects.DESCRIPTION OF THE DRAWINGS

[0010] The appended figures depict certain aspects and are therefore not to be considered limiting of the scope of this disclosure.

[0011] FIG. 1 depicts an example system for training and using a machine learning model to predict thermodynamic process parameter(s) for carbon capture, utilization, and storage process(es) simulation.

[0012] FIG. 2 depicts an example machine learning model, including two sub-models, trained to determine thermodynamic process parameters for carbon capture, utilization, and storage process(es) simulation.

[0013] FIGS. 3A-3B depict the accuracy of an example machine learning model trained to determine thermodynamic process parameter(s) for carbon capture, utilization, and storage process(es) simulation.

[0014] FIG. 4 depicts example computational efficiency achieved when using a machine learning model for thermodynamic process parameter(s) prediction.

[0015] FIG. 5 depicts an example method of carbon capture, utilization, and storage process simulation.

[0016] FIG. 6 depicts an example method training a machine learning model to predict thermodynamic process parameters for carbon capture, utilization, and storage process simulation.

[0017] FIG. 7 depicts an example processing system on which aspects of the present disclosure can be performed.

[0018] To facilitate understanding, identical reference numerals have been used, where possible, to designate identical elements that are common to the drawings. It is contemplated that elements and features of one embodiment may be beneficially incorporated in other embodiments without further recitation.DETAILED DESCRIPTION

[0019] Several conventional approaches exist to compute the aqueous solubility of carbon dioxide, with or without consideration of the water solubility in the carbon dioxide phase. However, most of these approaches are computationally expensive, thereby requiring a large number of resources (e.g., compute power and / or time) to compute the solubility of carbon dioxide and / or water. Further, most of these approaches are too computationally intensive for their incorporation into efficient CCUS process simulators for simulation of carbon dioxide injection and storage in a subsurface model.

[0020] For example, a commonality among each of these approaches includes the calculation of a thermodynamic process parameter for carbon dioxide and / or water, and more specifically, a K-value for carbon dioxide and / or water. A K-value, also referred to as a “vapor-liquid equilibrium ratio,” is a thermodynamic ratio that determines the phase split of a component (e.g., carbon dioxide, water, etc.) in the vapor and aqueous phase. For example, given a K-value for a specific component at certain conditions, the magnitude will determine the affinity the component has to be in the vapor phase (e.g., a K-value greater than 1) or the aqueous phase (e.g., a K-value smaller than 1). Estimating accurate K-values may require the use of multiple nested loops of equations that significantly increase the complexity of the calculation.

[0021] For example, one conventional approach that exists to compute the mutual solubilities of carbon dioxide and water includes the approach developed by Nicolas Spycher and Karsten Pruess. Specifically, Spycher and Pruess developed a method for calculating the mutual solubility of carbon dioxide and water for pressures up to 600 bar and temperatures between 12°C and 300°C, while also accounting for the salinity effects of chloride brines (e.g., 0-6 molal sodium chloride (NaCl) and 0-4 molal calcium chloride (CaCb)). The method solves equilibrium equations forcarbon dioxide and water to calculate the mole fraction of carbon dioxide and water in the CCh- rich and aqueous phases. The equilibrium equations for carbon dioxide and water are defined in accordance with Equations 1 and 2, respectively:where where (p is the fugacity coefficient for each component in the CCh-rich phase, y is the mole fraction of each component in the CCh-rich phase, P is the total pressure of system, K° is a function of temperature T and reference pressure P° and is the thermodynamic equilibrium constant for each component, V is the average partial molar volume of each component over the range of P° to P, R is a gas constant, and acis the activity of carbon dioxide or water. Thus, the equilibrium equations for carbon dioxide and water (e.g., Equation 1 and Equation 2, respectively) are functions of pressure (P), temperature (7), and composition.

[0022] An iterative approach, developed by Spycher and Pruess using Equations 1 and 2 above, is used to calculate K-values for carbon dioxide and water. For example, the iterative approach begins by determining an initial guess for wCO2and yH2O, where wCO2is the mole fraction of carbon dioxide in aqueous phase and yH20is the mole fraction of water. For a system with two components, such as carbon dioxide and water, one mole fraction of one of the components in needed for each phase. For example, for the gas phase, an initial guess for the mole fraction of water, yH20, may be determined and yC02may be calculated as yCO2= 1 — yH20. For the aqueous phase, an initial guess for the mole fraction of carbon dioxide, wC02, may be determined and wH20may be calculated as wH20= 1 — wC02. The mole fraction of the components in the aqueous phase are embedded in the activities of carbon dioxide and water in Equations 1 and 2 above.

[0023] As an example, wC02may be initially estimated as 0.0009 for T > 100°C. Further, yH20may be initially estimated per Equation 3 :Psat_ H2O ( 3 )VH2O ~ p where P^o is the saturation pressure of water at a specific temperature. K-values are then calculated using the initial guesses of wC02and yH2o>and the phase composition is re-calculated using these K-values. With the new phase composition, new K-values are calculated. This process of calculating K-values and phase composition is repeated until the solution converges. Molalities of salts are treated as inputs and may remain unchanged during the iterations; however, the carbon dioxide molality may be updated.

[0024] Due to the iterative nature and complexity of such calculations, calculating K-values may be computationally inefficient and require a large number of computational resources. Further, a single change in pressure, temperature, and / or salinity may require the re-calculation of K-values for carbon dioxide and water, again using the same iterative approach. For example, different subsurface locations for storing carbon dioxide and / or where carbon dioxide may migrate may require the re-calculation of K-values for carbon dioxide and water at these locations due to changes in pressure, temperature, and / or salinity. As such, conventional approaches, like the Spycher and Pruess method, for computing the mutual solubilities of carbon dioxide and water are time consuming and resource intensive. Accordingly, there is a need for a technical solution that accelerates thermodynamic process parameter computation, such as K-value computation, for CCUS process simulation.

[0025] Embodiments described herein help to overcome the aforementioned technical problems of conventional approaches and improve upon the state of the art by providing an approach for thermodynamic process parameter determination, such as K-value determination, using a trained machine learning (ML) model. The ML model may be configured to predict a thermodynamic process parameter for one or more thermodynamic components based on one or more thermodynamic properties. For example, the ML model may be configured to predict K- values for carbon dioxide and water in the presence of salts for different pressures and temperatures. These K-values predicted by the model may be used to simulate CCUS process(es) in a subsurface model to enable the efficient, effective, and safe design of CCUS systems. As described in detail below, the ML model may include any arbitrary number of piecewise trainedsub-models for predicting thermodynamic process parameters) to help attain desired accuracy levels for the ML model.

[0026] The improved approach for determining thermodynamic process parameter(s), described herein, provides significant technical effects and advantages over existing iterative algorithms used for thermodynamic process parameter(s) computation, including a significant reduction in time and resources (e.g., compute and power) for computation. In particular, the ML model described herein may use an algorithm to leam and generalize from thermodynamic process parameters historically determined for various thermodynamic properties (e.g., determined using conventional iterative algorithms) in order to make thermodynamic process parameter predictions for new input data. As such, the ML model may be able to produce thermodynamic process parameter predictions more quickly than using conventional methods for determining the same values, thereby saving time and resources that would have previously been expended to perform iterative calculations for thermodynamic process parameters calculations. Use of the ML model further allows for accelerated thermodynamic process parameter determination if one or more thermodynamic properties are changed. As such, thermodynamic process parameters may be determined and provided as input to a simulator in a short period of time to allow for the simulation of CCUS process(es) in various subsurface environments (e.g., having different thermodynamic properties, such as temperature, pressure, etc.). Thus, by improving the computational bottlenecks associated with determining thermodynamic process parameters and thus simulating CCUS process(es), decisions made based on CCUS process simulation(s) may be expedited.Example System for CCUS Process(es) Simulation

[0027] FIG. 1 depicts an example system 100 for training and using an ML model to predict thermodynamic process parameter(s) for CCUS process(es) simulation. As shown in FIG. 1, training an ML model for predicting thermodynamic process parameter(s), at 106, includes training data generation 110 and training 112. Further, using the ML model for predicting thermodynamic process parameter(s) for CCUS process(es) simulation includes thermodynamic process param eter(s) prediction 122, optionally, derivative(s) prediction 124, and CCUS process(es) simulation 126.

[0028] Training data generation 110 includes generating a plurality of training data instances that may be used to train the ML model for thermodynamic process parameter(s) prediction. Incertain embodiments, Spycher’s and Pruess’s iterative method for calculating K-values, described in detail above (e.g., using Equations 1, 2, and 3 above), is used to generate the training data instances. For example, Spycher’s and Pruess’s iterative method may be used to calculate K-values for one or more thermodynamic components (e.g., carbon dioxide, water, etc.) over a range of pressure, temperature, and salt molality values (e.g., a range of thermodynamic properties). In certain embodiments, the range for pressure is between 0 and 600 bar. In certain embodiments, the range for temperature is between 12°C and 350°C. In certain embodiments, the ranges for salt molality include 0-6 molal solutions for sodium chloride (NaCl), 0-5 molal solutions for calcium chloride (CaCh), and / or 0-1 molal solutions for calcium carbonate (CaCOi). Thus, each training data instance generated may include (1) a training output including a K-value determined for a combination of pressure, temperature, and salt molality values, using Spycher’s and Pruess’s iterative method, and (2) a training input including the pressure, temperature, and salt molality values (e.g., thermodynamic properties) used to generate the respective K-value.

[0029] Training 112 includes training an ML model for thermodynamic process parameter(s) prediction. The ML model may be a neural network model (e.g., such as a fully connected neural network model having fully connected layers) and may include one or more hidden layers. For example, the ML model may be trained to predict a thermodynamic process parameter for a thermodynamic component using the training data instances generated for training data generation 110. In particular, the ML model may predict a thermodynamic process parameter, such as a K- value, using the thermodynamic properties (e.g., training input) associated with each training data instance. The K-value predicted for each training data instance may be compared to the K-value included in the training output of the respective training data instance used for the K-value prediction. This comparison may be performed to evaluate the similarity of the model’s predicted K-values to the true expected K-values (e.g., training output K-values). Various parameters may be modified for the ML model based on the comparisons to optimize the model for thermodynamic parameter(s) prediction.

[0030] In certain embodiments, evaluating the similarity of the ML model’s predicted K- values to the true K-values, for different thermodynamic properties, is performed using a loss function. The loss function may be a modified mean squared error (e.g., the average squared difference between a predicted K-value value and the true K-value) that is weighted by the true K- value to refine the estimates for small K-values. However, other loss functions may be used.

[0031] In certain embodiments, two or more piecewise sub-models may make up the ML model. As such, training 112 may include training each sub-model of the ML model to achieve desired accuracy levels for the ML model. As an illustrative example, to train an ML model to accurately predict thermodynamic process parameters, e.g., K-values, for two thermodynamic components (e g., carbon dioxide and water), training 112 may include training four sub-models. Lwo of the sub-models, e.g., a first sub-model and a second sub-model, may each be trained to predict a thermodynamic process parameter for the first thermodynamic component (e.g., carbon dioxide), while the remaining two sub-models, e.g., a third sub-model and a fourth sub-model, may each be trained to predict a thermodynamic process parameter for the second thermodynamic component (e.g., water).

[0032] The first sub-model and the second sub-model may be trained using the training data instances generated for training data generation 110 and associated with the first thermodynamic component (e.g., K-values calculated for carbon dioxide). While all the training data instances associated with the first thermodynamic component may be used to train the first sub-model, only a subset of the training data instances associated with the first thermodynamic component may be used to train the second sub-model. More specifically, to enable the ML model to make more accurate smaller thermodynamic process parameter (e.g., smaller K-value) predictions for the first thermodynamic component, the second sub-model may be trained with training data instances associated with the first thermodynamic component and having thermodynamic process parameters below a first threshold (e.g., for carbon dioxide, the first threshold may be K-value = 50).

[0033] In addition to training the first and second sub-models of the ML model to predict thermodynamic parameters for the first thermodynamic component, the ML model may also be configured to select a final thermodynamic process parameter for the first thermodynamic component as the output of the first sub-model or the output of the second sub-model. More specifically, the ML model may be configured to select the output thermodynamic process parameter from the first sub-model as the final thermodynamic process parameter when the output thermodynamic process parameter from the first sub-model is greater than the first threshold. Alternatively, the ML model may be configured to select the output thermodynamic process parameter from the second sub-model as the final thermodynamic process parameter when the output thermodynamic process parameter from the first sub-model is less than, or equal to, the firstthreshold (e.g., given the second sub-model is better suited for predicting smaller K-values than the first sub-model, given the second sub-model is trained with smaller K-value training data instances).

[0034] Similarly, the third sub-model and the fourth sub-model may be trained using the training data instances generated for training data generation 110 and associated with the second thermodynamic component (e.g., K-values calculated for water). While all the training data instances associated with the second thermodynamic component may be used to train the third sub-model, only a subset of the training data instances associated with the second thermodynamic component may be used to train the fourth sub-model. More specifically, to enable the ML model to make more accurate smaller thermodynamic process parameter (e.g., smaller K-value) predictions for the second thermodynamic component, the fourth sub-model may be trained with training data instances associated with the second thermodynamic component and having thermodynamic process parameters below a second threshold K-value (e.g., for water, the second threshold may be K-value = 0.5).

[0035] In addition to training the third and fourth sub-models of the ML model to predict thermodynamic parameters for the second thermodynamic component, the ML model may also be configured to select a final thermodynamic process parameter for the second thermodynamic component as the output of the third sub-model or the output of the fourth sub-model. More specifically, the ML model may be configured to select the output thermodynamic process parameter from the third sub-model as the final thermodynamic process parameter when the output thermodynamic process parameter from the third sub-model is greater than the second threshold. Alternatively, the ML model may be configured to select the output thermodynamic process parameter from the fourth sub-model as the final thermodynamic process parameter when the output thermodynamic process parameter from the third sub-model is less than the second threshold (e.g., given the fourth sub-model is better suited for predicting smaller K-values than the third sub-model, given the fourth sub-model is trained with smaller K-value training data instances).

[0036] In certain embodiments, the ML model may be configured to select the final thermodynamic process parameter for the first thermodynamic component and / or the final thermodynamic process parameter for the second thermodynamic component using a Heavisidefunction. The Heaviside function may be defined in accordance with Equations 4, 5, and 6, respectively:H^X. XQ) = 0.5 * sign(x — x0) + 1 ( 4 ) when x < 0 sign(x) = 0, when x = 0( 1, when x > 0 ( 5)where H is the Heaviside function, T is the threshold (e.g., K-value threshold) for the respective thermodynamic component (e.g., first threshold or second threshold), yfUu is the output thermodynamic process parameter predicted by the first sub-model or the third sub-model, yspecis the output thermodynamic process parameter predicted by the third sub-model or the fourth submodel, and ypredis the overall prediction of the thermodynamic process parameter for the first thermodynamic component or the second thermodynamic component. This piecewise training and use of a Heaviside function for predicting thermodynamic process parameters helps to increases overall model accuracy compared using to a single network that predicts thermodynamic process parameters for the first and second thermodynamic components over the entire range of thermodynamic process parameters (e.g., training only one sub-model per thermodynamic component over the entire range of K-values).

[0037] Although the above example illustrates the training of a ML model including four submodels to predict thermodynamic process parameters for two thermodynamic components, in other examples, more or fewer sub-models may make up the ML model, thermodynamic process parameters may be predicted for more than two thermodynamic components, and / or more or fewer than two sub-models may be associated with each thermodynamic component.

[0038] In certain embodiments, training 112 further includes training the ML model to compute one or more derivatives for each thermodynamic component for which the model predicts a thermodynamic process parameter. Each derivative may be based on one of the thermodynamicproperties provided as input into the ML model (e.g., pressure, temperature, etc.). Each derivative may be computed using automatic differentiation for the respective thermodynamic property. Each derivative computed may measure the rate of change of a final thermodynamic process parameter predicted for a thermodynamic component when the respective thermodynamic property changes.

[0039] After training, at 106, is complete, the ML model may be deployed for inferencing (e g., deployed for predicting thermodynamic process param eter(s) for CCUS process(es) simulation 120). When deployed, the ML model may perform thermodynamic process parameter(s) prediction 122, and further in some cases, derivative(s) prediction 124. Thermodynamic process param eter(s) prediction 122 may include the ML model (or each of its sub-models) processing one or more thermodynamic properties to generate one or more thermodynamic process parameters for one or more thermodynamic components. The thermodynamic property(ies) may include a temperature property, a pressure property, and / or one or more salinity properties, to name a few. In certain embodiments, the one or more thermodynamic process parameters predicted by the ML model (and / or its sub-models) are Revalues. Derivative(s) prediction 124 may include the ML model computing a derivative of the thermodynamic process parameter predicated for each thermodynamic component based on one of the thermodynamic properties.

[0040] Additional details regarding thermodynamic process parameter(s) prediction 122 and derivative(s) prediction 124 are provided herein with respect to FIG. 2.

[0041] CCUS process(es) simulation 126 includes simulating one or more CCUS processes in a subsurface model using the thermodynamic process parameter(s) and / or derivative(s) predicted for one or more thermodynamic components. In some cases, the ML model may be coupled with a CCUS process simulator to provide such values for CCUS process(es) simulation.Example Thermodynamic Process Parameters and Derivatives Prediction

[0042] FIG. 2 depicts an example ML model 200, including four sub-models, trained to determine thermodynamic process parameters and derivatives for CCUS process(es) simulation. More specifically, the ML model 200 may include a first sub-model 232 and a second sub-model 234 used to predict K-values for a first thermodynamic component, such as carbon dioxide. Further, the ML model 200 may include a third sub-model 236 and a fourth sub-model 238 used to predict K-values for a second thermodynamic component, such as water.

[0043] The first sub-model 232 and the second sub-model 234 may have been previously trained to predict K-values for carbon dioxide based on training data instances including K-values calculated for carbon dioxide for various thermodynamic properties and ranges. However, the second sub-model 234 may be trained using only those training data instances associated with Revalues below a first threshold K-value of 50. For example, if 10,000 training data instances exist for carbon dioxide (e.g., have K-values associated with carbon dioxide) and only 2,000 of those training data instances are associated with K-values less than 50, then only 2,000 of those training data instances may have been used to train the second sub-model 234. However, the 10,000 training data instances may have been used to train the first sub-model 232.

[0044] Similarly, the third sub-model 236 and the fourth sub-model 238 may have been previously trained to predict K-values for water based on training data instances including K- values calculated for water for various thermodynamic properties and ranges. However, the fourth sub-model 236 may be trained using only those training data instances associated with K-values below a second threshold K-value of 0.5.

[0045] To initiate inferencing by the ML model 200, inputs 202 may be provided to the ML model 200. Inputs 202 may include one or more thermodynamic properties. For example, the thermodynamic properties may include a temperature property, a pressure property, and / or one or more salinity properties.

[0046] The first sub-model 232 may process inputs 202 and thereby generate a first K-value for carbon dioxide. Further, the second sub-model 234 may process inputs 202 and thereby generate a second K-value for carbon dioxide. The ML model 200 may select a final K-value 208 for carbon dioxide using a Heaviside function 206. More specifically, the ML model 200 may select the final K-value 208 for carbon dioxide as (1) the first K-value when the first K-value is greater than the first threshold K-value and (2) the second K-value when first K-value is less than the first threshold K-value (e.g., such prediction switching is implemented using Heaviside function 216).

[0047] Gradient tapes 210 are then used to calculate derivatives 212 and 214 for final K-value 208. Gradient tapes 210 may be the derivative tool of TensorFlow®, e.g., an end-to-end platform for machine learning. Derivative 212 may be the derivative of final K-value 208 with respect to a first thermodynamic property in inputs 202, such as temperature. Derivative 214 may be thederivative of final K-value 208 with respect to a second thermodynamic property in inputs 202, such as pressure.

[0048] Additionally, the third sub-model 236 may process inputs 202 and thereby generate a first K-value for water. Further, the fourth sub-model 238 may process inputs 202 and thereby generate a second K-value for water. The ML model 200 may select a final K-value 218 for water using a Heaviside function 216. More specifically, the ML model 200 may select the final K-value 218 for water as (1) the first K-value when the first K-value is greater than the second threshold K-value or (2) the second K-value when first K-value is less than the second threshold K-value (e g., such prediction switching is implemented using Heaviside function 216).

[0049] Gradient tapes 220 are then used to calculate derivatives 222 and 224 for final K-value 218. Derivative 222 may be the derivative of final K-value 218 with respect to a first thermodynamic property in inputs 202, such as temperature. Derivative 224 may be the derivative of final K-value 218 with respect to a second thermodynamic property in inputs 202, such as pressure.

[0050] The final outputs for the ML model 200 may include (1) final K-value 208, (2) derivative 212, (3) derivative 214, (4) final K-value 218, (5) derivative 222, and (6) derivative 224. These six output values may be provided as input into a simulator used to simulate one or more CCUS processes.Example Accuracy and Computation Efficiency Achieved when Using an ML Model for Thermodynamic Process Parameter(s) Prediction

[0051] FIGS. 3A-3B depict the accuracy of an example ML model trained to predict thermodynamic process parameter(s). More specifically, FIG. 3A depicts the error in the prediction obtained when using an ML model to predict K-values for carbon dioxide for a full range of pressure, temperature, and salinity (e.g., molality) inputs. When comparing the predicted K-values to the true, expected K-values, the maximum error in the K-values predicted by the ML model is equal to 5%, while 99% of the predictions are below a 2% error. As such, the ML model may not only provide efficient computation of K-values, but also a high percentage of accuracy for K-values predicted. In other words, the model is both more efficient and more performant.

[0052] FIG. 3B shows the accuracy of the ML model’s K-value predictions for varying temperature inputs for a given sample of fluid. The green curve represents the true K-values and the blue curve represents the K-values predicted by the model. Further, the red line represents the true derivative values while the black and purple lines represent the derivatives as obtained by finite difference using a small and large step size, respectively. Thus, as shown in FIG. 3B, the ML model may have high prediction accuracy given the lines are nearly the same for true and predicted K-values and derivative values.

[0053] FIG. 4 depicts example computational efficiency achieved when using an ML model for thermodynamic process parameter(s) prediction (e.g., such as described with respect to FIG. 2). For example, FIG. 4 depicts an example graph plotting the computational time (e.g., in seconds) needed to calculate K-values (1) by a human, using C++ and Spycher and Pruess’s iterative method (e.g., exhaustive method) and (2) by an ML model trained to make K-value predictions, for various sample sizes. While for sample sizes below 105, the time needed for computation using both methods only varies slightly, for sample sizes above 105, the computational time for calculating K-values using the ML model is substantially less than when the iterative method is used. In particular, the ML model is about 137 times faster for large samples and shows an almost constant time prediction for most practical batch sizes. As such, the ML model provides a more efficient means to determine K-value(s), which thereby reduces the amount of time needed for CCUS process(es) simulation (e.g., where the simulation is based on the determined K-value(s)) and further any decision making based on such simulation (e.g., for designing CCUS systems, selecting a site for carbon dioxide injection, etc.). Further, improved simulations may not only save time but also money in designing CCUS systems.Example Operations for CCUS Process Simulation

[0054] FIG. 5 depicts an example method 500 of CCUS process simulation. Method 500 may be performed by one or more processor(s) of a computing device, such as processor(s) 702 of processing system 700 described below with respect FIG. 7.

[0055] Method 500 begins, at step 502, with processing, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component. The plurality of input features may include one or more thermodynamic properties.

[0056] Method 500 proceeds, at step 504, with processing, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component.

[0057] Method 500 proceeds, at step 506, with selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold.

[0058] Method 500 proceeds, at step 508, with providing as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component.

[0059] Use of the ML model, including both the first sub-model and the second sub-model, to determine a final thermodynamic process parameter (e.g., such as a K-value) for the first thermodynamic component allows for accelerated thermodynamic process parameter determination. For example, the use of the ML model helps to produce a thermodynamic process parameter prediction more quickly than when using conventional methods (e.g., Spycher and Pruess method, described above) for determining the same values. As such, significant time and resources, that would have previously been expended, are saved. Further, quicker thermodynamic process parameter determination may lead to quicker CCUS process(es) simulation, which may allow for more efficient decision making based on such simulation.

[0060] In certain embodiments, method 500 further includes processing, with a third submodel of the ML model, the plurality of input features to generate a third thermodynamic process parameter for a second thermodynamic component. In certain embodiments, method 500 further includes processing, with a fourth sub-model of the ML model, the plurality of input features to generate a fourth thermodynamic process parameter for a second thermodynamic component. In certain embodiments, method 500 further includes selecting, by the ML model, a final thermodynamic process parameter for the second thermodynamic component as: the third thermodynamic process parameter generated for the second thermodynamic component when the third thermodynamic process parameter is greater than a second threshold; or the fourth thermodynamic process parameter generated for the second thermodynamic component when thefourth thermodynamic process parameter is less than the second threshold. In certain embodiments, method 500 further includes providing as a second output from the ML model the selected final thermodynamic process parameter for the second thermodynamic component.

[0061] In certain embodiments, method 500 further includes simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the final thermodynamic process parameter for the second thermodynamic component.

[0062] In certain embodiments, method 500 further includes for at least one of the one or more thermodynamic properties, computing a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property and simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the derivative of the final thermodynamic process parameter for the first thermodynamic component computed for the at least one of the one or more thermodynamic properties.

[0063] In certain embodiments, selecting, by the ML model, the final thermodynamic process parameter for the first thermodynamic component comprises using a Heaviside function to select one of the first thermodynamic process parameter generated for the first thermodynamic component or the second thermodynamic process parameter generated for the first thermodynamic component.

[0064] In certain embodiments, the one or more thermodynamic properties comprise at least one of a temperature property, a pressure property, or one or more salinity properties.

[0065] In certain embodiments, the first thermodynamic component comprises a gas or a liquid.

[0066] In certain embodiments, the first thermodynamic component comprises carbon dioxide (CO2) or dihydrogen oxide (H2O).

[0067] In certain embodiments, each of the first thermodynamic process parameter for the first thermodynamic component, the second thermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.

[0068] Note that FIG. 5 is just one example of a method, and other methods including fewer, additional, or alternative steps are possible consistent with this disclosure.Example Operations for Training an ML Model to Predict Thermodynamic Process Parameters for CCUS Process Simulation

[0069] FIG. 6 depicts an example method 600 of training an ML model to predict thermodynamic process parameters for CCUS process simulation. Method 600 may be performed by one or more processor(s) of a computing device, such as processor(s) 702 of processing system 700 described below with respect FIG. 7.

[0070] Method 600 begins, at step 602, with obtaining a first plurality of training data instances. Each of the first plurality of training data instances may include a first training input comprising one or more thermodynamic properties and a first training output comprising a thermodynamic process parameter of a first thermodynamic component based on the one or more thermodynamic properties.

[0071] Method 600 proceeds, at step 604, with training a first sub-model of the ML model to predict a first thermodynamic process parameter for the first thermodynamic component using the first plurality of training data instances.

[0072] Method 600 proceeds, at step 606, with training a second sub-model of the ML model to predict a second thermodynamic process parameter for the first thermodynamic component below a first threshold using a subset of the first plurality of training data instances.

[0073] Method 600 proceeds, at step 608, with configuring the ML model to select a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is greater than the first threshold or the second thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold.

[0074] In certain embodiments, method 600 further includes obtaining a second plurality of training data instances. Each of the second plurality of training data instances may include a second training input comprising the one or more thermodynamic properties and a second training output comprising a thermodynamic process parameter of a second thermodynamic component based onthe one or more thermodynamic properties. In certain embodiments, method 600 further includes training a third sub-model of the ML model to predict a third thermodynamic process parameter for the second thermodynamic component using the second plurality of training data instances. In certain embodiments, method 600 further includes training a fourth sub-model of the ML model to predict a fourth thermodynamic process parameter for the second thermodynamic component below a second threshold using a subset of the second plurality of training data instances. In certain embodiments, method 600 further includes configuring the ML model to select a final thermodynamic process parameter for the second thermodynamic component as: the third thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is greater than the second threshold; or the fourth thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is less than the second threshold.

[0075] In certain embodiments, method 600 further includes training the ML model to, using automatic differentiation for at least one of the one or more thermodynamic properties, compute a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property.

[0076] In certain embodiments, the ML model may be configured to select the final thermodynamic process parameter for the first thermodynamic component as the first thermodynamic process parameter predicted for the first thermodynamic component or the second thermodynamic process parameter predicted for the first thermodynamic component using a Heaviside function.

[0077] In certain embodiments, the one or more thermodynamic properties comprise at least one of a temperature property, a pressure property, or one or more salinity properties.

[0078] In certain embodiments, the one or more thermodynamic properties comprise: a pressure property less than or equal to 600 bar, a temperature property greater than or equal to 12 degrees Celsius and less than or equal to 100 degrees Celsius, and one or more salinity properties, each of the one or more salinity properties comprising a molality of a chloride brine greater than or equal to 0 molal and less than or equal to 6 molal.

[0079] In certain embodiments, the first thermodynamic component comprises a gas or a liquid.

[0080] In certain embodiments, the first thermodynamic component comprises carbon dioxide (CO2) or dihydrogen oxide (H2O).

[0081] In certain embodiments, each of the first thermodynamic process parameter for the first thermodynamic component, the second thermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.

[0082] Note that FIG. 6 is just one example of a method, and other methods including fewer, additional, or alternative steps are possible consistent with this disclosure.Example Processing System for CCUS Process Simulation

[0083] FIG. 7 depicts an example processing system 700 configured to perform various aspects described herein, including, for example, method 500 as described above with respect to FIG. 5 and method 600 as described above with respect to FIG. 6.

[0084] Processing system 700 is generally an example of an electronic device configured to execute computer-executable instructions, such as those derived from compiled computer code, including without limitation personal computers, tablet computers, servers, smart phones, smart devices, wearable devices, augmented and / or virtual reality devices, and others.

[0085] In the depicted example, processing system 700 includes one or more processors 702, one or more input / output devices 704, one or more display devices 706, one or more network interfaces 708 through which processing system 700 is connected to one or more networks (e.g., a local network, an intranet, the Internet, or any other group of processing systems communicatively connected to each other), and computer-readable medium 770. In the depicted example, the aforementioned components are coupled by a bus 710, which may generally be configured for data exchange amongst the components. Bus 710 may be representative of multiple buses, while only one is depicted for simplicity.

[0086] Processor(s) 702 are generally configured to retrieve and execute instructions stored in one or more memories, including local memories like computer-readable medium 770, as well as remote memories and data stores. Similarly, processor(s) 702 are configured to store application data residing in local memories like the computer-readable medium 770, as well as remote memories and data stores. More generally, bus 710 is configured to transmit programminginstructions and application data among the processor(s) 702, display device(s) 706, network interface(s) 708, and / or computer-readable medium 770. In certain embodiments, processor(s) 702 are representative of one or more central processing units (CPUs), graphics processing unit (GPUs), tensor processing unit (TPUs), accelerators, and other processing devices.

[0087] Input / output device(s) 704 may include any device, mechanism, system, interactive display, and / or various other hardware and software components for communicating information between processing system 700 and a user of processing system 700. For example, input / output device(s) 704 may include input hardware, such as a keyboard, touch screen, button, microphone, speaker, and / or other device for receiving inputs from the user and sending outputs to the user.

[0088] Display device(s) 706 may generally include any sort of device configured to display data, information, graphics, user interface elements, and the like to a user. For example, display device(s) 706 may include internal and external displays such as an internal display of a tablet computer or an external display for a server computer or a projector. Display device(s) 706 may further include displays for devices, such as augmented, virtual, and / or extended reality devices. In various embodiments, display device(s) 706 may be configured to display a graphical user interface.

[0089] Network interface(s) 708 provide processing system 700 with access to external networks and thereby to external processing systems. Network interface(s) 708 can generally be any hardware and / or software capable of transmitting and / or receiving data via a wired or wireless network connection. Accordingly, network interface(s) 708 can include a communication transceiver for sending and / or receiving any wired and / or wireless communication.

[0090] Computer-readable medium 770 may be a volatile memory, such as a random access memory (RAM), or a nonvolatile memory, such as nonvolatile random access memory (NVRAM), or the like. In this example, computer-readable medium 770 includes training data generation component 720, training component 722, thermodynamic process parameter(s) prediction component 724, derivative(s) prediction component 726, CCUS process(es) simulation component 728, ML model 730, sub-models 732, thermodynamic properties 734, thermodynamic process parameter(s) 736, derivative(s) 738, training data instances 740, subsurface model 742, processing logic 744, selecting logic 746, providing logic 748, simulating logic 750, computing logic 752, obtaining logic 754, training logic 756, configuring logic 758, and using logic 760.

[0091] In certain embodiments, processing logic 744 includes logic for processing, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component. In certain embodiments, processing logic 744 includes logic for processing, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component. In certain embodiments, processing logic 744 includes logic for processing, with a third sub-model of the ML model, the plurality of input features to generate a third thermodynamic process parameter for a second thermodynamic component. In certain embodiments, processing logic 744 includes logic for processing, with a fourth sub-model of the ML model, the plurality of input features to generate a fourth thermodynamic process parameter for a second thermodynamic component. In certain embodiments, process logic 744 is used to perform step 502 and step 504 in FIG. 5.

[0092] In certain embodiments, selecting logic 746 includes logic for selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component. In certain embodiments, selecting logic 746 includes logic for selecting, by the ML model, a final thermodynamic process parameter for the second thermodynamic component. In certain embodiments, selecting logic 746 is used to perform step 506 in FIG. 5.

[0093] In certain embodiments, providing logic 748 includes logic for providing as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component. In certain embodiments, providing logic 748 includes logic for providing as a second output from the ML model the selected final thermodynamic process parameter for the second thermodynamic component. In certain embodiments, providing logic 748 is used to perform step 508 in FIG. 5.

[0094] In certain embodiments, simulating logic 750 includes logic for simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the final thermodynamic process parameter for the second thermodynamic component. In certain embodiments, simulating logic 750 includes logic for simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the derivative of the finalthermodynamic process parameter for the first thermodynamic component computed for the at least one of the one or more thermodynamic properties.

[0095] In certain embodiments, computing logic 752 includes logic for computing a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property.

[0096] In certain embodiments, obtaining logic 754 includes logic for obtaining a first plurality of training data instances. In certain embodiments, obtaining logic 754 includes logic for obtaining a second plurality of training data instances, wherein each of the second plurality of training data instances. In certain embodiments, obtaining logic 754 is used to perform step 602 in FIG. 6.

[0097] In certain embodiments, training logic 756 includes logic for training a first sub-model of the ML model, to predict a first thermodynamic process parameter for the first thermodynamic component using the first plurality of training data instances. In certain embodiments, training logic 756 includes logic for training a second sub-model of the ML model to predict a second thermodynamic process parameter for the first thermodynamic component below a first threshold using a subset of the first plurality of training data instances. In certain embodiments, training logic 756 includes logic for training a third sub-model of the ML model to predict a third thermodynamic process parameter for the second thermodynamic component using the second plurality of training data instances. In certain embodiments, training logic 756 includes logic for training a fourth submodel of the ML model to predict a fourth thermodynamic process parameter for the second thermodynamic component below a second threshold using a subset of the second plurality of training data instances. In certain embodiments, training logic 756 includes logic for training the ML model to, using automatic differentiation for at least one of the one or more thermodynamic properties, compute a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property. In certain embodiments, training logic 756 is used to perform step 604 and step 606 in FIG. 6.

[0098] In certain embodiments, configuring logic 758 includes logic for configuring the ML model to select a final thermodynamic process parameter for the first thermodynamic component. In certain embodiments, configuring logic 758 includes logic for configuring the ML model to select a final thermodynamic process parameter for the second thermodynamic component. In certain embodiments, configuring logic 758 is used to perform step 608 in FIG. 6.

[0099] In certain embodiments, using logic 760 includes logic for using a Heaviside function to select one of the first thermodynamic process parameter generated for the first thermodynamic component or the second thermodynamic process parameter generated for the first thermodynamic component.

[0100] Note that FIG. 7 is just one example of a processing system consistent with aspects described herein, and other processing systems having additional, alternative, or fewer components are possible consistent with this disclosure.Example Clauses

[0101] Implementation examples are described in the following numbered clauses:

[0102] Clause 1: A method of carbon capture, utilization, and storage (CCUS) process simulation, comprising: processing, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component, wherein the plurality of input features comprise one or more thermodynamic properties; processing, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold; and providing as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component.

[0103] Clause 2: The method of Clause 1, further comprising: processing, with a third submodel of the ML model, the plurality of input features to generate a third thermodynamic process parameter for a second thermodynamic component; processing, with a fourth sub-model of the ML model, the plurality of input features to generate a fourth thermodynamic process parameter for a second thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the second thermodynamic component as: the third thermodynamic process parameter generated for the second thermodynamic component when the third thermodynamicprocess parameter is greater than a second threshold; or the fourth thermodynamic process parameter generated for the second thermodynamic component when the fourth thermodynamic process parameter is less than the second threshold; and providing as a second output from the ML model the selected final thermodynamic process parameter for the second thermodynamic component.

[0104] Clause 3: The method of Clause 2, further comprising simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the final thermodynamic process parameter for the second thermodynamic component.

[0105] Clause 4: The method of any one of Clauses 1-3, further comprising: for at least one of the one or more thermodynamic properties, computing a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property; and simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the derivative of the final thermodynamic process parameter for the first thermodynamic component computed for the at least one of the one or more thermodynamic properties.

[0106] Clause 5: The method of any one of Clauses 1-4, wherein selecting, by the ML model, the final thermodynamic process parameter for the first thermodynamic component comprises using a Heaviside function to select one of the first thermodynamic process parameter generated for the first thermodynamic component or the second thermodynamic process parameter generated for the first thermodynamic component.

[0107] Clause 6: The method of any one of Clauses 1-5, wherein the first thermodynamic component comprises a gas or a liquid.

[0108] Clause 7: The method of any one of Clauses 1-6, wherein the first thermodynamic component comprises carbon dioxide (CO2) or dihydrogen oxide (H2O).

[0109] Clause 8: The method of any one of Clauses 1-7, wherein the one or more thermodynamic properties comprise at least one of: a temperature property; a pressure property; or one or more salinity properties.

[0110] Clause 9: The method of any one of Clauses 1-8, wherein each of the first thermodynamic process parameter for the first thermodynamic component, the second thermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.[0U1] Clause 10: A method of training a machine learning (ML) model to predict thermodynamic process parameters for carbon capture, utilization, and storage (CCUS) process simulation, comprising: obtaining a first plurality of training data instances, wherein each of the first plurality of training data instances comprises: a first training input comprising one or more thermodynamic properties; and a first training output comprising a thermodynamic process parameter of a first thermodynamic component based on the one or more thermodynamic properties; training a first sub-model of the ML model to predict a first thermodynamic process parameter for the first thermodynamic component using the first plurality of training data instances; training a second sub-model of the ML model to predict a second thermodynamic process parameter for the first thermodynamic component below a first threshold using a subset of the first plurality of training data instances; and configuring the ML model to select a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is greater than the first threshold; or the second thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold.

[0112] Clause 11 : The method of Clause 10, further comprising: obtaining a second plurality of training data instances, wherein each of the second plurality of training data instances comprises: a second training input comprising the one or more thermodynamic properties; and a second training output comprising a thermodynamic process parameter of a second thermodynamic component based on the one or more thermodynamic properties; training a third sub-model of the ML model to predict a third thermodynamic process parameter for the second thermodynamic component using the second plurality of training data instances; training a fourth sub-model of the ML model to predict a fourth thermodynamic process parameter for the second thermodynamic component below a second threshold using a subset of the second plurality of training data instances; and configuring the ML model to select a final thermodynamic processparameter for the second thermodynamic component as: the third thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is greater than the second threshold; or the fourth thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is less than the second threshold.

[0113] Clause 12: The method of any one of Clauses 10-11, further comprising training the ML model to, using automatic differentiation for at least one of the one or more thermodynamic properties, compute a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property.

[0114] Clause 13: The method of any one of Clauses 10-12, wherein the ML model is configured to select the final thermodynamic process parameter for the first thermodynamic component as the first thermodynamic process parameter predicted for the first thermodynamic component or the second thermodynamic process parameter predicted for the first thermodynamic component using a Heaviside function.

[0115] Clause 14: The method of any one of Clauses 10-13, wherein the one or more thermodynamic properties comprise at least one of: a temperature property; a pressure property; or one or more salinity properties.

[0116] Clause 15: The method of any one of Clauses 10-14, wherein the one or more thermodynamic properties comprise: a pressure property less than or equal to 600 bar; a temperature property greater than or equal to 12 degrees Celsius and less than or equal to 100 degrees Celsius; and one or more salinity properties, each of the one or more salinity properties comprising a molality of a chloride brine greater than or equal to 0 molal and less than or equal to 6 molal.

[0117] Clause 16: The method of any one of Clauses 10-15, wherein the first thermodynamic component comprises a gas or a liquid.

[0118] Clause 17: The method of any one of Clauses 10-16, wherein the first thermodynamic component comprises carbon dioxide (CO2) or dihydrogen oxide (H2O).

[0119] Clause 18: The method of any one of Clauses 10-17, wherein each of the first thermodynamic process parameter for the first thermodynamic component, the secondthermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.

[0120] Clause 19: A processing system, comprising: a memory comprising computerexecutable instructions; and a processor configured to execute the computer-executable instructions and cause the processing system to perform a method in accordance with any one of Clauses 1-18.

[0121] Clause 20: A processing system, comprising means for performing a method in accordance with any one of Clauses 1-18.

[0122] Clause 21 : A non-transitory computer-readable medium storing program code for causing a processing system to perform the steps of any one of Clauses 1-18.

[0123] Clause 22: A computer program product embodied on a computer-readable storage medium comprising code for performing a method in accordance with any one of Clauses 1-18.Additional Considerations

[0124] The preceding description is provided to enable any person skilled in the art to practice the various embodiments described herein. The examples discussed herein are not limiting of the scope, applicability, or embodiments set forth in the claims. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments. For example, changes may be made in the function and arrangement of elements discussed without departing from the scope of the disclosure. Various examples may omit, substitute, or add various procedures or components as appropriate. For instance, the methods described may be performed in an order different from that described, and various steps may be added, omitted, or combined. Also, features described with respect to some examples may be combined in some other examples. For example, an apparatus may be implemented or a method may be practiced using any number of the aspects set forth herein. In addition, the scope of the disclosure is intended to cover such an apparatus or method that is practiced using other structure, functionality, or structure and functionality in addition to, or other than, the various aspects of the disclosure set forth herein. It should be understood that any aspect of the disclosure disclosed herein may be embodied by one or more elements of a claim.

[0125] As used herein, a phrase referring to “at least one of’ a list of items refers to any combination of those items, including single members. As an example, “at least one of: a, b, or c” is intended to cover a, b, c, a-b, a-c, b-c, and a-b-c, as well as any combination with multiples of the same element (e.g., a-a, a-a-a, a-a-b, a-a-c, a-b-b, a-c-c, b-b, b-b-b, b-b-c, c-c, and c-c-c or any other ordering of a, b, and c).

[0126] As used herein, the term “determining” encompasses a wide variety of actions. For example, “determining” may include calculating, computing, processing, deriving, investigating, looking up (e.g., looking up in a table, a database or another data structure), ascertaining and the like. Also, “determining” may include receiving (e.g., receiving information), accessing (e.g., accessing data in a memory) and the like. Also, “determining” may include resolving, selecting, choosing, establishing and the like.

[0127] The methods disclosed herein comprise one or more steps or actions for achieving the methods. The method steps and / or actions may be interchanged with one another without departing from the scope of the claims. In other words, unless a specific order of steps or actions is specified, the order and / or use of specific steps and / or actions may be modified without departing from the scope of the claims. Further, the various operations of methods described above may be performed by any suitable means capable of performing the corresponding functions. The means may include various hardware and / or software component(s) and / or module(s), including, but not limited to a circuit, an application specific integrated circuit (ASIC), or processor. Generally, where there are operations illustrated in figures, those operations may have corresponding counterpart means-plus- function components with similar numbering.

[0128] The following claims are not intended to be limited to the embodiments shown herein, but are to be accorded the full scope consistent with the language of the claims. Within a claim, reference to an element in the singular is not intended to mean “one and only one” unless specifically so stated, but rather “one or more.” Unless specifically stated otherwise, the term “some” refers to one or more. No claim element is to be construed under the provisions of 35 U.S.C. §112(f) unless the element is expressly recited using the phrase “means for” or, in the case of a method claim, the element is recited using the phrase “step for.” All structural and functional equivalents to the elements of the various aspects described throughout this disclosure that are known or later come to be known to those of ordinary skill in the art are expressly incorporatedherein by reference and are intended to be encompassed by the claims. Moreover, nothing disclosed herein is intended to be dedicated to the public regardless of whether such disclosure is explicitly recited in the claims.

Claims

CLAIMSWhat is claimed is:

1. A method of carbon capture, utilization, and storage (CCUS) process simulation, comprising: processing, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component, wherein the plurality of input features comprise one or more thermodynamic properties; processing, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold; and providing as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component.

2. The method of Claim 1, further comprising: processing, with a third sub-model of the ML model, the plurality of input features to generate a third thermodynamic process parameter for a second thermodynamic component; processing, with a fourth sub-model of the ML model, the plurality of input features to generate a fourth thermodynamic process parameter for a second thermodynamic component; selecting, by the ML model, a final thermodynamic process parameter for the second thermodynamic component as:the third thermodynamic process parameter generated for the second thermodynamic component when the third thermodynamic process parameter is greater than a second threshold; or the fourth thermodynamic process parameter generated for the second thermodynamic component when the fourth thermodynamic process parameter is less than the second threshold; and providing as a second output from the ML model the selected final thermodynamic process parameter for the second thermodynamic component.

3. The method of Claim 2, further comprising simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the final thermodynamic process parameter for the second thermodynamic component.

4. The method of Claim 1, further comprising: for at least one of the one or more thermodynamic properties, computing a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property; and simulating one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the derivative of the final thermodynamic process parameter for the first thermodynamic component computed for the at least one of the one or more thermodynamic properties.

5. The method of Claim 1, wherein selecting, by the ML model, the final thermodynamic process parameter for the first thermodynamic component comprises using a Heaviside function to select one of the first thermodynamic process parameter generated for the first thermodynamic component or the second thermodynamic process parameter generated for the first thermodynamic component.

6. The method of Claim 1, wherein the first thermodynamic component comprises a gas or a liquid.

7. The method of Claim 1, wherein the first thermodynamic component comprises carbon dioxide (CCh) or dihydrogen oxide (H2O).

8. The method of Claim 1, wherein the one or more thermodynamic properties comprise at least one of a temperature property; a pressure property; or one or more salinity properties.

9. The method of Claim 1, wherein each of the first thermodynamic process parameter for the first thermodynamic component, the second thermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.

10. A method of training a machine learning (ML) model to predict thermodynamic process parameters for carbon capture, utilization, and storage (CCUS) process simulation, comprising: obtaining a first plurality of training data instances, wherein each of the first plurality of training data instances comprises: a first training input comprising one or more thermodynamic properties; and a first training output comprising a thermodynamic process parameter of a first thermodynamic component based on the one or more thermodynamic properties; training a first sub-model of the ML model to predict a first thermodynamic process parameter for the first thermodynamic component using the first plurality of training data instances; training a second sub-model of the ML model to predict a second thermodynamic process parameter for the first thermodynamic component below a first threshold using a subset of the first plurality of training data instances; and configuring the ML model to select a final thermodynamic process parameter for the first thermodynamic component as:the first thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is greater than the first threshold; or the second thermodynamic process parameter predicted for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold.

11. The method of Claim 10, further comprising: obtaining a second plurality of training data instances, wherein each of the second plurality of training data instances comprises: a second training input comprising the one or more thermodynamic properties; and a second training output comprising a thermodynamic process parameter of a second thermodynamic component based on the one or more thermodynamic properties; training a third sub-model of the ML model to predict a third thermodynamic process parameter for the second thermodynamic component using the second plurality of training data instances; training a fourth sub-model of the ML model to predict a fourth thermodynamic process parameter for the second thermodynamic component below a second threshold using a subset of the second plurality of training data instances; and configuring the ML model to select a final thermodynamic process parameter for the second thermodynamic component as: the third thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is greater than the second threshold; or the fourth thermodynamic process parameter predicted for the second thermodynamic component when the third thermodynamic process parameter is less than the second threshold.

12. The method of Claim 10, further comprising training the ML model to, using automatic differentiation for at least one of the one or more thermodynamic properties, compute a derivative of the final thermodynamic process parameter for the first thermodynamic component based on the respective thermodynamic property.

13. The method of Claim 10, wherein the ML model is configured to select the final thermodynamic process parameter for the first thermodynamic component as the first thermodynamic process parameter predicted for the first thermodynamic component or the second thermodynamic process parameter predicted for the first thermodynamic component using a Heaviside function.

14. The method of Claim 10, wherein the one or more thermodynamic properties comprise at least one of a temperature property; a pressure property; or one or more salinity properties.

15. The method of Claim 10, wherein the one or more thermodynamic properties comprise: a pressure property less than or equal to 600 bar; a temperature property greater than or equal to 12 degrees Celsius and less than or equal to 100 degrees Celsius; and one or more salinity properties, each of the one or more salinity properties comprising a molality of a chloride brine greater than or equal to 0 molal and less than or equal to 6 molal.

16. The method of Claim 10, wherein the first thermodynamic component comprises a gas or a liquid.

17. The method of Claim 10, wherein the first thermodynamic component comprises carbon dioxide (CO2) or dihydrogen oxide (H2O).

18. The method of Claim 10, wherein each of the first thermodynamic process parameter for the first thermodynamic component, the second thermodynamic process parameter for the first thermodynamic component, and the final thermodynamic process parameter for the first thermodynamic component comprises a K-value for the first thermodynamic component.

19. A processing system comprising: a memory comprising computer-executable instructions; and a processor configured to execute the computer-executable instructions and cause the processing system to: process, with a first sub-model of a machine learning (ML) model, a plurality of input features to generate a first thermodynamic process parameter for a first thermodynamic component, wherein the plurality of input features comprise one or more thermodynamic properties; process, with a second sub-model of the ML model, the plurality of input features to generate a second thermodynamic process parameter predicted for the first thermodynamic component; select, by the ML model, a final thermodynamic process parameter for the first thermodynamic component as: the first thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is greater than a first threshold; or the second thermodynamic process parameter generated for the first thermodynamic component when the first thermodynamic process parameter is less than the first threshold; and provide as a first output from the ML model the selected final thermodynamic process parameter for the first thermodynamic component.

20. The processing system of Claim 19, wherein the processor is configured to execute the computer-executable instructions and further cause the processing system to: process, with a third sub-model of the ML model, the plurality of input features to generate a third thermodynamic process parameter for a second thermodynamic component; process, with a fourth sub-model of the ML model, the plurality of input features to generate a fourth thermodynamic process parameter for a second thermodynamic component; select, by the ML model, a final thermodynamic process parameter for the second thermodynamic component as:the third thermodynamic process parameter generated for the second thermodynamic component when the third thermodynamic process parameter is greater than a second threshold; or the fourth thermodynamic process parameter generated for the second thermodynamic component when the fourth thermodynamic process parameter is less than the second threshold; provide as a second output from the ML model the selected final thermodynamic process parameter for the second thermodynamic component; and simulate one or more CCUS processes in a subsurface model using the final thermodynamic process parameter for the first thermodynamic component and the final thermodynamic process parameter for the second thermodynamic component.

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