Aqueous nanobubble dispersions and gas supersaturation at high pressure

Abstract

Techniques are described for preparing a dispersion of nanobubbles in an aqueous fluid (e.g., water or brine) at high pressure to produce a dispersion having a large amount of one or more gases that are typically immiscible with the aqueous fluid. The composition of the aqueous fluid may be adjusted to contain an optimized amount of gas under desired pressure conditions. The gas may be present in the dispersion as an amount dissolved in the aqueous fluid and as dispersed nanobubbles. The thermodynamic model may be used to determine the amount of gas that may be present in the dispersion of nanobubbles and / or to determine or optimize the composition of the fluid.

Description

Cross - Reference to Related Applications

[0001] This application claims the benefit and priority of U.S. Provisional Application No. 63 / 401,857, filed on August 29, 2022, the entire content of which is incorporated herein by reference. Technical Field

[0002] This application pertains to the field of nanobubble dispersions. Generally speaking, the present invention relates to techniques for supporting large amounts of water - immiscible gases in aqueous fluids by preparing aqueous nanobubble dispersions under high - pressure conditions, as well as techniques for preparing and optimizing such aqueous nanobubble dispersions. Background Art

[0003] Many gases are immiscible with water. Adding or bubbling large amounts of such gases into water or other aqueous fluids, or via water or other aqueous fluids, generally does not result in the dissolved amount of such gases exceeding their solubility limits. Summary of the Invention

[0004] This document describes techniques (including methods) for preparing dispersions of nanobubbles in an aqueous fluid (such as water or brine) under high pressure, which enable the dispersions to contain a large amount of one or more gases that are typically immiscible with the aqueous fluid. The composition of the aqueous fluid can be adjusted to contain an optimized amount of gas under desired pressure conditions. The gas exists in the dispersion in an amount dissolved in the aqueous fluid and as an amount of dispersed nanobubbles. In some examples, a relatively large amount exists under saturated or supersaturated solvation conditions, and a relatively small amount exists as a stable dispersion of nanobubbles. In other examples, a relatively small amount exists under saturated or supersaturated solvation conditions, and a relatively large amount exists as a stable dispersion of nanobubbles. The dispersion of nanobubbles in an aqueous fluid may be referred to herein as a dispersion of nanobubbles or an aqueous nanobubble fluid or an aqueous NB fluid. Thermodynamic models can be used to determine the amount of gas that can be present in a dispersion of nanobubbles (including dissolved and nanobubble forms), where the thermodynamic models take into account the composition of the fluid, the identity of the gas, and conditions (such as temperature and pressure). The thermodynamic models can also or alternatively be used to determine the composition of the fluid, which can be adjusted or optimized to contain the amount of gas in the dispersion of nanobubbles under a set of specific conditions (such as temperature and pressure). The nanobubble dispersions can be used for a variety of purposes, including storing gas in an aqueous nanobubble dispersion, for underground reservoirs (such as for enhanced oil recovery processes), as a fluid containing a large amount of gas for use as a reactant in a chemical reaction or process (such as mineralization). Although any gas can be used in the techniques described herein, specific advantages can be achieved for gases that are considered immiscible in an aqueous fluid (such as water or brine), since the disclosed techniques can allow a large amount of such immiscible gas to be present in the aqueous fluid. In some cases, the dispersed nanobubbles can also be used to adjust the fluid properties of the aqueous fluid, such as viscosity or density.

[0005] In one aspect, this document provides a method for preparing a nanobubble dispersion. In some examples, the method of this aspect can include: determining a target composition of an aqueous fluid for a dispersion of nanobubbles of a gas at a specified temperature and a specified pressure; preparing the aqueous fluid according to the target composition; mixing the gas in the aqueous fluid at the specified temperature and the specified pressure to form a supersaturated solution of the gas in the aqueous fluid; and subjecting the gas and the aqueous fluid to a bubble generation process to form a dispersion of nanobubbles of the gas in the aqueous fluid at the specified temperature and the specified pressure.

[0006] As described above, any suitable gas can be used, but in some examples, the gas is immiscible in the aqueous fluid or has a solubility in water at standard temperature and pressure of less than 2 g / L. In some cases, the solubility of the gas in water at standard temperature and pressure is less than or about 2 g / L, less than or about 1.75 g / L, less than or about 1.5 g / L, less than or about 1.25 g / L, less than or about 1 g / L, less than or about 0.75 g / L, less than or about 0.5 g / L, less than or about 0.25 g / L, less than or about 0.2 g / L, less than or about 0.15 g / L, less than or about 0.1 g / L, or less than or about 0.05 g / L. In some examples, the gas includes CO2, H2, N2, O2, He, methane, ethane, ethylene, acetylene, propane, propylene, methylacetylene, cyclopropane, allene, butane, butene, butyne, cyclobutane, butadiene, hydrocarbon gas, or a combination thereof. In some examples, the gas includes a hydrocarbon gas suspended in or contained in an inert gas, a diatomic gas, or a gas having a low molecular weight (e.g., less than about 50 amu).

[0007] Any suitable temperature and pressure can be used to specify the pressure, but exemplary methods include those in which the process includes determining the composition of the aqueous fluid at the specified temperature and pressure and then forming a dispersion of nanobubbles in the aqueous fluid at that specified temperature and pressure. As described above, the disclosed methods are particularly useful at high pressures. In some examples, the specified pressure is from 1 MPa to 105 MPa, such as from 1 MPa to 5 MPa, from 5 MPa to 10 MPa, from 10 MPa to 15 MPa, from 15 MPa to 20 MPa, from 20 MPa to 25 MPa, from 25 MPa to 30 MPa, from 30 MPa to 35 MPa, from 35 MPa to 40 MPa, from 40 MPa to 45 MPa, from 45 MPa to 50 MPa, from 50 MPa to 55 MPa, from 55 MPa to 60 MPa, from 60 MPa to 65 MPa, from 65 MPa to 70 MPa, from 70 MPa to 75 MPa, from 75 MPa to 80 MPa, from 80 MPa to 85 MPa, from 85 MPa to 90 MPa, from 90 MPa to 95 MPa, from 95 MPa to 100 MPa, or from 100 MPa to 105 MPa. In some examples, the specified temperature is greater than or about 0 °C, greater than or about 10 °C, greater than or about 20 °C, greater than or about 30 °C, greater than or about 40 °C, greater than or about 50 °C, greater than or about 60 °C, greater than or about 70 °C, greater than or about 80 °C, greater than or about 90 °C, greater than or about 100 °C, greater than or about 110 °C, greater than or about 120 °C, greater than or about 130 °C, greater than or about 140 °C, greater than or about 160 °C, greater than or about 160 °C, greater than or about 170 °C, or greater than or about 180 °C.

[0008] The size of the nanobubbles in the dispersion can be within a certain range, but usually has a nanoscale diameter, such as less than 1000 nm. In some examples, the diameter of the nanobubbles is from 1 nm to 1000 nm, such as from 1 nm to 25 nm, from 25 nm to 50 nm, from 50 nm to 75 nm, from 75 nm to 100 nm, from 100 nm to 150 nm, from 150 nm to 200 nm, from 200 nm to 250 nm, from 250 nm to 300 nm, from 300 nm to 350 nm, from 350 nm to 400 nm, from 400 nm to 450 nm, from 450 nm to 500 nm, from 500 nm to 600 nm, from 600 nm to 700 nm, from 700 nm to 800 nm, from 800 nm to 900 nm or from 900 nm to 1000 nm. In some cases, at least a portion of the nanobubbles have a charged surface, creating a repulsive force between them and suppressing the small buoyancy of the bubbles. In some cases, the nanobubble dispersion can be stable for a duration of up to 30 days, such as up to 1 day, up to 2 days, up to 5 days, up to 10 days, up to 14 days, up to 20 days, up to 25 days or up to 30 days or longer, at a specified temperature and a specified pressure.

[0009] Nanobubbles can provide a high concentration of gas present in an aqueous fluid for a dispersion of nanobubbles. For example, the dispersion of nanobubbles can correspond to a gas concentration in the aqueous fluid of from 0.05 mol / L to 20 mol / L, such as from 0.05 mol / L to 0.5 mol / L, from 0.5 mol / L to 1 mol / L, from 1 mol / L to 2 mol / L, from 2 mol / L to 3 mol / L, from 3 mol / L to 4 mol / L, from 4 mol / L to 5 mol / L, from 5 mol / L to 6 mol / L, from 6 mol / L to 7 mol / L, from 7 mol / L to 8 mol / L, from 8 mol / L to 9 mol / L, from 9 mol / L to 10 mol / L, from 10 mol / L to 11 mol / L, from 11 mol / L to 12 mol / L, from 12 mol / L to 13 mol / L, from 13 mol / L to 14 mol / L, from 14 mol / L to 15 mol / L, from 15 mol / L to 16 mol / L, from 16 mol / L to 17 mol / L, from 17 mol / L to 18 mol / L, from 18 mol / L to 19 mol / L, from 19 mol / L to 20 mol / L or greater. In some examples, the amount (e.g., molar amount or mass) of gas dissolved or present in the aqueous fluid (e.g., present in or dissolved in the aqueous phase, such as in the form of a supersaturated amount) in the dispersion of nanobubbles is greater than the amount of gas in the nanobubbles in the dispersion of nanobubbles (e.g., present in the gas phase as gas nanobubbles). In other words, the amount of gas atoms or molecules in the liquid phase of the dispersion of nanobubbles can be higher than the amount in the gas phase of the dispersion of nanobubbles. In other examples, the amount (e.g., molar amount or mass) of gas dissolved or present in the aqueous fluid (e.g., present in or dissolved in the aqueous phase, such as in the form of a supersaturated amount) in the dispersion of nanobubbles is less than the amount of gas in the nanobubbles in the dispersion of nanobubbles (e.g., present in the gas phase as gas nanobubbles). In other words, the amount of gas atoms or molecules in the liquid phase of the dispersion of nanobubbles can be lower than the amount of gas atoms or molecules in the gas phase of the dispersion of nanobubbles.

[0010] Advantageously, the presence of nanobubbles can affect or increase the supersaturation amount of gas in an aqueous fluid. That is, when nanobubbles are present as a dispersion in an aqueous fluid, the aqueous fluid can support or contain a greater amount of gas in a dissolved state compared to when nanobubbles are not present in the aqueous fluid. In other words, a dispersion of nanobubbles can enhance the supersaturation of an aqueous fluid with a gas. For example, a dispersion of a gas in nanobubbles in an aqueous fluid can exhibit a greater supersaturation amount than a supersaturated solution of the gas in the aqueous fluid (e.g., in the absence of nanobubbles). Further benefits can be achieved through the presence of nanobubbles. For example, a dispersion of nanobubbles can increase the intensity and / or kinetics of mineral dissolution, carbonation saturation, and / or precipitation in a subterranean reservoir to convert at least a portion of the gas in the subterranean reservoir into solid minerals. For example, when the gas is CO2, the gas can undergo mineralization to form carbonate minerals.

[0011] A variety of aqueous fluids can be used in the methods described herein. In some examples, the aqueous fluid includes water, seawater, reservoir resident water, produced water, river water, pond water, brine, engineered brine, or any combination thereof. In an example, the aqueous fluid can be prepared by mixing one or more of the foregoing fluids and adding one or more soluble or insoluble components. For example, the aqueous fluid can contain one or more salts, one or more electrolytes, one or more acids, one or more bases, monovalent anions, monovalent cations, divalent anions, divalent cations, trivalent anions, trivalent cations, formate, or any combination thereof. Optionally, the aqueous fluid contains additives selected from surfactants, foaming agents, polymers, nanoparticles, alcohols, oxygenated solvents, or any combination thereof. In some examples, the additives are present or dissolved in the aqueous fluid at a concentration of less than or about 3 wt%, such as less than or about 2.5 wt%, less than or about 2 wt%, less than or about 1 wt%, less than or about 0.5 wt%, less than or about 0.25 wt%, less than or about 0.2 wt %, less than or about 0.1 wt% or 0 wt%. However, the additives are optional, and in some examples, the aqueous fluid does not contain or contains one or more additives selected from surfactants, foaming agents, polymers, nanoparticles, alcohols, oxygenated solvents, or any combination thereof. In other words, in some examples, the aqueous fluid excludes one or more additives selected from surfactants, foaming agents, polymers, nanoparticles, alcohols, oxygenated solvents, or any combination thereof.

[0012] Optionally, in some examples, the step of determining the target composition of the aqueous fluid includes determining the ionic composition or ionic strength of the aqueous fluid. Optionally, the ionic strength can be from 0 mol / L to 6 mol / L, such as from 0 mol / L to 0.25 mol / L, from 0.25 mol / L to 0.5 mol / L, from 0.5 mol / L to 1 mol / L, from 1 mol / L to 1.5 mol / L, from 1.5 mol / L to 2 mol / L, from 2 mol / L to 2.5 mol / L, from 2.5 mol / L to 3 mol / L, from 3 mol / L to 3.5 mol / L, from 3.5 mol / L to 4 mol / L, from 4 mol / L to 4.5 mol / L, from 4.5 mol / L to 5 mol / L, from 5 mol / L to 5.5 mol / L, or from 5.5 mol / L to 6 mol / L. In some specific examples, the ionic composition comprises one or more ions selected from H + , Na + , K + , Mg 2+ , Ca 2+ , Fe 2+ , NH4 + , OH-, F - , Cl - , Br - , I - , SO4 2- , NO3 - and CO3 2- , HCO3-, PO4 3- , HCOO - or any combination of these.

[0013] Optionally, determining the target composition of the aqueous fluid includes determining the target pH of the aqueous fluid. The pH can be any suitable pH, for example, 1 - 14. For various reasons, it may be useful to control the pH of the fluid. In some examples, the pH can affect the solubility of a gas in the aqueous fluid. In some examples, the pH can affect the thermodynamic conditions or state within the aqueous fluid and also affect the amount of gas that can be dispersed as nanobubbles in the aqueous fluid.

[0014] A variety of bubble generation and mixing processes can be used in the methods in this regard. In some examples, mixing a gas in an aqueous fluid and subjecting the gas and the aqueous fluid to a bubble generation process can be combined. Optionally, the bubble generation process includes injecting a gas into the aqueous fluid through a porous membrane. Optionally, the bubble generation process includes co-injecting a gas and an aqueous fluid through a porous membrane. Optionally, the bubble generation process includes injecting a gas into the aqueous fluid using one or more (e.g., an array of) nozzles (such as high-speed nozzles). Optionally, the bubble generation process includes co-injecting a gas and an aqueous fluid together using one or more (e.g., an array of) nozzles (such as high-speed nozzles). Optionally, the bubble generation process includes at least temporarily subjecting a supersaturated solution of a gas in an aqueous fluid to a reduced pressure to initiate bubble nucleation. Optionally, the bubble generation process includes subjecting a supersaturated solution of a gas in an aqueous fluid to ultrasonic energy to initiate bubble nucleation. Optionally, the bubble generation process includes subjecting a supersaturated solution of a gas in an aqueous fluid to shear stress to initiate bubble nucleation.

[0015] In some examples, in the methods in this regard, determining the target composition of an aqueous fluid includes providing at least specified temperature, specified pressure, and the identity information of a gas to a thermodynamic model. The thermodynamic model can determine the properties of the dispersion, including the amount of gas present as nanobubbles in the dispersion or the amount of gas loaded as nanobubbles in the dispersion. Determining the target composition of an aqueous fluid can include or further include providing the identity information of one or more salts, one or more electrolytes, one or more acids, one or more bases, or one or more additives for the aqueous fluid to the thermodynamic model. The thermodynamic model can evaluate the characteristics of the dispersion of nanobubbles, such as the interfacial tension at a given capillary pressure, where there is a net zero mass transfer across the curved interface of the nanobubbles, treating the dispersion of nanobubbles as a closed system. Optionally, the thermodynamic model uses empirical data determined by preparing a test nanobubble dispersion under fixed temperature, pressure, and aqueous fluid composition conditions and evaluating the amount of gas present in the test nanobubble dispersion. Such empirical data can be used to adjust or calibrate the thermodynamic model.

[0016] As described above, the nanobubble dispersion can be used for a variety of applications. In some examples, the methods of this aspect can include or further include injecting a dispersion of nanobubbles into a subterranean reservoir. Optionally, the dispersion of nanobubbles can be generated from the subterranean reservoir, for example, after injection. In some examples, injecting a dispersion of nanobubbles into a subterranean reservoir includes or can be used to store gas as a dispersion of nanobubbles in the subterranean reservoir. In this way, large amounts of gas can be stored in a reservoir containing an aqueous fluid. For example, according to the disclosed method, hydrogen ((H2) can be effectively stored in a subterranean reservoir. The storage of hydrogen according to the disclosed technology can optionally be enhanced with other storage technologies, such as where hydrogen is stored in another chemical form, such as in the form of a carboxylate (e.g., formate), as described in PCT International Application No. PCT / US2022 / 027116, filed April 29, 2022, which is incorporated herein by reference.

[0017] Optionally, the dispersion of nanobubbles undergoes a mineralization process in the subterranean reservoir to convert at least a portion of the gas into a solid mineral in the subterranean reservoir. For example, a dispersion of CO2 nanobubbles in an aqueous fluid can be injected into a subterranean reservoir for carbon sequestration. In some cases, CO2 dissolved in the aqueous fluid and / or present as nanobubbles in the aqueous fluid can mineralize at a relatively high rate due to the large amount of CO2 available in the aqueous fluid. Optionally, the composition of the aqueous fluid can be controlled or optimized to support a high or higher CO2 mineralization rate, such as when subjected to the temperature and pressure conditions within the subterranean reservoir. The storage / sequestration of carbon according to the disclosed technology can optionally be enhanced with other storage technologies, such as where carbon is stored in another chemical form, such as in the form of a carboxylate (e.g., formate), as described in PCT International Application No. PCT / US2022 / 027116.

[0018] In a specific example, the present disclosure also provides a carbon sequestration method. In some examples, the methods disclosed above can be used for carbon sequestration, such as when the gas contains carbonaceous materials (e.g., hydrocarbons or CO2). Exemplary carbon sequestration methods include preparing an aqueous fluid for a nano-bubble solution of CO2 in a subterranean reservoir; mixing CO2 in the aqueous fluid to form a supersaturated solution of CO2 in the aqueous fluid; subjecting the supersaturated solution to a bubble generation process to form a dispersion of nano-bubbles of CO2 in the aqueous fluid, wherein the dispersion of nano-bubbles of CO2 in the aqueous fluid exhibits a greater amount of supersaturation than the supersaturated solution of CO2 in the aqueous fluid; and injecting the dispersion of nano-bubbles of CO2 in the aqueous fluid into the subterranean reservoir, wherein the dispersion of nano-bubbles of CO2 in the aqueous fluid undergoes a mineralization process in the subterranean reservoir to convert at least a portion of the CO2 injected into the subterranean reservoir into carbonate minerals in the subterranean reservoir. In some examples, the dispersion of nano-bubbles of CO2 in the aqueous fluid exhibits a higher intensity and / or faster kinetics of mineral dissolution, carbonic acid saturation, and / or precipitation than the supersaturated solution of CO2 in the aqueous fluid.

[0019] Without being bound by any particular theory, beliefs or understandings of the basic principles related to the present invention may be discussed herein. It should be recognized that regardless of the ultimate correctness of any mechanical explanations or assumptions, the embodiments of the present invention can still be effective and useful. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1A A schematic diagram showing a volume of an aqueous fluid containing a saturated or supersaturated amount of a gas.

[0021] Figure 1B A schematic diagram providing a volume of a dispersion of aqueous nano-bubbles, which contains a plurality of nano-bubbles of a gas dispersed in an aqueous fluid at a specified temperature and pressure.

[0022] Figure 2 An overview of an exemplary method for preparing and using a dispersion of aqueous nano-bubbles is provided.

[0023] Figure 3A and Figure 3B A sample calculation of the phase equilibrium of an N2-water binary system at 297K with a bubble radius of 10 nm using the Peng-Robinson equation of state is provided.

[0024] Figure 4 A graph of the interfacial tension between the external aqueous phase and the bubble for varying bubble radii is provided.

[0025] Figure 5 A calculation example is provided where the energy released by phase separation is equal to the energy required for the bubble to create interfacial area in the system.

[0026] Figure 6 A schematic diagram of the experimental setup for gas content measurement is provided.

[0027] Figure 7 The results of N2 gas content measurement are provided.

[0028] Figure 8 The mass density of the aqueous nanobubble fluid is provided.

[0029] Figure 9 A schematic diagram of the experimental apparatus for stability assessment is provided.

[0030] Figure 10 provides a photograph of a sapphire cell containing an aqueous nanobubble fluid at approximately 1800 psig at room temperature: ( Figure 10A ) without an N2 gas cap, ( Figure 10B ) with an N2 gas cap.

[0031] Figure 11 A schematic diagram of the experimental setup for apparent viscosity measurement is provided.

[0032] Figure 12 The pressure difference during the apparent viscosity measurement of an aqueous nanobubble fluid with brine and N2 using Berea sand cores is provided.

[0033] Figure 13 A graph showing the equilibrium mole fractions of water in the gas phase and nitrogen in the aqueous phase is provided.

[0034] Figure 14 A graph showing the pseudo co-volume of the calibration of water / N2 is provided.

[0035] Figure 15 A graph showing the calibrated parameter model of the interfacial tension between water and nitrogen at various temperatures and pressures is provided.

[0036] Figure 16 A graph showing the temperature-dependent coefficient χ of the modified Parachor model is provided.

[0037] Figure 17 A schematic diagram of the experimental setup for generating an aqueous nanobubble fluid is provided.

[0038] Figure 18 A schematic diagram of the experimental setup for measuring the thermodynamic properties of an aqueous nanobubble fluid is provided.

[0039] Figure 19 A graph showing the solution of the thermodynamic equilibrium model of, for example, an aqueous nanobubble fluid sample is provided.

[0040] Figure 20A graph showing the reduced total Helmholtz free energy of, for example, an aqueous nanobubble fluid sample is provided.

[0041] Figure 21 Graphs are provided showing the mass of water, bubble radius, bubble number density, N2 content, fraction of N2 in the bubbles, interfacial area, interfacial tension, and capillary pressure of N2 in water (e.g., an aqueous nanobubble fluid sample).

[0042] Figure 22 A flowchart is provided that gives an overview of an algorithm for example rapid calculations. Detailed Description

[0043] Techniques are described herein for preparing a dispersion of nanobubbles in an aqueous fluid (e.g., water or brine) at high pressure to produce a dispersion having a large amount of one or more gases that are typically immiscible with the aqueous fluid. The composition of the aqueous fluid can be adjusted to contain an optimized amount of gas under desired pressure and temperature conditions. The gas can be present in the dispersion both as an amount dissolved in the aqueous fluid and as dispersed nanobubbles. Thermodynamic models can be used to determine the amount of gas that can be present in the dispersion of nanobubbles and / or to determine the composition of the fluid.

[0044] Figure 1A A schematic diagram of a volume 105A of an aqueous fluid 110 is shown that contains a saturated or supersaturated amount of a gas, such as an immiscible gas or a gas having a low solubility limit (e.g., less than 2 g / L at standard temperature and pressure). The aqueous fluid 110 can be water, brine, or any other suitable aqueous fluid, such as fresh water, seawater, reservoir resident water, produced water, river water, pool water, brine, engineered brine, or any combination thereof. The aqueous fluid 110 can include any suitable composition, such as including one or more salts, one or more electrolytes, one or more acids, one or more bases, monovalent anions, monovalent cations, divalent anions, divalent cations, trivalent anions, trivalent cations, formate, or any combination thereof. Specific example ions present in the aqueous fluid 110 include, but are not limited to, H + 、Na + 、K + 、Mg 2+ 、Ca 2+ 、Fe 2+ 、NH4 + 、OH - 、F - 、Cl - 、Br - 、I - 、SO4 2- 、NO3 - and CO3 2- 、HCO3−、PO4 3-, HCOO - or any combination thereof. Optionally, the aqueous fluid 110 may include one or more additives in an amount of up to about 3 wt%, such as surfactants, foaming agents, polymers, nanoparticles, alcohols, or oxygenated solvents, but in some examples, such materials are absent from or excluded from the aqueous fluid 110. In some examples, the ionic strength of the aqueous fluid 110 may be from 0 mol / L to 6 mol / L. In some examples, the aqueous fluid 110 may have any suitable pH, such as from 1 to 14.

[0045] Figure 1B A schematic diagram of a dispersion of aqueous nanobubbles of a certain volume 105B is provided, which includes a plurality of nanobubbles 115 of gas dispersed in the aqueous fluid 110 at a specified temperature and pressure. In an example, the specified pressure is from 1 MPa to 105 MPa. In an example, the specified temperature is between 0 °C and the boiling point of the aqueous fluid 110 at the specified pressure. It should be understood that the depiction of the plurality of nanobubbles 115 is merely a two-dimensional illustration, and the nanobubbles present in the dispersion of aqueous nanobubbles may include different sizes, numbers, number densities, or distributions of nanobubbles throughout the dispersion. In an example, the nanobubbles 115 may have a diameter ranging from 1 nm to 1000 nm. The dispersion of aqueous nanobubbles may correspond to, for example, a gas concentration in the aqueous fluid 110 of from 0.05 mol / L to 20 mol / L.

[0046] Example gases include but are not limited to CO2, H2, N2, O2, He, methane, ethane, ethylene, acetylene, propane, propylene, methylacetylene, cyclopropane, allene, butane, butene, butyne, cyclobutane, butadiene, hydrocarbon gases, or combinations thereof. In some cases, some amount of a hydrocarbon having a low vapor pressure may be suspended or distributed in a low molecular weight gas or an inert gas to provide the hydrocarbon as part of the gas in the form of nanobubbles in the dispersion of aqueous nanobubbles.

[0047] Various techniques can be used to prepare the aqueous nanobubble dispersions described herein. For example, Figure 2An overview of an exemplary method 200 for preparing and using a dispersion of aqueous nanobubbles is provided. Method 200 includes determining a target composition of an aqueous fluid at block 205. This can include determining a specified temperature and pressure of the aqueous fluid. For example, in some cases, the specified temperature and pressure can correspond to the temperature and pressure in a subterranean reservoir. In some examples, determining the composition of the aqueous fluid can include providing information about the aqueous fluid and / or the gas to be dispersed therein to a thermodynamic model. For example, temperature, pressure, fluid components (e.g., identity information of salts, electrolytes, anions, etc.), gas identity information (including gas mixtures), etc. can be provided as inputs to the thermodynamic model. The thermodynamic model can determine or provide the amount of gas that can be dispersed in the aqueous fluid in the form of nanobubbles and / or dissolved gas. The thermodynamic model can determine the composition of the aqueous fluid, such as the amount or properties of one or more salts, one or more electrolytes, one or more acids, one or more bases, or one or more additives for the aqueous fluid. The thermodynamic model can evaluate characteristics of the dispersion of nanobubbles, such as the interfacial tension at a given capillary pressure, where there is net zero mass transfer across the curved interface of the nanobubbles, treating the dispersion of nanobubbles as a closed system. Optionally, the thermodynamic model uses empirical data determined by preparing a test dispersion of nanobubbles under fixed temperature, pressure, and aqueous fluid composition conditions and evaluating the amount of gas present in the test dispersion of nanobubbles. Such empirical data can be used to adjust or calibrate the thermodynamic model.

[0048] In some examples, the thermodynamic model is provided or used as a software package or algorithm, such as where inputs to the thermodynamic model (e.g., temperature, pressure, gas identity information, aqueous fluid component identity information, etc.) are input into the software package or algorithm, and the amount and / or identity information of the gas and / or identity information for the aqueous fluid and / or the amount and / or identity information of one or more salts, one or more electrolytes, one or more acids, one or more bases, or one or more additives are output.

[0049] At block 205, method 200 includes preparing an aqueous fluid. The aqueous fluid can be prepared by mixing water, brine, or any other suitable aqueous fluid (e.g., fresh water, seawater, reservoir resident water, produced water, river water, pond water, brine, engineered brine, or any combination thereof) with an appropriate amount of one or more salts, electrolytes, acids, bases, monovalent anions, monovalent cations, divalent anions, divalent cations, trivalent anions, trivalent cations, and optionally a surfactant, foaming agent, polymer, nanoparticle, alcohol, or oxygenated solvent.

[0050] At block 215, method 200 includes mixing a gas in an aqueous fluid at a specified temperature and pressure to form a saturated or supersaturated solution of the gas in the aqueous fluid. In some examples, the gas can be mixed in the aqueous fluid by bubbling the gas through the fluid at the specified temperature and pressure or at other temperature and / or pressure conditions and then returning the fluid to the specified temperature and pressure.

[0051] At block 220, method 200 includes subjecting the aqueous fluid to a bubble generation process. The bubble generation process can form a dispersion of nanobubbles of the gas in the aqueous fluid at the specified temperature and pressure. A variety of techniques can be used for the bubble generation process, and several of these techniques can also optionally be used for the mixing step of block 215. In some examples, the bubble generation process includes injecting the gas into the aqueous fluid through a porous membrane or through a nozzle or nozzle array. In some examples, the bubble generation process includes co-injecting the gas and the aqueous fluid through a porous membrane, or co-injecting the gas and the aqueous fluid through a nozzle or nozzle array. In some examples, the use of a nozzle or nozzle array can be used to generate bubbles downhole in a well (such as at, adjacent to, or into a subterranean reservoir). Optionally, the bubble generation process includes subjecting a supersaturated solution of the gas in the aqueous fluid to at least a temporary pressure reduction to initiate bubble nucleation. In some cases, the pressure reduction can correspond to changing the pressure from a value above the specified pressure to a value that matches the specified pressure.

[0052] In some examples, method 200 can include various other steps. For example, method 200 can include the step of injecting the dispersion of nanobubbles into a subterranean reservoir. In some examples, method 200 can include a method for carbon sequestration, such as where the dispersion of nanobubbles includes a dispersion of CO2 in an aqueous fluid. In some examples, the dispersion of nanobubbles can be used to store an amount of gas in a subterranean reservoir for later retrieval. Thus, method 200 can optionally include the step of producing the dispersion of nanobubbles from the subterranean reservoir after injection. In some examples, method 200 can include a method of storing an energy-containing gas (e.g., H2, CH4, natural gas, air, etc.) as a dispersion of aqueous nanobubbles in a subterranean reservoir. In some cases, the dispersion of nanobubbles serves as a composition for enhanced oil recovery. Thus, method 200 can optionally include the step of producing a hydrocarbon-containing fluid from the subterranean reservoir after injection.

[0053] The present invention can be further understood by the following non-limiting examples. Example 1

[0054] Many gaseous substances such as CO2, H2, N2, and light hydrocarbons are highly immiscible with water, and their equilibrium concentrations in aqueous fluids (e.g., water or brine) are typically very small under a wide range of conditions. However, if these immiscible gaseous substances can be included as an effective homogeneous phase in an aqueous fluid, various industrial processes would benefit.

[0055] The present disclosure provides techniques capable of effectively producing such an aqueous fluid that can contain a large amount of immiscible gas or gas mixture at high pressure in a controlled and scalable manner. Advantageously, the gaseous substances can be stably dispersed in the aqueous fluid as small bubbles (typically on the nanoscale) and gas molecules dissolved in the aqueous fluid. These two modes of accommodation can together enable the total concentration of the gaseous substances to be several orders of magnitude greater than its thermodynamic solubility in the aqueous fluid. Such an aqueous fluid with a bubble / molecule dispersion is referred to as an "aqueous NB fluid" in this and subsequent embodiments.

[0056] Aspects of the process can include the following general steps:

[0057] Step 1. Specify operating conditions such as temperature, pressure, aqueous fluid composition, gaseous substances, mixing method, bubble generation method, etc.

[0058] Step 2. Mix the gaseous substances and the aqueous fluid under the specified conditions.

[0059] Step 3. Generate bubbles of the gaseous substances in the aqueous fluid under the specified conditions. This bubble generation step can optionally be combined with the above mixing step.

[0060] Step 4. Stabilize the resulting fluid as a closed system under the specified conditions (e.g., temperature and pressure). As needed, the bulk gas phase caused by the excess gaseous substances is displaced from the system for recycling so that the aqueous phase can contain the gaseous substances as a dispersion of stable bubbles and dissolved molecules.

[0061] In Step 1, in some examples, the temperature can be greater than 273K and lower than the boiling temperature of the aqueous fluid at the specified pressure. The pressure is generally greater than atmospheric pressure because there are advantages in achieving a significant increase in gas accommodation using pressure. The aqueous fluid can be water or naturally occurring brine or engineered brine with a specific ionic composition and / or any additives for optimizing the application. Although foaming agents such as polymers and surfactants are not required, these or other electrolytes can be optimized as needed so that gas accommodation can be enhanced. The gaseous substances can be a single-component gas or a gas mixture that is immiscible with the aqueous fluid. Step 1 can employ software or algorithms that calculate the resulting properties of the gas-containing aqueous fluid for the specified conditions. The software can use computational algorithms based on thermodynamics and thermodynamic models and optionally existing experimental data / correlations.

[0062] In step 2, in some examples, the mixing method causes (supersaturation) of the aqueous fluid by a gaseous substance under operating conditions. The concentration of the gaseous substance in the aqueous fluid can be used in step 3, where the bubbles should be stably dispersed in the aqueous fluid.

[0063] For low-pressure conditions, different methods can be used for step 3, but an effective and simple method for high-pressure applications is to use a porous membrane (e.g., ceramic and / or stainless steel). When a porous membrane is used in step 3, the injection rates of the gaseous substance and the aqueous fluid should be designed for a given membrane with known properties. The injection rates (and their ratios) can significantly affect the amount of the gaseous substance in the aqueous fluid and thus the physical and transport properties of the resulting fluid. For example, for the membrane used, the permeability, porosity, material, and gas-water relative permeability should be known and can be adjusted in a thermodynamic model. It should be understood that other techniques for generating bubbles can be used, and the use of the porous membrane is not intended to be restrictive. In other examples, bubble generation can be achieved using any suitable technique, such as cavitation, application of ultrasonic energy, decompression of a supersaturated aqueous phase, application of shear stress to a supersaturated aqueous phase, subjecting a supersaturated aqueous phase to turbulent conditions, etc. Various properties, flow conditions, etc. can affect the number density of the bubbles, the gas supersaturation level in the aqueous phase, the bubble size, and the total gas concentration by hydrodynamic mixing, gas snap-off, gas nucleation in the convection of the two immiscible phases (gas and water) in the porous membrane, etc., such as the gas and liquid injection rates, liquid flow rate, pressure, container size and size variation, etc. for a given porous membrane.

[0064] The goal of this method is to generate a thermodynamically stable state under desired conditions (e.g., temperature and pressure) in a closed system with an aqueous phase having supersaturated gas and dispersed bubbles. The two phases should be prepared to be stable in the closed system under the specified thermodynamic conditions, where the continuous aqueous phase with an interfacial tension at a given capillary pressure contains a large number density of bubbles and the net mass transfer across the curved interface is zero. For some cases, most of the gas will be in the form of bubbles and the rest will be in the form of gas dissolved in molecular form in the aqueous phase. For example, this may occur when the gas is highly immiscible with water, but this doesn't have to be the case in all examples. For other cases, in an aqueous NB fluid, most of the gas will be in the form of gas dissolved in molecular form in the aqueous phase and the rest will be in the form of bubbles. This can happen even if the gas is generally considered immiscible or highly immiscible with water. In some examples, the presence or suspension of nanobubbles in the aqueous phase can be used to create supersaturated conditions. Nanoscale bubbles can have charged surfaces, creating a repulsive force between them and suppressing the small buoyancy of the bubbles. In some examples, the upper limit of the nanobubble number density for a given operating condition of a stable aqueous NB fluid can be estimated by software or an algorithm.

[0065] Generally, if the system contains a bulk gas phase, it is less stable; that is, it is more desirable to adopt step 4, where the excess gas is removed. As the pressure increases, the total gas concentration in the aqueous fluid so prepared will be greater. Therefore, the generation of an aqueous NB fluid will be more efficient even when operating at low pressure and open to the atmosphere. Such low-pressure applications may experience a reduction in the gas content in the fluid over time and with any changes in thermodynamic variables.

[0066] Industrial processes. The techniques described in this example can enable immiscible gaseous substances to be stably dispersed as bubbles and dissolved molecules in an aqueous fluid. For the stability of the aqueous NB fluid during preparation, the system needs to be a closed system. By leveraging pressure, the present invention finds its most promising applications in subsurface processes mediated by aqueous fluids and high-pressure surface processes.

[0067] High-pressure surface processes that can benefit from the disclosed techniques include CO2 electrochemical reaction processes and any other reactions that require a high concentration of gaseous substances as reactants. Aqueous NB fluids can be used for high-pressure gas storage, such as H2, in tanks, pipelines, and other pressure vessels. Some surface processes do not require the long-term stability of nanobubbles because they use gaseous substances for reactions (consumption); thus, such processes can optionally be given an aqueous NB fluid with a larger amount of gas than other processes (such as long-term gas storage).

[0068] Subsurface applications include enhanced oil recovery (EOR) by gas injection and geological storage of gases in hydrocarbon reservoirs and aquifers. Typical gases for EOR are light hydrocarbons (e.g., methane, ethane, and propane), CO2, and N2; typical gases for geological storage are light hydrocarbons, CO2, H2, helium, air, and N2. These applications include energy storage as compressed gases based on renewable energy, which is sometimes intermittent and requires short-term storage.

[0069] In gas EOR, the injected gas not only rapidly passes through high-permeability layers and / or fracture networks but also gravitates to the upper region of the target reservoir. This undesirable flow regime causes the injected gas to quickly penetrate into the production wells, resulting in poor volumetric sweep efficiency and costly recycling of the injected gas. To mitigate this problem, water alternating gas (WAG) injection is commonly employed; however, water and gas may quickly separate, losing their effectiveness. A low concentration of specially formulated surfactants can be added to the water, thereby creating a surfactant-stabilized gas foam bank. In the case of the high apparent viscosity of the foam phase, better mobility control of gas injection is expected. However, two major drawbacks of this gas foam technology are (i) the difficulty in controlling the stability of the foam flowing in the reservoir pores and (ii) the use of surfactants increases the complexity and cost of field operations.

[0070] The aqueous NB fluid and related methods described herein can effectively reduce the mobility of the injected gas as it flows together with the external aqueous phase as a carrier without the risk of gas bubbles being trapped at the rock pores. The apparent viscosity of the aqueous NB fluid is shown to be slightly greater than that of the separate external phase without nanobubbles. Thus, compared to the simultaneous flow of two phases with relative permeability, the mobility of the gaseous substances contained in the aqueous NB fluid is significantly reduced by a factor of 10 in the experimental case with a Berea sandstone core. The reduced gaseous substance mobility is beneficial for both EOR and gas storage applications.

[0071] The aqueous NB fluid prepared according to the disclosed technology contains gaseous substances as nanoscale bubbles and can flow in geological formations like ordinary brine or other aqueous fluids. The dispersion of nanobubbles can substantially suppress buoyancy compared to injecting the gas as a bulk gas phase in the presence of water. Additionally, compared to conventional gas injection, the use of the aqueous NB fluid can reduce the density difference between the injected fluid and the reservoir oil. For example, the mass density of the aqueous NB fluid can be close to the mass density of the reservoir oil to be displaced.

[0072] For example, when the aqueous NB fluids and methods described herein are used for geological CO2 sequestration, they can significantly enhance the kinetics of carbon mineralization to achieve robust carbon sequestration. As mineralization occurs, the buoyancy reduction due to CO2 being contained as nanobubbles in the brine can mitigate the potential leakage of CO2 to the surface through any hydraulic pathways (e.g., faults and old wells).

[0073] Many biogas reservoirs are available for CO2 sequestration, but the contamination of the reservoir gas by the injected CO2 is a major issue. Using the present invention, the mixing of CO2 and natural gas (primarily methane) can be controlled by including CO2 in the injected aqueous phase.

[0074] In some examples, gas nanobubbles can be generated not only in aqueous fluids (e.g., water or brine), but also in aqueous solutions of other chemicals. Thus, the rheology and / or density of drilling fluids, fracturing fluids, and completion cements can be controlled or adjusted by including nanobubbles in these fluids.

[0075] In addition, the combination of CO2 sequestration and formate (HCOO - dissolved in water) can provide additional benefits. The use of carboxylates for carbon sequestration, EOR, and hydrogen storage is described in PCT International Application No. PCT / US2022 / 027116, filed on April 29, 2022, which is incorporated herein by reference. In examples, carboxylate-containing fluids can be modified to include nanobubbles of CO2 to enhance the carbon sequestration ability of the fluid. In examples, carboxylate-containing fluids can be modified to include nanobubbles of H2 to enhance the hydrogen storage capacity of the fluid.

[0076] Bubbles have applications in food, agriculture, wastewater treatment, mineral processing, pharmaceuticals, and other industries. However, these prior applications have been mainly limited to atmospheric pressure, where bubbly water is generated in an open system near atmospheric pressure. Without the discontinuous addition of energy, such a large-volume aqueous bubble system tends to be unstable at atmospheric bubble number densities. As described above, aqueous NB fluids can be generated with a significantly larger amount of gaseous material at elevated pressures and find more useful applications at elevated pressures. In addition, the advantage provided by using nanoscale bubbles is that the bubbles can remain dispersed in the aqueous fluid, which is generally not the case for the larger-sized bubbles applied in many conventional systems. However, no method has been found for controlling and designing the physical and transport properties of such gas-containing fluids at high pressures. This example and the present disclosure achieve this at least in part by obtaining a fundamental understanding of the thermodynamics involved in the formation of stable aqueous NB fluids and by using software and algorithms that embody such understanding. In addition, the use of an experimentally determined measurement database can enhance the performance and predictive ability of the thermodynamic model.

[0077] The current technology can be used for the generation and industrial application of a large number of bubbles coexisting with an external aqueous phase of a supersaturated gas in a closed system. From a thermodynamic perspective, this is very different from a single bubble or multiple bubbles in an open system at low pressure.

[0078] Sample data and results. Stability of aqueous NB fluids. A theoretical understanding of bubble stability is beneficial for the disclosed technology. Algorithms and software have been developed for performing thermodynamic calculations involving fluid phases with curved interfaces, including bubbles in aqueous fluids. The algorithms and software can be used to explore a fundamental understanding of the various factors affecting the formation of aqueous NB fluids, and for determining the optimal or beneficial fluid formulation for supporting a stable nanobubble dispersion.

[0079] Based on Gibbs' original work, a theoretical framework for phase stability analysis has been formed, but there is no rigorous solution to the phase stability problem in the presence of capillary pressure. Therefore, for phase stability and equilibrium calculations under capillary pressure, fundamental changes are made to the theoretical formulation by using the Helmholtz free energy instead of the Gibbs free energy. The inherent consistency between the Helmholtz and Gibbs free energies has been confirmed and the new framework developed here has been verified.

[0080] Assuming the stability of a single bubble, the thermodynamic model can estimate the properties of an aqueous NB fluid under given thermodynamic conditions (e.g., number of moles of components, temperature, and volume), such as phase composition, bubble size, and phase amounts. Figure 3A and Figure 3B shows sample calculations of the phase equilibrium of a water - N2 binary system at 298K with a bubble radius of 10 nm at two different pressures ( Figure 3A : 1.01 bar and Figure 3B : 140 bar). The solutions are evaluated by minimizing the Helmholtz free energy using the relevant algorithm, but for clarity, the results are shown in terms of the Gibbs free energy. These figures show that at an overall pressure of 1.01 bar, the displacement of the Gibbs free energy surface at the gas phase pressure is more significant ( Figure 3A ), because when the overall pressure is low, the relative magnitude of the gas phase pressure to the overall pressure is more significant. Compared with the prior art at ambient pressure, this highlights an advantageous aspect of the technology described herein, where high - pressure conditions are focused on in this technology.

[0081] Previous studies have speculated that the interfacial tension between the external aqueous phase and the bubble depends on the bubble size. As Figure 4 shown, due to the predicted relationships between variables such as phase composition, pressure, surface area, and interfacial tension, the software and related algorithms developed for the technology described herein naturally predict size - dependent interfacial tension. This figure is obtained by varying Figure 3Bobtained from the bubble sizes of the water-N2 binary examples shown.

[0082] When the aqueous NB fluid is formed from gas-saturated water, sufficient energy is available for the interfacial area required for the bubbles contained in the external aqueous phase in the system. When the system is set at a given temperature and total volume, the Helmholtz free energy of the gas-saturated single-phase fluid for the mixture is reduced to the Helmholtz free energy of the aqueous NB fluid consisting of two phases (the external aqueous phase and the bubbles). In theory, the Helmholtz free energy obtained by phase separation is used for the interfacial area for forming the bubbles. Figure 5 An exemplary calculation is shown where the amount of Helmholtz free energy released by forming the aqueous NB fluid is equal to the energy required to cause the interfacial area of the bubbles in the system. However, in practice, any dissipation will require an excess amount of energy over that theoretically required. Thus, the theoretical framework can be supplemented with experimental data, as shown in the next subsection.

[0083] Since the aqueous NB fluid in the current technology involves an aqueous phase of a gas-saturated gas in equilibrium with bubbles, it is useful for the thermodynamic model to be reliable in the metastable region. The example calculations shown in this section use the Peng-Robinson equation of state (EOS), but other models such as the GERG-2008 EOS can be used without a fundamental change to the method.

[0084] When the aqueous NB fluid contains many bubbles, the stability of the multiple bubbles is indicated by the upper limit of the bubble number density (the number of bubbles per unit volume). This maximum number density depends in part on the molecular-level details near the interface, which is not easily quantitatively predicted for general realistic conditions. In some cases, the number density can be estimated by supplementing a database of experimentally determined information to provide guidance for the values generated using the thermodynamic model, such as applying a calibration or correction factor to the modeled values.

[0085] Gas content measurement. In this example, the amount of gaseous substance in the aqueous NB fluid is referred to as the "gas content". It is one of the most fundamental data and substantially affects various applications of the technology, such as geological CO2 sequestration. A database of gas content under a wide range of conditions is useful, not only because it is not easily quantitatively predicted using theoretical models, but also because it depends on the mixing and bubble generation methods (Steps 2 and 3). For example, when Step 3 uses a porous membrane, for a given set of conditions (pressure, temperature, composition of the fluid, properties of the porous membrane, etc.), the gas content depends on the injection rates of the gas and water. The gas content measurement is described below for a set of conditions.

[0086] Experimental setup. Experiments using N2 are described here. The aqueous samples are deionized (DI) water or NaCl brine with a salinity of 50,000 ppm. The stainless-steel porous membrane used has a porosity of 37%, an average pore size of 5 μm (maximum 10 μm), an outer diameter of 25.4 mm, and a length of 3 mm. The stainless steel consists of 16 - 18% Cr, 11 - 14% Ni, 2 - 3% Mo, <0.03% C, <2% others, and Fe (the balance).

[0087] Figure 6 A schematic diagram of the experimental setup for gas content measurement is shown. The setup uses reservoirs for DI water (or NaCl brine) and N2, a pressure pump for maintaining the pressure of the test sample in the reservoir, a Hassler core holder for accommodating the porous membrane, a hydraulic hand pump for maintaining the overpressure in the core holder, and a sapphire visualization cell. The sapphire cell is used for optimal observation of the test fluid and has an internal volume of 8 mL. It can withstand a high pressure of up to 700 bar and a temperature of up to 423 K. An additional reservoir (receiver) is connected to the outlet of the sapphire cell to collect the effluent sample. One of the receiver reservoirs (2c) is placed to collect the fluid from the sapphire cell during the co-injection period. Another receiver reservoir (2d) is placed to collect the depressurized gas after the co-injection period.

[0088] Experimental procedure. To prepare the aqueous NB fluid, several variables were tested - pressure, injection rate (volume co-injection ratio), salinity. The experimental pressure was from 500 psi to 4000 psi, and the temperature was 294 K (room temperature). Two injection rates were used: rate 1 was 25 mL / h and rate 2 was 100 mL / h. The volume co-injection ratio was ratio 1 (90% N2 and 10% DI water or brine) or ratio 2 (50% N2 and 50% DI water or brine). At rate 2 and ratio 2, for example, 50 mL / h of N2 and 50 mL / h of DI water or brine were co-injected into the porous membrane, where the volume rate was at the operating pressure and temperature. The salinity variable was tested using 50,000 ppm NaCl brine. The procedure remained the same for each pressure, injection rate, co-injection ratio, and salinity configuration. The experimental process for an example configuration is described below.

[0089] Evacuate the tops of the pipeline, core holder, sapphire cell, and receiver accumulator for 1 hour. Saturate the system with DI water or brine up to the top of the receiver accumulator 2c while keeping valve V9b closed. Co-inject N2 and DI water or brine at a constant flow rate (rate 1 or 2) at a specified co-injection ratio (ratio 1 or 2) through the filter and through the sapphire visualization cell for a period of 2 hours to fill the cell with an aqueous NB fluid. The receiver accumulator (2c) receives the co-injected fluid at a constant refill flow rate (rate 1 or 2) to maintain the pressure in the system. After the co-injection period, isolate the sapphire cell by closing valves V8 and V9a. Determine the N2 content in the aqueous NB fluid by gradually depressurizing the system to atmospheric pressure. Valve V9b is first opened to fill the pipeline with depressurized N2, then valve V12 fills the dead volume of accumulator 2d, and then valve V13 collects the displacement fluid corresponding to the volume of the accumulator filled with depressurized N2. The volume of the collected fluid, the volume of the pipeline, and the dead volume of accumulator 2d represent the volume of N2 at atmospheric pressure assuming no N2 in the remaining aqueous phase in the sapphire cell and no water in the expanded gas phase. Then calculate the volume of N2 in the aqueous NB fluid at the experimental pressure using the following equation: [PV / Z] exp =[PV / Z] atm where P, V, and Z are the pressure, volume, and compressibility factor. The subscript exp represents the experimental conditions and the subscript atm represents the atmospheric pressure conditions. In the above equation, the right side is the measured value, assuming Z atm =1.0 (ideal gas). Divide this value by the product of the universal gas constant and the experimental temperature to obtain the number of moles of N2. Then the gas content is expressed in mole fraction as follows: where n is the number of moles of the substance.

[0090] When measuring the mass of the remaining water in the sapphire cell, correct the above procedure. Subtract the mass divided by the water density at that temperature and pressure from the volume of the sapphire cell to obtain a more accurate volume of N2 in the sapphire cell after depressurization.

[0091] Results. The initial phase of the experiment has generated a preliminary data set based on the assumption of no water in the expanded gas volume at atmospheric pressure as described above. Figure 7Shows the mole fraction of N2 in the aqueous NB fluid with 50% N2 and 50% water or brine at a total injection rate of 100 mL / h under different pressures. For example, the mole fraction of N2 obtained in the case of DI water is 0.038 at 4023 psia, and the mole fraction of N2 obtained in the case of brine is 0.042 at 4031 psia. The thermodynamic solubility of N2 in water at the same temperature and pressure is 0.002. That is to say, the N2 content in the former is 19 times greater than the thermodynamic solubility, and the N2 content in the latter is 21 times greater than the thermodynamic solubility.

[0092] Figure 8 Shows Figure 7 The mass density of the resulting NB fluid shown. The mass density of the NB fluid prepared with DI water is 0.881 g / mL at 4023 psia, and the mass density of the NB fluid prepared with brine is 0.798 g / mL at 4031 psia.

[0093] Apparent viscosity. The presence of gas bubbles in the aqueous NB fluid can be confirmed by the gas content measured under reduced pressure. Applying the aqueous NB fluid to a subterranean formation, such as geological CO2 sequestration, requires knowledge of the apparent viscosity in a porous medium. It is expected that gas bubbles in the aqueous NB fluid increase the apparent viscosity, similar to other dispersed particles, such as oil-in-water emulsions.

[0094] Therefore, use as Figure 11 shown core flood device to measure the apparent viscosity of the aqueous NB fluid. The setup consists of a pressurized pump, an accumulator containing the aqueous NB fluid, a core holder housing a Berea sandstone core, a pressure gauge, and a graduated cylinder for collecting effluent samples. The length of the Berea sandstone core is 9 inches and the diameter is 1 inch.

[0095] First, a sample of the aqueous NB fluid is prepared and stored in the accumulator. The sample is prepared by co-injecting N2 and DI water at a co-injection ratio of 50% N2 and 50% DI water (or brine) at 100 mL / h through a stainless-steel porous membrane. The pressure is 1800 psi and the co-injection is at room temperature. Then, the system is evacuated for 1 hour. The sandstone core is saturated with DI water (or brine) to determine the porosity and permeability of the core. Then, the DI water (or brine) in the system is displaced with the aqueous NB fluid at a flow rate of 50 mL / h, and the pressure drop across the core is determined. The apparent viscosity is calculated using Darcy's law.

[0096] Figure 12Shows the pressure difference during the measurement of the apparent viscosity of an aqueous NB fluid with brine and N2 using the Berea sandstone core as described above. In this figure, the red and blue dots show the data during the brine injection phase and the aqueous NB fluid injection phase, respectively. The pressure difference increases from 10 psi to 11 psi, indicating a 10% increase in apparent viscosity. This indicates the presence of gas bubbles in the tested aqueous NB fluid.

[0097] The transport of N2 as an aqueous NB fluid and the transport of N2 in a water-gas two-phase flow can be compared by using the mole fraction of N2, the molar density and viscosity of the aqueous NB fluid, and the water-gas relative permeability of the measured Berea sandstone core (Chen et al. 2016). The results show that the transport of N2 in the aqueous NB fluid is one order of magnitude smaller than the transport in the two-phase flow with relative permeability. The main factor reducing N2 transport is the reduced mobility of the gas-containing phase; that is, the aqueous NB fluid with a slightly increased apparent viscosity transports N2 much slower than N2 transport because the gas phase flows simultaneously with the water phase.

[0098] Description of the drawings. Figure 3A and Figure 3B . Sampling calculations of the phase equilibrium of the N2-water binary system at 297 K with a bubble radius of 10 nm using the Peng-Robinson equation of state. ( Figure 3A ) An overall pressure of 1.01 bar and ( Figure 3B ) An overall pressure of 140 bar. At 1.01 bar, the aqueous phase has two Gibbs free energy surfaces, where the cubic EOS has two real roots.

[0099] Figure 4 . The interfacial tension between the external aqueous phase and the bubble is used to change the radius of the bubble based on in-house software. Except for the varying bubble radius, the conditions are the same as those of Figure 3B .

[0100] Figure 5 . An example calculation where the energy released by phase separation is equal to the energy required for the bubble to create an interfacial area in the system. The vertical axis is the energy that can be released by forming two phases from a single phase, the dimensionless Helmholtz free energy divided by the molar volume (Helmholtz free energy density). The horizontal axis is the component molar density space (dimensionless) scaled between the equilibrium tie lines.

[0101] Figure 6 . Schematic diagram of the experimental setup for gas content measurement.

[0102] Figure 7 . Gas content measurement results under the assumption that there is no water in the expanded gas phase during depressurization.

[0103] Figure 8 . Figure 7The mass density of the aqueous NB fluid shown in

[0104] Figure 9 . Schematic diagram of the stability test device.

[0105] Figure 10. Photograph of a sapphire cell containing an aqueous NB fluid at room temperature and approximately 1800 psig: ( Figure 10A ) without an N2 gas cap, ( Figure 10B ) with an N2 gas cap. Due to the white background, the second sample appears white in the aqueous NB fluid, but it is transparent, just like the first sample above.

[0106] Figure 11 . Schematic diagram of the apparent viscosity measurement device.

[0107] Figure 12 . Pressure difference during the apparent viscosity measurement of an aqueous NB fluid with brine and N2 using Berea sand cores. Example 2: Thermodynamic Modeling of Dispersions of Aqueous Nanobubbles

[0108] The amount of gaseous substances in water or brine can be greatly increased in the form of nanobubble (NB) dispersions. Aqueous NB dispersions have great industrial applications and are potentially used in enhanced oil recovery and carbon dioxide (CO2) sequestration to control the mobility of gaseous substances. An appropriate understanding of the thermodynamic properties of aqueous NB dispersions allows for the further development of such NB technologies. The purpose of this example is to analyze the thermodynamic stability of aqueous NB dispersions and apply a thermodynamic equilibrium model to analyze experimental data.

[0109] This example presents a thermodynamic formula for simulating aqueous NB dispersions, which clarifies that aqueous NB dispersions occur in an aqueous phase supersaturated with gaseous substances in the system. That is, gaseous substances exist in two modes: dispersion of bubbles under capillary pressure and molecular dispersion (supersaturation) in the outer aqueous phase. This thermodynamic system is called an aqueous NB fluid in this example and is specified by (NC + 3) variables (e.g., temperature, total volume, number of moles of components, and capillary pressure), where NC is the number of components. Then, this example presents a novel implementation of the GERG-2008 equation of state (EOS) that minimizes the Helmholtz free energy to solve for the equilibrium properties of the aqueous NB fluid. GERG-2008 is used in this example because it is suitable for simulating an aqueous phase supersaturated with gaseous substances.

[0110] The thermodynamic equilibrium model was applied to experimental data of aqueous NB fluids with nitrogen (N2) at pressures up to 277 bar (4019 psia) and 295.15 K (71.6 °F). Application of the model to the experimental data indicated that most of the total N2 (0.8 - 0.9) was in the form of molecular dispersion, but such supersaturation of the aqueous phase was possible because of the presence of NB dispersions with capillary pressure. That is, as a thermodynamic system, the NB dispersion can increase the gas content in the aqueous NB fluid by supersaturating the gas in the aqueous phase. Despite the experimental uncertainties leading to a possible range of equilibrium properties of the aqueous NB fluid at high pressures, extrapolating the computed results to atmospheric pressure yielded bubble radii and number densities within the range of data reported in the literature.

[0111] Many gaseous substances such as CO2, H2, N2, and light hydrocarbons are highly immiscible with water, and their equilibrium concentrations in aqueous fluids (water or brine) are generally very small under a wide range of conditions. However, if these immiscible gaseous substances can be effectively homogeneously incorporated in an aqueous fluid, where the external aqueous phase contains immiscible bubbles with a large number density, various industrial processes can benefit.

[0112] Bubbles have many applications in food, agriculture, wastewater treatment, mineral processing, pharmaceuticals, and other industries. However, these applications are mainly limited to atmospheric pressure, where bubbling water is generated in an open system near atmospheric pressure. Such aqueous bubbles are not thermodynamically stable because the system is open and not kinetically stable at a large number density without continuous addition of energy.

[0113] This example relates to the development of a nanobubble technology that produces such aqueous fluids containing a large amount of immiscible gas or gas mixture at elevated pressures in a controlled and scalable manner. The technology aims to stably disperse gaseous substances as small bubbles (usually on the nanoscale) and dissolved molecules in an aqueous fluid. These two modes of accommodation (bubble dispersion and molecular dispersion) can together enable the total concentration of the gaseous substance to be greater than its thermodynamic solubility in the aqueous fluid. Such an aqueous fluid with bubble / molecular dispersion is referred to as an "aqueous NB fluid" in this example.

[0114] As shown in further detail below, aqueous NB fluids can be produced with a larger amount of gaseous substances at higher pressures, and thus, it finds more useful applications at elevated pressures. From a thermodynamic perspective, this is completely different from other technologies that address the problem of single or multiple bubbles in an open system at low pressures. However, to date, no method has been found to control and design the physical and transport properties of such gas-containing fluids at high pressures, which may be due to the lack of rigorous thermodynamic analysis and engineering tools for aqueous NB fluids.

[0115] High-pressure non-subsurface processes that can benefit from NB technology include CO2 electrochemical reaction processes and any other reactions that require a high concentration of gaseous substances as reactants in an aqueous reaction medium. This technology can be used for high-pressure gas storage in tanks, pipelines, and other pressure vessels, such as H2. Some surface processes do not require the long-term stability of NB because they use gaseous substances for reactions (consumption).

[0116] Underground applications of NB technology include enhanced oil recovery (EOR) by gas injection and geological storage of gases in hydrocarbon reservoirs and aquifers. In gas EOR, the injected gas not only flows through high-permeability layers and / or fracture networks but also undergoes gravity segregation to the upper region of the target reservoir. This undesirable flow state leads to rapid breakthrough of the injected gas into the production well, resulting in inefficient volumetric sweep and expensive recycling of the injected gas. To mitigate this problem, water alternating gas (WAG) injection is commonly employed; however, water and gas may separate, thereby losing the effectiveness of WAG. A low concentration of specially formulated surfactants can be added to water to create a surfactant-stabilized gas foam bank. In the case of the high apparent viscosity of the foam phase, better mobility control of gas injection is expected. However, two major drawbacks of this gas foam technology are (i) the difficulty in controlling the stability of the foam flowing in reservoir pores and (ii) the use of surfactants increases the complexity and cost of field operations.

[0117] NB technology can effectively reduce the mobility of the injected gas because it flows together with the external aqueous phase as a carrier without the risk of gas bubbles being trapped at rock pores. The apparent viscosity of the aqueous NB fluid shows a slightly greater value than that of the separate external phase without NB. Therefore, compared with the two-phase slip flow with relative permeability, in the experimental case with a Berea sandstone core, the mobility of the gaseous substances contained in the aqueous NB fluid will be significantly reduced by a factor of 10. The reduced gaseous substance mobility is beneficial for both EOR and gas storage applications.

[0118] An aqueous NB fluid containing gaseous substances as nanoscale bubbles can flow like ordinary brine in geological formations. Compared with injecting the gas as a bulk gas phase in the presence of water, the NB dispersion can substantially suppress buoyancy.

[0119] When this technology is applied to geological CO2 sequestration, it can significantly enhance the kinetics of carbon mineralization to achieve robust carbon sequestration. Along with mineralization, the buoyancy reduction due to including CO2 as NB in the brine can mitigate the potential leakage of CO2 to the ground through any hydraulic pathways (faults and old wells). Many biogas reservoirs can be used for CO2 sequestration, but the contamination of the reservoir gas by the injected CO2 is a major issue. Using the nanobubble technology, the mixing of CO2 and natural gas (mainly methane) can be controlled by including CO2 in the injected aqueous phase.

[0120] The theoretical understanding of aqueous NB fluids can be used to develop nanobubble technology. Software has been developed to perform thermodynamic calculations of fluid phases with curved interfaces, including bubbles in aqueous fluids. This example presents a thermodynamic equilibrium model that enables a basic understanding of the various factors affecting the properties of aqueous NB fluids. In this example, the aqueous NB fluid is modeled as a thermodynamically stable state of a closed system, where the external aqueous phase and the bubble phase coexist, and there is no bulk gas phase for water and gas substances.

[0121] After Gibbs' original work, the thermodynamic formula for phase stability analysis has been established, but there is no rigorous solution to the phase stability problem in the presence of capillary pressure. Therefore, for phase stability and equilibrium calculations under capillary pressure, a fundamental change is made to the theoretical formula by using the Helmholtz free energy instead of the Gibbs free energy. However, in addition, modeling the properties of aqueous NB fluids utilizes an equation of state (EOS) that can model water (a polar substance). Furthermore, the external aqueous phase is supersaturated with gaseous substances in the aqueous NB fluid; thus, the EOS used for this example must be reliable under metastable conditions.

[0122] Although cubic EOSs have traditionally been mainly used for hydrocarbon mixtures, they are not suitable for simulating strong intermolecular interactions caused by polarity, such as hydrogen bonding and dipole interactions in the liquid phase. The GERG-2004 EOS was developed to accurately predict the thermodynamic properties of fluids. The EOS was calibrated for 18 substances commonly present in natural gas, such as alkanes, water, and CO2. The accuracy of the GERG-2004 EOS depends on a large fluid database from 650 experimental data sources, covering different types of thermodynamic properties, such as PVT data, vapor-liquid equilibrium data, saturated liquid density, and enthalpy changes. Then, the GERG-2008 EOS extended the GERG-2004 model to 21 substances. The new model also extended the applicable conditions from 450 K to 700 K and from 35 MPa to 70 MPa, thus covering the vapor, liquid, supercritical, and multiphase regions. The GERG-2008 EOS has shown to be superior to cubic EOSs in predicting liquid density under a wide range of temperature and pressure conditions.

[0123] The GERG-2008 equation adopts an explicit form of the reduced Helmholtz free energy as a function of the reduced temperature, reduced density, and composition, which facilitates thermodynamic calculations based on the minimization of the Helmholtz free energy. In addition, GERG-2008 EOS has been compared with other EOSs to obtain the ability to reproduce the spinodal limits and metastable regions of pure components. It is found that GERG-2008 is more accurate than other Helmholtz-based EOSs (such as SAFT EOS). Therefore, in this embodiment, GERG-2008 EOS is adopted for the phase equilibrium calculation of aqueous NB fluids.

[0124] There are some challenges in using GERG-2008 EOS for modeling aqueous NB fluids. For example, GERG-2008 is not very accurate for the phase boundary prediction of CO2-containing mixtures and the solubility of gases in water. As will be shown in this embodiment, in GERG-2008, the residual part of the reduced Helmholtz free energy consists of two parts, namely the linear combination of the residuals of each component in the mixture and the departure function. The departure function is calibrated only for 7 hydrocarbon binaries. The matching of the water / CO2 mixture is improved by calibrating the departure correlation coefficient. This embodiment is re-modified in terms of the departure function and further improves the accuracy of GERG-2008 for the water / N2 mixture.

[0125] In addition, determining the correct compressibility factor using GERG-2008 is more challenging than using cubic EOS. GERG-2008 can have more than three roots, and there is no analytical solution for the root-finding problem. Commercial codes (such as REFPROP) may lead to convergence problems due to incorrect compressibility factors. A more robust algorithm for the compressibility factor using GERG-2008 is developed here.

[0126] This embodiment first gives the equations and algorithms for calculating the properties of aqueous NB fluids using GERG-2008 EOS. Then this model is used to match and analyze the experimental data of aqueous NB fluids with N2. It is believed that this is the first time to model aqueous NB fluids using the strict thermodynamic principle with a quantitatively reliable EOS, GERG-2008.

[0127] Equations. This article provides the equations and algorithms for calculating the equilibrium properties of aqueous NB fluids. The thermodynamic model can estimate the properties of aqueous NB fluids under given thermodynamic conditions (such as the number of moles of components, temperature, volume, and bubble radius), assuming a uniform bubble size.

[0128] Thermodynamic stability and equilibrium of aqueous nano-bubble fluids. Phase equilibrium with capillary pressure is most naturally modeled by minimization of the Helmholtz free energy. The iterative solution of the phase equilibrium problem using an EOS is highly nonlinear, but using the Helmholtz free energy involves only one energy surface, which is different from the conventional method using the Gibbs free energy and is independent of the number of phases with capillary pressure. The pressure of different equilibrium phases (i.e., capillary pressure) is inherently modeled as part of the minimization of the Helmholtz free energy. A brief review of the equations is provided, and the equilibrium properties of aqueous NB fluids are also given.

[0129] When the Helmholtz free energy of the system cannot be reduced by any possible perturbation, at a fixed temperature T, total volume V total and N C total number of moles n of components i (i = 1, 2,..., N C ) the closed system is in equilibrium. That is, for any perturbation of the thermodynamic variables, if dA total = dA V + dA σ + dA L ≥ 0 (1) then the system is stable. In the above equation, dA total , dA V , dA σ and d A L represent the changes in the Helmholtz free energy of the system, gas phase, interface, and liquid phase, respectively. The changes in the Helmholtz free energy of the V and L phases are and the change in the Helmholtz free energy of the interface is In the above equation, S is entropy, T is temperature, P is pressure, V is volume, and is the partial molar Gibbs free energy of component i, σ is the interfacial tension (IFT) between the V and L phases, a is the interfacial area, n i is the number of moles of component i, and N C is the number of components.

[0130] T, V total and n i The thermodynamic specification of dn iV +dN iσ +dN iL =0 (5) dV V +dV σ +dVL = 0 (6) dT V = dT σ = dT L = 0. (7) These conditions yield Due to dV σ and dn iσ being relatively small, the second and fourth terms can be neglected compared to the other terms on the right side of the above equation. Then, dA total tends to zero and the net mass transfer between the V and L phases decreases; i.e., dA total = 0 and Equation 10 requires the following condition: (P V - P L )dV V = σda, or P V - P L = σda / dV V . (11) Then, Equations 10 and 11 are used to define the first-order necessary conditions for the Helmholtz free energy to be minimized at given T, V total and n i (i = 1, 2,..., N C ). Note that Equation 11 applies to the equilibrium phase.

[0131] The minimization of the Helmholtz free energy is subject to the molar volume constraint. V j > V limj (12) where for the L and V phases (j = V or L) and the positivity of the number of moles n ij > 0 (13) where i = 1, 2,..., N C and j = V or L. In Equation 12, V limj represents the minimum possible molar volume of the EOS used. For cubic EOS [e.g., Peng-Robinson EOS], V limj is the co-volume parameter.

[0132] Equation 9 or 11 clarifies that the interfacial area a gives the state variable P of the thermodynamic aqueous NB fluid V - P L, which is constantly zero for the phase equilibrium state with a planar interface between fluid phases. Assume V V N at equilibrium b The uniform radius r of the bubble, V V = 4πr 3 N b / 3 (14) And the total surface area a is a=4πr 2 N b. (15) Using equations 14 and 15, the capillary pressure P C (=P V -P L ) is P C = σda / dV V =2σ / r. (16) Note that in equation 16, P C depends on r, assuming that the V phase is a plurality of spherical bubbles with a uniform radius r. Therefore, in addition to T, V total and n i (i = 1, 2,..., N C ), the value of P C can also be specified by specifying the values or functions of r and σ. For a given equilibrium solution, the number of bubbles N b can be calculated by using equation 14.

[0133] The problem of the thermodynamic aqueous NB fluid given above is quantitatively solved by using the GERG - 2008 EOS in this embodiment. The existence of a thermodynamically valid solution using such a quantitatively accurate EOS indicates the feasibility or stability of individual NB in the water phase supersaturated with gaseous substances. Finding such a valid solution contradicts the process called Laplace Pressure Bubble Catastrophe, which has been qualitatively discussed and not even specified the system of interest in the NB - related literature. Note that the many - body stability of NB cannot be analyzed in the above - mentioned thermodynamic framework, and detailed experiments may be important at the current research stage.

[0134] Bubble nucleation. When forming an aqueous NB fluid from a mixture of water and gaseous substances using a specific device, sufficient energy must be obtained to bring the interfacial area of the bubbles in the external water phase in the system to equilibrium. When such a system is set at a given temperature and total volume, the total Helmholtz free energy of the mixture is reduced to the total Helmholtz free energy of the aqueous NB fluid composed of two phases (the external water phase and the bubbles). The Helmholtz free energy ΔA totalThis reduction must be greater than the total Helmholtz free energy of the interface. This is a theoretical thought process without specifying the process for generating such an aqueous NB fluid; thus, the nucleation criteria given in this section are not as strict as those in an actual process. For example, any dissipation will require an additional amount of energy beyond the theoretically required amount.

[0135] The Helmholtz free energy of the original mixture is A I , while the Helmholtz free energy of the aqueous NB fluid is (A V + A σ + A L ). For the latter state to be thermodynamically more stable than the former, A I > (A V + A σ + A L ) or A I – (A V + A L ) > A σ = σa (17) Assume that the number of moles of the components and the volume of the interface are small such that A σ = G σ - P σ V σ + σa can be approximated as A σ = σa. The total volume V total of the system is common for the initial and final (equilibrium) states. Divide Equation 17 by V total RT to get A RI –(A RV S V + A RL S L ) > ε, (18) where A RI = A I / V total RT, A RV = A V / V V RT, A RL = A L / V L RT, S V = V V / V total , S L = V L / V total , and ε = σa / V total RT. A RI is the reduced Helmholtz free energy density in the initial state (assumed to be a single phase), A Rjis the reduced Helmholtz free energy density of phase j, S j is the equilibrium volume fraction (i.e., saturation) of phase j, and R is the universal gas constant.

[0136] Material balance of component i n i = n iV + n iL (19) can be expressed as d i = sd iV + (1 – s)d iL (20) where d i =n i / V total ,d iV =n iV / V V ,d iL =n iL / V L 。We use s instead of S V to analyze the nucleation criterion (Equation 18) in s space. That is, if D(s) = A RI (s) – [s A RV + (1 – s)A RL > ε, (21) then for a specified temperature, total volume, and number of moles of components, the aqueous NB fluid has a smaller Helmholtz free energy than the assumed single phase.

[0137] The D function is non-linear with s, while ε increases linearly with s with a slope of 3σ / rRT because ε=3σs / rRT. Note that at s=0, D=ε=0. Therefore, if the gradient of D with respect to s is greater than 3σ / rRT, then for small s values, D>ε. The gradient of D is where the Gibbs-Duhem equation is used. At s=0, the gradient becomes (P V -(P L ) / RT. Then, if P V – P L – 3σ / r > 0. (23) then bubble nucleation for small s values may be stable.

[0138] As in the current thermodynamic analysis, if P V -P L= 2σ / r (see Equation 16), Equation 23 cannot be satisfied. Note that Equation 23 is similar to the widely used expression for the nucleation energy barrier. The criterion (Equation 23) can be temporarily satisfied during gas nucleation, but such bubbles may not be thermodynamically stable unless a more fundamental criterion (Equation 21) is satisfied at equilibrium. This analysis shows that the thermodynamic stability of aqueous NB fluids requires a minimum amount of gaseous species in the system such that the criterion shown in Equation 21 can be satisfied.

[0139] Thermodynamic models. Equation of state. One challenge in accurately modeling the multiphase behavior including capillary pressure is that the equilibrium phases at lower pressures lie on the metastable part of the free energy surface. This part of the free energy lies outside the conventional range of the thermodynamic variables used to calibrate the EOS. As a result, most EOSs are uncertain in terms of the accuracy of modeling metastable phases. The GERG-2008 EOS is relatively accurate in modeling metastable phases.

[0140] The GERG-2008 EOS is a multi-parameter EOS and gives the values of the Helmholtz free energy as a function of composition, temperature, and molar density. This section gives the equations for the Helmholtz free energy given by the GERG-2008 EOS. Analytical expressions for other thermodynamic variables such as pressure and fugacity have been described. The dimensionless form of the EOS is where δ is the reduced density, δ = d / d r (x), (25) τ is the reciprocal of the reduced temperature, τ = T r (x) / T, (26) α 0 represents the contribution from an ideal gas mixture using d, T, and x, and α r represents the residual mixing behavior using δ, τ, and x. In Equations 24 and 25, d r and T r are the reduced molar density and temperature, defined as and where β vij , γ vij , β Tij and γ TijCalibration parameters that can be adjusted to match experimental data. The code for the GERG-2008 EOS was developed by converting FORTRAN77 code to modern FORTRAN (FORTRAN2003) and by adding missing routines for the pressure derivative with respect to the number of moles, the logarithm of the fugacity, and the derivative of the logarithm of the fugacity.

[0141] The calibration parameter β for the reduced temperature, molar density, and the residual component of the Helmholtz free energy for the water / gas system vij , γ vij , β Tij and γ Tij are available. However, this calibration did not use enough data to accurately calibrate the binary deviation parameters for mixtures of water and gases such as nitrogen ((N2) and carbon dioxide (CO2)). Another calibration of the binary deviation EOS for mixtures of water with various gases including N2 and CO2.

[0142] Figure 13 Shows experimental measurements and calculated values using different calibrations of the GERG-2008 EOS for the equilibrium water / N2 mole fractions in the liquid and gas phases at different temperatures and pressures. Figure 13 , inset a (left) shows the mole fraction of water in the gas phase, Figure 13 , inset b (right) shows the mole fraction of N2 in the liquid phase.

[0143] The REFPROP software developed by the National Institute for Science and Technology uses various EOS to calculate thermodynamic properties. It includes a fast liquid-vapor calculation using the GERG-2008 EOS. Figure 13 The open squares in are the results using REFPROP. The dashed lines show the equilibrium mole fractions calculated by the present implementation of the GERG-2008 EOS, which match the REFPROP values. The open triangles show the pressure values when the fast calculation of REFPROP fails. The GERG-2008 EOS implemented in this example converges to the correct solution at all pressures. This demonstrates the improved robustness of the fast calculation algorithm used in this example.

[0144] The dashed lines represent the equilibrium mole fractions calculated by the EOS-CG calibration of the GERG parameters. For water / N2, neither GERG nor EOS-CG matches the data well. Therefore, the GERG parameters are recalibrated to match the data. The recalibrated GERG parameters are shown in Tables 1 and 2.

[0145] Table 1. Binary parameters for the reduced parameter function for density and temperature. Table 2. Binary deviation functions Coefficients and exponents. N2 / H2O was calibrated by minimizing the residuals using the Scipy implementation of the Nelder-Mead algorithm.

[0146] One drawback of the multi-parameter GERG-2008 EOS is that it does not explicitly give an expression for the co-volume parameter, which is used in some algorithms to calculate the physical limits of the molar volume constrained by Equation 12. A model was developed for the pseudo co-volume parameter to match the molar volume that yields a pressure prediction of 2 × 10 7 bar; i.e., b = V (P = 2 × 10 7 bar).

[0147] First, the pseudo co-volume values of pure N2 and water were determined based on the GERG-2008 EOS calibrated elsewhere as given in Table 3.

[0148] Table 3. Pseudo co-volumes of pure substances based on GERG-2008. <![CDATA[N2]]> <![CDATA[H2O]]> b, cc / mol 5.41358 4.83885 Two models were calibrated for the co-volume of the water / N2 mixture. The first model uses the geometric mean for the attractive parameter, such as the van der Waals mixing rule. where k ij is the binary interaction parameter for the binary component pair i and j. The second model uses the mixing rule for the reduced density mixing rule from the GERG-2008 EOS. where c b,ij = 2β b,ij γ b,ij b ij , (31) β b,ij and γ b,ij are calibration parameters. Figure 14 The values of the pseudo co-volume parameters calculated by the above definitions were compared. Tables 4 - 7 show the co-volumes of pure substances and the calibration parameters for the two models.

[0149] Table 4. Co-volumes of pure substances. <![CDATA[N2]]> <![CDATA[H2O]]> b, cc / mol 5.41358 4.83885

[0150] Table 5. Optimal BIP value k ij for the geometric mean. <![CDATA[N2]]> <![CDATA[H2O]]> <![CDATA[N2]]> 0 -0.2234 <![CDATA[H2O]]> -0.2234 0

[0151] Table 6. Co-volume parameter β of the GERG-type mixing rules b,ij 。 <![CDATA[N2]]> <![CDATA[H2O]]> <![CDATA[N2]]> 0 1.0023 <![CDATA[H2O]]> 1.0023 0

[0152] Table 7. Co-volume parameter γ of the GERG-type mixing rules b,ij 。 <![CDATA[N2]]> <![CDATA[H2O]]> <![CDATA[N2]]> 0 1.2212 <![CDATA[H2O]]> 1.2212 0

[0153] The interfacial tension (IFT) of water and N2. Equation 11 is one of the main equations solved by the phase separation calculation algorithm for the equilibrium properties of the aqueous NB fluid in this example. This equation is given by the pressure modeled by the EOS and the capillary pressure for a given r. The equilibrium IFT is usually a function of the equilibrium phase compositions L and V, where the L phase is in the metastable region of the free energy hypersurface. This subsection presents the development of the IFT model for water / N2 nanobubbles, which takes into account the L-phase composition and density in the metastable region.

[0154] Data calibration of IFT based on the modified Parachor model. where χ is the temperature-dependent coefficient. This modification can be achieved simply by changing the value of Π in the input file i to χΠ i The calculated IFT and the experimentally measured values are shown in Figure 15 using solid and hollow symbols at various temperatures and pressures. Table 8 shows the Parachor coefficients and the calibrated Parachor exponents. Figure 16 shows the values of the χ parameter at different temperatures, which can be linearly correlated as χ = -0.5191(T - 273.15) + 173.2. (35)

[0155] Table 8. Parachor coefficients and Parachor exponents of water and N2.

[0156] Algorithm. This section gives a brief description of the fast calculation algorithm for a given composition and total molar volume, as well as two important developments necessary to implement the GERG-2008 EOS in minimizing the Helmholtz free energy. These models and algorithms include the correlation of the pseudo co-volume parameters for the gas-water mixture and a new procedure for estimating the initial guess for stability analysis and phase separation calculations.

[0157] Fast calculation. The algorithm uses the Successive Substitution (SS) method followed by the Newton-Raphson (NR) algorithm. SS is based on Adaptation of Michelsen's (1982) algorithm by Firoozabadi (2011) for minimizing the Helmholtz free energy. A switch from SS to NR occurs when the criterion is satisfied, where for i = 1, … N C , F i is F i = ln f iV - ln f iL = 0 (36) and the capillary pressure equation The NR algorithm uses the number of moles of the vapor phase and the total volume as independent variables.

[0158] Each SS iteration consists of two main steps: composition update and volume update. The composition update is based on the traditional method of Rachford and Rice for solving the material balance of ln K i . ln K i = lnx iV – lnx iL . (38) The Rachford-Rice routine is used in this embodiment. The volume is updated by the solution of the pressure equation according to the volume balance.

[0159] A brief description of the sequential iteration scheme of the SS algorithm is given below, and Figure 22 the flow chart of the algorithm is shown in

[0160] Step 1. Initialize ln K and V. If the reference phase is inherently stable, use stability analysis; otherwise, use the Wilson correlation at the specified total molar volume. Initialize the iteration index k: k ← 1.

[0161] Step 2. If then switch to the Newton-Raphson algorithm.

[0162] Step 3. Calculate and the SS sub-relaxation factor

[0163] Step 4. Update the capillary pressure using sub-relaxation based on the capillary pressure model evaluated at the composition and as well as the molar volume and . ​

[0164] Step 5. Update the phase composition. Update lnK using the SS step lnK i k ←(1 - ζ SS )lnK i k-1 + ζ SS (lnφ iL P L - lnφ iV P V ), where i = 1, …, N c . For the phase composition and and the phase mole fractions and Solve the Rachford-Rice equation.

[0165] Step 6. Update the phase molar volumes by solving Equation 13 using the Newton method.

[0166] Step 7. If the low-pressure phase is inherently unstable, use bisection to reduce its molar volume until it lies on the limit of inherent stability (the spinodal boundary).

[0167] Step 8. Check for convergence. If then stop. Otherwise, k ← k + 1 and return to Step 2. In this embodiment, ε F is set to 10 -10 .

[0168] In Step 2, evaluate the switching criterion from SS to . By setting ε NR to a value lower than ε NR , the SS algorithm can be executed until convergence without switching to the NR method. A description of the sequential iteration scheme when the switching criterion is met and the NR algorithm is activated is presented below. Calculate the definite and indefinite solutions of the Jacobian determinant using specific expressions.

[0169] Step 3. Calculate the gradient F k and the Jacobian determinant

[0170] Step 4. Solve for the Newton direction according to Equation

[0171] Step 5. Calculate the under-relaxation factor ζ NR required to enforce the feasibility constraints of Equations 14 and 15.

[0172] Step 6. Update the gas phase and the liquid phase in terms of number of moles and volume.

[0173] Step 7. Check for convergence. If then stop. Otherwise, k ← k + 1 and return to Step 3. In this embodiment, ε F is set to 10 -10 .

[0174] Initial guess. Raoult's law does not give accurate K-values as an initial guess for stability and phase separation calculations in this study. Also, N2 and water are strongly immiscible; thus, a specific initial estimate of the K-values is possible as presented in this subsection. The component index i = 1 is defined as the component index for water. To find the initial aqueous phase, the initial guess for the composition is x i = 10 -9 , i = 2, …, N C , and x1 = 1.0 - (N C - 1) × 10 -9 . The molar volume is set to V = max(18 × 10 -6 , 1 + 10 -4 b(x)) (39) Search for the initial aqueous phase. To search for the initial gas phase, for i = 2, …, N C and x1 = 10 -9 / t, the initial guess for the composition is x i = z i / t, where the molar volume is set to V = V total / (1.0 – z1) (40) to search for the initial gas phase.

[0175] If the Hessian of the reduced Helmholtz free energy is positive definite, the initial guess composition for phase separation calculations is the same as described elsewhere. However, the initial guess molar volume is determined by solving L P V = P V = β L V L + β V V V using the Newton-Raphson algorithm subject to P

[0176] Step 1. Set P k ← 10 bar and k ← 1, P min ← 10-9 , P max ← 2 × 10 -9

[0177] Step 2. Solve the EOS for the molar volumes of the liquid k and vapor V L at pressure P V V , and calculate the derivatives of the pressure with respect to volume for the two phases. Calculate the total volume V t = V L + V V . If V t < V total , then set P max ← P k . Otherwise, set P min ← P k .

[0178] Step 3. Update the pressure If |V t - V total | / V total < 10 -7 , then the algorithm converges. Use the liquid and gas phase compositions and volumes as initial guesses for the fast calculation. Otherwise, set k ← k + 1 and return to Step 2.

[0179] If the Hessian of the reduced Helmholtz free energy is not positive definite, then it is unconditionally unstable. The L-phase mole fraction and initial guess composition are set as follows: where i = 2, …, N c , and

[0180] The V-phase mole fraction and initial guess composition are set as follows: where i = 2, …, N c , and Then use the Newton - Raphson algorithm above to calculate the volumes of the two phases.

[0181] Apply the thermodynamic equilibrium model to aqueous nanobubble fluids with N2. This section first describes the experiments and results for aqueous NB fluids with N2, and then presents the application of the thermodynamic equilibrium model to analyze the data. The modeling part includes the calibration of the GERG - 2008 EOS, the water / gas interfacial tension model, and the calculation of the equilibrium properties of aqueous NB fluid samples.

[0182] Dispersion of aqueous nanobubbles that produce N2 at elevated pressures. Figure 17 Figure showing a schematic of the experiment to produce the aqueous NB fluid in this example. Deionized (DI) water and high purity N2 gas are pressurized in an accumulator equipped with a piston. They are co-injected at an equal volume rate of 50 cc / hr (100 cc / hr total) at the test pressure into a core holder in which three porous stainless steel membranes are placed. The confining pressure on the core holder is 35 bar greater than the test pressure. Each membrane has a diameter of 1 inch and a thickness of 3 mm, with uniform pores of 5 μm. One possible mechanism for this porous membrane to produce an aqueous NB dispersion is that when water and gas flow through the pores, hydrodynamic mixing and gas mutation produce dispersed bubbles in the aqueous phase, which are supersaturated with the gas component. Due to two modes of dispersion: bubble dispersion as the internal phase and molecular dispersion in the external phase, the water leaving these three membranes contains a greater amount of N2 than the saturation amount. Then the prepared aqueous NB fluid is transferred to a receiver accumulator for storage at high pressure.

[0183] Figure 18 Figure showing a schematic of the experiment to measure the thermodynamic properties of the aqueous NB fluid. According to the procedure given previously, an aqueous NB fluid sample is transferred from the receiver accumulator to a sapphire cell at pressure P1. The sapphire cell provides an observation window to observe the behavior of the aqueous NB fluid, and it can withstand pressures up to 350 bar. The volume of the sapphire cell is known and named V cell . Then, the cell is connected to the top side of an accumulator containing a piston and a pressure gauge. The piston is initially set at the top of the accumulator, and the dead volumes (V d ) in the pipeline connecting the sapphire cell to the accumulator and the pipeline connecting the accumulator to the pressure gauge are evacuated. Next, the cell is gradually depressurized by opening the cell to fill the dead volume with N2 from the aqueous NB fluid. Then the bottom side of the accumulator is opened to the atmosphere. When the aqueous NB fluid sample is depressurized or expanded, water is collected to measure the displacement of the piston. The collected water corresponds to the volume of the depressurized N2 in the aqueous NB fluid. The mass of the collected water is denoted as m w2 , and the pressure at the top side of the accumulator after depressurization is P2. Finally, the remaining water in the cell is collected and its mass m w3 is measured.

[0184] These experiments were conducted in Austin, Texas during the week of April 3, 2023. In Austin, Texas, during this time period, the average atmospheric pressure was 1.0135 bar, the minimum was 1.000 bar, and the maximum was 1.026 bar. This pressure is used as P3 in the calculations. Each measurement was recorded at a temperature of 295.15 K.

[0185] Analyze aqueous NB fluids with N2. This subsection first shows the application of the previously described thermodynamic framework to analyze the experimental data of aqueous NB fluids with N2 and calculate the apparent radius of the bubbles for each aqueous NB fluid sample. Although the size distribution of nanobubbles has been measured and reported for low-pressure (mainly atmospheric pressure) samples using light scattering, spectroscopy, and high-resolution imaging techniques in the literature, such measurements for high-pressure aqueous NB samples are not an easy task and require a specific design for the high-pressure sample containers used. The bubble sizes estimated in this section enable an understanding of the overall behavior of aqueous NB fluids with N2 from a thermodynamic perspective.

[0186] First, analyze the data by using a thermodynamic equilibrium model based on the following assumptions: 1. Measure the data at equilibrium. 2. The mass of water measured in step 3 ( Figure 18 ) is in equilibrium with the N2 gas cap in the sapphire cell. 3. The mass of water remaining inside the sapphire cell in the form of droplets is negligible compared to the measured mass m w3 . 4. Close the system during the pressure reduction process from P2 to P3.

[0187] As described above, the phase equilibrium including capillary pressure can be specified by (N C + 3) variables; for example, temperature, total volume, total number of moles of components, and capillary pressure. Here, a thermodynamic model is used for temperature, total volume, total number of moles of components, and external phase pressure, which are measurable (directly or indirectly) for the aqueous NB fluid sample in this embodiment.

[0188] The following process first explains how to estimate the total number of moles ( Figure 18 ) in the sapphire cell in step 1 of the experiment, and then how to determine the apparent radius of the bubbles for the external phase pressure P1. - Perform a quick calculation for an equimolar mixture of the water / N2 binary system at P3 (atmospheric pressure) and 295.15 K. Assume the mixture is only equimolar to obtain the equilibrium water phase composition in step 3. The volume of the water phase is calculated as V w3 = m w3 V L / M L , where V L and M L are the equilibrium water phase molar volume and weight. The number of moles of water in the water phase is n w3 = m w3 / M L = d 1L V w3。 - Perform a quick calculation at P2 and 295.15 K. The total volume of the aqueous phase in step 2 is V L2 = n w3 / d 1L where d 1L is the molar density of water in the obtained aqueous phase. - Perform a quick calculation on a binary water / N2 mixture at P3 and 295.15 K, where N2 (as an approximate composition of air) is in equilibrium with the water collected in step 2. Thus, the volume of the water collected is V w2 = m w2 V L / M L where V L and M L are the equilibrium aqueous phase molar volume and weight. Thus, the total volume of the mixture at P2 is V t2 = V cell + V w2 + V d where V d is the dead volume contained in the pipeline connecting the sapphire cell and the accumulator and the pipeline connecting the accumulator to the pressure gauge. - Determine the total number of moles in the system between the sapphire cell and the accumulator, which gives the liquid volume V L2 and the gas volume V t2 - V L2 。 - Perform a quick calculation at the total volume V cell and the number of moles of water and N2, with bubble radii of 1 nm and 104 nm. If the outer phase pressure P1 lies between the values of 1 nm and 104 nm, perform a bisection to find the bubble radius that gives the outer phase pressure P1.

[0189] Table 9 shows the measured data in the experiment on an aqueous NB fluid with N2. For the temperature (295.15 K), the total volume (V cell ), the number of moles of water (n w ) and the number of moles of N2 (n N2 ) and the outer phase pressure (P1), use the data in Table 9 and the procedure given above to generate the possible bubble radii. Among these input parameters, m w3 is the most uncertain and is found to have an impact on the bubble radius generated in the calculation. Table 9 shows that the uncertainty of m w3 is ±3 g. For example, if m w3If it is less than 0.1 g, it can increase the apparent radius of the calculated bubbles by an order of magnitude. Therefore, it is impossible to quantitatively determine the apparent radius of the bubbles of these data with order-of-magnitude accuracy solely by using thermodynamic calculations. Nevertheless, for the actual experimental conditions, the presence of bubbles with an actual apparent radius indicates the possibility of a thermodynamic aqueous NB fluid, where the gas component is molecularly dispersed and also exists as bubbles in the external aqueous phase with capillary pressure.

[0190] Table 9. Experimental data for aqueous NB of N2 at 295.15 K. Parameter <![CDATA[P1]]> <![CDATA[P2]]> <![CDATA[P3]]> <![CDATA[m w2 > <![CDATA[m w3 > <![CDATA[V cell > <![CDATA[V d > Unit bar bar bar g G mL mL Experiment 1 34.59 1.22 1.013 4.54 10.765±3 13.69 6.705 Experiment 2 68.93 1.29 1.013 11.4 10.930±3 13.69 6.705 Experiment 3 104.2 1.15 1.013 23.58 11.405±3 13.69 6.705 Experiment 4 103.3 1.29 1.013 19.49 11.310±3 13.69 6.705 Experiment 5 103.4 1.29 1.013 21.22 11.295±3 13.69 6.705 Experiment 6 138.2 1.22 1.013 32.01 11.040±3 13.69 6.705 Experiment 7 207.8 1.22 1.013 57.41 11.835±3 13.69 6.705 Experiment 8 277.1 1.22 1.013 71.92 12.040±3 13.69 6.705

[0191] To analyze the experimental data, a thermodynamic equilibrium model is solved for the overall composition, total molar volume, and bubble radius of the water / N2 binary system at a specified temperature. Since the mass m of water collected from the sapphire cell w3 is relatively uncertain, for each experiment within the possible value range shown in Table 9, the thermodynamic calculations are repeated for multiple values of m w3 . For each calculation, based on m w3 , the number of moles of water n w and the volume of the L phase are adjusted. The number of moles of nitrogen n N2 is based on the volume of the V phase in Step 2, using the mass m of water collected from the receiver accumulator in Table 9 w2 . Then, for the system specified at fixed T, n N2 , n w , V cell and P L , the radius of the bubbles is determined.

[0192] Figure 19 The total N2 mole fraction z is shown by a thick black line N2 , the mole fraction of N2 in the aqueous phase x is shown by a black dashed line N2,W , and the mole fraction of N2 for changing the bubble radius in the absence of capillary pressure x N2,W (P C = 0) is shown by a dotted line. The stability criterion C (= D - ε, see Equation 21) is plotted on the auxiliary y-axis with a black dash-dotted line. The bubble radius at C = 0 is the minimum radius that satisfies the stability criterion. The minimum radius of the small bubbles is calculated as Figure 19 60.8 nm in Figure a (Experiment 1 at 34.59 bar), Figure 19 39.1 nm in Figure b (Experiment 2 at 68.93 bar), Figure 19 25.4 nm in Figure c (Experiment 3 at 104.2 bar), Figure 19 27.0 nm in Figure d (Experiment 4 at 103.3 bar), Figure 1923.3 nm of small figure e (Experiment 5 at 103.4 bar), Figure 19 16.5 nm of small figure f (Experiment 6 at 138.2 bar), Figure 19 8.54 nm of small figure g (Experiment 7 at 207.8 bar), and Figure 19 7.14 nm of small figure h (Experiment 8 at 277.1 bar). Table 10 shows n N2 and n w , as well as the corresponding masses of N2 and water used for calculations with the experimental data sets of Experiments 1 - 8.

[0193] Figure 20 Shows the total reduced Helmholtz free energy using a thick black line, and the total Helmholtz free energy of the gas phase and the interface plotted against the secondary y - axis using a dotted line. For all experimental data, the free energy decreases monotonically as the bubble radius decreases. That is, based on the thermodynamic equilibrium model and experimental data in this embodiment, for a given temperature, total molar volume, and external phase pressure, the total composition corresponding to C = 0 results in the minimum possible Helmholtz free energy for an aqueous NB fluid with N2.

[0194] Table 10. For each experiment at 295.15 K and 13.69 mL volume, the bubble radius, component moles and masses at C = 0.

[0195] To give an overview of the calculated properties of the aqueous NB fluid samples in this embodiment, for each pressure of each aqueous NB fluid sample, the apparent radius of the bubble corresponding to the total composition with C = 0 is calculated using a thermodynamic equilibrium model. Once the radius of the bubble is set, the model gives various equilibrium properties of the aqueous NB fluid sample. Figure 21 Small figure a of shows the mass of water m used for calculations at each pressure w3 within the uncertainties given in Table 9. Figure 21 Also shown are the bubble radius, bubble number density, the amount of N2 in the bubble and the amount of N2 dissolved in the external aqueous phase in molecular form, the total interfacial area, IFT, and the capillary pressure relative to the external (water) phase pressure (P L ). Figure 21 The N2 content in small figure d is calculated as for the gas phase and for the liquid water phase where β V is the gas - phase mole fraction (as the total amount of the bubble), and β L is the water - phase mole fraction. The dotted line labeled "saturated" represents the situation when N2 and water are in equilibrium without bubbles and thus have a single planar interface between the two bulk phases in the system. Figure 21 Insert figure e shows the N2 fraction contained in the bubbles, calculated as The error bar was determined as half of the difference between the minimum and maximum values at 104 bar, since the experiment was repeated three times for Experiments 3, 4, and 5.

[0196] Figure 21 Insert figures b and c show the calculated bubble radius and number density decreasing with increasing P L . Extrapolation to atmospheric pressure using two data points at the lowest pressure yields a bubble radius of 80 nm and a number density of 10 9 / mL. This extrapolated radius lies within the range of the measured bubble radii of 25 - 200 nm at atmospheric pressure. Similarly, the extrapolated number density is within the measured values of 10 6 -10 9 mL -1 at atmospheric pressure.

[0197] Figure 21 Insert figures d and e show that most of the N2 in the system is dissolved in the external aqueous phase in molecular form. This is a valuable finding from this study; namely, more N2 is added through molecular dispersion (supersaturation) in the aqueous phase compared to inclusion of N2 as bubbles, and the presence of bubbles increases the N2 content in the system. The presence of bubbles in the aqueous NB fluid at equilibrium tends to increase the supersaturation level in the external aqueous phase with capillary pressure. The results show that this supersaturation is the main contribution to the amount of N2 in the aqueous NB fluid. Since gas content is one of the most fundamental properties of the aqueous NB fluid, this insight obtained through the thermodynamic equilibrium model in this example has a fundamental impact on the research and development of NB technology, such as for the devices and applications of surface and subsurface processes.

[0198] Previous studies hypothesized that the IFT between the external aqueous phase and the bubbles depends on the bubble size. Due to the thermodynamic relationships between variables such as phase composition, pressure, surface area, and interfacial tension, the thermodynamic equilibrium model developed in this study naturally predicts a size-dependent interfacial tension, as Figure 21 shown.

[0199] Conclusion. This example presents a thermodynamic equilibrium model of an aqueous NB fluid using the GERG-2008 EOS. The model was applied to experimental data of an aqueous NB dispersion of N2 at pressures up to 277 absolute bar (4019 psia) at 295.15 K (71.6°F). Thermodynamic analysis of the experimental data led to the following conclusions: - A thermodynamic system of an aqueous NB fluid is possible if bubbles are dispersed in an external aqueous phase supersaturated with a gaseous substance and without a bulk gas phase. The bubble nucleation criterion obtained in this embodiment indicates that the thermodynamic stability of the aqueous NB fluid requires a minimum amount of gaseous substance in the system. - Applying a thermodynamic model to high-pressure experimental data shows that the aqueous NB fluid system gives the minimum possible Helmholtz free energy at the overall composition corresponding to the bubble nucleation limit for a given temperature, overall volume, and bubble radius. - As shown by the experimental data, the amount of gas in the aqueous NB fluid increases with increasing pressure of the external aqueous phase. Thus, the model shows that as the aqueous phase pressure increases, the bubble radius decreases and the bubble number density increases. Extrapolation to atmospheric pressure yields a bubble radius of 80 nm and a number density of 10 9 mL -1 within the range of the data measured at atmospheric pressure. - Analysis of the data shows that most (0.8 - 0.9) of the gaseous substance N2 in the system is dissolved in the aqueous phase in molecular form. Thus, the presence of bubbles is important for increasing the N2 supersaturation level in the aqueous phase, but in this embodiment, the amount of N2 as bubbles is not the main contribution to the total amount of N2 in the aqueous NB fluid. The thermodynamic equilibrium model developed in this embodiment naturally predicts that the IFT between the external aqueous phase and the bubbles depends on the bubble size because of the thermodynamic relationships between variables such as phase composition, pressure, surface area, and interfacial tension.

[0200] Description of the drawings of Embodiment 2.

[0201] Figure 13 . Equilibrium mole fractions of water in the gas phase and nitrogen in the aqueous phase; (inset a) shows the mole fraction of water in the gas phase from bottom to top at 273.15 K, 283.15 K, 323.15 K, and 422.4 K; (inset b) shows the mole fraction of nitrogen in the aqueous phase from bottom to top at 323.15 K and 298.15 K. Hollow squares and dotted lines show the equilibrium mole fractions calculated using the implementation of REFPROP (RPGERG) and the GERG developed herein (TGRGERG), respectively. The solid line shows the calibrated GERG model with the tuning parameters shown in Tables 1 and 2.

[0202] Figure 14 . Calibrated pseudo - co - volume of water / N2. Hollow red circles show the root of the molar volume for a pressure of 2 x 10 7 bar. For a BIP of 0, the dark dashed line and the thick line show the matching co - volumes using the geometric mixing rule and the reference mixing rule, respectively. The dotted line represents the matching pseudo - co - volume using the GERG - type mixing rule.

[0203] Figure 15 . Calibration parameter model of IFT of water and nitrogen at various temperatures and pressures. Experimental data are shown by black circles at 298.15K, red squares at 313.15K, blue diamonds at 333.15K, green triangles at 353.15K, and yellow downward triangles at 373.15K.

[0204] Figure 16 . In this embodiment, the temperature correlation coefficient χ of the modified Parachor model.

[0205] Figure 17 . Schematic diagram of the experimental apparatus for generating aqueous NB fluid.

[0206] Figure 18 . Schematic diagram of the experimental apparatus for measuring the thermodynamic properties of aqueous NB fluid.

[0207] Figure 19 . Solutions of the thermodynamic equilibrium model for aqueous NB fluid samples in Experiments 1 - 8. The auxiliary y-axis is the stability criterion C = D - ∈ (see Equation 21) multiplied by 10 3 .

[0208] Figure 20 . For Experiments 1 to 8, the total Helmholtz free energy [A R and (A V + A σ ) / RT] of aqueous NB fluid with N2 at 295.15K decreases.

[0209] Figure 21 . For the nanobubble solution in Experiments 1 to 8 at 295.15K, the mass of water in the sapphire cell, bubble radius, bubble number density, N2 content, fraction of N2 in the bubble, interfacial area, interfacial tension of N2 in water, and capillary pressure.

[0210] Figure 22 . Flowchart of the fast calculation algorithm. References

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[0265] All references in this application, such as patent documents, including issued or granted patents or equivalents and patent application publications, and non-patent literature documents or other source materials, are incorporated herein by reference in their entirety as if individually incorporated by reference.

[0266] All patents and publications mentioned in the specification represent the state of the art of those skilled in the art to which the present invention pertains. The references cited herein are incorporated herein by reference in their entirety to indicate the state of the prior art, in some cases as of their filing date, and it is intended that this information can be used herein, if needed, to exclude (e.g., disclaim) particular embodiments of the prior art.

[0267] When a group of substituents is disclosed herein, it is understood that all individual members of these groups and all subgroups and classes that can be formed using the disclosed substituents are individually disclosed. When a Markush group or other grouping is used herein, all individual members of the group and all possible combinations and subcombinations of the group are intended to be individually included in the disclosure. As used herein, “and / or” means that one, all, or any combination of the items in the list separated by “and / or” is included in the list; for example, “1, 2 and / or 3” is equivalent to “1, 2, 3, 1 and 2, 1 and 3, 2 and 3, or 1, 2 and 3”.

[0268] Unless otherwise indicated, each formula or combination of components described or exemplified can be used to practice the present invention. The specific names of materials are intended to be exemplary since it is known that one of ordinary skill in the art can name the same materials differently. It should be understood that methods, device elements, starting materials, and synthetic methods other than those specifically exemplified can be used in the practice of the present invention without undue experimentation. All known functional equivalents of any such methods, device elements, starting materials, and synthetic methods are intended to be included in the present invention. Whenever a range is given in the specification, such as a temperature range, a time range, or a composition range, all intermediate ranges and sub-ranges, as well as all individual values included in the given range, are intended to be included in this disclosure.

[0269] As used herein, "comprising" is synonymous with "including", "containing", or "characterized by", and is inclusive or open-ended and does not exclude additional unrecited elements or method steps. As used herein, "consisting of" does not include any element, step, or ingredient not specified in the claim element. As used herein, "consisting essentially of" does not exclude materials or steps that do not substantially affect the basic and novel characteristics of the claim. Any recitation of the term "comprising" herein, particularly in the description of the components of a composition, in the description of a method, or in the description of the elements of a device, should be understood to encompass those compositions, methods, or devices that consist essentially of the recited components or elements (optionally in addition to other components or elements) or consist of them. The present invention, as described illustratively herein, can be practiced appropriately without any element, plurality of elements, limitation, or plurality of limitations not specifically disclosed herein.

[0270] The terms and expressions that have been employed are used as terms of description and not of limitation, and there is no intention, in the use of such terms and expressions, of excluding any equivalents of the features shown and described or portions thereof, but it is recognized that various modifications are possible within the scope of the invention as claimed. Accordingly, it should be understood that although the present invention has been specifically disclosed by way of example, embodiments, and optional features, modifications and variations of the concepts disclosed herein may be employed by those skilled in the art, and such modifications and variations are considered to be within the scope of the invention as defined by the appended claims.

Claims

1. A method, comprising: Determining a target composition of an aqueous fluid in a nano-bubble solution for a gas at a specified temperature and a specified pressure; Preparing the aqueous fluid according to the target composition; Mixing a gas in the aqueous fluid at the specified temperature and the specified pressure to form a supersaturated solution of the gas in the aqueous fluid; And Subjecting the gas and the aqueous fluid to a bubble generation process to form a dispersion of nano-bubbles of the gas in the aqueous fluid at the specified temperature and the specified pressure.

2. The method according to claim 1, wherein the gas is immiscible in the aqueous fluid or has a solubility in water of less than 2 g / L at standard temperature and pressure.

3. The method according to claim 1, wherein the specified temperature is greater than 0 °C and less than the boiling point of the aqueous fluid at the specified pressure.

4. The method according to claim 1, wherein the specified pressure is from 1 MPa to 105 MPa.

5. The method according to claim 1, wherein The dispersion of nano-bubbles of the gas in the aqueous fluid exhibits a greater amount of supersaturation than the supersaturated solution of the gas in the aqueous fluid.

6. The method according to claim 1, wherein Compared with the supersaturated solution of the gas in the aqueous fluid, the dispersion of nano-bubbles of the gas in the aqueous fluid exhibits a higher intensity and / or faster kinetics of mineral dissolution and / or precipitation.

7. The method according to claim 1, wherein the gas comprises CO2, H2, N2, O2, He, methane, ethane, ethylene, acetylene, propane, propylene, methylacetylene, cyclopropane, allene, butane, butene, butyne, cyclobutane, butadiene, hydrocarbon gas or a combination thereof.

8. The method according to claim 1, wherein the gas comprises a hydrocarbon gas suspended in or contained in an inert gas.

9. The method according to claim 1, wherein the nano-bubbles have a diameter of 1 nm to 1000 nm.

10. The method according to claim 1, wherein the dispersion of nano-bubbles corresponds to a concentration of the gas in the aqueous fluid of 0.05 mol / L to 20 mol / L.

11. The method according to claim 1, wherein the amount or mass of the gas dissolved in the aqueous fluid in the dispersion of nano-bubbles is greater than the amount or mass of the gas in the nano-bubbles in the dispersion of nano-bubbles.

12. The method according to claim 1, wherein the amount or mass of the gas in the nano-bubbles in the dispersion of nano-bubbles is greater than the amount or mass of the gas dissolved in the aqueous fluid in the dispersion of nano-bubbles.

13. The method according to claim 1, wherein the aqueous fluid comprises water, seawater, reservoir resident water, produced water, river water, pond water, brine, engineered brine or any combination thereof.

14. The method according to claim 1, wherein the aqueous fluid comprises one or more salts, one or more electrolytes, one or more acids, one or more bases, monovalent anions, monovalent cations, divalent anions, divalent cations, trivalent anions, trivalent cations, formate, or any combination thereof.

15. The method according to claim 1, wherein the aqueous fluid comprises an additive selected from the group consisting of surfactants, foaming agents, polymers, nanoparticles, alcohols, oxygenated solvents, or any combination thereof.

16. The method according to claim 15, wherein the additive is present or dissolved in the aqueous fluid at a concentration of less than or about 3 wt%.

17. The method according to claim 1, wherein the aqueous fluid does not contain or contains one or more additives selected from the group consisting of surfactants, foaming agents, polymers, nanoparticles, alcohols, oxygenated solvents, or any combination thereof.

18. The method according to claim 1, wherein determining the target composition of the aqueous fluid comprises determining the ionic composition or ionic strength of the aqueous fluid.

19. The method according to claim 18, wherein the ionic strength is from 0 mol / L to 6 mol / L.

20. The method according to claim 18, wherein the ionic composition comprises one or more ions selected from the following: H + , Na + , K + , Mg 2+ , Ca 2+ , Fe 2+ , NH4 + , OH - , F - , Cl - , Br - , I - , SO4 2- , NO3 - and CO3 2- , HCO3-, PO4 3- , HCOO - or any combination thereof.

21. The method according to claim 1, wherein the bubble generation process comprises injecting the gas into the aqueous fluid through a porous membrane, co-injecting the gas and the aqueous fluid through a porous membrane, injecting the gas into the aqueous fluid through one or more nozzles, co-injecting the gas and the aqueous fluid through one or more nozzles, subjecting a supersaturated solution of the gas in the aqueous fluid to decompression to initiate bubble nucleation, subjecting a supersaturated solution of the gas in the aqueous fluid to ultrasonic energy, subjecting a supersaturated solution of the gas in the aqueous fluid to shear stress, or a combination thereof.

22. The method according to claim 1, wherein determining the target composition of the aqueous fluid comprises determining the target pH of the aqueous fluid.

23. The method according to claim 1, wherein determining the target composition of the aqueous fluid comprises providing at least the specified temperature, the specified pressure, and the identity information of the gas to a thermodynamic model.

24. The method according to claim 23, wherein the thermodynamic model determines the properties of the dispersion, the properties including the amount of the gas present in the dispersion as the nanobubbles.

25. The method according to claim 23, wherein determining the target composition of the aqueous fluid further comprises providing to the thermodynamic model the identity information of one or more salts, one or more electrolytes, one or more acids, one or more bases, or one or more additives for the aqueous fluid.

26. The method according to claim 23, wherein the thermodynamic model uses empirical data determined by the following process: preparing a nanobubble dispersion under conditions of fixed temperature, pressure, and aqueous fluid composition, and evaluating the amount of gas present in the nanobubble dispersion.

27. The method according to claim 1, wherein the dispersion of the nanobubbles is stable for a duration of up to 30 days at the specified temperature and the specified pressure.

28. The method according to claim 1, further comprising injecting the dispersion of the nanobubbles into a subterranean reservoir.

29. The method according to claim 28, further comprising producing a dispersion of nanobubbles from the subterranean reservoir.

30. The method according to claim 28, wherein injecting the dispersion of the nanobubbles into the subterranean reservoir comprises storing the gas as a dispersion of nanobubbles in the subterranean reservoir.

31. The method according to claim 28, wherein the dispersion of the nanobubbles undergoes a mineralization process in the subterranean reservoir to convert at least a portion of the gas into a solid mineral in the subterranean reservoir.

32. The method according to claim 28, wherein, The dispersion of the nanobubbles enhances the supersaturation of the aqueous fluid with CO2 and increases the intensity and / or kinetics of mineral dissolution, carbonic acid saturation, and / or precipitation in the subterranean reservoir to convert at least a portion of the CO2 in the subterranean reservoir into a solid mineral.

33. A carbon sequestration method, comprising: preparing an aqueous fluid for a nanobubble solution of CO2 in a subterranean reservoir; mixing CO2 in the aqueous fluid to form a supersaturated solution of CO2 in the aqueous fluid; subjecting the supersaturated solution to a bubble generation process to form a dispersion of nanobubbles of CO2 in the aqueous fluid, wherein the dispersion of nanobubbles of CO2 in the aqueous fluid exhibits a greater amount of supersaturation than the supersaturated solution of CO2 in the aqueous fluid; and injecting the dispersion of the nanobubbles of CO2 in the aqueous fluid into the subterranean reservoir, wherein the dispersion of the nanobubbles of CO2 in the aqueous fluid undergoes a mineralization process in the subterranean reservoir to convert at least a portion of the CO2 injected into the subterranean reservoir into carbonate minerals in the subterranean reservoir.

34. The carbon sequestration method according to claim 33, wherein, The dispersion of the nanobubbles of CO2 in the aqueous fluid exhibits a higher intensity and / or faster kinetics of mineral dissolution, carbonic acid saturation, and / or precipitation than the supersaturated solution of CO2 in the aqueous fluid.

35. The carbon sequestration method according to claim 33, wherein the preparing, the mixing, and the subjecting comprise the method according to any one of claims 1-32.

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