Fluid Surfactant Research Articles

Determining interfacial tension and critical micelle concentrations of surfactants from atomistic molecular simulations

HypothesisAtomistically-detailed models of surfactants provide quantitative information on the molecular interactions and spatial distributions at fluid interfaces. Hence, it should be possible to extract from this information, macroscopical thermophysical properties such as interfacial tension, critical micelle concentrations and the relationship between these properties and the bulk fluid surfactant concentrations.Simulations and ExperimentsMolecular-scale interfacial of systems containing n-dodecyl β-glucoside (APG12) are simulated using classical molecular dynamics. The bulk phases and the corresponding interfacial regions are all explicitly detailed using an all-atom force field (PCFF+). During the simulation, the behaviour of the interface is analyzed geometrically to obtain an approximated value of the critical micelle concentration (CMC) in terms of the surfactant area number density and the interfacial tension is assessed through the analysis of the forces amongst molecules.New experimental determinations are reported for the surface tension of APG12 at the water/air and at the water/n-decane interfaces.FindingsWe showcase the application of a thermodynamic framework that inter-relates interfacial tensions, surface densities, CMCs and bulk surfactant concentrations, which allows the in silico quantitative prediction of interfacial tension isotherms.

Efficient second-order accurate scheme for fluid–surfactant systems on curved surfaces with unconditional energy stability

Accurately simulating the interplay between fluids and surfactants is a challenge, especially when ensuring both mass conservation and guaranteed energy stability. This study proposes a highly accurate numerical scheme for the water–oil–surfactant system coupled with the Navier–Stokes equation. We use the second-order accurate discrete operators on triangular grids representing these surfaces. We use the Crank–Nicolson method to achieve the second-order temporal accuracy. To handle high-order nonlinearities, we employ the consistency-enhanced Scalar Auxiliary Variable method. Additionally, the projection method tackles the Navier–Stokes equations. These techniques guarantee the unconditional stability. Consequently, larger time steps are permissible. Our method achieves the high accuracy with lower computational cost. This efficiency stems from solely utilizing surface information, eliminating the need for calculations across the entire 3D space. The proposed scheme’s accuracy, stability, and robustness can be confirmed through various numerical experiments.

The effect of fir wood SLS surfactant concentration on the characteristics of light crude oil

As time progresses, oil production will gradually depletes considering limited oil reserves. This is why, an advanced stage method known as tertiary oil recovery is required. One of these methods is known as Enhanced Oil Recovery method. In this laboratory study, one specific surfactant fluid was used, namely Fir wood sodium lignosulfonate (SLS) with varying concentrations of 0.50; 1.00; 1.50; 2.00; 2.50; and 3.00% each crude oil 39 ° API. This study aims to witness the stability of SLS surfactant fluid in chemical injection. SLS surfactant injection is carried out to increase oil production in the reservoir. In this study, there are various stages in order to test the characteristics of the SLS surfactant, so it can be declared as effective in oil sweeping, namely phase behaviour test, density testing, phase behaviour test, interfacial tension test, and adsorption test. Density test is carried out to determine the density of a fluid. Phase behaviour test is intended to see the stability of emulsion obtained from the utilization of SLS surfactant. The main objective of surfactant utilization is to reduce interfacial tension which leads to IFT test. The IFT (interfacial tension) results of the SLS surfactant fluid are determined from the results of the stable phase behaviour test which evidently shows the critical micelle concentration (CMC) point, so it can properly reduce the interfacial tension of oil and formation water in the reservoir. Interfacial tension test was carried out to determine the interfacial tension between SLS surfactant and oil. Adsorption test is carried out to witness the level of fluid adsorption onto the rock surface. On static adsorption test, the result showed for 2 % surfactant concentration is 9.526 mg/gr. Dynamic adsorption test was conducted on the same concentration show results of respectively 1.865 mg/gr.

A high temperature resistance and hyper‐dispersed nanoparticle grafted by multi‐monomer via in‐situ polymerization: Preparation, characterization, and its imbibition performance

AbstractIn recent years, the excellent cleaning‐oil capacity of nanofluid has attracted extensive attention and it has been widely used in oilfields as an imbibition agent. To solve the poor dispersion stability of nanoparticles in high‐temperature and high‐salt reservoir, this paper has prepared a hyper‐dispersed nanoparticle, polymer grafted nanosilica (PNS) that is anti‐salt monomer and anti‐temperature monomer simultaneously grafting on the surface of nanosilica via in‐situ polymerization reaction. Its imbibition performance has been discussed. Results show that (1) The two monomers are all successfully grafted on the surface of nanosilica via optimization of in‐situ polymerization reaction conditions. This hyper‐dispersed nanoparticle has 14.5% final grafting rate, approximately 18 nm in particle size, and −41.2 mV of zeta potential; (2) PNS fluid has excellent dispersion stability and its grain size has no obvious change in 20 wt.% of NaCl or 4 wt.% of CaCl2 fluids at room temperature (25°C), as well as in 18 wt.% of NaCl or 4 wt.% of CaCl2 fluids at 130°C after 1 week; (3) Crude oil–water interface tension can be decreased and the hydrophilicity is significantly boosted by this PNS fluid. Meanwhile, the 10−3 mN/m of interface tension can be obtained and the contact angle of water phase is decreased to 12.8° by surfactant erucamide propyl hydroxysulfobetaine (EHSB) synergizing with PNS fluid; (4) Oil recovery efficiency replaced by PNS in surfactant fluid has reached 39.3%. That is mainly because the hyper‐dispersed nanoparticle provides a stronger spreading force to enhance the efficiency of cleaning oil.

The Effect of Crude Oil Stripped by Surfactant Action and Fluid Free Motion Characteristics in Porous Medium.

The surfactant solution is crucial in facilitating the spontaneous imbibition process for the recovery of oil in tight reservoirs. Further investigation is required to examine the fluid flow in porous mediums and the process of crude oil stripping by a surfactant solution during spontaneous imbibition. Hence, this study aims to determine the free motion properties of oil and water in porous mediums using the finite-element approach to solve the multiphase flow differential equation, taking into account the capillary pressure. An investigation was conducted to examine the impact of oil viscosity and interfacial tension on the mean liquid flow rate and oil volume fraction. An experimental study was conducted to investigate the impact of surface tension, interfacial tension, and wetting angle on crude-oil-stripping efficiency. The findings indicate that the stripped crude oil migrated through porous mediums as individual oil droplets, exhibiting a degree of stochasticity in its motion. When the interfacial tension is reduced, the average velocity of the fluid in the system decreases. The crude oil exhibited a low viscosity, high flow capacity, and a high average flow rate within the system. Once the concentration of the surfactant solution surpasses a specific threshold, it binds with the oil to create colloidal aggregates, resulting in the formation of micelles and influencing the efficiency of the stripping process. As the temperature rises, the oil-stripping efficiency also increases. Simultaneously, an optimal range of wetting angle, surface tension, and interfacial tension could enhance the effectiveness of removing oil using surfactant solutions. The research results of this paper enrich the enhanced oil recovery mechanism of surfactant and are of great significance to the development of tight reservoirs.

Surface phase-field surfactant fluid model and its practical closest point type finite difference computation

To investigate the fluid surfactant material on three-dimensional objects, we herein develop a simple and practical model based on phase-field method and design its efficient algorithm. The binary fluids and surfactant are represented by two order parameters. The fluid evolution is governed by the incompressible Navier–Stokes equations. To achieve high-performance computation, a linear semi-implicit scheme with stabilizers is proposed for the phase-field type equations in time. The projection method with pressure correction is used to decouple the velocity and the pressure. Based on the closest-point type embedded narrow domain method and a simple pseudo-Neumann boundary treatment, the calculation on curved surface is extended into a narrow band region including the surface. The surface spatial operators are approximately replaced by the standard spatial operators. In the three-dimensional narrow band, the finite difference method is used to discretize the equations on staggered grids. The mass compensation and vector projection techniques are designed to obtain physically meaningful solutions. In each time iteration, the proposed algorithm is efficient to implement. Numerical results indicate that the proposed method is capable to simulate surfactant-laden phase separation, fluid instabilities, and coarsening dynamics with variable mobility on various surfaces.

Monitoring Rheological Changes Using Acoustic Emissions for Complex Formulated Fluids Manufacturing

AbstractThe measurement capabilities of a newly developed in‐situ rheometric device based on a single passive acoustic emission sensor and machine learning algorithms were investigated. Two surfactant structured fluids demonstrating complex non‐Newtonian rheology (Power‐law and Herschel‐Bulkley models) were examined. Furthermore, a static evaluation on the laboratory scale in comparison to dynamic processing on the pilot scale was conducted. The results indicate that the machine learning algorithms of this technology can identify, in > 90 % of scenarios, the correct type of rheology or the manufacturing process step across both scales. This identification is based on solving a classification problem using quadratic support vector machine learning algorithms, which have proven to deliver the most robust predictions across a choice of 24 different algorithms tested. Additionally, a new format of in situ rheology display was introduced, referred to as RRF™ factor.

Emulsion Formation in Palm Oil Methyl Ester Sulfonate Surfactant to Light Crude Oil

The Enhanced Oil Recovery method is a method that can be attempted to increase the recovery of petroleum. One of the materials that can be used is Methyl Ester Sulfonate surfactant from palm oil, as a vegetable surfactant whose raw materials are widely available in Indonesia. In this study, the compatibility test of Methyl Ester Sulfonate surfactant was carried out on light crude oil type T samples. The study was carried out with various surfactant concentrations, starting from 0.25%, 0.3%, 1%, 1.5%, and 2%. In the aqueous stability test, the results obtained for all clear conditions for the surfactant concentration were measured for 3 days in an oven with a temperature of 60oC. Whereas in the phase behavior test, good results of the upper phase emulsion were obtained at concentrations of 0.3%, 1%, 1.5%, and 2%. The volume of the top phase emulsion ranges from 25% to 37.5%. (Normal). From the results of this study, it can be concluded that for the crude oil sample T, palm oil MES surfactant is stable for use as a surfactant injection fluid, with a surfactant concentration composition that produces a fairly large upper phase emulsion of around 25% - 37.5% at a surfactant concentration of 0.5% - 2%.

Rheology, viscoelasticity and microstructural properties of OAPB-SDS mixtures at different temperature and pH conditions

Viscoelastic surfactant (VES) fluids are widely used in the hydraulic fracturing process to increase oil and gas productivity. Zwitterionic (carbon-18) surfactant solution, which is commonly used in VES fluids, has high critical micelle concentration, resulting in high used concentration and lack of economy. Furthermore, it is not applicable to high-temperature conditions. The oleylamidopropyl betaine (OAPB, carbon-25) with longer carbon chain has lower critical micelle concentration (CMC) and better high temperature resistance. In addition, it behaves better viscosity increasing capacity combining with anionic sodium dodecyl sulfate (SDS) surfactant. In this study, the viscoelasticity and microstructural properties of OAPB-SDS (OADS) mixtures at different temperature and pH conditions were investigated deeply. Rheology and structural morphology properties of the OADS mixed fluids were investigated by rheometer, and transmission electron cryo-microscopy. The results showed that OADS solution demonstrated elastic gel-like fluid behavior with zero shear viscosity of 3.5 × 106 mPa.s at neutral pH and room temperature, while OAPB solution demonstrated viscous fluid behavior with zero shear viscosity (ηo) of 62 mPa.s. The viscoelasticity and microstructural properties of OADS solution were influenced by concentration, pH and temperature. It was gel-like fluid at 25–40 °C, viscoelastic fluid at 60–80 °C and totally viscous fluid at 90 °C. The OADS was viscous at 0.5 wt% concentration, viscoelastic at 0.6 wt% concentration and elastic at 0.75 wt% concentration. The OADS solution showed viscous, viscoelastic and elastic behaviors at pH value of 3, 4, and 7 respectively. The fluid exhibited viscosity switch ability by reversibly altering pH values. The Cryo-TEM images confirmed that the OADS micelle experience microstructural transformed from long wormlike micelles (WLMs) to spherical micelles as the pH changes. The mixture fluid improved viscoelastic and aggregation properties than that of individual surfactant component, possessing lower used surfactant concentration. This study is useful in understanding the properties of mixed zwitterionic-anionic fluids, which is thermo-pH responsive, valuable in the fracturing.

An efficient dimension splitting p-adaptive method for the binary fluid surfactant phase field model

An efficient dimension splitting p-adaptive method for the binary fluid surfactant phase field model

Enhanced bitumen extraction from oil sands using CO2-responsive surfactant combined with low-salinity brine: Toward cleaner production via CO2 utilization

With a recent concern on more sustainable production, oil sands as an affordable energy resource requires more efficient and cleaner technology to extract bitumen from its deposits. Recent study conceptualized the combination of greener bitumen recovery and CO2 utilization, which shows promising potential. Using CO2-responsive surfactants that could ‘switch’ the bitumen-water interfacial behavior, oil-water separation process can be greatly improved, although its workability in bitumen aeration stage and co-presence with brines are not yet fully examined. In the current study, influence of a combination of CO2-responsive surfactant and NaCl brine fluids to bitumen liberation and aeration stages were investigated. Two interfacial phenomena (i.e., bitumen-water interfacial tension and bitumen-water-substrate contact angle) were studied as dominant parameters to oil sands processing. Although an ultra-low interfacial tension at high mixture concentration (6 mM surfactant + 500 mM NaCl) promises an advantage for bitumen extraction via a spontaneous bitumen pinch-off, some bitumen residual was left unproduced on substrate. While the low-salinity brine at the same surfactant concentration (6 mM surfactant + 10 mM NaCl) resulted in a much-reduced bitumen-substate contact area, which could practically enhance bitumen liberation. Furthermore, CO2-responsive surfactant suggests a good switchability in such a high-salinity environment for bitumen-water demulsification, owing to the CO2-induced acidification. In aeration stage, CO2 bubble was found a greater ‘attachability’ to bitumen surface compared to typical air bubble. This observation suggests a promising CO2 utilization as an alternative flotation gas carrier for bitumen aeration. The findings in the current study provide fundamental guidance on bitumen extraction process enhanced by both surfactant and brine fluids. The study also confirms a holistic improvement for the whole extraction process with CO2 utilization toward a cleaner production that couples both climate action and affordable energy sustainable goals.

Pulmonary surfactant structure as solved by neutron reflectometry and atomic force microscopy.

In order to sustain breathing mechanics, the alveolar surface needs to be covered by pulmonary surfactant, a lipid/protein system that provides with the required surface tension reduction to avoid alveolar collapse at the end of expiration. Any disruption of this system could impair its function leading to severe respiratory pathologies. Pulmonary surfactant is composed by 90 % lipids and 10 % hydrophilic (SP-A and SP-D) and hydrophobic (SP-B and SP-C) proteins. After secretion, surfactant lipids form a complex structure at the alveolar air-liquid interface consisting of an adsorbed monolayer connected to a membranous reservoir in the subphase maintained thanks to the action of both hydrophobic proteins. The molecular mechanism of surfactant proteins is still not fully understood, making the finding of treatments for some respiratory pathologies a challenge. Model lipid systems mimicking pulmonary surfactant composition (DPPC/POPC/POPG 50:25:15 w:w:w) in the presence of SP-B and/or SP-C, as well as a native surfactant isolated from animal lungs, have been used as models for the study of the structure and function of pulmonary surfactant films. In this work, we have characterized these models with different biophysical technics such as neutron reflectometry and atomic force microscopy. The results point to the importance of hydrophobic proteins in the formation of three-dimensional structures associated to highly compressed surfactant films. Furthermore, a recently isolated human amniotic fluid surfactant has also been studied. This material is thought to maintain the properties of a freshly synthetized and secreted surfactant that could cover the air-liquid interface in a more efficient way, with physiological importance to develop new surfactant therapies. Here we show that amniotic fluid surfactant exhibits a similar behavior than animal-derived surfactant once it coats the interface.

Smart Fluids and Their Applications in Drilling Fluids to Meet Drilling Technical Challenges

This article presents extensive analysis and review on recent developments in smart fluids as well as future opportunities of smart drilling fluids utilization in oil and gas well drilling while focusing on the following smart fluids: smart nanoparticles, electrorheological, magnetorheological, and viscoelastic surfactant (VES) fluids. The distinctive properties of nanoparticles such as tiny particle sizes, high specific surface area, mechanical strength, and thermal stability make them suitable for utilization in drilling fluids. In bentonite water-based drilling fluid systems, this review suggests that charged nanoparticles are capable of displacing exchangeable ions in between bentonite clay platelets, thereby forming intercalates which can interact with clay surfaces through electrostatic attraction or repulsion. In improving wellbore stability, it is presented in this review that nanoparticles are able to invade and plug ultratiny pore spaces in shale formations, thereby further enhancing shale formations’ mechanical strength and wellbore stability. According to this review, the magnitude of changes in properties of smart electrorheological and magnetorheological fluids largely depends on the intensity of applied electric and magnetic fields. The intensity of smart fluids properties alteration due to applied field would equally depend on wt.% concentration and chemical compositions of particles susceptible to electric and magnetic fields. Based on review carried out on VES smart fluids, attractive and repulsive forces in the smart VES fluids solution result in the formation of micelles which can cause changes in viscoelastic property of the formulated smart viscoelastic fluids. The more the concentration of charged ions in the base fluid which VES fluids come in contact with, the higher the viscoelasticity of the smart VES fluids. According to this review, utilization of smart materials in drilling fluids can result in meeting oil and gas well drilling technical challenges including enhancing wellbore stability, improving hole cleaning performance, lost circulation control, fluid loss control, enhancing rate of penetration, pressure drop control, and easing cutting carrying efficiency of drilling fluids. This review equally suggests that the utilization of smart fluids such as smart magnetorheological and electrorheological fluids would facilitate drilling automation and real-time data acquisition processes, which is the future technology in oil and gas drilling.

Platform for Exposing Aerosolized Substances to Lung Surfactant and Alveolar Cells at the Air-Liquid Interface

Lung surfactant lowers surface tension in the alveoli, playing a critical role in lung function and immune defense. Inhaled aerosol particles may induce adverse health effects via the interruption of lung surfactant surface tension. Previous generations of surfactometers have been developed and used to characterize surfactants and their response to various exposures. However, these devices do not allow for simultaneous exposure with multiple aerosols, the incorporation of multiple aerosolization methods, or the co-exposure scenario involving both lung surfactant fluid and pulmonary cells/tissues. Herein, we introduce a new configuration, termed the aerosol exposure surfactometer (AESM), that addresses all of these limitations. The results indicate correlation of surface tension changes in concordance with aerosol properties while preventing unwanted cell death. Further investigation using this method may elucidate mechanisms of pathogenesis related to surfactant dysfunction and provide the foundation for predictive models.

Influence of divalent ion concentration on the adhesion behaviour of sulfonate self-assembled monolayers (SAM)

Surfactant-assisted oil recovery is usually employed for the production of residual oil after primary and secondary recovery techniques have been exhausted. The loss of injected surfactants via adsorption on to the porous media surfaces impede the efficiency of the procedure and greatly impact process economics. To address this issue, the choice of surfactant and aqueous fluid composition are varied. In particular, the divalent ion concentration is a property that potentially influences surfactant adsorption significantly. It is this aspect which has been addressed in this study. In this study, atomic force microscope (AFM). tips were functionalised with a self-assembled monolayer (SAM) of the alkanethiol, sodium 11-mercaptoundecanesulfonate (otherwise known as MUS) with the –SO3-headgroups oriented outwards towards the aqueous solutions, this is a model for the well-studied surfactant, sodium dodecyl sulfate, SDS. The adhesion forces between these “surfactant-functionalised” tips and Bandera Brown sandstone surfaces were measured in brine solutions of varying CaCl2 concentrations. Observations deviate from previous studies where adsorption of surfactant headgroups in the bulk solution is enhanced via Ca2+ bridging with the surface. Rather, measured adhesion forces decreased with increase in CaCl2 concentration. The results are reversible and also occurs in a reducing environment when the iron in the Bandera brown is reduced for iron (III) to iron (II). The observed behaviour is interpreted in terms of Ca2+ preferentially bridging between neighbouring headgroups on the tip due to the dense packing of molecules non-representative of respective bulk behaviours and acting as a barrier to adhesive contact. Thus, this supposed micellization at the tip aided by the formation of Ca2+ salt bridges between alternate headgroups more closely mimics a surfactant micelle, rather than dispersed individual monomers. The findings of this study provide insight into nanoscale anionic surfactant interactions in general and within sandstone reservoirs in particular where surfactant adsorption is driven largely by monomers rather than micelles. Investigating surfactant adsorption using microscopic techniques such as AFM allow for the determination of interactions at mineral-fluid interfaces and constitute an effective screening methodology for ascertaining enhanced oil recovery process feasibility.

Development of CO2-Sensitive Viscoelastic Fracturing Fluid for Low Permeability Reservoirs: A Review

There are economic and technical challenges to overcome when increasing resource recovery from low permeability reservoirs. For such reservoirs, the hydraulic fracturing plan with the development of clean and less expensive fracturing fluid plays a vital aspect in meeting the energy supply chain. Numerous recent published studies have indicated that research on worm-like micelles (WLMs) based on viscoelastic surfactant (VES) fluid has progressed substantially. This study looks at the development of CO2-sensitive viscoelastic fracturing fluid (CO2-SVFF), its applications, benefits, limitations, and drawbacks of conventional fracturing fluids. The switchable viscoelasticity of CO2-SVFF system signifies how reusing of this fluid is attained. Compared to conventional surfactants, the CO2-SVFF system can be switched to high viscosity (to fracture formation and transporting proppants) and low viscosity (easy removal after causing fracture). The effect of pH, conductivity, temperature, and rheological behaviors of CO2-SVFFs are also highlighted. Further, the aid of Gemini surfactants and nanoparticles (NPs) with low concentrations in CO2-SVFF can improve viscoelasticity and extended stability to withstand high shear rates and temperatures during the fracturing process. These studies provide insight into future knowledge that might lead to a more environmentally friendly and successful CO2-SVFFs in low-permeability reservoirs. Despite the increased application of CO2-SVFFs, there are still several challenges (i.e., formation with high-temperature range, pressure, and salinity).

Study of the Surfactant Transport Law Based on an Improved Adsorption Model with an Artificial Seismic Wave

To explore the law and mechanism of enhanced surfactant flooding with a low-frequency artificial seismic wave, for single-phase fluids in porous media, a heterogeneous two-stage adsorption model for a surfactant with a low-frequency artificial seismic wave is introduced into the surfactant transport equation of a single-phase fluid. With this model, the surfactant fluid transport model in porous media with an artificial seismic wave is obtained. The model is solved using the C-N difference and chasing method. The migration law of the surfactant is simulated and quantitatively analyzed for different vibration accelerations, injection slug sizes, displacement speeds, and reservoir parameters with the action of low-frequency artificial seismic waves. The results show that artificial seismic waves can increase the effective range of the surfactants and reduce the number of chemical agents through reduced adsorption. Low-frequency vibration with the same surfactant injection rate can increase the effective range by a factor greater than one. For the same effective action distance, the dose of chemical agents can be reduced by more than 60%, and the optimal acceleration and the injection slug size are 0.3 m/s2 and 0.4 PV, respectively. With the increase of the injection rate, the effect of low-frequency vibration on the diffusion and transport of the surfactant decreases. A low-frequency wave combined surfactant has a better effect on the low permeability reservoirs. The research results provide important support for further understanding of the low-frequency artificial seismic wave composite surfactant flooding law and the optimization of the field parameters.

An efficiently linear and totally decoupled variant of SAV approach for the binary phase-field surfactant fluid model

In this work, an efficiently linear, totally decoupled, and unconditionally energy-stable time-marching scheme is developed for solving the Cahn–Hilliard (CH) type phase-field incompressible surfactant fluid model. The proposed scheme is based on a variant of scalar auxiliary variable (SAV) approach. By defining several time-dependent auxiliary variables, the original governing equations are reformulated into equivalent forms which provide the foundation to construct the time-discretized numerical method. Different from the original SAV approach, the proposed method achieves totally decoupled computations of all variables. In each time step, the surfactant is explicitly calculated, then the phase-field function is updated by solving linear elliptic type equations. The velocity and pressure fields are calculated by the projection method. The time-discretized energy dissipation law is estimated in detail. The numerical validations indicate that the proposed method not only has desired energy stability but also works well for surfactant-laden droplets dynamics.

Dynamic proppant-carrying performance of VES-CO2 foam fracturing fluid in the pipeline and the fracture

A viscoelastic surfactant (VES) fluid blends with CO 2 to form the foam fracturing fluid. To obtain the dynamic proppant-carrying behaviors of the VES-CO 2 foam fluid, an experimental system with a horizontal transparent tube and a visual fracture is built. In the horizontal pipeline, it is displayed that the critical settling flow velocity of the ceramsite proppant in the flowing VES-CO 2 foam fluid increases with the temperature. Further, the critical settling flow velocity initially decreases and then increases with both the increases of the foam quality and the proppant ratio, and its transition points are at the foam quality of 0.75–0.80 and at the proppant ratio of 0.25, respectively. In addition, considering the influencing parameters in the experiments, we obtain a correlation equation of the critical settling flow velocity. In the experiments of the fracture observation section, the height of the equilibrium sand bank and the angle of repose are mainly investigated. Both of these two parameters decrease as the foam quality, as well as the injection flow velocity, is increased. Especially, it is found that the angle of repose is below 20° at larger injection flow velocity. • The dynamic proppant-carrying behaviors of the degradable VES-CO 2 foam fracturing fluid are studied. • A correlation equation of the critical settling flow velocity of the proppant-carrying foam fluid is obtained. • The angle of repose in the fracture is generally below 20° at larger flow velocity. • This work provides a reference for the related prediction in the fracturing project.

Fully-discrete, decoupled, second-order time-accurate and energy stable finite element numerical scheme of the Cahn-Hilliard binary surfactant model confined in the Hele-Shaw cell

We consider the numerical approximation of the binary fluid surfactant phase-field model confined in a Hele-Shaw cell, where the system includes two coupled Cahn-Hilliard equations and Darcy equations. We develop a fully-discrete finite element scheme with some desired characteristics, including linearity, second-order time accuracy, decoupling structure, and unconditional energy stability. The scheme is constructed by combining the projection method for the Darcy equation, the quadratization approach for the nonlinear energy potential, and a decoupling method of using a trivial ODE built upon the “zero-energy-contribution” feature. The advantage of this scheme is that not only can all variables be calculated in a decoupled manner, but each equation has only constant coefficients at each time step. We strictly prove that the scheme satisfies the unconditional energy stability and give a detailed implementation process. Various numerical examples are further carried out to prove the effectiveness of the scheme, in which the benchmark Saffman-Taylor fingering instability problems in various flow regimes are simulated to verify the weakening effects of surfactant on surface tension.