3.2 Contact angle and wettability

Contact angle and wettability are crucial concepts in multiphase flow. They describe how fluids interact with solid surfaces, affecting fluid distribution and flow behavior in porous media. Understanding these phenomena is essential for predicting and optimizing fluid transport in various applications.

These concepts play a significant role in determining relative permeability, capillary pressure, and displacement efficiency. By grasping contact angle fundamentals and wettability effects, we can better model and analyze multiphase flow systems, leading to improved predictions and more effective fluid management strategies.

Contact angle fundamentals

• Contact angle quantifies the wettability of a solid surface by a liquid, determined by the balance of adhesive and cohesive forces at the liquid-solid-gas interface
• Plays a crucial role in understanding the interaction between fluids and solid surfaces in multiphase flow systems, impacting fluid distribution, flow behavior, and displacement efficiency

Young's equation for equilibrium

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• Describes the equilibrium contact angle ($\theta$) as a function of interfacial tensions between solid-liquid ($\gamma_{sl}$), solid-gas ($\gamma_{sg}$), and liquid-gas ($\gamma_{lg}$) phases: $\gamma_{sg} = \gamma_{sl} + \gamma_{lg} \cos \theta$
• Assumes an ideal smooth, homogeneous, and rigid solid surface, with no chemical reactions or surface deformation
• Provides a theoretical basis for understanding wettability and contact angle, although real surfaces often deviate from these assumptions

Factors affecting contact angle

• Surface roughness increases the apparent contact angle for hydrophobic surfaces and decreases it for hydrophilic surfaces, as described by the Wenzel and Cassie-Baxter models
• Surface chemistry, such as the presence of functional groups or coatings, can alter the surface energy and wettability (fluoropolymers, silanes)
• Fluid properties, including surface tension, viscosity, and density, influence the contact angle and spreading behavior (water, oil)
• Environmental conditions, such as temperature, pressure, and humidity, can affect the interfacial tensions and contact angle

Measuring contact angles

• Sessile drop method involves placing a liquid droplet on a solid surface and measuring the angle formed at the three-phase contact line using a goniometer or image analysis software
• Tilting plate method determines the advancing and receding contact angles by tilting the solid surface until the droplet starts to move, providing insight into contact angle hysteresis
• Wilhelmy plate method measures the force acting on a thin plate partially immersed in a liquid, allowing the calculation of the contact angle based on the plate dimensions and liquid surface tension

Wettability concepts

• Wettability describes the preference of a solid surface to be in contact with one fluid phase over another in a multiphase system, influencing fluid distribution, flow behavior, and displacement efficiency
• Plays a critical role in various applications, such as enhanced oil recovery, groundwater remediation, and microfluidic devices

Wetting vs non-wetting fluids

• Wetting fluid preferentially spreads on and adheres to the solid surface, displaying a contact angle less than 90° (water on clean glass)
• Non-wetting fluid tends to minimize contact with the solid surface, forming a contact angle greater than 90° and being displaced by the wetting fluid (mercury on glass)
• In a porous medium, the wetting fluid occupies smaller pores and crevices, while the non-wetting fluid occupies larger pores and channels

Hydrophilic vs hydrophobic surfaces

• Hydrophilic surfaces have a strong affinity for water, exhibiting contact angles less than 90° and facilitating water spreading (clean glass, quartz)
• Hydrophobic surfaces repel water, displaying contact angles greater than 90° and resisting water spreading (Teflon, waxed surfaces)
• Superhydrophobic surfaces exhibit extremely high water contact angles (>150°) and low contact angle hysteresis, leading to self-cleaning and water-repellent properties (lotus leaf, nanostructured coatings)

Wettability alteration mechanisms

• Surface coating or chemical treatment can modify the surface energy and wettability by introducing functional groups or changing the surface composition (silanization, fluorination)
• Adsorption of surfactants or polymers can alter the wettability by forming a thin film on the solid surface, modifying the interfacial tensions (anionic surfactants, polyelectrolytes)
• Surface roughness and texture can be engineered to control wettability through the Wenzel or Cassie-Baxter states, leading to enhanced hydrophobicity or hydrophilicity (micro/nanostructured surfaces)
• Wettability alteration in porous media can occur due to aging, adsorption of polar compounds, or changes in fluid composition, affecting fluid distribution and flow behavior

Wettability effects on flow

• Wettability significantly influences fluid flow and distribution in porous media, impacting relative permeability, capillary pressure, and displacement efficiency
• Understanding the role of wettability is crucial for optimizing multiphase flow processes in various applications, such as enhanced oil recovery, groundwater remediation, and fuel cell technology

Wettability impact on relative permeability

• Relative permeability quantifies the ability of each fluid phase to flow in the presence of other phases, depending on fluid saturation and wettability
• In water-wet systems, water occupies smaller pores and forms a continuous film on the solid surface, leading to higher water relative permeability at low water saturations compared to oil-wet systems
• In oil-wet systems, oil occupies smaller pores and crevices, resulting in higher oil relative permeability at low oil saturations compared to water-wet systems
• Wettability affects the shape and endpoint values of relative permeability curves, with mixed-wet systems exhibiting intermediate behavior between water-wet and oil-wet cases

Wettability influence on capillary pressure

• Capillary pressure is the pressure difference between the non-wetting and wetting phases in a porous medium, arising from the curvature of the fluid-fluid interface and the interfacial tension
• In water-wet systems, capillary pressure is positive, with water spontaneously imbibing into the porous medium and displacing oil
• In oil-wet systems, capillary pressure is negative, with oil spontaneously imbibing and displacing water
• Wettability affects the magnitude and sign of capillary pressure, as well as the shape of the capillary pressure curve, with mixed-wet systems displaying more complex behavior

Wettability role in fluid distribution

• Wettability governs the microscopic fluid distribution in porous media, determining which fluid phase occupies the smaller pores and crevices and which phase forms a continuous film on the solid surface
• In water-wet systems, water occupies the smaller pores and forms a continuous film, while oil occupies the center of larger pores (pendular rings, corner filaments)
• In oil-wet systems, oil occupies the smaller pores and forms a continuous film, while water occupies the center of larger pores (inverse pendular rings)
• Mixed-wet systems exhibit a combination of water-wet and oil-wet regions, leading to complex fluid distributions and flow behavior (mixed-wet large, mixed-wet small)

Wettability characterization techniques

• Various experimental methods are used to characterize the wettability of porous media, providing quantitative or qualitative measures of the preference for one fluid phase over another
• Wettability characterization is essential for understanding fluid-rock interactions, predicting flow behavior, and optimizing recovery processes in multiphase flow systems

Contact angle measurement methods

• Direct measurement of contact angles on flat mineral surfaces or polished rock samples using sessile drop, tilting plate, or Wilhelmy plate techniques
• Provides a quantitative measure of wettability at the microscopic level, but may not fully represent the complex pore structure and heterogeneity of natural porous media
• Can be used to study the effects of fluid composition, temperature, and pressure on wettability (brine salinity, crude oil components)

Amott-Harvey wettability index

• Measures the ratio of spontaneous imbibition to forced displacement of water and oil in a porous medium, providing a macroscopic measure of wettability
• Involves four steps: spontaneous imbibition of water, forced displacement of oil by water, spontaneous imbibition of oil, and forced displacement of water by oil
• Wettability index ranges from -1 (completely oil-wet) to +1 (completely water-wet), with 0 indicating neutral wettability
• Widely used in the oil industry for characterizing reservoir wettability and screening wettability modifiers

USBM wettability index

• Measures the area under the capillary pressure curve obtained from centrifuge or porous plate methods, providing a macroscopic measure of wettability
• Compares the work required to displace water by oil (drainage) and oil by water (imbibition) in a porous medium
• Wettability index is the logarithm of the ratio of the areas under the drainage and imbibition capillary pressure curves
• Positive values indicate water-wet conditions, negative values indicate oil-wet conditions, and near-zero values suggest neutral wettability
• Complements the Amott-Harvey method by considering the capillary pressure data and providing additional information on wettability

Wettability in porous media

• Porous media, such as rocks, soils, and engineered materials, exhibit complex wettability behavior due to their heterogeneous pore structure, mineralogy, and surface chemistry
• Understanding wettability in porous media is crucial for predicting fluid flow, distribution, and recovery in various applications, such as petroleum engineering, hydrology, and fuel cell technology

Wettability heterogeneity in reservoirs

• Reservoir rocks often display spatial variations in wettability due to differences in mineralogy, pore structure, and fluid history
• Wettability heterogeneity can occur at various scales, from pore-level (mixed-wet) to core-scale (fractional wettability) and field-scale (regional variations)
• Heterogeneous wettability affects fluid distribution, flow paths, and recovery efficiency, leading to complex flow behavior and oil trapping (by-passed oil, capillary end effects)
• Characterizing and modeling wettability heterogeneity is essential for accurate reservoir description and performance prediction

Mixed-wet systems

• Mixed-wet systems contain both water-wet and oil-wet regions within the porous medium, resulting from the adsorption of polar compounds or the presence of different minerals
• Mixed-wettability can be classified as mixed-wet large (larger pores are oil-wet, smaller pores are water-wet) or mixed-wet small (smaller pores are oil-wet, larger pores are water-wet)
• Mixed-wet systems exhibit unique fluid distribution and flow behavior, with the wetting phase occupying the corresponding pore sizes and the non-wetting phase forming droplets or ganglia
• Recovery from mixed-wet systems depends on the balance between capillary forces and viscous forces, as well as the connectivity of the wetting and non-wetting phases

Wettability effects on recovery mechanisms

• Wettability plays a critical role in various recovery mechanisms, such as waterflooding, gas injection, and enhanced oil recovery processes
• In water-wet systems, waterflooding is efficient due to the spontaneous imbibition of water and the displacement of oil from smaller pores, leading to high recovery rates and low residual oil saturation
• In oil-wet systems, waterflooding is less efficient due to the preference for oil to occupy smaller pores and the lack of spontaneous imbibition, resulting in higher residual oil saturation and slower recovery rates
• Gas injection in water-wet systems can lead to gas trapping and reduced sweep efficiency, while in oil-wet systems, gas can more easily displace oil from smaller pores and improve recovery
• Wettability alteration through the use of surfactants, low salinity water, or other chemicals can enhance oil recovery by modifying the fluid-rock interactions and promoting favorable wettability conditions

Modeling wettability in simulations

• Incorporating wettability effects in numerical simulations of multiphase flow is essential for accurate prediction of fluid behavior, distribution, and recovery in porous media
• Various approaches have been developed to model wettability in pore-scale and continuum-scale simulations, ranging from simple contact angle modifications to complex multi-physics models

Incorporating wettability in flow equations

• In continuum-scale models (Darcy's law, Buckley-Leverett), wettability effects are typically included through the relative permeability and capillary pressure functions
• Wettability-dependent relative permeability curves can be obtained from experimental data or empirical correlations (Corey, Brooks-Corey, van Genuchten)
• Capillary pressure functions can be modified to account for wettability effects using the Leverett J-function or other scaling approaches (Skjaeveland, Li-Horne)
• Pore-scale models (Lattice Boltzmann, pore network) can explicitly incorporate wettability by specifying contact angles or surface energy parameters at the fluid-solid interfaces

Wettability functions and correlations

• Empirical functions and correlations have been developed to relate wettability to other rock and fluid properties, such as porosity, permeability, and fluid saturation
• The Leverett J-function scales the capillary pressure based on porosity and permeability, allowing for the comparison of capillary pressure curves across different rock types and wettability conditions
• The Amott-Harvey and USBM indices can be correlated with other wettability measures, such as contact angles or relative permeability endpoints, to provide input for numerical simulations
• Wettability hysteresis models (Carlson, Killough) account for the difference between drainage and imbibition processes, capturing the dynamic nature of wettability during fluid displacement

Challenges in modeling wettability effects

• Accurate characterization of wettability in porous media remains a challenge due to the complex pore structure, mineralogy, and surface chemistry of natural rocks
• Upscaling wettability effects from pore-scale to continuum-scale models requires careful consideration of sub-grid heterogeneity and averaging techniques (dynamic pore network models, multi-scale mortar methods)
• Modeling wettability alteration processes, such as surfactant adsorption or low salinity waterflooding, involves coupling flow equations with geochemical reactions and surface chemistry (ion exchange, electric double layer)
• Validation of wettability models against experimental data is essential for ensuring the reliability and predictive capability of numerical simulations in multiphase flow systems