Complexities of immiscible oil-water flow through a horizontal pipe

Liquid-liquid interface forms when two liquids that don’t mix are in contacts with each other, such as oil and water. The co-current flow of two immiscible liquids in pipes is commonly encountered in a number of industrial applications, e.g., reactors, mixers, and crude oil wells and pipelines. In this discussion, the crude oil-water rheological issues have been focused on.

Crude oil

Crude oil is a mixture of comparatively volatile liquid hydrocarbons with some nitrogen, sulfur, and oxygen. Those elements form a large variety of complex molecular structures, some of which cannot be readily identified. Generally, all crude oil ranges from 82 to 87 percent carbon by weight and 12 to 15 percent hydrogen by weight.

Rheological properties of crude oil vs water: Three key drivers: Viscosity, Density, and

Complex rheology of crude oil-water flow

Viscosity, Density, and Surface tension together make the rheological properties of Crude – Water difficult and unpredictable. [1] The wide difference in the viscosities of crude oil and water generates phase separation and different flow velocities, [2] Similar densities promote emulsification, and [3] Interfacial tension between crude oil and water makes the phases merge together into one continuous phase. These three factors continuously compete with each other. Each of these properties is temperature and pressure-dependent. Each of these properties is different at bulk and at the interface.

Viscosity: Viscosity is the measure of the resistance of a fluid to flow. Pressure and temperature are also considered when talking about the viscosity of a liquid. If the viscosity does not change with pressure, we describe something as being a Newtonian fluid. A non-Newtonian fluid is a fluid that does not follow Newton's law of viscosity, i.e., constant viscosity independent of stress. In non-Newtonian fluids, viscosity can change when under force. There is no direct relation between viscosity and density. However, both Viscosity and density are affected by temperature. In general, for any fluids, when the temperature is increased, its density decreases, thus the fluid becomes less viscous

Viscosity controls the relative velocity between the liquid layers within the liquid and the solid wall. Velocity controls the hydrodynamic entry length of the flow. The hydrodynamic entry length is the point at which the velocity profile is fully developed in the tube from the point of entry for the fluid.

When there are two fluids moving together their hydrodynamic entrance length is different. They do not form a fully developed flow at the same point.

Density: Large density difference promotes separation, and generates stratified flow where the lighter phase flows above and significantly faster than the heavier phase. In the case of crude oil-water flow, the density ratio is close to unity and that is a great disadvantage in contrast to gas-liquid flows. This has many implications [1] change of flow character from the stratified to disperse flow [2] oil-water emulsification [3] phase inversion: the dispersed phase can invert to form continuous phase and vice versa under certain conditions. This unique phenomenon is called phase inversion.

Interfacial tension: Interfacial tension represents and predicts the phase stability of the interfaces. The interfacial rheological properties of the interfacial layer will give indications on how well the interface can resist coalescence. Interfacial forces provide wetting characteristics that play an important role in the development of flow. Fundamentally, interfacial tension is the force of attraction between the molecules at the interface of two fluids.

Surface tension – Viscosity relation

Reports suggest, that the solutions with a higher viscosity than water had either less or the same surface tension as water. Indirectly it means that the viscosity of a fluid is influenced more by the friction caused by the interactions between large molecules with a lot of polar atoms, causing an attraction between them.

Example: Flow of two immiscible liquids with different viscosities and densities 

This is a typical case where there are two immiscible liquids are flowing together. The top one is less dense and less viscous and the bottom one is denser and more viscous.

You can see the flow profile is not exactly parabolic. The vertex of the parabola is shifted to the light/less viscous fluid. You may also see a break in the continuity of the flow profile shown by the arrow. The reason is that the entrance hydrodynamic length where flow develops fully is not the same for both. While at the top the low viscosity liquid has reached fully developed flow.

Summary: The design of pipelines for the transportation of crude oil is based upon a knowledge of the rheology of the oil under the anticipated operating pressure and temperature. Many crude oils exhibit normal or Newtonian consistency behavior but some are not so simply described. This is especially the case under lower operating temperatures. Liquid-liquid flows are characterized by complex interactions between both liquids in which interfacial forces and wetting characteristics play an important role in the development of the flow. The density ratio in liquid-liquid flows is close to unity, in contrast to gas-liquid flows. Large density difference promotes separation, and thus there is a strong tendency to form stratified flow where the lighter phase flows above and significantly faster than the heavier phase. In liquid-liquid flows, both phases flow at similar velocities for which complex phase configurations are observed. Oil and water flow could become even more complex since the resulting mixed fluid can turn into an emulsion

Flow regime:

Just visualize the situation in the pipe. [1] The wide difference in the viscosities of crude oil and water generates phase separation and different flow velocities, [2] Similar densities promote emulsification, and [3] Interfacial tension between crude oil and water makes the phases to merge together into one continuous phase. These three factors continuously compete with each other. Varying temperature and pressure making the situation completely unpredictable.

As explained, transportation of oil and water can result in different characteristic distributions of oil and water. The different distributions are often called flow regimes or flow patterns. Reliable estimation of the flow regimes in oil-water pipe flows is required for many processes in the petroleum industry. The pressure gradient of horizontal pipe flows can be very much dependent on the flow regimes that occur. Better prediction of flow the pattern will yield a better design of multiphase pipeline systems in the petrochemical industry.

Oil - Water flow regime

Left side from top to bottom

Densely packed water droplets

Inhomogeneous water in oil

Right side from top to bottom

Densely packed oil droplets

Inhomogeneous oil in water

Different researchers have used different classifications of the flow patterns. In the present study, two main flow regimes are considered important are [1] stratified flow and [2] dispersed flow.

The above shows examples of different flows that are classified as dispersed flows.

Dispersed flow

Dispersed flow is characterized by the flow where one phase is dispersed in the other continuous phase. Dispersed flows have only one continuous phase.

Both flow regimes can be divided into sub regimes with a more detailed description of the flow structures. The other phase is dispersed in the continuous phase in the form of droplets. The droplets can be dispersed over the whole pipe cross-section, but they can also form a densely packed layer. Furthermore, the dispersion over the whole pipe cross-section can be either homogeneous or inhomogeneous.

Mass momentum and energy transfer between phases

One of the most important features common to all types of dispersed flows is that mass, momentum, and energy transfer between the phases are carried out from each particle (here, particle means solid particle, bubble, a droplet in gas and liquid) to the surrounding continuous phase. Therefore, the mechanisms of mass, momentum, and energy transfer from a single particle basically control the interaction between phases, although, of course, multiparticle effects must be considered. The correlations for phase interactions are usually based on that for a single particle, with some modification, due to the multiparticle effect of volume fraction or mass fraction of the dispersed phase.

Drag force

Among the interaction terms between phases, the most important one is the drag force acting on the particle, since this reflects two-phase flow effects in determining the flow fields of the dispersed and continuous phases. The drag force, Fd, is given in terms of drag coefficient, CD, which is defined by:

Fd = Cd A ½ ρc [uc – ud] x [uc – ud], where ρ is the density; u, velocity; suffixes c and d denote the continuous and dispersed phases; and A is the projected area of a particle in its flow direction.

Drag force is = Coefficient of drag x [density x [velocity]^2 ] / 2 x Reference area

Stratified flow

The flow in many fluids varies with density and depends upon gravity. Due to which the fluid with lower density is always above the fluid with higher density. A stratified fluid may be defined as the fluid with density variations in the vertical direction. A stratified flow is a flow in layers.

Please refer to the above image: Stratified flows have two separate layers, each with a different continuous phase. Each layer can be partly or fully dispersed the interface between the two continuous layers can be either smooth or wavy.

Pressure gradient: Different studies show that the flow regime affects the pressure gradient of multiphase pipe flow.

It has been observed a small decrease in the pressure gradient when the flow transits from stratified to dispersed

Concentration distribution: In stratified oil-water flow, complete separation does not occur. There is always a small amount of water dispersed in the oil layer (> 1.5%).

Stratified -------- > Dispersed ----- > Stratified flow transition

Sratified flow challenges

The stability of the oil-water stratified flow in a horizontal pipe is strongly related to oil viscosity, gravity, and interfacial intension. For viscous oils, the influence of shear stress becomes much more obvious and can be characterized by ignoring the velocity of the viscous phase. Usually, the flow pattern of oil-water in horizontal pipe switches from stratified structure to dispersed structure with increasing flow rate, and the oil-water interaction is also presented during this change.

 In stratified flow, the determination of pressure drop and liquid hold-up requires an accurate prediction of the friction at the wall and at the interface. Indeed, for fully developed flow, the pressure drop is controlled by the friction at the wall of each phase and by the weight of the liquid, which is related to the hold-up. As a consequence, pressure drop and liquid hold-up are strongly coupled in stratified flow: they must be predicted simultaneously. Another interesting feature of stratified flow is that the difference of velocity between phases can be high, suggesting that the momentum transfer between phases is ineffective. As this transfer is controlled by the interfacial friction, it may be anticipated that it will play a central role in the flow.

At low enough velocity the interface is maintained smooth by gravity and surface tension. The interfacial friction which depends on interfacial roughness, and roughness itself depends on the phase velocities, makes the problem difficult to solve. This is a twofold problem that is regarded as the central issue of stratified flow

Dispersed flow challenges

In dispersed flow, as the viscosity increases, oil droplets become harder to break up, meaning that the ability of droplets to recover deformation becomes stronger. It is more difficult for o/w dispersed flow to be formed in viscosity oil.

The dispersed phase is determined mainly by the flow rates of both phases since the interface between both phases is deformable, and the dispersed phase coalesces when the interfacial tension comes to closure and finally becomes the continuous phase as the flow rate increases.