Thermo-Hydrodynamics of Core-Annular Flow of Water, Heavy Oil and Air Using CFX ()
1. Introduction
The worldwide heavy oil reserves are estimated to be 3 trillion barrels [1], while light oil reserves have shown a progressive decline in the last decade. This fact leads to an increased economic interest for the reserves of heavy oil which consequently stimulates further research to make production of heavy oil economically feasible. Currently, Brazil is one of the important worldwide producers of oil, and that most of the Brazilian reserves consist of heavy oil in deep waters, generating technical difficulties in exploitation of such resources. Heavy oil is considered to have API between 10 and 20, a density greater than 0.90 g/ml, a viscosity between 10 cP and 100 cP at reservoir conditions and from 100 cP to 10,000 cP at surface conditions [2]. At present, these oils do not have significant economic value due to the low concentration of smaller chain hydrocarbons. However, with the decline of production of light oil, the importance, and consequently the price of these energy sources are likely to increase. The major obstacle of utilizing heavy oil is its relatively high viscosity, which makes it difficult to transport and higher density which increases the cost of refining. Thus, the transportation of heavy and ultraviscous oil is a main technological challenge in the petroleum industry. This fact is related to the high pressure drop or friction due to viscous effects of this type of oil during its flow.
According to Trevisan [3], because of unfavorable characteristics of heavy oils, their transport from the production areas to the processing and refining plants is the biggest obstacle encountered for the production of heavy oils. The author also mentions that the alternatives currently used are to transport by truck or heated pipeline. However, these methods are very expensive and are applicable only for short distances. For efficient transportation at considerable distances, it is necessary to use conventional pipelines, but most of these pipelines have viscosity specifications lower than 0.1 Pa∙s, which is not true for heavy oils. In order to overcome the difficulties inherent in the production and transport of heavy and ultra-viscous oil, several techniques have been used, so that a decrease in pressure drop during the flow can be provided, thereby a reduction in the viscosity effect of the fluids present can occur. Among the techniques used one can mention: adding heat to the system, diluting the heavy crude oil with a lighter one and forming emulsions using emulsifying agents. However, each of these alternatives has limitations in their use, both technical and economic.
One technique that has higher efficiency compared to other methods is the core-flow technique. This technique consists in injecting a less viscous liquid, usually water, adjacent to the pipeline wall. This prevents the contact of oil with the inner side of the pipeline. It results in a greater reduction in the pressure drop of the flow and consequently in a reduction in the transport cost of such oil. A drawback of this technique is when the oil comes in contact with the inner wall of the pipeline during transport. This may cause a large increase in the system pressure, which can result in a serious damage to the transportation system and the environment [4].
The most important feature of the core-flow technique is that it does not modify the viscosity of the oil but changes the flow pattern and reduces friction during the transport of very viscous products, such as heavy oil. This reduction in friction also causes a reduction in the longitudinal pressure drop and consequently, a reduction in pumping costs. Several papers have reported research works related to the improvement of the core-flow technique [4-9].
However, in oil production, oil and water rarely flow separately and a gas fraction is generally present, which is characterized as a multiphase flow. Such flow can be defined as a system in which fluid components are immiscible and separated by interfaces. The occurrence of multiphase flow in the oil industry is very common in the units of production, transportation and processing of hydrocarbons of an oil field.
Thus, it is important to analyze the influence of the presence of a third phase (gas) in the annular flow (water-oil) with respect to the pressure drop. In order to verify three-phase flow characteristics some experimental studies have been performed [10-13].
Bannwart et al. [10] studied the pressure drop and flow patterns of a three phase flow observed in a glass tubing with a diameter of 2.84 cm containing heavy oil (3.4 Pa∙s and 970 kg/m3 at 20˚C), water and air under several combinations of individual compositions and tube inclination (horizontal, vertical and inclined). In their study nine flow patterns were verified. According to these authors, when compared to the two-phase flow of heavy oil-water only, the presence of gas increases considerably the mixture velocity and consequently the pressure drop is increased.
Poesio et al. [12] made an experimental study related to the core-annular flow with the aim of providing a new database for the three-phase (ultra-viscous oil, water and air) flow and to propose a simple model for the determination of the pressure drop. They observed the effect of the air injection on the pressure drop of the annular liquid-liquid flow and noticed an error less than ±15% of measured value in relation to that of the proposed model.
Strazza et al. [13] presented an experimental study of the three-phase flow using water, air and high viscosity oil. The attention was focused on the effect of the gas presence in the core-annular liquid-liquid flow. The experimental flow map, obtained by them, showed that the increase in gas flow breaks up the integrity of the oil core, resulting in a chaotic flow regime. Values for the pressure drop were compared with the proposed theoretical model for the three-phase core flow. The difference between the experimental and the predicted pressure drop was of more or less 20%.
In this background, the objective of this work is to study numerically the three-phase annular flow of heavy oil, water and air (core-flow), at different conditions of temperature and volume fraction of the air.
2. Mathematical Modeling
2.1. Physical Domain of Study
The study domain consists of a 3 meter long and 2.84 cm inner diameter horizontal tube, in which the flow of heavy oil-water-gas takes place. This is shown in Figure 1.
2.2. Computational Domain
To study numerically the annular flow behavior of oilwater in the presence of gas, it is necessary to represent the geometry or domain of study in a computational domain or mesh. For this a mesh of hexahedral structured elements was employed. This mesh was made with the ICEM-CFD commercial package available in ANSYS CFX.
To draw up the computational domain, initially, a tube with two inlets, one annular for water injection and another circular for the oil together with gas, was created. This can be seen in Figure 1. The ring or the annular space between tube wall and the oil core has a thickness of 1.7 mm. The mesh used in the present work consisted
Figure 1. (a) Tube dimensions and details of water and oil inlet sections. (b) Details of the expanded mesh at the inlet region and (c) at the outlet region.
of 464,000 hexahedral elements.
2.3. Mathematical Model
To study the three-phase flow within a horizontal pipe following conditions have been considered:
1) Incompressible and steady state flow;
2) No chemical reactions;
3) Existence of gravitational and drag effects;
4) The viscosities of water, gas and ultra-viscous heavy oil are functions of temperature;
5) There is no interfacial mass transfer between water, oil and gas phases;
Thus, the conservation equations of mass, momentum and energy applied to the multiphase flow are reduced to:
2.3.1. Conservation Equations
1) Mass Conservation Equation
(1)
where
, 
e 
correspond to the volume fraction, density and velocity vector of phase
, respectively.
2) Momentum Conservation Equation
(2)
where 
is pressure, 
represents a term for the external forces acting on the system per unit volume and 
describes the total forces per unit volume (interfacial drag force).
In the mixture model, available in ANSYS CFX, the total forces per unit volume only consider the interfacial forces (drag) and are given by:
(3)
where 
is the drag coefficient and the sub-indexes 
and 
correspond to the phases 
and 
present in the flow.
In Equation (3), 
corresponds to the interfacial contact area between the phases 
and 
which is given by:
(4)
where in 
and 
represent the volume fraction and the diameter of the particle of the phase
, respectively. Adopting the particle model, 
represents the continuous phase (heavy oil or water) and 
being the dispersed phase (gas).
For the mixture model the interfacial contact area between phases 
and 
is given by:
(5)
where 
is the length of the mixture.
3) Energy Conservation Equation
(6)
where
, 
and 
describe static enthalpy, thermal conductivity and temperature respectively of 
phase and 
describes heat transfer to the 
phase through the interfaces with the other phases, which is given by:
(7)
where:
(8)
The heat transfer through the boundary is usually described in terms of a coefficient of overall heat transfer, 
, which is the amount of heat energy through a unit area per unit time per unit of temperature difference between the phases.
Thus, the rate of heat transfer, 
, per unit of time through the phase interfacial boundary area, per unit volume
, of phase 
to phase 
is given by:
(9)
Many times it is convenient to express the coefficient of heat transfer in terms of the dimensionless Nusselt number, defined by Equation (10):
(10)
In the particle model the thermal conductivity (l) is considered as being the thermal conductivity of the continuous phase, and the length d is considered to be the diameter of the dispersed phase. So it can be written as:
(11)
2.3.2. Turbulence Model
As turbulence model, the standard 
model was used, where it is assumed that the Reynold’s tensors are proportional to the mean velocity gradients, with the proportionality constant being characterized by turbulent viscosity (idealization known as Boussinesq hypothesis).
The characteristic of this type of model is that two transport equations modeled separately are solved for the turbulent length and the time scale or solved for any two linearly independent combinations of them. The transport equations for the turbulent kinetic energy, 
, and turbulent dissipation rate, 
, respectively are:
(12)
(13)
where 
is turbulent kinetic energy generated in the phase
, 
and 
are empirical constants. Also, in this equation, 
the dissipation rate of turbulent kinetic energy of phase 
and 
the turbulent kinetic energy for phase
, are defined by:
(14)
(15)
where 
is the length of spatial scale, 
is the velocity scale, 
is an empirical constant.
The variable 
is the turbulent viscosity and is given by the equation:
(16)
where, the constants used in the above equations are:
;
; 
and
.
2.3.3. Boundary Conditions
1) In the annular section referring to water inlet a prescribed and not null value, for the axial velocity component and volume fraction of water in the 
direction, was adopted such that:
where
, 
e 
correspond to the velocity vector components in the
, 
and 
directions, in this order, the sub-indices
, 
and 
represent water, oil and gas phases respectively, and T the temperature.
2) In the core section referring to oil inlet a prescribed and not null value, for the axial velocity component and volume fraction of oil and air in the 
direction, was adopted such that:
3) At the borders referring to the tube wall the condition of non-slip was considered, namely:
4) At the outlet section (x = L), a constant mean pressure pest = 101,325 Pa, was prescribed, where L is the length of the tube.
In the present work a root mean square (RMS) residue equal to 10−7 kg/s was considered as the convergence criterion. The thermo-physical properties of the fluids used in the simulation are presented in Tables 1 and 2. Table 3 summarizes all the cases of this study.
3. Results and Discussion
3.1. Influence of the Air Phase on Flow Hydrodynamics
Figures 2 and 3 depict the superficial velocity profiles for oil and water, respectively. The two-phase flow (oilwater) refers to the case 01, and the three-phase (oil-water-air), refers to the case 04 (Table 3), at four positions of the axial direction, Z = 0 m and were obtained under the same conditions.
By observing the velocity profiles in Figures 2 and 3, it can be noted that the introduction of the air phase in two-phase flow (water-oil), causes a significant change
Table 1. Thermo-physical properties of the fluids (25˚C) used in the simulations.
(a)
(b)
Figure 2. Superficial velocity profiles of the oil: (a) three-phase (water-oil-air) flow and (b) two-phase (water-oil) flow.
(a)
(b)
Figure 3. Superficial velocity profiles of the water: (a) Three-phase (water-oil-air) flow and (b) Two-phase (water-oil) flow.
Table 2. Dynamic viscosity of the fluid as a function of temperature (in ˚C).
*Equation fitted to the data provided by [17]; **Applied in the range of 0˚C ≤ T ≤ 100˚C.
in fluid-dynamics of water and oil phases. It affects the velocity gradient in the lower region of the pipe due to the increase in water flow in this region. A similar behavior was observed independently by [10-13]. This effect can be better seen in Figures 4(a) and (b), where the behavior of the volumetric fraction field of oil in the pipe, at different axial positions, is illustrated. Here it is clearly perceived that the presence of air creates a greater elevation of the oil core and, thus increases the area occupied by annular section of water in the lower region of the pipe, close to the wall. Therefore, it can be said that the divergence between buoyancy and lubrication forces are more intense in three phase flow than in two-phase flow.
3.2. Effect of Temperature on Flow Hydrodynamics
Figure 5 depicts the superficial velocity profiles, at different temperatures (288.15 K, 303.15 K and 323.15 K) for the cases: 02, 03 and 05, on the axial position equal to 1.0 m and direction Z = 0 m. It is noted that an increase in the temperature of the phases, at the entrance of the pipe, causes a small variation in the oil phase superficial velocity due to the change in the viscosity.