In the scenery of the oil industry, the remaining resources associated with light oils have an increasingly smaller share in the natural energy resources available to man, and in return the importance of resources associated with heavy oils has increased significantly. One of the drawbacks of this type of oil is associated with its low mobility due to the high viscosity in reservoir conditions, making the transport in pipelines very difficult, especially through pumping methods that require high powers. Thus, the development of new techniques and optimization of some existing technologies, aiming at the commercial use of heavy oil accumulations plays an important role. A viable technique that has been used is the core annular flow, in which small amounts of water are injected close to the pipe wall, lubricating the oil core, reducing friction and decreasing the pressure drop during the flow. In this sense, this work aims to perform, numerically, an energetic and hydrodynamic analysis of a heavy oil-water two-phase flow, using the core-flow technique, in curved pipes, in the Ansys CFX software. Results of the velocity, pressure, and volume fraction distribution of the involved phases are presented and analyzed. It was observed that the proposed mathematical model was able to accurately represent the analyzed phenomena and that a reduction factor in the pressure drop of 28.4 was obtained as compared to the heavy oil single-phase flow.
In the world oil production scenario, light oils, also called conventional oils, have dominated the market throughout history. These oils are technically easier to produce, have a lower production cost, higher performance after being refined, in addition to providing high-value products [
Heavy oils are composed of high molecular weight hydrocarbons, consequently, they have a high relative density, related to the presence of unwanted product contents such as asphaltenes, metallic components (nickel and vanadium) and sulfur. Furthermore, they are characterized by having a low API degree, between 10 and 20, and high viscosity ranging from 100 cP (0.1 Pa·s) to 10,000 cP (10 Pa·s). The production of this type of oil is, on average, twice as expensive in terms of production cost and energy consumption. This fact is related to low mobility due to its high viscosity in reservoir conditions, along with the presence of unwanted components already mentioned, making it more difficult to produce, transport and refine these oils.
In Brazil, the Campos Basin is the location that contains the largest amount of heavy oil in deep waters, being responsible for approximately 90% of the oil production in the country [
Core Annular Flow (CAF) can be defined as an alternative technique for transporting heavy oils. This technique uses parietal lubrication, that is, the annular flow of water in the pipe to carry the heavy oil in the center, thus, reducing friction effects [
Sarmadi et al. developed a methodology for transporting heavy oil using an annular flow with three layers. The third layer, next to the wall, is a lubricating layer. These authors verified that the addition of the extra layer ensures the stability of the transport, allowing a stable annular flow. Furthermore, they authors verified that the method produces a significant reduction in pressure drop.
Ameri et al. [
Strazza et al. [
During the Core Annular Flow, numerous difficulties related to the transportation of heavy oils are encountered. Given the importance of the physical problem under discussion, there is a need for further studies on the development and optimization of existing techniques, thus allowing the commercial use of these reserves from a technical and economic point of view. Therefore, in complement of this topic, this work aims to perform, numerically, an energetic and hydrodynamic analysis of a heavy oil-water two-phase flow, using the core-flow technique, in non-conventional ducts (curved pipes).
The physical problem to be studied herein consists of the two-phase flow (core-flow type) of heavy oil in a curved pipe (
In the present work, a structured three-dimensional mesh representing the study domain was generated in the ICEM CFD module of the ANSYS CFX 12.0 software. This mesh was created using a set of points, curves, surfaces, and solids describing its shape (curved pipe) and dimensions (diameter and length). The
modeling of the physical problem with appropriated boundary conditions were specified in the Ansys CFXÒ.
The heavy oil-water two-phase flow in curved pipes is governed by general conservation laws, as follows:
1) Mass Conservation Equation:
∂ ∂ t ( f α ρ α ) + ∇ ( f α ρ α U α ) = S M S α + ∑ β = 1 N p Γ α β (1)
where the sub-indices α and β correspond to the involved phases; f is the volume fraction, ρ is the density, U is the velocity vector; S M S is the mass source term and Γ α β is the mass transfer term between the fluid phases.
2) Momentum Equation:
∂ ∂ t ( f α ρ α U α ) + ∇ ⋅ [ f α ( ρ α U α ⊗ U α ) ] = − f α ∇ p α + ∇ ⋅ { f α μ α [ ∇ U α + ( ∇ U α ) T ] } + ∑ β = 1 N p ( Γ α β + U β − Γ β α + U α ) + S M α + M α (2)
where μ is the dynamic viscosity, p is the pressure, ⊗ is tensor product, S M represents the term of the external forces acting on the system per volume unit. In the term referring to the momentum transfer induced by the interfacial mass transfer (the third term on the right side of the equation), Γ α β + corresponds to the mass flow rate per unit volume of the phase β to phase α and vice-versa.
The tensor product of two vector is given by:
U ⊗ U = ( U x U x U x U y U x U z U y U x U y U y U y U z U z U x U z U y U z U z ) (3)
and the term ∇ ⋅ ( f ρ U ⊗ U ) can be obtain by:
∇ ⋅ ( f ρ U ⊗ U ) = ( ∂ ∂ x ( f ρ U x U x ) ∂ ∂ y ( f ρ U x U y ) ∂ ∂ z ( f ρ U x U z ) ∂ ∂ x ( f ρ U y U x ) ∂ ∂ y ( f ρ U y U y ) ∂ ∂ z ( f ρ U y U z ) ∂ ∂ x ( f ρ U z U x ) ∂ ∂ y ( f ρ U z U y ) ∂ ∂ z ( f ρ U z U z ) ) (4)
In Equation (2), M describes the interfacial force per unit volume over the phase α due to the interaction with the phase β. This parameter represents the sum of several forces, such as wall lubrification force, lift force, interfacial drag force, virtual mass force, turbulent dispersion force and solids pressure force. In the work, we use the mixing model at the interface between the phases. In this case, only the interfacial drag force is considered, being given by:
M α = C D ρ α β A α β | U β − U α | ( U β − U α ) (5)
where CD = 0.44 is the drag coefficient [
ρ α β = f α ρ α + f β ρ β (6)
The viscosity of the fluid mixture is given by:
μ α β = f α μ α + f β μ β (7)
The interfacial area density per volume unit, A α β , defines the treatment model for interfacial transfer (particle, mixture and free surface models). In this research we use the following equation:
A α β = | Δ f α | (8)
3) Turbulence equations:
The k-ε turbulence model was used to describe the flow of the water phase. This is a turbulent viscosity model where Reynolds tensors are assumed to be proportional to the mean velocity gradients, with the constant of proportionality being characterized by the turbulent viscosity (idealization known as Boussinesq’s hypothesis).
The characteristic of this type of model is that two transport equations modeled separately are solved for the turbulent length and the time scales or any two combinations linearly independent of them. The variable k represent the transport equation for the turbulent kinetic energy, and ε represent the turbulent kinetic energy dissipation rate, as follows:
∂ ∂ t ( ρ α f α k α ) + ∇ ⋅ { f α [ ρ α U α k α − ( μ + μ t α σ k ) ∇ k α ] } = f α ( G α − ρ α ε α ) (9)
∂ ∂ t ( ρ α f α ε α ) + ∇ ⋅ { f α ρ α U α ε α − ( μ + μ t α σ ε ) ∇ ε α } = f α ε α k α ( C 1 G α − C 2 ρ α ε α ) (10)
where Gα is the generation of turbulent kinetic energy within phase α, C1 and C2 are empirical constants. The dissipation rate of turbulent kinetic energy and the turbulent kinetic energy of phase α, are, respectively, defined by:
ε α = c μ q α 3 l α (11)
k α = q α 2 2 (12)
where lα is the length of the spatial scale, qα is the velocity scale and, cμ is an empirical constant, being as follows:
c μ = 4 c α 2 (13)
where cα is an empirical constant and μtα corresponds to turbulent viscosity, defined by:
μ t α = c μ ρ α k α 2 ε α (14)
The value of the constants used in the Equation (7) and Equation (8) are: C1 = 1.44, C2 = 1.92, Cμ = 0.09, σk = 1.0, and σε = 1.3. These information can be found in the literature.
As an initial condition, it was considered that the entire pipe was filled with water. The boundary conditions applied to the study domain are as follows:
1) An annular section for the inlet of water:
R i < r < R e ⇒ { Q ˙ w = 4.0779 kg / s f w = 1.0 U 0 z = f 0 = 0 (15)
2) An inlet section for oil:
0 < r < R i ⇒ { Q ˙ 0 = ( 15 − 1.5 t 2 ) kg / s ∴ 0 ≤ t ≤ 10 s f 0 = 1.0 U w z = f w = 0 (16)
where t is the time.
3) At the boundaries of the pipe wall: a roughness value of 4.5 × 10−5 m and the no-slip condition were considered.
r = { U w r = U w θ = U w z = 0 U 0 r = U 0 θ = U 0 z = 0 (17)
The properties of the fluids used in the numerical simulation of the heavy oil-water two-phase flow, using the core-flow technique, are shown in
Regarding the numerical simulation of the physical problem, some assumptions were made, which are shown in
The numerical simulation was carried out in a transient state with a total process time equal to t = 10 s and a time-step Δt = 0.05 s. As evidenced in the initial and boundary conditions, the water flow rate is constant (iqual to 4 kg/s), while the oil flow rate is a time-dependent function with decreasing behavior (decreasing from 15 to 0 kg/s), as shown in
| Property | Heavy oil | Water |
|---|---|---|
| Density (kg/m3) | 989 | 997 |
| Dynamic viscosity (Pa·s) | 10 | 8.89 × 10−4 |
| Surface tension (N/m) | 0.072 | |
| Properties | Assumptions |
|---|---|
| Classification of fluid flow | Two-phase flow (oil-water), three-dimensional, transient, incompressible, isothermal, turbulent (water)/laminar (oil) |
| Turbulence model | k-ε Standard |
| Multiphase model | Non-homogeneous |
| Interfacial transfer model | Mixing model |
| Interfacial force | Drag |
| Pressure interpolation scheme | Trilinear |
| Velocity interpolation scheme | Trilinear |
| Advection scheme | High Resolution |
this physical situation to a real process such as a performance reduction of the oil pump due to a problem in the suction of the pipeline or even a variation in the engine rotation velocity done manually to attend operational requirements.
The pressure field at time t = 3 s and 6.5 s are shown in
pipe wall, especially in the curvature region, as expected for at this geometry type.
In the petroleum industry always is desirable to transport crude oil as possible at fixed pressure drop. Thus, to compare the performance of the core-flow technique plays important role. For heavy oil single-phase flow, the pressure drop achieved was ΔP = 81780.9 Pa. Therefore, a reduction factor of 28.4, which is the relationship between the pressure drop of the oil single-phase flow and the two-phase flow using the core-flow technique, was verified. There was a reduction in pressure drop equivalent to 96.48% when using the core-flow technique for transporting heavy oil, thus showing its efficiency in terms of the high-energy gain in the process, that is essential to make the production of heavy oils to be optimized and economically attractive.
mainly due to the difference in density between the two fluids, inducing interfacial waves in the core-annular flow and at the same time increasing, even more, its hydrodynamic stability. This behavior can be seen clearly in
Regarding the oil velocity behavior illustrated in
that it does not touch the pipe wall, not even in the curvature region, confirming the oil core lubrication performed by the water flow, reaching a maximum superficial velocity of 0.56 m/s.
From the obtained results, it can be concluded that:
1) The core-flow technique proved to be an excellent alternative solution for the transport of heavy oils due to the reduction in the energy consumption used in the process;
2) The use of the core-flow technique for the proposed problem presented a reduction factor in the pressure drop of 28.4 compared to the heavy oil single-phase flow;
3) The use of the core-flow technique provided a maximum reduction in pressure drop equal to ΔP = 2879.37 Pa and the maximum required power of 41.14 W;
4) The reduction in pressure drop when using the core-flow technique was 96.48%;
5) During the entire process, the oil core was stable and non-concentric, not even touching the pipe wall;
6) In pipeline projects for transporting heavy oils, the radius of curvature must be analyzed during the design process, to avoid breaking the stability of the core-flow pattern due to its high local pressure drop.
The authors thank CNPq, CAPES, FINEP, and ANP (Brazilian Research Agencies) for financial support.
The authors declare no conflicts of interest in this paper.
Silva, B.F., Magalhães, H.L.F., Gomez, R.S., de Morais Cabral, E., Batista, F.A., da Costa Pereira, A.B., de Lima, W.M.P.B. and de Lima, A.G.B. (2020) Isothermal Transport (Core-Flow Type) of Heavy and Ultraviscous Oil in Curved Pipes: A Transient Study by CFD. Open Journal of Fluid Dynamics, 10, 122-134. https://doi.org/10.4236/ojfd.2020.102008