- Email: [email protected]
Nanopaint application for flow assurance with electromagnetic pig
Accepted Manuscript Nanopaint application for flow assurance with electromagnetic pig Ningyu Wang, Mas̆a Prodanović, Hugh Daigle PII:
S0920-4105(19)30482-6
DOI:
https://doi.org/10.1016/j.petrol.2019.05.028
Reference:
PETROL 6077
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 14 January 2019 Revised Date:
15 April 2019
Accepted Date: 7 May 2019
Please cite this article as: Wang, N., Prodanović, Mas̆., Daigle, H., Nanopaint application for flow assurance with electromagnetic pig, Journal of Petroleum Science and Engineering (2019), doi: https:// doi.org/10.1016/j.petrol.2019.05.028. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Nanopaint Application for Flow Assurance with Electromagnetic Pig Ningyu Wang, Ma˘sa Prodanovi´c⇤, Hugh Daigle
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Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
Abstract
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Wax, hydrates, and asphaltenes precipitate in subsea pipelines and restrict the transportation of hydrocarbons. Traditional wax deposition prevention and dewaxing methods include thermal, chemical, and mechanical approaches. This paper investigates a new electromagnetic pigging method combined with a ferromagnetic nanopaint for potentially high heating efficiency and low maintenance cost. The electromagnetic pig could be inserted into the pipeline to generate induction heat and a nanopaint coating on the inner wall of the pipeline enhances
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the heating e↵ect. To evaluate the e↵ectiveness of the proposed system, the concept of maximum pig speed is introduced. Systems with higher maximum pig speed can dewax a pipeline in shorter time. Numerical models are used to analyze the heating performance for di↵erent system configurations. Simulation
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results show that the proposed pigging tool can e↵ectively heat and melt the deposited wax. The maximum pig speed is a function of the pig induction coil length and radius. The hydraulic shape of the pig does not impact the heating
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e↵ectiveness.
Keywords: nanopaint, superparamagnetic nanoparticles, flow assurance, dewaxing, pigging, subsea pipeline
⇤ Corresponding
author Email address: [email protected] (Ma˘sa Prodanovi´ c)
Preprint submitted to Journal of Petroleum Science and Engineering
January 14, 2019
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Nanopaint Application for Flow Assurance with Electromagnetic Pig Ningyu Wang, Ma˘sa Prodanovi´c∗, Hugh Daigle
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Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
Abstract
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Wax, hydrates, and asphaltenes precipitate in subsea pipelines and restrict the transport of hydrocarbons. Traditional wax prevention and dewaxing methods include thermal, chemical, and mechanical approaches. This paper investigates a new electromagnetic pigging method combined with a ferromagnetic nanopaint for potentially high heating efficiency and low maintenance cost. The electromagnetic pig could be inserted into the pipeline to generate induction heating; a nanopaint coating on the inner wall of the pipeline enhances the heating effect.
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To evaluate the effectiveness of the proposed system, we calculate the maximum pig speed, which is the fastest a pig can move through the pipeline and effectively dislodge wax deposits by heating. Systems with a higher maximum pig speed can dewax a pipeline in a shorter time. Numerical models are used to
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analyze the heating performance for different system configurations. Simulation results show that the proposed pigging tool can effectively heat and melt the deposited wax. The maximum pig speed is a function of the pig induction coil
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length and radius. The hydraulic shape of the pig does not impact the heating effectiveness.
Keywords: nanopaint, superparamagnetic nanoparticles, flow assurance, dewaxing, pigging, subsea pipeline
∗ Corresponding
author Email address: [email protected] (Ma˘sa Prodanovi´ c)
Preprint submitted to Journal of Petroleum Science and Engineering
May 17, 2019
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1. Introduction
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Offshore pipelines are one of the major means of transporting oil from offshore oil facilities and to onshore facilities. As deepwater drilling expands,
pipeline installations move to deeper and deeper water. For instance, pipelines 5
in the Gulf of Mexico, offshore West Africa, offshore Brazil, and offshore Aus-
tralia have entered regions deeper than 1000 m (Randolph et al. (2011)), and
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sometimes deeper than 2300 m (Ekweribe et al. (2008)).
Subsea pipelines are deployed at the sea floor where the typical temperature is as low as about 4o C. To pump the oil and gas through the pipelines, the transported fluids are subjected to pressures of 14.5 MPa (2100 psi) (Ekweribe
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et al. (2008)) or even higher. The low temperature and high pressure can lead to precipitation of hydrates, wax, and asphaltenes from the fluids. Wax deposition in the pipelines is a common and intensively researched phenomenon (Leiroz and Azevedo (2005); Ekweribe et al. (2008); Hilbert (2010); 15
Aiyejina et al. (2011); Semenov (2012); Zheng et al. (2017)). When the oil
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is cooler than 40o C, the wax begins to separate from the oil and deposit in the pipeline (Burger et al. (1981); Roenningsen et al. (1991); Hammami and Raines (1997); Roehner and Hanson (2001)). While the mechanism that leads to the deposition of wax is complex, the temperature required for melting of the 20
deposited wax is about 40-50o C (Aiyejina et al. (2011)).
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Hydrates are a major risk in high-pressure natural gas transport lines (Jassim et al. (2008)). At high pressure and low temperature, such as commonly encountered around subsea pipelines, the wet gas in the pipelines will form gas
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hydrates that attach to the pipelines (Sloan (2003); Koh et al. (2007); Nicholas
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et al. (2009); Koh and Sum (2010)). Finally, the precipitation and deposition of asphaltenes are more compli-
cated (Zhu et al. (2010); Eskin et al. (2011)) and the treatment required is not addressed in this work. If any of these substances deposit onto the pipeline, flow can be inhibited or
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even stopped completely, posing safety, environmental, and economic risks. In
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this paper, we focus on oil pipelines, where wax deposition is a major concern.
pipelines but is not directly addressed by our modeling. 1.1. Flow Assurance Methods 35
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Our proposed heating method should also work for hydrates removal in gas
Flow assurance refers to the process of removing deposits and preventing
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future deposition in the pipeline. Methods of flow assurance fall into three cate-
gories: chemical methods, mechanical methods, and thermal methods (Aiyejina et al. (2011); Wang et al. (2014)).
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The chemical approach is focused on preventing the precipitation and deposition of solids by injecting inhibitors or by applying different coatings. The main types of wax inhibitors include ethylene copolymers, comb polymers, wax dispersants, polar crude fractions, and short-chain alkanes (Argo et al. (1997); Haghighi et al. (2009); Aiyejina et al. (2011); Chi et al. (2016); Hashmi and Firoozabadi (2016)). The main types of hydrate inhibitors include polyvinyl45
caprolactam (PVCap) and polyvinylpyrrolidone (PVP). (Lederhos et al. (1996);
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Sloan et al. (1998); Kelland (2006); Koh and Sum (2010); Abrahamsen and Kelland (2018)). The disadvantages of chemical deposition control are the cost associated with continuous injection of chemicals, the corresponding environmental risks, as well as the need to select the inhibitor mixture for the mixed 50
hydrocarbon flowing in a pipeline (Hill et al. (2002); Kondapi and Moe (2013);
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Borden (2013)). Some chemical coatings have been developed to decrease the deposition of wax and hydrates (Liang et al. (2015, 2016); Lahin et al. (2017)).
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Mechanical removal of the deposited sediments typically requires a pipeline inspection gauge, or ’pig’ for short, and the process itself is called ’pigging’(Wang
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et al. (2015); Huang et al. (2017)). Although pigging has been applied in flow assurance for quite a long time and practical guides are available (Schaefer (1991)), pigging still interferes with the hydrocarbon transport in the pipelines and it is common for the tool to get stuck. Conventional thermal removal of deposits involves electrical heating of the
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pipelines. This method has the smallest environmental hazard and does not 3
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interfere with the oil transport. Either a conductive layer or a wire or coil
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is applied inside or outside the pipeline to introduce Joule heating (Nysveen et al. (2005)). By heating the deposited wax and hydrates above the melting temperature, they may flow away with the hydrocarbon. 65
The problems of the above thermal removal methods include the maintenance of the heating system and the associated electricity cost. In these systems,
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a coil is permanently deployed in or around the pipeline at the sea floor. The coil may deteriorate and any maintenance of permanent infrastructure under several hundred meters of seawater would be expensive. List (2017) designed and
analyzed a magnetic pig built with no coils but a rotating array of permanent
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magnets driven by a turbine to induce the alternating magnetic field. 1.2. Enhanced Induction Heating with Nanopaint
A nanopaint is a paint or coating that is nanostructured. A nanopaint that contains nanometer size ferromagnetic material is a ferromagnetic nanopaint, 75
and is studied in this work. Nanopaint starts as a ferrofluid, i.e. a stable
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dispersion of superparamagnetic nanoparticles (SMNPs) in a liquid carrier, and solidifies in the process.
Unlike the eddy currents that cause Joule heating in the metal conductors, the heating effect of SMNPs is based on the magnetization of the particle. Mag80
netic materials have magnetic domains inside them. Each magnetic domain has
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its own magnetic moment which aligns with the external magnetic field. When the size of the ferromagnetic material decreases to several tens of nanometers,
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there is only one magnetic domain in the particle. If the external magnetic field is alternating, the magnetic moment of the magnetic domain of the nanoparticle
85
will oscillate with the magnetic field, converting the electromagnetic energy to heat. In the absence of a magnetic field, the individual domain orientations are randomized. This behavior is referred to as superparamagnetism. The resulting heat power density can be much higher than conventional induction heating by eddy currents under the same magnetic field, which will be shown later in this
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paper. 4
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SMNP heating has been studied in magnetic hyperthermia for many years
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(Chou (1990); Jordan et al. (1993); Sonvico et al. (2005); Fortin et al. (2007); Prigo et al. (2015); Obaidat et al. (2015); Yao et al. (2017)). Magnetic hyperthermia uses an alternating magnetic field to induce heat in magnetic agent, 95
e.g. SMNPs. With proper coating, SMNPs can selectively attach to tumor
cells. Then an external alternating magnetic field is applied so that the SM-
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NPs generate localized heat. The heat can effectively kill tumor cells at above
43o C (Hildebrandt et al. (2002)). The magnetic field frequency used in most research on magnetic hyperthermia is on the order of several hundred thousand Hz, lower than the reported safety threshold (Atkinson et al. (1984); Johnson
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et al. (1993)).
In petroleum engineering, Yahya et al. (2012) discussed heating the reservoir oil with SMNPs and an external alternating magnetic field.
The feasibility of using SMNPs in flow assurance was briefly discussed in the 105
book by Huh et al. (Huh et al. (2019)).
The heating power of unit weight of SMNPs is evaluated by the specific
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absorption rate (SAR) (Chou (1990); Jordan et al. (1993)).
SAR =
2(πmHf τN )2 2 τN KB T V ρ(1 + (2πf )2 )τN
where m is the magnetic moment of the particle, H is the magnetic field
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strength, f is the frequency of the magnetic field, V is the particle volume, KB is the Boltzmann constant, T is the temperature, ρ is the density of the SMNP,
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and τN is the N´eel relaxation time (Rosensweig (1985)). KV
τN = τ0 e KB T
where τ0 is a constant, K is the volumetric magnetic anisotropy. The SAR can be measured in the lab by
SAR =
cp ∆T WN P ∆t
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where cp is the heat capacity, ∆T is the temperature increase, WN P is the mass, and ∆t is the heating time.
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To be applied in pipeline heating, the nanopaint has to withstand the working temperature of the system, which means the SMNP has to keep its superparamagnetism and the paint matrix should not deteriorate. The typical ambi-
ent temperature at the sea floor is 4o C, and a typical melting point of paraffin wax is 42o C. The SMNP becomes paramagnetic above its Curie temperature
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and returns to a superparamagnetic state when the temperature decreases. The Curie temperature of magnetite (F e3 O4 ), a cheap material for SMNP, is over
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550o C (Schult (1970); Maher and Taylor (1988)). Magnetite nanoparticles with Curie temperature of 553o C have been reported by Woltz et al. (2006). The 125
paints being used in oil and gas pipelines can work at up to 85o C (Guan et al. (2005)). Some polypropylene paints are used for transporting hot, erosive fluids up to 170o C (Guidetti et al. (1996)). More paints and coatings under development can work at 600o C (Ho et al. (2014)) or even up to 650o C (Ho and Iverson (2014)). In short, there are no expected operational issues for the nanopaint in pipeline heating.
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Another factor of the nanopaint is its durability. The life and sustainability of the nanopaint is determined by both the SMNP and the paint matrix. Magnetism is a long-term property of materials. The paint itself may last shorter
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than the embedded SMNPs, but little to no maintenance would be required during the limited life. Even if the nanopaint layer were partly destroyed, the heat would still be generated at each of the SMNPs in areas that still had the
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nanopaint.
1.3. Nanopaint Applications in Pipeline Heating Davidson et al. (2012) proposed to paint a layer of superparamagnetic nanopar-
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ticles in the pipeline to heat the hydrocarbon. They measured the specific absorption rate of different dispersion settings of superparamagnetic nanoparticles and measured the induction heat transferred to the fluid inside the pipe. However, the induction coil in that (laboratory) work was installed outside the 6
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pipe. A similar idea was proposed by Haindade et al. (2012) for dewaxing in production wells. Mehta et al. (Mehta et al. (2014); Mehta (2015)) performed
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experiments to quantify the specific absorption rate of different superparamagnetic nanoparticles for the coil placed outside the pipeline.
Mehta (2015) first proposed injecting an electromagnetic coil in a pipeline painted with nanopaint for wax removal in her MS thesis. This work was mostly
experimental. She set up a numerical model of the electromagnetic pigging
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process and concluded that higher current and higher nanoparticle concentration in the nanopaint both accelerate the wax melting process. The numerical model
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was preliminary with fewer than 10 total simulations and the oil phase was modeled as static. Further, these simulations were not published in the peer 155
reviewed literature before.
In this paper, we perform a thorough study of induction oil shape (radius/length ratio) with over 240 simulations, and improve modeling of oil (in other words, we incorporate the cooling effect of flowing hydrocarbon).
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2. Electromagnetic Pigs
The most straightforward way to generate an alternating magnetic field inside the pipeline is to place a coil within. The coil should be packed in a pig together with proper power units and control units. There are countless designs
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for pigs (Tiratsoo (1992); Okamoto et al. (1999); Nguyen et al. (2001); Han et al. (2004); Hiltscher et al. (2006); Tur and Garthwaite (2010); Shukla and 165
Karki (2016)). Two simple cylindrical pigs, one hollow and one non-hollow, are
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studied in this research, as shown in Fig. 1. The cross section of the non-hollow pig is shown in Fig. 2. The power unit and the control unit are not shown. The polymer support helps decelerate the pig and keep it from hitting the pipe wall. If we neglect the distance between adjacent wires in the coil, the magnetic
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field of a co-axial coil in the pipeline is axisymmetric, as shown in Fig. 3. As the pig travels through the pipeline, the alternating magnetic field heats the surrounding metallic materials axisymmetrically. This induction heat is then
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(b)
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Figure 1: Cylindrical pig designs. (a) hollow. (b) non-hollow.
transported to the precipitated material. With enough heat, the material will melt from the layer contacting the pipe wall. Once the inner layer of material 175
melts, it no longer adheres to the pipe wall and will peel off due to the shear
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forces of the flowing hydrocarbon in the pipeline. This process is similar to the conventional pigging operation since they both involve the deposited material peeling off from the pipeline when the pig passes. Thus the operation proposed
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in this paper can be called electromagnetic pigging.
3. Coupled Modeling of Flow, Heat Transfer, and Magnetic Field In an oil pipeline, coupled flow and heat transfer happens when the oil flows
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through the pipeline. A k- turbulent flow model (Chac´on Rebollo and Lewandowski (2014)) is
used to describe the flow of the oil.
ρ
∂~u 2 + ρ(~u · ∇)~u = ∇ · [−pI + (µ + µT )(∇~u + (∇~u)T ) − ρkI)] + F~ ∂t 3 ρ∇ · ~u = 0
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A
SECTION A-A
Figure 2: Side view and the cross section labeled A-A’ of the hollow cylindrical pig.
ρ ρ
∂k µT + ρ(~u · ∇)k = ∇ · [(µ + )∇k] + Pk − ρ ∂t σk
∂ µT 2 + ρ(~u · ∇) = ∇ · [(µ + )∇] + C1 Pk − C2 ρ ∂t σ k k
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= ep
µT = ρCµ
k2
Pk = µT [∇~u : (∇~u + (∇~u)T )]
where k is the turbulent kinetic energy, is the turbulent dissipation, ~u is
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the velocity, rho is the density, I is the unit tensor, µ is the viscosity, µT is the turbulent viscosity, F~ is the body force, σk , σ , C1 , C2 , and Cµ are constants.
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The oil is much warmer than the sea water. The heat transfer can be de-
scribed by
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ρCp
∂T + ρCp ~u · T = ∇ · (k∇T ) + Q + Wp ∂t
where ρ is the density, Cp is the heat capacity at constant pressure, T is the
temperature, t is the time, ~u is the flow rate, Q is the heat input, and Wp is the external work.
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mT 0.2
35
m -0.2
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0
30
-0.4
0.6
m
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0.4
25
0.2
0
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0.2
y
15
10
5
0
x
m
-0.2
0
Figure 3: The magnetic flux density (B) in the pipeline.
At the interfaces between different media, the temperature is continuous.
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At the wax-oil interface, the heat flux is
q = hoil−wax (Toil − Twax )
At the pipe-sea water interface, the heat flux is
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q = hpipe−sea (Tpipe − Tsea )
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When the pig is injected into the pipeline, an additional magnetic field is introduced by the alternating current in the induction coil. The electromagnetic field is described by ~ + ∇ × (µ−1 µ−1 B) ~ − σ~v × B ~ = J~e (jωσ − ω 2 0 r )A r 0 ~ =∇×A ~ B
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where j is the imaginary unit, ω is the angular frequency of the current, σ 200
is the electrical conductivity, 0 is the vacuum permittivity, r is the relative
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~ is the vector potential, µ0 is the vacuum permeability, µr is the permittivity, A ~ is the magnetic flux density, ~v is the velocity relative magnetic permeability, B of the circuit, J~e is the current density.
The magnetic field induces heat in the nanopaint. The induction heat power density is
q=
1 SAR ρ
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where ρ is the density of the nanopaint, SAR is the specific absorption rate. The induction heat in the metal is
q=
1 ~ ·H ~ ∗) Re(jω B 2
~ = H/(µ ~ ~∗ where B 0 µr ) is the magnetic flux density, H is the conjugate of ~ the magnetic field strength H.
Numerical implementation of the above equations exists in COMSOL soft-
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ware, which we use in this work. Our goal is to evaluate when the temperature of wax reaches melting point, and we do not specifically model what happens to the wax after that (it is presumably carried away by oil).
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4. Geometry Description and Model Parameters The pigs shown in Fig. 1 are modeled in the commercial software COMSOL.
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The model for the hollow pig is shown in Fig. 4. The pipeline in this model has an insulation layer (2) between the two steel layers (1) to decrease the heat loss to the seawater (3). The nanopaint (4) is painted on the inner wall of the pipeline. The oil (5) flows through the pipeline. We assume wax (6) precipitated
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and deposited on the nanopaint layer. We also assume the pig (7) moves along the pipe axis. The induction coil (8) is inside the pig (7). The geometric and physical parameters are listed in Table 1 and Table 2. The pig inner channel exists only in the hollow pig model. The coil radius and 11
(4)
0.6
(5)
(6)
0.4
(7)
(1)
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(8)
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(3)
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0.2
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0.7 m
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0
0
0.1
0.2
0.3
0.4
0.5 m
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Figure 4: (1) Pipeline steel layer. (2) Pipeline insulation layer. (3) Seawater. (4) Nanopaint layer. (5) Oil. (6) Wax deposited in the pipeline. (7) Pig. (8) Induction coil.
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coil length will change, but the distance between the coil and the pig shell is the same. In the hollow pig, the difference between pig diameter and inner channel
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diameter are kept constant.
We perform simulations for Reynolds number 5.95 × 104 , in particular for a
fluid of temperature 25o C, density 746kg/m3 , viscosity 5.02 × 104 P a · s (0.5cp), nominal velocity 0.1m/s and in a tube of diameter 0.4m. Depending on the
assumed oil flowing in the pipe: e.g. light oil of density 738.9kg/m3 (60o AP I)
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and viscosity 1.6 × 10−3 (1.6cp), to heavy oil of density 960.6kg/m3 (15.8o AP I) and viscosity 2.003P a · s (2003cp), the simulation conditions are equivalent to
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oil velocity range of 0.39m/s to 310m/s. Note that thermal properties of the simulation fluid are heat capacity at constant pressure of 2082J/kg · K, thermal 235
conductivity 0.1156W/kg · K. And they do not change much for light or heavy oil. Thus the assumed fluid velocity if not as restrictive as it seems. We are modeling relative movement where pig is fixed in space and the oil is moving around it. At time zero, a 300A, 500kHz alternating current is applied in the induction coil. There are 25turns in the coil. These values are selected within the range of published work (Mehta (2015)). Technically speaking, the
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current multiplied by the number of turns is what is fixing the maximum magnetic field strength around the coil to the single value examined in this work. From the numerical standpoint, we model the coil as a cylinder without going
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into the number of turns it has (it could have had 100A and 75turns, for example, with the same result). For that maximum field strength, we then focus on changing the shape of the field (i.e., by changing the normalized radius and
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length of the coil). The maximum field strength ultimately determines required power supply to the pig, which is an important practical design parameter but not to be researched at this stage.
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Nanoparticles, when dispersed in the paint, can significantly change the ther-
mal conductivity of the mixture and the thermal conductance of the nanopaint layer. However, due to the fact that the thickness of the paint layer is three orders of magnitude smaller than the thickness of the pipeline, the nanopaint has negligible impact on the thermal conductance of the painted pipeline system. A 13
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value
pipeline outer diameter
0.8 [m]
pipeline inner diameter
0.4 [m]
thickness of nanopaint
0.4 [mm]
thickness of wax
5 [mm]
thickness of insulation layer
0.1 [m]
thickness of outer steel layer
0.05 [m]
thickness of inner steel layer
0.05 [m]
pig length
0.1525 [m]
0.22 [m]
pig inner channel diameter
0.0625 [m]
induction coil diameter
0.06 [m]
induction coil length
0.18 [m]
detailed explanation can be found in Appendix A.
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pig diameter
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Table 1: geometrical parameters
5. Evaluation of Heating Effectiveness and Maximum Pig Speed The pig travels in the pipeline with the flowing product. To evaluate whether
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the pig can effectively melt and remove the wax, we define the maximum pig speed, which is the fastest speed the pig can travel and melt a wax deposit. If the pig travels slower than the maximum pig speed, the pig can effectively melt
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the wax adhering to the pipeline and let it peel off in the flowing oil or gas. This maximum speed provides a valuable design parameter for hydraulic design. This concept is illustrated using the simulation results for the pig described in
Table 1. The magnetic flux density and temperature field for the pig described
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in Table 1 after 150s heating are shown in Fig. 5. The white zone in the temperature field is where the temperature is above the wax melting point. The corresponding heating power density in the nanopaint and at the inner 14
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Table 2: physical parameters of solids
coil
steel
insulation
wax
nanopaint
relative magnetic permeability
1
1
1
1
2.1
relative electrical permittivity
1
1
1
1
2.1
electrical conductivity [S/m]
6.0e7
4.03e6
2.50e-8
1.0e-8
1.0e-8
heat capacity [J/(kg·K)]
385
475
2000
3430
3430
density [kg/m3 ]
8700
7850
750
900
900
thermal conductivity [W/(m·K]
400
44.5
0.17
0.25
0.25
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steel surface of the pipeline is shown in Fig. 6. The peak SMNP heating power density generated by nanopaint is 450% higher than the induction heat in the 270
adjacent steel layer in the pipeline.
Melting Zone. The melting zone is any zone in the wax layer that is hotter
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than the melting temperature. The melting zone at t = 150s is shown in Fig. 7 accompanied by the heating power in the nanopaint. The heat is transferred to the wax across the wax-nanopaint interface, so the wax near this interface 275
melts first. Thus the melting zone length can be defined as the width of the melting zone at the wax-nanopaint interface. The melting zone depth is defined
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as the distance that the melting zone extends into the wax layer. After 150 s of heating, the melting zone grew to what is shown in Fig. 7.
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Minimum Melting Zone Depth and Minimum Melting Zone Length. When the
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melting zone depth reaches a threshold, the wax will be peeled off by the oil or gas flow. This depth threshold is defined as the minimum melting depth and can be measured in the lab. The corresponding melting zone length is the minimum melting zone length. The melting zone length is a measure of the heating locality. Long melting zone length indicates both heating power
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dispersion and heat dissipation.
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Figure 5: Simulation result of (a) magnetic flux density and (b) temperature at t = 150s. The white zone is where the temperature is above the wax melting point.
Minimum Heating Time. If the pig is moving, the local induction heat power
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density will change with time. As long as the local heating power is over a threshold for a long enough time, the local wax can be melted to the minimum melting depth. This time threshold is defined as the minimum heating time. Thus, the maximum pig speed can be defined as
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maximum pig speed =
minimum melting zone length minimum heating time
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6. Simulation Results
Pigs with different coil geometries were modeled in the commercial multi-
physics simulation software COMSOL (version 5.3a). Each model was simulated using the frequency-transient solver in COMSOL for 200 s. The modules
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required to implement models presented here are ’Turbulent Flow, k- (spf)’, ’Heat Transfer in Solids (ht)’, ’Heat Transfer in Fluids (ht)’, and ’Magnetic Fields (mf)’. The following ’Multiphysics’ modules are used for coupling them: 16
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Figure 6: Heating power density near the pipe-nanopaint interface. Blue solid line: the SMNP heating in the nanopaint. Red dashed line: the conventional induction heating in the steel pipe.
’Non-Isothermal Flow (nitf)’, ’Electromagnetic Heat Source (emh)’, ’Boundary
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Electromagnetic Heat Source (bemh)’, and ’Temperature Coupling (tc)’. One difficulty in finding the melting zone is that, once the wax is melted, it is no longer a solid phase and thus the original model should be dynamically changed as the wax is melting. To compensate for this inaccuracy, we focus on very shallow melting zone depths. The melting result is studied at minimum
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melting depths of 1, 3, and 5 layers of mesh cells in the wax nearest to the nanopaint, corresponding to 0.000575, 0.00173, and 0.002885 times the pipeline
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inner radius.
The simulation results are shown in Fig. 8. The dependence of minimum
heating time and melting zone length on the coil radius and coil length are similar at different assumed minimum melting depths. The results are the same
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for both the hollow and non-hollow pigs, which makes sense given that in both cases the material (or fluid) inside the pig is modeled as non-magnetic. The heating is faster and more localized with coils of shorter axial length and larger radius. 17
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Figure 7: The melting zone at t = 150s and the corresponding heating power density in nanopaint. The melting zone is a zone in the wax layer that is hotter than the melting
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temperature.
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Figure 8: (a) Minimum heating time and (b) melting zone length measured at different assumed minimum melting depths for a pipeline with nanopaint, hollow and non-hollow pigs
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alike. The coil radius, the coil length, the minimum melting depth, and the melting zone length are normalized with respect to the pipeline inner radius. The three studied minimum melting depths correspond to layers 1, 3, and 5 mesh cells deep from the wax-nanopaint in-
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terface into the wax. White color in the minimum heating time graph means the wax did not reach the melting point within the 200 s of simulation time at this assumed minimum melting depth, coil radius, and coil length combination. Zero melting zone length means the wax did not reach the melting point during the simulation.
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The minimum heating time and melting zone length measured at an assumed minimum melting length of 5 mesh cells deep or 0.002885r are further analyzed
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315
to generate formulae by least squares fitting. The quality of the generated
formulae is measured by the R2 value, where R2 = 1 means perfect fitting or interpolating and R2 = 0 refers to a total failure.
Minimum Heating Time. The minimum heating time is shown in Fig. 9. All the lengths are normalized with respect to the pipeline inner radius (0.2 m).
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320
The results for the hollow and non-hollow pigs are the same. It can be seen that the smaller the coil length and the larger the coil radius, the faster the wax
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melts. The results can be fitted by the following formula: 3
time = a + b · ec/r · ed·L
where r is the normalized coil radius and L is the normalized coil length. 325
The fitted coefficients are a = 4.837, b = 0.02989, c = 0.07873, d = 2.062. The fitting quality is R2 = 0.9939.
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The 1/r3 term is motivated by the decline of the magnetic field of a dipole/coil with distance. The time does not reach zero due to the finite resolution of the numerical simulation. 330
Minimum Melting Zone Length. The minimum melting zone length is shown
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in Fig. 10. All the lengths are normalized with respect to the pipeline inner radius (0.2 m). The results for the hollow and non-hollow pigs are the same. It can be seen that shorter coil length leads to shorter or more localized heating,
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while the effect of the coil radius is negligible. The results can be fitted by the
335
following formula:
length = f + g · r + h · L
where r is the normalized coil radius and L is the normalized coil length.
The fitted coefficients are f = 1.998, g = 0.001028, h = 1.498. The fitting
20
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0.2
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1
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coil radius
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time [s]
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coil length
Figure 9: Minimum heating time for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius and coil length are normalized with respect to the pipeline inner radius (0.2 m).
quality is measured by R2 = 1. If the fitting parameter g = 0, the result is still
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R2 = 1.
It is interesting that the melting zone length is at least 2 times the inner radius of the pipeline, though the mechanism behind this phenomenon is beyond the scope of this paper.
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Maximum Pig Speed. The maximum pig speed is shown in Fig. 10. All the lengths are normalized with respect to the pipeline inner radius (0.2 m). The results for the hollow and non-hollow pigs are the same. It can be seen that the smaller the coil radius and the larger the coil length, the faster the pig may
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345
travel. The results can be fitted by the following formula which is the division of the minimum melting zone length by the minimum heating time:
speed =
f +g·r+h·L a + b · ec/R3 · ed·L
or
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3 2 0.4 0.6
0.2
0.4
0.6
0.8
1
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coil radius
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length
4
coil length
Figure 10: Minimum melting zone length for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius, coil length, and minimum melting zone length are normalized by the pipeline
speed =
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(f /a) + (g/a) · R + (h/a) · L 1 + (b/a) · ec/R3 · ed·L
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inner radius 0.2m.
where r is the normalized coil radius and L is the normalized coil length. The fitted coefficients are a = 4.837, b = 0.02989, c = 0.07873, d = 2.062, f = 1.998, g = 0.001028, h = 1.498. The fitting quality is measured by R2 = 0.9914. When
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g = 0, R2 drops to 0.9883. Impact of Pig Hydraulic Shape. From the above simulations, the results for hollow and non-hollow pigs are exactly the same. This indicates that the hydraulic
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shape of the pig doesn’t have a big impact on the heating process. Impact of Hydrocarbon Flow Rate. The hydraulic shape of the pig impacts the flow field of the hydrocarbon near the pig. The flow in the annulus between the pig and the pipeline in the case of the hollow pig is slower than in the case of
360
the non-hollow pig, leading to weaker heat dissipation from the heated wax to
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0.5
0 1 0.8 0.6 0.4 0.2
0.6
0.4
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coil length
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speed [1/s]
1
coil radius
Figure 11: Maximum pig speed for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius, coil length, and velocity are normalized with respect to the pipeline inner radius (0.2 m).
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the hydrocarbon. Since the impact of the pig’s hydraulic shape is small, it is possible that the impact of the flow rate on the heating process is limited. Impact of Nanopaint. The heating power of eddy currents in the steel pipe is much lower than that of the nanopaint, as shown in Fig. 6. We performed the same simulation for models with exactly the same pipe and pig but no
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nanopaint, of which the results are shown in Fig. 12. Only several pigs with the largest possible radius created a deep enough melting zone within the 200 s
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simulation time, which would be too slow for pigging.
7. Conclusion
370
We developed a numerical model to investigate the benefits of superpara-
magnetic nanoparticles embedded in a nanopaint coating for flow assurance applications in subsea pipelines using a pig traveling through the pipeline and emitting an electromagnetic field.
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Figure 12: (a) Minimum heating time and (b) melting zone length measured at different assumed minimum melting depths for a pipeline without nanopaint, hollow and non-hollow
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pigs alike. The coil radius, the coil length, the minimum melting depth, and the melting zone length are normalized with respect to the pipeline inner radius. The three studied minimum melting depths correspond to depths of 1, 3, and 5 layers of mesh cells from the wax-nanopaint
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interface into the wax. White color in the minimum heating time graph means the wax did not reach the melting point within the 200 s simulation time at this assumed minimum melting depth, coil radius, and coil length combination. Zero melting zone length means the wax did not reach the melting point.
24
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The simulation results showed that a pig emitting an electromagnetic field could heat and melt the precipitated wax in the pipeline. To evaluate the heat-
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375
ing effectiveness and optimize the pig, the maximum pig speed was calculated. Longer and fatter coils led to higher maximum pig speed and better heating
effectiveness. Formulae were generated to predict the minimum melting zone length and minimum heating time for a given coil length and coil radius combination.
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380
The nanopaint, though as thin as 0.4 mm, significantly improved the heating efficiency. The heating power density in the nanopaint was several times higher
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than in the steel pipe. For the same pig and pipe, the nanopaint could decrease the minimum melting time by two orders of magnitude. 385
The hydraulic shape of the pig had little impact on the heating process. The only requirement for the pig was to have enough inner volume for the coil, battery, and control circuits.
This paper was based on a static pig model and studied the effectiveness of the heating system. The estimated maximum pig speed was probably overly conservative. The hydrocarbon flow rate had potentially negligible an impact
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on the heating process, but this point should be verified. A moving pig model should be developed to further analyze the heating efficiency and the heat loss rate. Further, estimating the practical aspects of building the proposed pigging
8. Acknowledgement
Support for HD was provided by the Nanoparticles for Subsurface Engineer-
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395
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system was beyond the scope of this preliminary study.
ing Industrial Affiliates Program (member companies Nissan Chemical America, Baker Hughes, and Foundation CMG) at the University of Texas at Austin.
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Appendix A. Thermal Resistance of the Nanopaint Layer
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For a cylindrical thermal medium of inner radius rin , outer radius rout , thermal conductivity k, and length L, we have the heat transfer equation 1 d dT kr =0 r dr dr
T = c1 ln r + c2 400
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Integrate to get the temperature field
Assuming the temperature at the inner surface (r = rin ) is Tin and the temper-
c1 =
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ature at the outer surface (r = rout is Tout , we get
Tout − Tin Tout / ln rout − Tin / ln rin , c2 = ln rout − ln rin 1/ ln rout − 1/ ln rin
The radial heat flow is
q=−
1 dT (Tout − Tin ) = −k 2πrL R dr
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where R is the radial thermal resistance. Substituting c1 and c2
−
dT Tout − Tin 1 (Tout − Tin ) = −k 2πrL = −k 2πL R dr ln rout − ln rin
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the radial thermal resistance is
R=
ln (rout /rin ) 2πLk
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The radial thermal resistance of a cylindrical thermal medium of N concen-
tric layers is the linear superposition of resistances of each layer and the contact thermal resistance between the contacting layers:
405
R=
N N X X ln (rout /rin ) ( )i + (Rcontact )i 2πLk i=1 i=1
For the thin layer of nanopaint, ln (rout /rin ) ∼ 1 × 10−5 . For the steel layer, ln(rout /rin ) ∼ 1 × 10−1 . The nanopaint has limited impact on the system 26
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thermal resistance as long as the thermal conductivity is of the same order of
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magnitude with steel or smaller. Since we are proposing a nanopaint with less than 5wt% nanoparticles, we used the thermal conductivity of the wax, which 410
is a better approximation compared to the steel, as the thermal conductivity of the nanopaint.
We have also performed simulations for nanopaint thermal conductivity
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within the range of 2.5 × 10−3 ∼ 2.5 × 101 W/(m · K), which spans a range
2 orders of magnitude smaller than wax to the same order of magnitude as steel. No noticeable change has been observed.
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415
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Highlights: • We numerically investigate a new electromagnetic pigging method combined with a ferromagnetic nanopaint.
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• The simulation results show that a pig emitting magnetic field can heat and melt the precipitated wax in the oil pipeline.
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• The nanopaint with embedded superparamagnetic particles, though as thin as 0.4mm, significantly improves the heating efficiency.
1
S0920-4105(19)30482-6
DOI:
https://doi.org/10.1016/j.petrol.2019.05.028
Reference:
PETROL 6077
To appear in:
Journal of Petroleum Science and Engineering
Received Date: 14 January 2019 Revised Date:
15 April 2019
Accepted Date: 7 May 2019
Please cite this article as: Wang, N., Prodanović, Mas̆., Daigle, H., Nanopaint application for flow assurance with electromagnetic pig, Journal of Petroleum Science and Engineering (2019), doi: https:// doi.org/10.1016/j.petrol.2019.05.028. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Nanopaint Application for Flow Assurance with Electromagnetic Pig Ningyu Wang, Ma˘sa Prodanovi´c⇤, Hugh Daigle
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Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
Abstract
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Wax, hydrates, and asphaltenes precipitate in subsea pipelines and restrict the transportation of hydrocarbons. Traditional wax deposition prevention and dewaxing methods include thermal, chemical, and mechanical approaches. This paper investigates a new electromagnetic pigging method combined with a ferromagnetic nanopaint for potentially high heating efficiency and low maintenance cost. The electromagnetic pig could be inserted into the pipeline to generate induction heat and a nanopaint coating on the inner wall of the pipeline enhances
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the heating e↵ect. To evaluate the e↵ectiveness of the proposed system, the concept of maximum pig speed is introduced. Systems with higher maximum pig speed can dewax a pipeline in shorter time. Numerical models are used to analyze the heating performance for di↵erent system configurations. Simulation
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results show that the proposed pigging tool can e↵ectively heat and melt the deposited wax. The maximum pig speed is a function of the pig induction coil length and radius. The hydraulic shape of the pig does not impact the heating
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e↵ectiveness.
Keywords: nanopaint, superparamagnetic nanoparticles, flow assurance, dewaxing, pigging, subsea pipeline
⇤ Corresponding
author Email address: [email protected] (Ma˘sa Prodanovi´ c)
Preprint submitted to Journal of Petroleum Science and Engineering
January 14, 2019
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Nanopaint Application for Flow Assurance with Electromagnetic Pig Ningyu Wang, Ma˘sa Prodanovi´c∗, Hugh Daigle
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Hildebrand Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, TX 78712, USA
Abstract
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Wax, hydrates, and asphaltenes precipitate in subsea pipelines and restrict the transport of hydrocarbons. Traditional wax prevention and dewaxing methods include thermal, chemical, and mechanical approaches. This paper investigates a new electromagnetic pigging method combined with a ferromagnetic nanopaint for potentially high heating efficiency and low maintenance cost. The electromagnetic pig could be inserted into the pipeline to generate induction heating; a nanopaint coating on the inner wall of the pipeline enhances the heating effect.
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To evaluate the effectiveness of the proposed system, we calculate the maximum pig speed, which is the fastest a pig can move through the pipeline and effectively dislodge wax deposits by heating. Systems with a higher maximum pig speed can dewax a pipeline in a shorter time. Numerical models are used to
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analyze the heating performance for different system configurations. Simulation results show that the proposed pigging tool can effectively heat and melt the deposited wax. The maximum pig speed is a function of the pig induction coil
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length and radius. The hydraulic shape of the pig does not impact the heating effectiveness.
Keywords: nanopaint, superparamagnetic nanoparticles, flow assurance, dewaxing, pigging, subsea pipeline
∗ Corresponding
author Email address: [email protected] (Ma˘sa Prodanovi´ c)
Preprint submitted to Journal of Petroleum Science and Engineering
May 17, 2019
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1. Introduction
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Offshore pipelines are one of the major means of transporting oil from offshore oil facilities and to onshore facilities. As deepwater drilling expands,
pipeline installations move to deeper and deeper water. For instance, pipelines 5
in the Gulf of Mexico, offshore West Africa, offshore Brazil, and offshore Aus-
tralia have entered regions deeper than 1000 m (Randolph et al. (2011)), and
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sometimes deeper than 2300 m (Ekweribe et al. (2008)).
Subsea pipelines are deployed at the sea floor where the typical temperature is as low as about 4o C. To pump the oil and gas through the pipelines, the transported fluids are subjected to pressures of 14.5 MPa (2100 psi) (Ekweribe
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et al. (2008)) or even higher. The low temperature and high pressure can lead to precipitation of hydrates, wax, and asphaltenes from the fluids. Wax deposition in the pipelines is a common and intensively researched phenomenon (Leiroz and Azevedo (2005); Ekweribe et al. (2008); Hilbert (2010); 15
Aiyejina et al. (2011); Semenov (2012); Zheng et al. (2017)). When the oil
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is cooler than 40o C, the wax begins to separate from the oil and deposit in the pipeline (Burger et al. (1981); Roenningsen et al. (1991); Hammami and Raines (1997); Roehner and Hanson (2001)). While the mechanism that leads to the deposition of wax is complex, the temperature required for melting of the 20
deposited wax is about 40-50o C (Aiyejina et al. (2011)).
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Hydrates are a major risk in high-pressure natural gas transport lines (Jassim et al. (2008)). At high pressure and low temperature, such as commonly encountered around subsea pipelines, the wet gas in the pipelines will form gas
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hydrates that attach to the pipelines (Sloan (2003); Koh et al. (2007); Nicholas
25
et al. (2009); Koh and Sum (2010)). Finally, the precipitation and deposition of asphaltenes are more compli-
cated (Zhu et al. (2010); Eskin et al. (2011)) and the treatment required is not addressed in this work. If any of these substances deposit onto the pipeline, flow can be inhibited or
30
even stopped completely, posing safety, environmental, and economic risks. In
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this paper, we focus on oil pipelines, where wax deposition is a major concern.
pipelines but is not directly addressed by our modeling. 1.1. Flow Assurance Methods 35
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Our proposed heating method should also work for hydrates removal in gas
Flow assurance refers to the process of removing deposits and preventing
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future deposition in the pipeline. Methods of flow assurance fall into three cate-
gories: chemical methods, mechanical methods, and thermal methods (Aiyejina et al. (2011); Wang et al. (2014)).
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The chemical approach is focused on preventing the precipitation and deposition of solids by injecting inhibitors or by applying different coatings. The main types of wax inhibitors include ethylene copolymers, comb polymers, wax dispersants, polar crude fractions, and short-chain alkanes (Argo et al. (1997); Haghighi et al. (2009); Aiyejina et al. (2011); Chi et al. (2016); Hashmi and Firoozabadi (2016)). The main types of hydrate inhibitors include polyvinyl45
caprolactam (PVCap) and polyvinylpyrrolidone (PVP). (Lederhos et al. (1996);
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Sloan et al. (1998); Kelland (2006); Koh and Sum (2010); Abrahamsen and Kelland (2018)). The disadvantages of chemical deposition control are the cost associated with continuous injection of chemicals, the corresponding environmental risks, as well as the need to select the inhibitor mixture for the mixed 50
hydrocarbon flowing in a pipeline (Hill et al. (2002); Kondapi and Moe (2013);
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Borden (2013)). Some chemical coatings have been developed to decrease the deposition of wax and hydrates (Liang et al. (2015, 2016); Lahin et al. (2017)).
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Mechanical removal of the deposited sediments typically requires a pipeline inspection gauge, or ’pig’ for short, and the process itself is called ’pigging’(Wang
55
et al. (2015); Huang et al. (2017)). Although pigging has been applied in flow assurance for quite a long time and practical guides are available (Schaefer (1991)), pigging still interferes with the hydrocarbon transport in the pipelines and it is common for the tool to get stuck. Conventional thermal removal of deposits involves electrical heating of the
60
pipelines. This method has the smallest environmental hazard and does not 3
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interfere with the oil transport. Either a conductive layer or a wire or coil
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is applied inside or outside the pipeline to introduce Joule heating (Nysveen et al. (2005)). By heating the deposited wax and hydrates above the melting temperature, they may flow away with the hydrocarbon. 65
The problems of the above thermal removal methods include the maintenance of the heating system and the associated electricity cost. In these systems,
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a coil is permanently deployed in or around the pipeline at the sea floor. The coil may deteriorate and any maintenance of permanent infrastructure under several hundred meters of seawater would be expensive. List (2017) designed and
analyzed a magnetic pig built with no coils but a rotating array of permanent
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magnets driven by a turbine to induce the alternating magnetic field. 1.2. Enhanced Induction Heating with Nanopaint
A nanopaint is a paint or coating that is nanostructured. A nanopaint that contains nanometer size ferromagnetic material is a ferromagnetic nanopaint, 75
and is studied in this work. Nanopaint starts as a ferrofluid, i.e. a stable
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dispersion of superparamagnetic nanoparticles (SMNPs) in a liquid carrier, and solidifies in the process.
Unlike the eddy currents that cause Joule heating in the metal conductors, the heating effect of SMNPs is based on the magnetization of the particle. Mag80
netic materials have magnetic domains inside them. Each magnetic domain has
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its own magnetic moment which aligns with the external magnetic field. When the size of the ferromagnetic material decreases to several tens of nanometers,
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there is only one magnetic domain in the particle. If the external magnetic field is alternating, the magnetic moment of the magnetic domain of the nanoparticle
85
will oscillate with the magnetic field, converting the electromagnetic energy to heat. In the absence of a magnetic field, the individual domain orientations are randomized. This behavior is referred to as superparamagnetism. The resulting heat power density can be much higher than conventional induction heating by eddy currents under the same magnetic field, which will be shown later in this
90
paper. 4
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SMNP heating has been studied in magnetic hyperthermia for many years
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(Chou (1990); Jordan et al. (1993); Sonvico et al. (2005); Fortin et al. (2007); Prigo et al. (2015); Obaidat et al. (2015); Yao et al. (2017)). Magnetic hyperthermia uses an alternating magnetic field to induce heat in magnetic agent, 95
e.g. SMNPs. With proper coating, SMNPs can selectively attach to tumor
cells. Then an external alternating magnetic field is applied so that the SM-
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NPs generate localized heat. The heat can effectively kill tumor cells at above
43o C (Hildebrandt et al. (2002)). The magnetic field frequency used in most research on magnetic hyperthermia is on the order of several hundred thousand Hz, lower than the reported safety threshold (Atkinson et al. (1984); Johnson
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et al. (1993)).
In petroleum engineering, Yahya et al. (2012) discussed heating the reservoir oil with SMNPs and an external alternating magnetic field.
The feasibility of using SMNPs in flow assurance was briefly discussed in the 105
book by Huh et al. (Huh et al. (2019)).
The heating power of unit weight of SMNPs is evaluated by the specific
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absorption rate (SAR) (Chou (1990); Jordan et al. (1993)).
SAR =
2(πmHf τN )2 2 τN KB T V ρ(1 + (2πf )2 )τN
where m is the magnetic moment of the particle, H is the magnetic field
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strength, f is the frequency of the magnetic field, V is the particle volume, KB is the Boltzmann constant, T is the temperature, ρ is the density of the SMNP,
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and τN is the N´eel relaxation time (Rosensweig (1985)). KV
τN = τ0 e KB T
where τ0 is a constant, K is the volumetric magnetic anisotropy. The SAR can be measured in the lab by
SAR =
cp ∆T WN P ∆t
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where cp is the heat capacity, ∆T is the temperature increase, WN P is the mass, and ∆t is the heating time.
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To be applied in pipeline heating, the nanopaint has to withstand the working temperature of the system, which means the SMNP has to keep its superparamagnetism and the paint matrix should not deteriorate. The typical ambi-
ent temperature at the sea floor is 4o C, and a typical melting point of paraffin wax is 42o C. The SMNP becomes paramagnetic above its Curie temperature
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and returns to a superparamagnetic state when the temperature decreases. The Curie temperature of magnetite (F e3 O4 ), a cheap material for SMNP, is over
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550o C (Schult (1970); Maher and Taylor (1988)). Magnetite nanoparticles with Curie temperature of 553o C have been reported by Woltz et al. (2006). The 125
paints being used in oil and gas pipelines can work at up to 85o C (Guan et al. (2005)). Some polypropylene paints are used for transporting hot, erosive fluids up to 170o C (Guidetti et al. (1996)). More paints and coatings under development can work at 600o C (Ho et al. (2014)) or even up to 650o C (Ho and Iverson (2014)). In short, there are no expected operational issues for the nanopaint in pipeline heating.
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Another factor of the nanopaint is its durability. The life and sustainability of the nanopaint is determined by both the SMNP and the paint matrix. Magnetism is a long-term property of materials. The paint itself may last shorter
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than the embedded SMNPs, but little to no maintenance would be required during the limited life. Even if the nanopaint layer were partly destroyed, the heat would still be generated at each of the SMNPs in areas that still had the
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nanopaint.
1.3. Nanopaint Applications in Pipeline Heating Davidson et al. (2012) proposed to paint a layer of superparamagnetic nanopar-
140
ticles in the pipeline to heat the hydrocarbon. They measured the specific absorption rate of different dispersion settings of superparamagnetic nanoparticles and measured the induction heat transferred to the fluid inside the pipe. However, the induction coil in that (laboratory) work was installed outside the 6
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pipe. A similar idea was proposed by Haindade et al. (2012) for dewaxing in production wells. Mehta et al. (Mehta et al. (2014); Mehta (2015)) performed
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experiments to quantify the specific absorption rate of different superparamagnetic nanoparticles for the coil placed outside the pipeline.
Mehta (2015) first proposed injecting an electromagnetic coil in a pipeline painted with nanopaint for wax removal in her MS thesis. This work was mostly
experimental. She set up a numerical model of the electromagnetic pigging
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process and concluded that higher current and higher nanoparticle concentration in the nanopaint both accelerate the wax melting process. The numerical model
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was preliminary with fewer than 10 total simulations and the oil phase was modeled as static. Further, these simulations were not published in the peer 155
reviewed literature before.
In this paper, we perform a thorough study of induction oil shape (radius/length ratio) with over 240 simulations, and improve modeling of oil (in other words, we incorporate the cooling effect of flowing hydrocarbon).
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2. Electromagnetic Pigs
The most straightforward way to generate an alternating magnetic field inside the pipeline is to place a coil within. The coil should be packed in a pig together with proper power units and control units. There are countless designs
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for pigs (Tiratsoo (1992); Okamoto et al. (1999); Nguyen et al. (2001); Han et al. (2004); Hiltscher et al. (2006); Tur and Garthwaite (2010); Shukla and 165
Karki (2016)). Two simple cylindrical pigs, one hollow and one non-hollow, are
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studied in this research, as shown in Fig. 1. The cross section of the non-hollow pig is shown in Fig. 2. The power unit and the control unit are not shown. The polymer support helps decelerate the pig and keep it from hitting the pipe wall. If we neglect the distance between adjacent wires in the coil, the magnetic
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field of a co-axial coil in the pipeline is axisymmetric, as shown in Fig. 3. As the pig travels through the pipeline, the alternating magnetic field heats the surrounding metallic materials axisymmetrically. This induction heat is then
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(b)
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Figure 1: Cylindrical pig designs. (a) hollow. (b) non-hollow.
transported to the precipitated material. With enough heat, the material will melt from the layer contacting the pipe wall. Once the inner layer of material 175
melts, it no longer adheres to the pipe wall and will peel off due to the shear
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forces of the flowing hydrocarbon in the pipeline. This process is similar to the conventional pigging operation since they both involve the deposited material peeling off from the pipeline when the pig passes. Thus the operation proposed
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in this paper can be called electromagnetic pigging.
3. Coupled Modeling of Flow, Heat Transfer, and Magnetic Field In an oil pipeline, coupled flow and heat transfer happens when the oil flows
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through the pipeline. A k- turbulent flow model (Chac´on Rebollo and Lewandowski (2014)) is
used to describe the flow of the oil.
ρ
∂~u 2 + ρ(~u · ∇)~u = ∇ · [−pI + (µ + µT )(∇~u + (∇~u)T ) − ρkI)] + F~ ∂t 3 ρ∇ · ~u = 0
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A
SECTION A-A
Figure 2: Side view and the cross section labeled A-A’ of the hollow cylindrical pig.
ρ ρ
∂k µT + ρ(~u · ∇)k = ∇ · [(µ + )∇k] + Pk − ρ ∂t σk
∂ µT 2 + ρ(~u · ∇) = ∇ · [(µ + )∇] + C1 Pk − C2 ρ ∂t σ k k
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= ep
µT = ρCµ
k2
Pk = µT [∇~u : (∇~u + (∇~u)T )]
where k is the turbulent kinetic energy, is the turbulent dissipation, ~u is
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the velocity, rho is the density, I is the unit tensor, µ is the viscosity, µT is the turbulent viscosity, F~ is the body force, σk , σ , C1 , C2 , and Cµ are constants.
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The oil is much warmer than the sea water. The heat transfer can be de-
scribed by
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ρCp
∂T + ρCp ~u · T = ∇ · (k∇T ) + Q + Wp ∂t
where ρ is the density, Cp is the heat capacity at constant pressure, T is the
temperature, t is the time, ~u is the flow rate, Q is the heat input, and Wp is the external work.
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mT 0.2
35
m -0.2
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0
30
-0.4
0.6
m
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25
0.2
0
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0.2
y
15
10
5
0
x
m
-0.2
0
Figure 3: The magnetic flux density (B) in the pipeline.
At the interfaces between different media, the temperature is continuous.
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At the wax-oil interface, the heat flux is
q = hoil−wax (Toil − Twax )
At the pipe-sea water interface, the heat flux is
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q = hpipe−sea (Tpipe − Tsea )
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When the pig is injected into the pipeline, an additional magnetic field is introduced by the alternating current in the induction coil. The electromagnetic field is described by ~ + ∇ × (µ−1 µ−1 B) ~ − σ~v × B ~ = J~e (jωσ − ω 2 0 r )A r 0 ~ =∇×A ~ B
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where j is the imaginary unit, ω is the angular frequency of the current, σ 200
is the electrical conductivity, 0 is the vacuum permittivity, r is the relative
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~ is the vector potential, µ0 is the vacuum permeability, µr is the permittivity, A ~ is the magnetic flux density, ~v is the velocity relative magnetic permeability, B of the circuit, J~e is the current density.
The magnetic field induces heat in the nanopaint. The induction heat power density is
q=
1 SAR ρ
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where ρ is the density of the nanopaint, SAR is the specific absorption rate. The induction heat in the metal is
q=
1 ~ ·H ~ ∗) Re(jω B 2
~ = H/(µ ~ ~∗ where B 0 µr ) is the magnetic flux density, H is the conjugate of ~ the magnetic field strength H.
Numerical implementation of the above equations exists in COMSOL soft-
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ware, which we use in this work. Our goal is to evaluate when the temperature of wax reaches melting point, and we do not specifically model what happens to the wax after that (it is presumably carried away by oil).
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4. Geometry Description and Model Parameters The pigs shown in Fig. 1 are modeled in the commercial software COMSOL.
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The model for the hollow pig is shown in Fig. 4. The pipeline in this model has an insulation layer (2) between the two steel layers (1) to decrease the heat loss to the seawater (3). The nanopaint (4) is painted on the inner wall of the pipeline. The oil (5) flows through the pipeline. We assume wax (6) precipitated
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and deposited on the nanopaint layer. We also assume the pig (7) moves along the pipe axis. The induction coil (8) is inside the pig (7). The geometric and physical parameters are listed in Table 1 and Table 2. The pig inner channel exists only in the hollow pig model. The coil radius and 11
(4)
0.6
(5)
(6)
0.4
(7)
(1)
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(8)
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0.7 m
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0
0
0.1
0.2
0.3
0.4
0.5 m
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Figure 4: (1) Pipeline steel layer. (2) Pipeline insulation layer. (3) Seawater. (4) Nanopaint layer. (5) Oil. (6) Wax deposited in the pipeline. (7) Pig. (8) Induction coil.
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coil length will change, but the distance between the coil and the pig shell is the same. In the hollow pig, the difference between pig diameter and inner channel
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diameter are kept constant.
We perform simulations for Reynolds number 5.95 × 104 , in particular for a
fluid of temperature 25o C, density 746kg/m3 , viscosity 5.02 × 104 P a · s (0.5cp), nominal velocity 0.1m/s and in a tube of diameter 0.4m. Depending on the
assumed oil flowing in the pipe: e.g. light oil of density 738.9kg/m3 (60o AP I)
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and viscosity 1.6 × 10−3 (1.6cp), to heavy oil of density 960.6kg/m3 (15.8o AP I) and viscosity 2.003P a · s (2003cp), the simulation conditions are equivalent to
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oil velocity range of 0.39m/s to 310m/s. Note that thermal properties of the simulation fluid are heat capacity at constant pressure of 2082J/kg · K, thermal 235
conductivity 0.1156W/kg · K. And they do not change much for light or heavy oil. Thus the assumed fluid velocity if not as restrictive as it seems. We are modeling relative movement where pig is fixed in space and the oil is moving around it. At time zero, a 300A, 500kHz alternating current is applied in the induction coil. There are 25turns in the coil. These values are selected within the range of published work (Mehta (2015)). Technically speaking, the
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current multiplied by the number of turns is what is fixing the maximum magnetic field strength around the coil to the single value examined in this work. From the numerical standpoint, we model the coil as a cylinder without going
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into the number of turns it has (it could have had 100A and 75turns, for example, with the same result). For that maximum field strength, we then focus on changing the shape of the field (i.e., by changing the normalized radius and
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length of the coil). The maximum field strength ultimately determines required power supply to the pig, which is an important practical design parameter but not to be researched at this stage.
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Nanoparticles, when dispersed in the paint, can significantly change the ther-
mal conductivity of the mixture and the thermal conductance of the nanopaint layer. However, due to the fact that the thickness of the paint layer is three orders of magnitude smaller than the thickness of the pipeline, the nanopaint has negligible impact on the thermal conductance of the painted pipeline system. A 13
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value
pipeline outer diameter
0.8 [m]
pipeline inner diameter
0.4 [m]
thickness of nanopaint
0.4 [mm]
thickness of wax
5 [mm]
thickness of insulation layer
0.1 [m]
thickness of outer steel layer
0.05 [m]
thickness of inner steel layer
0.05 [m]
pig length
0.1525 [m]
0.22 [m]
pig inner channel diameter
0.0625 [m]
induction coil diameter
0.06 [m]
induction coil length
0.18 [m]
detailed explanation can be found in Appendix A.
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pig diameter
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Table 1: geometrical parameters
5. Evaluation of Heating Effectiveness and Maximum Pig Speed The pig travels in the pipeline with the flowing product. To evaluate whether
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the pig can effectively melt and remove the wax, we define the maximum pig speed, which is the fastest speed the pig can travel and melt a wax deposit. If the pig travels slower than the maximum pig speed, the pig can effectively melt
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the wax adhering to the pipeline and let it peel off in the flowing oil or gas. This maximum speed provides a valuable design parameter for hydraulic design. This concept is illustrated using the simulation results for the pig described in
Table 1. The magnetic flux density and temperature field for the pig described
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in Table 1 after 150s heating are shown in Fig. 5. The white zone in the temperature field is where the temperature is above the wax melting point. The corresponding heating power density in the nanopaint and at the inner 14
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Table 2: physical parameters of solids
coil
steel
insulation
wax
nanopaint
relative magnetic permeability
1
1
1
1
2.1
relative electrical permittivity
1
1
1
1
2.1
electrical conductivity [S/m]
6.0e7
4.03e6
2.50e-8
1.0e-8
1.0e-8
heat capacity [J/(kg·K)]
385
475
2000
3430
3430
density [kg/m3 ]
8700
7850
750
900
900
thermal conductivity [W/(m·K]
400
44.5
0.17
0.25
0.25
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steel surface of the pipeline is shown in Fig. 6. The peak SMNP heating power density generated by nanopaint is 450% higher than the induction heat in the 270
adjacent steel layer in the pipeline.
Melting Zone. The melting zone is any zone in the wax layer that is hotter
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than the melting temperature. The melting zone at t = 150s is shown in Fig. 7 accompanied by the heating power in the nanopaint. The heat is transferred to the wax across the wax-nanopaint interface, so the wax near this interface 275
melts first. Thus the melting zone length can be defined as the width of the melting zone at the wax-nanopaint interface. The melting zone depth is defined
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as the distance that the melting zone extends into the wax layer. After 150 s of heating, the melting zone grew to what is shown in Fig. 7.
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Minimum Melting Zone Depth and Minimum Melting Zone Length. When the
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melting zone depth reaches a threshold, the wax will be peeled off by the oil or gas flow. This depth threshold is defined as the minimum melting depth and can be measured in the lab. The corresponding melting zone length is the minimum melting zone length. The melting zone length is a measure of the heating locality. Long melting zone length indicates both heating power
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dispersion and heat dissipation.
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Figure 5: Simulation result of (a) magnetic flux density and (b) temperature at t = 150s. The white zone is where the temperature is above the wax melting point.
Minimum Heating Time. If the pig is moving, the local induction heat power
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density will change with time. As long as the local heating power is over a threshold for a long enough time, the local wax can be melted to the minimum melting depth. This time threshold is defined as the minimum heating time. Thus, the maximum pig speed can be defined as
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maximum pig speed =
minimum melting zone length minimum heating time
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6. Simulation Results
Pigs with different coil geometries were modeled in the commercial multi-
physics simulation software COMSOL (version 5.3a). Each model was simulated using the frequency-transient solver in COMSOL for 200 s. The modules
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required to implement models presented here are ’Turbulent Flow, k- (spf)’, ’Heat Transfer in Solids (ht)’, ’Heat Transfer in Fluids (ht)’, and ’Magnetic Fields (mf)’. The following ’Multiphysics’ modules are used for coupling them: 16
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Figure 6: Heating power density near the pipe-nanopaint interface. Blue solid line: the SMNP heating in the nanopaint. Red dashed line: the conventional induction heating in the steel pipe.
’Non-Isothermal Flow (nitf)’, ’Electromagnetic Heat Source (emh)’, ’Boundary
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Electromagnetic Heat Source (bemh)’, and ’Temperature Coupling (tc)’. One difficulty in finding the melting zone is that, once the wax is melted, it is no longer a solid phase and thus the original model should be dynamically changed as the wax is melting. To compensate for this inaccuracy, we focus on very shallow melting zone depths. The melting result is studied at minimum
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melting depths of 1, 3, and 5 layers of mesh cells in the wax nearest to the nanopaint, corresponding to 0.000575, 0.00173, and 0.002885 times the pipeline
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inner radius.
The simulation results are shown in Fig. 8. The dependence of minimum
heating time and melting zone length on the coil radius and coil length are similar at different assumed minimum melting depths. The results are the same
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for both the hollow and non-hollow pigs, which makes sense given that in both cases the material (or fluid) inside the pig is modeled as non-magnetic. The heating is faster and more localized with coils of shorter axial length and larger radius. 17
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Figure 7: The melting zone at t = 150s and the corresponding heating power density in nanopaint. The melting zone is a zone in the wax layer that is hotter than the melting
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temperature.
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Figure 8: (a) Minimum heating time and (b) melting zone length measured at different assumed minimum melting depths for a pipeline with nanopaint, hollow and non-hollow pigs
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alike. The coil radius, the coil length, the minimum melting depth, and the melting zone length are normalized with respect to the pipeline inner radius. The three studied minimum melting depths correspond to layers 1, 3, and 5 mesh cells deep from the wax-nanopaint in-
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terface into the wax. White color in the minimum heating time graph means the wax did not reach the melting point within the 200 s of simulation time at this assumed minimum melting depth, coil radius, and coil length combination. Zero melting zone length means the wax did not reach the melting point during the simulation.
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The minimum heating time and melting zone length measured at an assumed minimum melting length of 5 mesh cells deep or 0.002885r are further analyzed
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315
to generate formulae by least squares fitting. The quality of the generated
formulae is measured by the R2 value, where R2 = 1 means perfect fitting or interpolating and R2 = 0 refers to a total failure.
Minimum Heating Time. The minimum heating time is shown in Fig. 9. All the lengths are normalized with respect to the pipeline inner radius (0.2 m).
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320
The results for the hollow and non-hollow pigs are the same. It can be seen that the smaller the coil length and the larger the coil radius, the faster the wax
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melts. The results can be fitted by the following formula: 3
time = a + b · ec/r · ed·L
where r is the normalized coil radius and L is the normalized coil length. 325
The fitted coefficients are a = 4.837, b = 0.02989, c = 0.07873, d = 2.062. The fitting quality is R2 = 0.9939.
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The 1/r3 term is motivated by the decline of the magnetic field of a dipole/coil with distance. The time does not reach zero due to the finite resolution of the numerical simulation. 330
Minimum Melting Zone Length. The minimum melting zone length is shown
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in Fig. 10. All the lengths are normalized with respect to the pipeline inner radius (0.2 m). The results for the hollow and non-hollow pigs are the same. It can be seen that shorter coil length leads to shorter or more localized heating,
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while the effect of the coil radius is negligible. The results can be fitted by the
335
following formula:
length = f + g · r + h · L
where r is the normalized coil radius and L is the normalized coil length.
The fitted coefficients are f = 1.998, g = 0.001028, h = 1.498. The fitting
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80 60 40 20 0 0.4 0.6
0.2
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0.8
1
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coil radius
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time [s]
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coil length
Figure 9: Minimum heating time for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius and coil length are normalized with respect to the pipeline inner radius (0.2 m).
quality is measured by R2 = 1. If the fitting parameter g = 0, the result is still
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R2 = 1.
It is interesting that the melting zone length is at least 2 times the inner radius of the pipeline, though the mechanism behind this phenomenon is beyond the scope of this paper.
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Maximum Pig Speed. The maximum pig speed is shown in Fig. 10. All the lengths are normalized with respect to the pipeline inner radius (0.2 m). The results for the hollow and non-hollow pigs are the same. It can be seen that the smaller the coil radius and the larger the coil length, the faster the pig may
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345
travel. The results can be fitted by the following formula which is the division of the minimum melting zone length by the minimum heating time:
speed =
f +g·r+h·L a + b · ec/R3 · ed·L
or
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3 2 0.4 0.6
0.2
0.4
0.6
0.8
1
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coil radius
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length
4
coil length
Figure 10: Minimum melting zone length for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius, coil length, and minimum melting zone length are normalized by the pipeline
speed =
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(f /a) + (g/a) · R + (h/a) · L 1 + (b/a) · ec/R3 · ed·L
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inner radius 0.2m.
where r is the normalized coil radius and L is the normalized coil length. The fitted coefficients are a = 4.837, b = 0.02989, c = 0.07873, d = 2.062, f = 1.998, g = 0.001028, h = 1.498. The fitting quality is measured by R2 = 0.9914. When
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g = 0, R2 drops to 0.9883. Impact of Pig Hydraulic Shape. From the above simulations, the results for hollow and non-hollow pigs are exactly the same. This indicates that the hydraulic
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shape of the pig doesn’t have a big impact on the heating process. Impact of Hydrocarbon Flow Rate. The hydraulic shape of the pig impacts the flow field of the hydrocarbon near the pig. The flow in the annulus between the pig and the pipeline in the case of the hollow pig is slower than in the case of
360
the non-hollow pig, leading to weaker heat dissipation from the heated wax to
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0.5
0 1 0.8 0.6 0.4 0.2
0.6
0.4
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coil length
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speed [1/s]
1
coil radius
Figure 11: Maximum pig speed for hollow and non-hollow pigs. The dots are the simulation results for different coil radii and coil lengths and the surface is the fitting result. The coil radius, coil length, and velocity are normalized with respect to the pipeline inner radius (0.2 m).
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the hydrocarbon. Since the impact of the pig’s hydraulic shape is small, it is possible that the impact of the flow rate on the heating process is limited. Impact of Nanopaint. The heating power of eddy currents in the steel pipe is much lower than that of the nanopaint, as shown in Fig. 6. We performed the same simulation for models with exactly the same pipe and pig but no
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nanopaint, of which the results are shown in Fig. 12. Only several pigs with the largest possible radius created a deep enough melting zone within the 200 s
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simulation time, which would be too slow for pigging.
7. Conclusion
370
We developed a numerical model to investigate the benefits of superpara-
magnetic nanoparticles embedded in a nanopaint coating for flow assurance applications in subsea pipelines using a pig traveling through the pipeline and emitting an electromagnetic field.
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Figure 12: (a) Minimum heating time and (b) melting zone length measured at different assumed minimum melting depths for a pipeline without nanopaint, hollow and non-hollow
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pigs alike. The coil radius, the coil length, the minimum melting depth, and the melting zone length are normalized with respect to the pipeline inner radius. The three studied minimum melting depths correspond to depths of 1, 3, and 5 layers of mesh cells from the wax-nanopaint
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interface into the wax. White color in the minimum heating time graph means the wax did not reach the melting point within the 200 s simulation time at this assumed minimum melting depth, coil radius, and coil length combination. Zero melting zone length means the wax did not reach the melting point.
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The simulation results showed that a pig emitting an electromagnetic field could heat and melt the precipitated wax in the pipeline. To evaluate the heat-
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375
ing effectiveness and optimize the pig, the maximum pig speed was calculated. Longer and fatter coils led to higher maximum pig speed and better heating
effectiveness. Formulae were generated to predict the minimum melting zone length and minimum heating time for a given coil length and coil radius combination.
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380
The nanopaint, though as thin as 0.4 mm, significantly improved the heating efficiency. The heating power density in the nanopaint was several times higher
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than in the steel pipe. For the same pig and pipe, the nanopaint could decrease the minimum melting time by two orders of magnitude. 385
The hydraulic shape of the pig had little impact on the heating process. The only requirement for the pig was to have enough inner volume for the coil, battery, and control circuits.
This paper was based on a static pig model and studied the effectiveness of the heating system. The estimated maximum pig speed was probably overly conservative. The hydrocarbon flow rate had potentially negligible an impact
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on the heating process, but this point should be verified. A moving pig model should be developed to further analyze the heating efficiency and the heat loss rate. Further, estimating the practical aspects of building the proposed pigging
8. Acknowledgement
Support for HD was provided by the Nanoparticles for Subsurface Engineer-
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395
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system was beyond the scope of this preliminary study.
ing Industrial Affiliates Program (member companies Nissan Chemical America, Baker Hughes, and Foundation CMG) at the University of Texas at Austin.
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Appendix A. Thermal Resistance of the Nanopaint Layer
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For a cylindrical thermal medium of inner radius rin , outer radius rout , thermal conductivity k, and length L, we have the heat transfer equation 1 d dT kr =0 r dr dr
T = c1 ln r + c2 400
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Integrate to get the temperature field
Assuming the temperature at the inner surface (r = rin ) is Tin and the temper-
c1 =
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ature at the outer surface (r = rout is Tout , we get
Tout − Tin Tout / ln rout − Tin / ln rin , c2 = ln rout − ln rin 1/ ln rout − 1/ ln rin
The radial heat flow is
q=−
1 dT (Tout − Tin ) = −k 2πrL R dr
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where R is the radial thermal resistance. Substituting c1 and c2
−
dT Tout − Tin 1 (Tout − Tin ) = −k 2πrL = −k 2πL R dr ln rout − ln rin
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the radial thermal resistance is
R=
ln (rout /rin ) 2πLk
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The radial thermal resistance of a cylindrical thermal medium of N concen-
tric layers is the linear superposition of resistances of each layer and the contact thermal resistance between the contacting layers:
405
R=
N N X X ln (rout /rin ) ( )i + (Rcontact )i 2πLk i=1 i=1
For the thin layer of nanopaint, ln (rout /rin ) ∼ 1 × 10−5 . For the steel layer, ln(rout /rin ) ∼ 1 × 10−1 . The nanopaint has limited impact on the system 26
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thermal resistance as long as the thermal conductivity is of the same order of
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magnitude with steel or smaller. Since we are proposing a nanopaint with less than 5wt% nanoparticles, we used the thermal conductivity of the wax, which 410
is a better approximation compared to the steel, as the thermal conductivity of the nanopaint.
We have also performed simulations for nanopaint thermal conductivity
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within the range of 2.5 × 10−3 ∼ 2.5 × 101 W/(m · K), which spans a range
2 orders of magnitude smaller than wax to the same order of magnitude as steel. No noticeable change has been observed.
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415
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Highlights: • We numerically investigate a new electromagnetic pigging method combined with a ferromagnetic nanopaint.
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• The simulation results show that a pig emitting magnetic field can heat and melt the precipitated wax in the oil pipeline.
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• The nanopaint with embedded superparamagnetic particles, though as thin as 0.4mm, significantly improves the heating efficiency.
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