IPTC 13420
Ca Studies on Simulation of Wax Deposition in Pipelines
Shu Pan, Jack Zhu, Dan Zhang, Ali Razouki, and Mike Talbot/Schlumberger; Scott Wierzchowski/Shell
Copyright 2009, International Petroleum Technology Conference
This paper was prepared for prentation at the International Petroleum Technology Conference held in Doha, Qatar, 7–9 December 2009.
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Abstract
The problem cad by wax deposition during production and transportation of waxy oil has been receiving an increasing attention from the industry, especially with the off-shore projects expansion recently. Due to the high cost of tho projects, an accurate modelling on wax precipitation and deposition is imperatively required to facilitate the design, development, and operation of tho projects. While the wax precipitation models depict the thermodynamic behaviour of waxy oil, the modelling of wax deposition in production facilities and pipelines focus on how soon wax would accumulate. The wax deposition simulation appears to be a more challenging task due to the high complexity and limited measured data available in the open literature. In this work, a compositional si
mulator is introduced to simulate the wax deposition in a pipeline. This model is founded on a thermodynamics model from our previous work and equipped with major wax deposition mechanisms as well as tuning function. Through four ca studies, the model, with its prediction and tuning capability, has demonstrated a practical tool in flow assurance simulation. The results also suggest that a promising methodology can be applied in flow assurance study when the simulator is tuned with measurements from the high pressure deposition cell.
2 IPTC 13420 Introduction
The problem caud by wax deposition during production and transportation of waxy oil has been receiving an increasing
attention from the oil and gas industry with the rapid expansion of off shore projects. This problem mainly happens when the
oil is cooled to a temperature below wax appearance temperature (WAT) due to lower environment temperature. Under such
a condition, wax solid will precipitate out and may accumulate in the pipeline and eventually plug the pipeline. Therefore, an
accurate modeling on wax precipitation and deposition is imperatively required to put this hazard situation under control and
facilitate the design, development, and operation of off shore projects.
A reliable wax precipitation model provides the thermodynamic properties and the driving forces to wax deposition model
and therefore rves as the foundation of flow assurance simulation. A couple of thermodynamic models have been propod
to depict wax precipitation phenomenon in the literature (Pedern [1], Lira-Galeana et al. [2], Pan et al [3], Coutinho et al [4]
and Zuo etal [5] [6]). The Zuo’s model has shown a good agreement with experimental data by adopting a framework with
the Peng-Robinson equation of state for describing the nonideality of the vapor and liquid phas and the predictive universal
quasi-chemical (UNIQUAC) for the solid (wax) pha. This model has been incorporated into a compositional flow
assurance simulator and will be ud in this work.
The modeling of wax deposition in production facilities and pipelines focus on how soon wax would accumulate on the
wall of pipeline. Compared to wax precipitation modeling, the wax deposition simulation demonstrates a more challenging
task due to the higher complexity and limited measured data available in the open literature. Many rearchers (Brown et al
[7], Burger et al [8], Svendn et al [9], Singh et al [10][11], Lindeloof et al [12], Edmonds et al [13], Rygg et al [14],
Matzain [15], etc.) have contributed to the modeling of wax deposition in pipeline. Their work revealed that a number of
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mechanisms, such as, molecular diffusion, shear dispersion, shear reduction, Brownian diffusion, thermophoresis, and
internal diffusion, appear to be responsible for the radial wax deposition in a pipeline. However, a quantitative prediction of
wax deposition remains to be a challenge.
In this work, an effort has been made to simulate wax deposition in a pipeline using a compositional wax deposition
simulator. A brief description of model is given, followed by four ca studies. In ca study 1, two alternative approaches
will be adopted to predict the wax deposition due to molecular diffusion in laminar boundary sublayer, which is widely
accepted as dominant mechanism for wax deposition in pipeline. The prediction results are compared against measured flow
loop data to justify current model. In ca study 2, the model is tuned using wax deposition data scaled up from a high
pressure deposition cell measurement. The tuned parameters are ud to predict the ca from the high pressure deposition
cell measurement. In ca study 3, one full scale pipeline ca is simulated either with or without the tuning parameters
obtained from ca study 2, and a comparison between the simulation results and data reported from literature is given. In
ca study 4, a scaling model is ud to simulate wax deposition in two pha flow. The results are prented together with a
single pha flow simulation. Some conclusions are summarized afterwards.
Model description
In this work, the pipeline is divided into gments over which the heat transfer and pressure drop are calculated. Since the
amount of wax deposition is very small relative to the total fluid within a reasonable time step, a steady state flow is assumed.
With this assumption, the pressure and temperature profile are obtained from the fluid dynamics and heat transfer modules,
and ud for further modeling of wax deposition on each gment.
As above mentioned, the modeling of wax deposition is established on a thermodynamic model by Zuo et al. [5] [6]. The
basic assumption that wax formers are normal paraffins heavier than nC17 has been inherited in the wax deposition model.寡人之于国也原文及翻译及注释
Therefore the wax deposition layer in a pipeline may be considered as a gel of normal paraffin solid and entrapped oil. The
volume fraction of entrapped oil in deposition layer is defined as porosity, which is usually found within a range of 40% to
90%. The porosity is introduced as an important input parameter for mass transfer calculation as shown below. The mass
transfer rate, i. e., the rate of wax deposition, is assumed to be a summation of mass transfer rate due to two major
mechanisms, molecular diffusion and shear removal.
1. Molecular diffusion
As the dominant mechanism of wax deposition, molecular diffusion in laminar boundary sublayer is considered in each ca
study of this work. Driven by the radial concentration gradient in oil pha, the deposition rate of wax formers (n-paraffins)
due to molecular diffusion may be calculated by the product of diffusion coefficient and the concentration gradient at the wall
as shown below, w i i i dr dC D J ⎟⎠⎞⎜⎝⎛−= (1)
IPTC 13420 3
where referes to each wax former, is the mass transfer rate (mol/m 2/s) due to molecular diffusion of component ,
is the diffusion coefficient (m 2/s) and i i J i i D w i dr dC ⎟⎠⎞⎜
⎝⎛ is the concentration gradient at the wall (1/m). Two approaches are usually adopted to calculate w
i dr dC ⎟⎠⎞⎜⎝⎛. The first approach is called heat-mass analogy method. In this method, the driving force is calculated through heat-mass analogy using concentration in bulk fluid and at the wall. The latter is esntially the saturate concentration of wax formers at the wall temperature.
怎样拆分单元格
i w
i C R Sh dr dC Δ−=⎟⎠⎞⎜⎝⎛2 (2) Here is the Sherwood number, Sh R is the pipeline inner radius, and i C Δ is the difference between concentrations in bulk
fluid and saturate concentration in oil at the wall temperature.
The cond approach is called solubility method, in which w
i dr dC ⎟⎠⎞⎜⎝⎛ is calculated through temperature gradient at the wall by assuming that wax formers are saturate everywhere in the oil near the wall. In other words, the temperature gradient will
determine the concentration gradient at the wall by
w
s i w i dr dT dT dC dr dC ⎟⎠⎞⎜⎝⎛⎟⎟⎠⎞⎜⎜⎝⎛=⎟⎠⎞⎜⎝⎛ (3) where w
dr dT ⎟⎠⎞⎜⎝⎛is the temperature gradient at the wall and is the saturate concentration of wax former i at temperature s i C T .
A study by Venkatesan et al [16] suggested that the actual concentration profile is located between the profiles from the
two approaches. That is, the solubility method may predict a lower limit while the heat-mass analogy may bring an upper
limit for actual concentration gradient at the wall.
In additional to the driving force, in this model the diffusion coefficients of tho wax formers (n-paraffins) are
approximated by the diffusion coefficients in infinite dilutions (i. e., a solution in which the concentration of component of
interest is approaching zero). This approximation can be justified by the fact that the solubility of wax formers in oil tend to
be of a low value. Like many other wax deposition models, the popular Hayduk-Minhas method [17] is ud for this
calculation.
i D
After obtaining the deposition rate of normal paraffins due to molecular diffusion, one need turn to tho non-wax formers. It
is worth mentioning that although the deposition rate of n-paraffin solid could be purely predicted from eq. (1)-(3), the
美女图片真人deposition rate of other components has to be obtained by compromisingly introducing wax porosity as an input parameter.
To be more specific, in this work the overall deposition rate due to molecular diffusion is scaled up from the deposition rate
of n-paraffins using the given wax porosity. This compromi comes from an implied assumption behind eq. (1) that the
molecular diffusion rate of a certain component is proportional to the concentration of this component itlf, which is valid
only for components with concentration approaching zero. On the other hand, let us suppo that this assumption can be
applied to each component. Then if wax deposition exists only the wax formers move towards the wall, while the remaining
components move in the opposite direction, since at the wall n-paraffins have concentration lower than concentration in bulk
fluid and the remaining components correspondingly have higher due to the precipitation of n-paraffins. This will result in
zero porosity, which is contradicted with the obrvation in experiments.
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2. Shear removal
When acting on a wax gel layer, the shear stress may slough off wax pieces from the deposition layer. This effect ems to be
the major mechanism to reduce the deposit thickness in most of cas. The negative mass transfer rate due to shear removal
may be related to the shear stress, thickness of wax gel layer, and strength of wax gel yield stress. Kern and Seaton [18]
have suggested that this term is proportional to the shear stress and deposit thickness. Recently it has been found by
sr J
4 IPTC 13420 Venkatesan [19] that the wax gel yield stress might be proportional to .2ωhere 3
, w ω is the mass fraction of wax in gel layer.
This finding has enabled Edmonds et al [13] to extend Kern Seaton’s work as 3.2/ωδτk J sr =
(4) where δ
is the deposit thickness, τis the shear stress and is a parameter. k
In this work, an additional parameter has been introduced to eq. (4) for a better fitting function, inspired by Venkatesan’s
[19] fitting that may be proportional to , instead of a sr J 9.1τ
τ. Hence may be expresd by sr J 3.2/ωδτa sr k J =
(5)
For a single pha flow, the mass transfer rates obtained from the above two mechanisms can be converted directly to the
wax deposition thickness. But the same strategy can not be applied to a two-pha flow region directly, since the wax
deposition in a two-pha flow may only occur at the oil wet interface and depend on veral two-pha flow characteristics.
Rearchers such as Rygg et al. [14] or Matzain et al. [15], have suggested that in additional to appropriate two-pha fluid
dynamics and heat transfer models, a scaling method, which incorporates characteristic parameters of two-pha flow, has to
been applied to scale wax deposition in a two-pha flow from a single-pha model. Following their strategy, a first
approximation has been taken in this work and a proposal was made that the wax deposition in two-pha flow is related to
liquid holdup and a ratio of wetting surface by
sp tp J H J βαΦ=
(6) Here is the mass transfer rate using single pha deposition model, sp J H is the liquid holdup,Φ is the ratio of wetting
surface, αand β are tuning parameters with a default value 0.5.
Results and Discussion
In this work, the model described above has been applied to four ca studies. The first two cas are bad on lab scale
measurements and the last two cas are given for full scale pipeline simulations.
CASE STUDY 1
Hernandez [20] conducted an investigation on the wax deposition under single-pha flow conditions using the flow loops
from the University of Tulsa. Two fluids, Garden Banks and South Pelto, were ud to study the effects of the flow rate and
the temperature difference on the wax deposition. Bad on the fluid and flow loops information given in ref. [20], a couple
of simulations have been performed using the propod model. In the simulations, only the molecular diffusion mechanism
is taken into account without any tuning, whereas the shear removal term is not considered. Two alternative approaches, heat
mass analogy method and solubility method, have been applied.
The simulation results are given in figs. (1)-(6). Figs. (1)-(3) compare the simulation results to the measured data from tests
for Garden Banks fluid, while Figs (4)-(6) give the comparison for South Pelto fluid. In the figures, markers reprent the
measured data, solid lines give the results from simulation using the heat-mass analogy method, and dash-dot lines refer to考研数学分数线
the simulation using the solubility method. Different markers indicate the deposition thickness measured by different
methods. The figures (1)-(6) show that the propod model provide a fare agreement with the experimental data. The
simulations using the heat-mass analogy method generally provide better predictions than the solubility method. Figs. (4)-(6)
show that for South Pelto fluid the heat-mass analogy method overpredicts the wax deposition, while the solubility method
tends to underpredict the deposition. This obrvation has confirmed the theoretical analysis given by Venkatesan et al [16].
In most cas of Garden Banks fluid, as shown in Figs. (1)-(3), the simulation results using heat-mass analogy lie among data
measured by different methods. This slight inconsistence with Venkatesan’ analysis might be caud by the deviation from
the thermodynamics or the transport property models. It might also be a result from uncertainties in the flow loop
measurements.
CASE STUDY 2
The experimental results given in ca 1 have suggested that the measurement of deposition thickness in flow loop test could
have significant discrepancies between results from the different measurement methods or from the different runs under the
same condition. This situation may come from the difficulties in maintaining an ideal operation condition for flow loops.
The discrepancies bring a non-negligible uncertainness if the data are ud for parameter tuning. Meanwhile, another tool,
the high pressure deposition cell has shown a promising performance in the study of wax deposition by scaling the cell data
to a pipeline gment [21]. Since the measured data from high pressure deposition are obtained with a relative small
discrepancy, the data may provide a good source to demonstrate the tuning function of the propod model.
IPTC 13420 5 In the propod model, the overall deposition rate can be given as, 3.22121/ωδτa i w i i sr i i overall C dr dC D C J C J C J ∑∑−⎟⎠⎞⎜⎝⎛−=−= (7)
Eq. (7) implies that three tuning parameters,, and may be ud for tuning. However, as three data points are provided in ref. [21], only two of the three parameters can be ud for the tuning. Following Venkatesan’s suggestion, is proportional to , parameter a has been fixed to be 1.9 and parameters,, are open for tuning.
1C 2C a sr J
我的幸福在哪里
9.1τ1C C 2
This ca study has been conducted using both the heat-mass analogy and the solubility methods for molecular diffusion using information given in Table 6 of ref. [21]. The simulation and tuning result
s are given in Table 1.
Table 1 The simulation and tuning results for the high pressure deposition cell measurement
Test number Moleculare diffusion model Measured deposition thickness (mm) Simulated deposition thickness (mm)
1C 2C EPS-1 Heat-mass analogy 0.037 0.037 1 6.6E-4 EPS-1 Solubility 0.037 1.5 6.6E-4 EPS-2 Heat-mass analogy 0.013 0.013 1 6.6E-4
EPS-2 Solubility 0.013 1.5 6.6E-4 EPS-3 Heat-mass analogy 0.004 0.00354 1 6.6E-4
EPS-3 Solubility 0.00355 1.5 6.6E-4
The tuning starts from parameter bad on test 1 of equivalent pipe ction (EPS-1), in which the shear stress is small. By neglecting the shear removal term, it has been found that no tuning is needed for molecular diffusion term when the heat-mass analogy is adopted. On the other hand, a multiplier 1.5 has to be applied while using the solubility method. This ems to be reasonable if we compare with the results obtained in Ca 1. After obtaining the optimized value of , test ESP-2 is ud to tune the value of . For both heat-mass analogy and solubility methods, 6.6E-4 ems to be a
n optimum value for . With this value, EPS-1 has been re-visited by taking into account both molecular diffusion and shear removal effect.
A negligible change has been obrved in this round. Therefore no iteration is needed to tune the parameters and . The parameters are directly ud for simulations of test EPS-3. A comparison with experimental data can be found in the last two rows of Table 1. It is shown that the propod model and the tuning method gives good predictions for test EPS-3. The results suggest that the simulation model combined with results from the high pressure deposition may provide a reliable tool to study wax deposition in real pipeline and optimize the design of offshore projects.
1C 1C 2C 2C 1C 2C
CASE STUDY 3
After performing simulations of wax deposition against the lab-scale measurements in ca studies 1 and 2, a ca of full scale pipeline was studied, which was reported as ca study 1 by Brown et al. in ref. [7]. The first run of simulation was performed without any tuning. Only molecular diffusion is considered by using the heat-mass analogy. The results from this simulation are given in figure 7. The total deposited wax volume has been obtained around 1,200 bbl. This value is clo to the resul
ts from other simulations, 1,070 bbl by Brown et al [7] or 995 bbl by Edmonds et al [13], but is much higher than the data reported from field, which is “more than 50 bbl”. This overprediction suggested that the shear removal effect may not be neglected for this ca. The simulation was then repeated by considering both molecular diffusion and shear removal mechanisms. Due to insufficient information from the literature, a customized tuning ems to be impossible, and the tuned parameter in Ca 2 was tentatively ud. Figure 8 gives the results from the cond run of simulation. The results show that a balance between molecular diffusion and shear removal has been achieved after about 80 days. And the total deposition wax volume was about 25 bbl. It is no surpri that this value does not agree very well with the measured “more than 50 bbl” since the totally different oil and pipeline configuration was ud to obtain the tuning parameters. Generally speaking, this simulation has confirmed the significance of shear removal in the wax deposition predictions.
CASE STUDY 4
In this ca, another full scale pipeline simulation has been conducted to deal with wax deposition in two-pha flow. The oil and pipeline information have been reported by Lindeloff and Krejbjerg in [12]. The simulation has mimicked two flow assurance scenarios with only molecular diffusion consid
ered by applying the heat-mass analogy method. In the first scenario, the pipeline is insulated by concrete and surrounded by a water. And the inlet pressure is as high as 100 atm to ensure a single pha flow. The simulation result is given in figure 9. It is shown that the deposition reach a peak near the
