EVALUATING THE MECHANISMS OF WAX DEPOSITION IN CRUDE OIL PIPELINES
A.A. Sulaimon1*, K. Gunasekaran1, S. Vatsa2
1Department of Petroleum Engineering Universiti Teknologi PETRONAS, Malaysia
2Department of Petroleum Engineering, IIT ISM Dhanbad, Jharkhand, India E-mail: [email protected]
ABSTRACT
Flow assurance standstill as a massive issue as it involves ensuring fluid flows in well, flowline and trunk line. One of the major decisive for flow assurance crude oil is its constitution and solid deposits successful management. Wax deposition challenges and its control can be determined with the right prediction from wax deposition modelling.
Certain factors like pipeline inclination that influences the rate of wax deposition need to be taken into consideration.
For inclined wells, the model is tuned to account for low concentration slurries under inclined angles. Regarding this, a complete wax deposition model is developed to predict the rate of wax deposition by investigating all the possible wax deposition mechanisms which contribute actively for better wax deposition management in the oil fields. A thorough analysis has been carried out to show the significance of each deposition mechanisms and parameters in wax deposition model like rate of wax deposition, deposit thickness, the temperature in the pipeline, pressure drop in the pipeline. Based on the results achieved, it can be deduced that the shear stripping and rate enhancement effect due to oil trap has the highest contribution towards the wax deposition in the pipeline but the gravity settling velocity cannot be neglected without valid assumptions.
Keywords: flow assurance, wax deposition, wax deposition mechanisms, wax deposition modelling, shear stripping, gravity settling velocity
INTRODUCTION
In subsea production fields formerly, flow assurance is essential for its economic growth. Subsea transportation of reservoir fluids has shown to be more troublesome, mainly due to a colder environment and longer shipping distances. Hence, the deposition of solids in production and conveying equipment has become a severe issue for the oil and gas industry.
Deposition of wax in subsea pipelines, flowlines, and wells diminish in operation efficiency. The deposits of crude wax consist of petite wax crystals that are readily available to agglomerate and form granular particles of wax around the size of coarse grains of normal salt [1].
Numerous studies on wax deposition were performed during the past decades. Most of them dealt with problem in pipelines, whose sectional homogeneity and improved traceability for experimental purposes allowed endeavouring very important results. Nevertheless, the wax deposition problem is extremely significant in wells [2]-[4]. Several laboratory test methods have been developed, including mathematical modelling, to forecast the rate of wax deposition in pipelines to time [5]. Deposition modelling consists of two major parts – pipeline modelling and depositional model. Pipeline model illustrates heat transfer and fluid flow calculation along the pipeline, whereas the deposition model
handles the calculation of wax deposition rate. The main objective of this study is to predict the wax deposition rate by investigating the possible wax deposition mechanisms which contribute actively to better wax deposition management in the oil fields.
Recently, the number of researches has been conducted on the modelling of wax deposition consists of only two out of four possible mechanisms, such as molecular diffusion, shear dispersion, Brownian diffusion, and gravity settling [6]-[8].
The involvement of all the possible coefficients represents their respective mechanisms will result in good accuracy of wax deposition in the pipeline [9]. The question arises about the importance of the other mechanisms and the impact on the flow of wax molecules in the wax deposition profile [10].
Not only that, certain factors like pipeline inclination that influences the rate of wax deposition, need to be taken into consideration [11].
Table 1 Properties of crude oil
Properties of Indian crude oil Values
Viscosity of oil (kg/ms) 28.8
Density of oil (kg/m3) 856
Actual velocity (m/s) 0.87
Ambient temperature (oC) 35
Heat capacity 1.8
Mass flow rate (kg/hr) 120
Input wax concentration in % 16.6
Velocity of oil in pipelines (m/s) 0.68 Inlet temperature of oil in the pipeline (oC) 57
However, due to some limitations of crude oil field data, there is a certain problem encountered during the validation of the developed model, which is the unit conversion, and the properties of crude oil might affect the accuracy of wax deposition profile prediction. In correlation with this problem, two objectives were targeted to be achieved to validate
the model using field data and to develop a relevant wax deposition model that incorporates all the possible mechanisms [12]. In most of the research, molecular diffusion and shear dispersion standstill are the main mechanisms, and it is driven by a radial concentration gradient [13].
A study on total wax deposition in pipeline entirely focusses on the results from a combination of molecular diffusion mechanism, Brownian diffusion mechanism, shear dispersion mechanism and gravity settling. A relevant wax depositional model is developed based on Indian crude oil properties to stimulate the rate of wax deposition across the pipeline. The temperature range is 30oC to 40oC.
Different properties of Indian crude oil with their respective values are shown in Table 1.
Wax Deposition Mechanisms
Different types of mechanisms have been suggested, such as molecular diffusion, thermophoretic diffusion, Brownian diffusion, particle agglomeration, gravity settling and shear dispersion [14]-[16]. All mechanisms are describing the radial transport of total precipitated
particles except molecular diffusion [12]. Bern at al. [17] and Brown et al. [18] concluded based on experiments that molecular diffusion is the mechanism predominately responsible for deposition. Burger et al. [6] concluded that molecular diffusion dominates at high temperatures and heat flux conditions [19].
Molecular diffusion and shear dispersion standstill in most of these research, as the main mechanism, and it is driven by a radial concentration gradient [13].
Wax Depositional Model
Matzain model is chosen to include the other influences by expanding or modifying it has a valid reason. One of the reasons is there is some empirical relation for the rate enhancement due to oil being trapped in the deposited wax layer. It also accounts for any other positive deposition rate that is not considered in Dow, turbulent mass diffusion [20]. Matzain et al. also came out with empirical relations for rate reduction due to shear stripping, which eases the linear equation calculation without conducting any lab experiment to collect certain data [9],[13]. They included the use of dimensionless variables and empirical constants from his experiments.
Table 2 Input constants
Input Matzain constant C1 15
Input Matzain constant C2 0.055 Input Matzain constant C3 1.4
Figure 1 Schematics of flow through a pipeline
Matzain et al. [9],[13] also figured out that wax deposition was dependent on the flow pattern. The only model was incorporating the effect of different flow regimes. Also, there were three empirical constants. C1, C2 and C3, which correlated from single- phase and two-phase flow data, and their values are written below in Table 2.
MODEL DEVELOPMENT Temperature profile
When crude oil flows through the subsea pipeline, wax deposition takes place due to the temperature gradient between the pipe wall and the bulk centre of the flowing fluid. Instant deposition rate will change strongly to the respective position in the pipeline with time. The fluid inside the pipe gets colder because of heat transmission from outside of the pipe [21]-[22].
The first procedure for the simulation purpose is to perform a complete calculation of temperature profile (Figure 1) by deriving the sub-gradient heat equation for the pipeline.
The thermal sub-gradient of heat is given by, dT
dr =Tb−Tw
λo xhwall
(1) where λo is the oil thermal conductivity (W/m.K), Tb is bulk average flow temperature (K), Tw is inner wall surface temperature (K), hwall is inner wall surface heat transfer coefficient (W/m2.K). This temperature-driven fluid cooling process occurs due to heat loss to the colder surrounding of the pipeline. Heat transmission from the outside of the pipe gives cooling of the fluid inside the pipeline.
(2) where Tamb is the ambient temperature (oC), Tinlet is inlet temperature of the pipeline (oC), D is the diameter of the pipeline (m), is heat transfer coefficient (W/m/oC), Cp is heat capacity, m is the mass flow rate (kg/hr), x is a distance of pipeline (m). The data required to analyse the temperature profile is given in Table 3.
regime dependent Reynold’s number, molecular diffusion mechanism, Brownian diffusion, gravity settling for incline flow and temperature gradient [13].
Change in wax thickness deposited on the wall with time (m/s) is simulated using the equation below,
(3)
where Π1 accounts for porosity effect on the rate of wax deposited, Π2 accounts for wax effect shear stripping, is the molecular diffusion coefficient (m2/s), Db is Brownian movement co-efficient (m2/s), U is gravity settling velocity (m/s), dCw
dT is wax solubility, dT
dr is temperature gradient (1/oC).
For inclined wells, the model is tuned to account for low concentration slurries under inclined angles. An approach was tried by Campos et al. [23].
Table 3 Input data for temperature profile
Input Data Value
Ambient temperature (oC) 36
Inlet temperature of oil in the pipeline (oC) 57
Diameter of the pipeline (m) 0.207
Overall heat transfer coefficient (W/m/C) 0.34
Heat capacity 1.8
Mass flow rate (kg/hr) 120
Wax deposition simulation
Matzain model has been chosen because it is the only model which incorporates the effect of flow regime as well as the empirical correlation for calculating the rate enhancement due to the trapped oil in the deposited wax layer.
Thus, this model has six main mechanisms such as reducing constant due to shear stripping effect, flow
(4)
where U is gravity settling velocity (m/s), g is the gravitational acceleration (m/s2), is particle diameter (m),
s is the ratio of particle density to fluid density, C is the volumetric concentration of particles, n is an exponent of the hindered settling term, D is pipe diameter (m), ρ is fluid density (kg/m3), μ is fluid viscosity (kg/m.s), do is reference sand size, 360 (μm), a is an empirical constant based on Roco’s data, a= 0.31, b is an empirical constant based on Roco’s data, b= 0.60, θ is an inclination angle measured from vertical (θ =90 is horizontal), degree, ξ is a fraction of turbulent eddies, (ξ =1) is used.
RESULTS AND DISCUSSION
Sensitivity Analysis
A thorough analysis has been carried out to show the significance of each deposition mechanisms and parameters in the wax deposition model. Gravity settling and molecular diffusion have a significant impact on wax deposition compared to the Brownian deposition mechanism, as shown in Figure 2.
Due to heat loss to the cold seawater surrounding the pipe, the fluid inside the pipe gets colder. Thus, the wax deposition thickness along the pipeline increases with time, as shown in Figure 3. The temperature falls when the length of pipeline increases as the crude oil flows through the subsea pipeline, as shown in Figure 4.
The temperature profile in the pipeline is generated in a spreadsheet using Equation 2.
As the deposition of wax inside the pipeline increases, the pipeline’s inner diameter decreases, and hence the pressure drop increases along the pipeline. The pressure drop profile in the pipeline is also generated in the spreadsheet, as shown in Figure 5. The values of input parameters for the rate of wax deposition simulation are recorded as in Table 4.
Figure 2 Effect of all possible mechanism towards rate of wax depositions
Figure 3 Total deposit thickness on different number of days
Figure 4 Temperature variation across length of pipeline
Figure 5 Pressure drop due to wax deposition increment in the pipeline
Table 4 Input data for the rate of wax deposition simulation
INPUT Data for simulation Value
Input Matzain constant C1 15
Input Matzain constant C2 0.055
Input Matzain constant C3 1.4
Wax layer thickness (m) 0.015
Diameter of the pipeline (m) 0.207
Overall heat transfer coefficient (W/m/oC) 0.35
Pour Point (K) 312.15
DISCUSSION
The result of the simulation has developed temperature profile, pressure profile and outlined the contribution of each specific wax deposition mechanism through the rate of wax deposition versus distance of pipeline plotted graphically. Based on the results shown in Figure 1 and graphs plotted in Figure 2, shear stripping and rate enhancement effect due
to oil trap have the highest contribution towards the wax deposition in the pipeline. Besides, the Brownian diffusion mechanism has the least contribution towards wax deposition in the pipeline, which is almost negligible. The gravity settling term plays an important role in wax deposition across the pipeline, which is considered as a significant compared to the Brownian diffusion mechanism.
Based on Figure 3, it is obvious that paraffin deposition for the proposed pipeline is expected to behave abruptly during start-up. The temperature would be lower during the start-up, and the heat fluxes would be higher compared to steady-state. This situation leads to a condition where significant wax deposition problem. The instant deposition rate will change strongly to the respective position in the pipeline with time.
The gravity settling affects by Burger et al. [6] in an oil layer under the deposition rate and is discovered through the centrifugation technique. It has been found that Oroskar & Turian [24] predicts the rate of deposition better than the modified Stokes’s Law recommended by Burger et al. [6] since it considers low concentration slurries, inclined pipe flow and multi-phase flow.
Moreover, the gravity settling expression retrieved from modified Stroke’s Law consist of two uncertainties (N’ and K’) known as viscosity power-law parameter for pseudo-plastic fluid which is relatively hard to speculate without any detail experimental work on the fluid or solvent. This inaccurate forecast of fluid properties will produce an error in the prediction of wax deposition rate, as shown in Figure 6.
CONCLUSION
The model is tested with the published field data;
graphical results show the contribution of each mechanism, respectively. Based on the graphical analysis of different parameters with the length of the pipeline, shear stripping and rate enhancement effect due to oil trap has the highest contribution towards the wax deposition in the pipeline. Gravity settling and molecular diffusion have a significant impact on wax deposition compared to the Brownian deposition mechanism. However, detail investigation is necessary to identify the possible mechanisms which contribute directly to wax deposition. A complete mathematical model that incorporates four possible mechanisms discussed above has been merged into a single term.
Thus, the diffusion coefficient is required for further calculation and it is important to determine the coefficient through empirical calculation technique which enables predicting the long-term effects of wax deposition on pipeline operations.
Figure 6 Comparison of gravity settling term by modified Stroke's law
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