Article pubs.acs.org/EF
Waxy Oil Pipeline Transportation through Cold Flow Technology: Rheological and Pressure Drop Analyses M. Margarone,*,† A. Bennardo,‡ C. Busto,§ and S. Correra† †
Exploration and Production Division, Eni, Via Emilia, 1, 20097 San Donato Milanese, Italy Refining and Marketing Division, Eni, Via Maritano, 26, 20097 San Donato Milanese, Italy § Istituto Donegani, Eni, Via G. Fauser, 4, 28100 Novara, Italy ‡
ABSTRACT: The cold flow of waxy slurries has been recently appointed as a potential method to avoid or partially reduce the wax deposition in a waxy oil transportation pipeline (Merino-Garcia, D.; Correra, S. Pet. Sci. Technol. 2008, 26, 446−459). An experimental investigation on a large flow loop with rough pipes (inner diameter = 5.08 cm; L ∼ 70 m) was then carried out with the aim to study the cold flow of waxy slurries. The wax slurry was constituted by a commercial paraffin wax distribution in ndecane, previously characterized from a rheological point of view. The influences of the wax concentration and flow rates on the pressure drop were investigated by loop runs. A comparison between the experimental pressure drop and modeling results was carried out by investigating friction factor correlations suitable for waxy slurry flow. Furthermore, the same set of data was used, regardless of the rheological characterization, to assess the rheological behavior of the suspensions. This second approach has allowed evidence for the importance of a correct estimation of bulk viscosity to correctly predict the pressure drop. The tests carried out constitute a proof of concept for the “waxy cold flow” transportation technology.
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INTRODUCTION Production of crude oils in offshore conditions is greatly affected by the formation of solid deposits, such as gas hydrates and waxes. Specifically, the presence of long-chain alkanes (with a carbon number ranging from 18 to 65), commonly known as waxes, may cause partial or complete blockage of pipelines and equipment because of waxy deposits that may form at the pipe wall.2 This leads to a production drawdown and an increase of the pressure drop, which affect crude oil delivery. Besides, restart issues after a production shutdown may compromise offshore transportation. In subsea pipelines, because of the heat exchange with the surrounding environment, the transported oil cools, reaching the seabed temperature. The temperature reduction induces a lower solubility of waxes in the oil matrix, causing separation of a waxy solid or semi-solid phase (deposit). Oil cools along the tube, and the deposition phenomenon begins when the internal wall temperature reaches the so-called wax appearance temperature (WAT or cloud point). Basically, the deposit forming at the pipe wall is a gel phase consisting of a waxy solid network entrapping a liquid phase. These gel networks have a complex morphology, and their characteristics are affected by different factors, such as the amount and nature of waxes, flow behavior, and time.3−10 At industrial level, a number of methods are nowadays used to prevent or remediate wax deposition.11 These include injection of chemicals to modify wax crystallization, crystal growth, and gelation, thermal insulation, heat tracing, and mechanical treatments. In offshore conditions, the longer the distances from production systems (wells and manifolds) to topside facilities, the worse the issues affecting design and remediation actions. All of the proposed remediation methods suffer some shortcoming, because of viability, costs, and environmental issues (e.g., chemical injection) thus the need for alternative technologies is becoming extremely important for industries © 2012 American Chemical Society
involved in developing long offshore pipelines and tieback to existing facilities. A proposed alternative technology is the so-called “waxy cold flow”.1,3 The idea is to transport a waxy slurry of crude oil at the seabed temperature (PP < T < WAT, where PP is the pour point), whereby wax crystals remain suspended in an oil matrix. It was claimed that, if the slurry is formed before entering a long pipe surrounded by a cold environment, it could be transported in a stable way without having deposition. From a theoretical point of view, when the temperature drops below the WAT, solid wax crystals start to form; however, this does not necessarily imply deposition.12 Wax precipitation is essentially a solid-phase separation, depending upon operative conditions, where the wax crystals form a tridimensional network, embedding the liquid phase. This is the wax deposit, and its formation is also affected by fluid dynamics, heat- and mass-transfer processes, and solidsurface interactions. Two main issues are to be taken into account to establish the waxy cold flow feasibility: first, a “cold flow unit” needs to be designed to make waxes precipitate and favor the waxy slurry flow in a pipeline system; second, waxy particles have to remain suspended. In addition to this, the increase in fluid overall viscosity because of particles in suspension lead to an increase of the pressure drop, which is difficult to deal with because of nonNewtonian behavior of solid−liquid mixtures. As a preliminary condition, if the fluid is transported at a temperature equal to the external surroundings (e.g., seabed), Special Issue: 13th International Conference on Petroleum Phase Behavior and Fouling Received: September 15, 2012 Revised: November 11, 2012 Published: December 4, 2012 1809
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there will be no driving force for the change of phase and, thus, no deposition. This would imply zero heat flux between bulk and external, and it has been demonstrated that this zero heat flux condition would lead to negligible deposition on the pipe wall.5,13−20 Several experimental evidence support the possibility of setup for the proposed waxy cold flow technology. At present, even though the heat transfer of wax deposition under cold flow conditions has been investigated, no work was devoted to deal with pressure drop behavior because of waxy slurry transport at isothermal conditions. Moreover, the feasibility evaluation of cold flow would require the pressure gradient behavior of waxy slurry as close as possible to field conditions. Thus, this work aims at fill this gap presenting a set of pressure drop measurements with an experimental flow loop (inner diameter = 5.08 cm; L ∼ 70 m), where slurry flow is formed in a stirred vessel and isothermal pressure drop is measured in pipes at cold flow conditions. Influences of the mixture temperature, wax concentration, and flow rates on the pressure drop were investigated. An analysis of literature pressure drop modeling compared to experiments is given. Furthermore, the same set of data was used, regardless of the rheological laboratory characterization, to assess the rheological behavior of the suspensions. This headed to an independent evaluation of the suspension rheological constitutive equation and highlighted some important issue: the setup of a cold flow technology will be possible only by means of a very reliable and unambiguous rheological comprehension of the whole system.
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Figure 2. Wax−decane mixture density as function of the temperature and wax concentration.
⎛ A ⎞ ρws = 103⎜A 0 − 14 T ⎟ ⎝ 10 ⎠
(1)
where T is the temperature (°C). The experimental fitting parameters obtained from the analyses were A0 = 0.7469 + 0.00066Ωw and A1 = −7.7433 + 0.0223Ωw, being Ωw the wax weight fraction. WAT and wax disappearance temperature (WDT) of mixtures were determined using a well accurate differential scanning calorimetry23−25 (DSC)-based method, which allowed for a simple determination of the wax solid formation by the analysis of enthalpy variations as function of the temperature. A Mettler-Toledo DSC 822 apparatus was used. Different mixtures were prepared to determine the WAT−WDT dependence upon the wax concentration. In practice, after sampling preparation, the temperature in the equipment was initially calibrated using the onset of indium and cyclohexane transition peaks. The temperature investigated were between 60 and −20 °C, using different cooling and heating rates (1−2 °C/min). An average value of 210 J g−1 was used as enthalpy of precipitation of the complex mixtures under investigation.25 The results are shown on the left panel of Figure 3, where WAT and WDT measurements as a function of Ωw are presented. It can be seen that the wax concentration has been varied and WAT resulted from 15.5 °C at 2.5% to 27 °C at 10%. The wax solubility has also been derived using the DSC-based method cumulative integral, and results are shown on the right panel of Figure 3 for two different mixtures (Ωw = 5 and 10%). For the purpose of this paper, it was important to ensure that cold flow conditions were guaranteed when loop tests were performed. In principle, the DSC-based method does not allow for precise determination of solid−liquid equilibrium because of finite cooling and heating rates,12,26,27 but the real solid−liquid equilibrium curve can be taken between WAT and WDT. This effect is clearly visible, observing that the estimated solubility curves for both cooling and heating experiments give different plots of the amount of solid waxes as function of the temperature. Because the WDT measurements are commonly higher than the WAT at a constant wax concentration, the solubility curve by heating scans would shift toward higher values, giving higher solid wax at a constant temperature. With the aim to be conservative and ensure that cold flow conditions were reached in loop experiments, in the present work the WAT curve was employed as the solid−liquid equilibrium curve. The rheological properties of waxy mixtures were analyzed to determine shear stress−shear rate dependence. A rotational stress rheoemeter STRESSTECH manufactured by Reologica Instruments AB was used for the analysis. Rheological behavior was analyzed in the range of 10−300 s−1 (shear rates) and 10−50 °C (temperature). Figure 4 shows shear stress dependence with temperature at constant shear rates. For both mixtures, the viscosity increased while the temperature decreased, as expected. For Ωw = 5%, viscosity changes from 0.001 to 0.01 Pa s, whereas for Ωw = 10%, an increase of the viscosity was observed below 18−20 °C for all of the shear rates investigated. The viscosity varied from 0.001 Pa s at a
EXPERIMENTAL SECTION
Materials and Analysis. The mixtures used for this study were composed by waxes (Carlo Erba Reagenti, Arese, Italy, quality > 99%, with carbon number ranging from C18 to C45) and n-decane (purity of 95%). The carbon number distribution is shown in Figure 1. It can be
Figure 1. Carbon number distribution of waxes (linear and isoparaffins). seen that only 69% of waxes was constituted by linear paraffins, while the rest was made up by isoparaffins. The melting point of waxes was within the range of 62−64 °C, with a density of around 0.90 kg/m3 at 20 °C. For the n-decane, the molecular weight and density were 142 kg/kmol and 735 kg/m3 at 18 °C, respectively. Viscosity and density of n-decane at the different temperatures were calculated by means of literature relationships.21,22 The density of mixtures was measured in the temperature range of 10−50 °C. The density dependence from both the temperature and wax concentration are shown in Figure 2. The density ρws (g/cm3) was estimated over the entire range of temperatures by the 1810
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Figure 3. (Left) WAT and WDT of waxy mixtures by DSC experiments and (right) estimated solubility curves for Ωw = 5 and 10%.
Figure 4. Shear stress as a function of the temperature at constant shear rates: (a) Ωw = 5% and (b) Ωw = 10%.
Figure 5. Shear stress as a function of the shear rate at a constant temperature: (a) Ωw = 5% and (b) Ωw = 10%. temperature between 30 and 50 °C to 0.01−0.1 Pa s at 10 °C. The higher viscosities observed at lower temperatures can be explained by the wax crystallization occurring at temperatures below 25 °C. A shearthinning behavior was seemingly observed for both mixtures, more pronounced for Ωw = 10%. The preliminary measurements allowed for an exclusion of a time dependence of the viscosity. Figure 5 shows the shear stresses as a function of shear rates at constant temperatures. At Ωw = 5%, a Newtonian behavior was observed at temperatures higher than 15 °C in the range of 10−100 s−1. The viscosity curve at 10 °C shows a weak shear-thinning behavior (the viscosity decreased by an order of magnitude when the shear rate ranged from 5 to 300 s−1). At Ωw = 10% mixtures, the shear-thinning behavior
occurred at higher temperatures, even though the values were lower than 20 °C. The rheological measurements yielded the evidence of the gelation effects because of the temperature drop. For the Ωw = 5% mixture, Figure 5 suggests that the effect of gelation is marginal because no abrupt viscosity variation occurred, at least in the range of temperatures investigated. A more pronounced effect was indeed observed for the Ωw = 10% mixture, observing the curve slope changes for temperatures lower than 20 °C. Flow Loop Description. The flowing behavior of the wax slurry behavior was investigated through a large flow loop built with the specific aim to create and keep an isothermal flow and to measure the 1811
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Figure 6. Flow loop for cold flow measurements. pressure drop at different flowing conditions. The objective was to determine the pressure drop behavior in a large-scale apparatus, bearing in mind the waxy slurry rheological behavior at different mixture temperatures. The flow loop was also designed to perform wax deposition tests, similar to other flow loops designed and used for this purpose.3,13,14 The loop schematic is shown in Figure 6. The main loop components are a test fluid circulation system with two different test sections (each with an independent cooling system), a stirred vessel with a hot bath, a circulating pump (Convex CXM-200), temperature and pressure gauges, massflow meter, and a data acquisition system. The test fluid circulation system was manufactured with stainlesssteel pipes. The inner pipe diameter and roughness were 50.8 mm and 50 μm, respectively, with a total loop length of approximately 70 m. The outer pipes have an external diameter of 76.2 mm. Water was used as a cooling medium to refrigerate test sections S1 and S2, in particular flowing counter-currently in the pipes annulus and back to a refrigerator unit (indicated with W1 and W2). Test section S1 was built using 13 straight pipes (3 m long each) and 12 180° bends, with a radius (0.6 m) chosen to minimize the concentrated pressure drop. The test section S2 was built using three straight pipes as per test section S1. The loop was entirely insulated to minimize heat transfer to the surroundings and to guarantee as close as possible an isothermal flow. The slurry preparation was carried out in a vessel (V-1), with 0.8 m3 volume, maintained in a diathermic oil bath for temperature regulation and equipped with an internal stirrer (power of 1.1 kW and maximum rotational velocity of 700 rpm) used with the 2-fold objective to enhance the wax dissolution in the solvent and maintain the wax particles suspended (at T < WAT), limiting the deposition on the vessel surface. The low shear pump P-1 was selected to minimize the shearing effect on the mixtures in cold flow conditions, thus limiting the effect of change in the bulk viscosity. The pump was mechanically driven, and its speed was regulated by changing the frequency of the electrical motor by means of dedicated inverters. Two main valves were present at the outlet of the stirred vessel and at the top of the loop, to bypass the vessel and allow for recirculation of the slurry mixtures. A dedicated acquisition system allowed for measuring and recording the flow parameters. Absolute pressure was measured at the V-1 and P-1 outlets. Differential pressure was measured across S1 and S2 (ΔP1 and ΔP2). Mass flow rates were measured using Coriolis metering (FIC) after pump P-1. The loop was also equipped with an online viscosimeter, with the aim to directly measure the suspension viscosities and investigate the rheological behavior in flowing conditions. Nevertheless,
throughout the experimental campaign, the instrument was always at full scale, leading to inconsistent measurements, and its measurements were not considered for the purposes of this study. Flow Loop Measurements. The first loop runs were performed using pure n-decane to hydraulically test the system and to calibrate the pressure gauges. The mass flow rates investigated were in the range of 1700−5000 kg/h, with a measured temperature in the range of 15−18 °C. In those conditions, the Reynolds number resulted between 11 900 and 32 000 (turbulent flow). The pressure drops also allowed for the determination of the loop equivalent length as the test section presents different bends. On the basis of the analysis, the equivalent length for the test section S1 resulted in 55 m. The experimental pressure gradient for the test section S1 was compared to the calculated pressure gradient using the Haaland friction factor correlation,28 and the errors were found less than 3% for all of the flow rates. After the tests using n-decane, the waxes were added to vessel V-1 through a dedicated opening at the top. The mixture was preheated to 70 °C for 1 h to destroy any thermal history. In addition to this, the mixtures were also continuously stirred at maximum velocity. The cooling process at a temperature below the WAT was driven by the surrounding temperature and resulted in a slow process because of high thermal inertia of the loop. This behavior allowed for the ensuring of the isothermal condition in the test section S1, regulating the water flow rate from W1 and the inlet water temperature T3 in the section S1. Even though the control system was set specifically to keep the flow isothermal, a small temperature gradient across the test section S1 (T2− T4) was always encountered, even though the highest deviation measured throughout the experimental campaign was always less than 1 °C. The mass flow rates were varied ranging from 1700 to 5000 kg/h to determine the steady-state ΔP1 measured through all of the loop runs with the wax slurry flow. For each test, the recorded mixture temperature (T2) changed in a quasi-static way (from 1 to 0.1 °C/h) and procedure was repeated. To ensure that cold flow conditions were reached, it is worthy saying that the WAT measurements were repeated through the DSC-based method on the real mixtures, thus taking into account the real wax concentration. This was performed through the extraction of mixture samples in a point located at the bottom of vessel V-1. The true concentrations were 4.1 and 8.5 wt %. The results of this process are shown in Table 1, where it is clear that cold flow conditions were reached. 1812
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In the first approach (“fluid dynamic”), viscosities of the wax suspensions were obtained from laboratory rheological measurements and then employed using suitable rheological models. The steady-state pressure drops were estimated using correlations for the friction factor for both Newtonian and non-Newtownian flows, even though, in the latter case, it would be difficult to define a suitable Reynolds number and to choose an appropriate friction factor correlation. These results were compared to the experimental results, to find the best correlations and estimate the error. The second approach tends rather to investigate the rheological behavior of the waxy slurries in cold flow conditions. It was decided to derive the slurry constitutive equation directly from experimental data. In a few words, the flow loop has been used as a viscosimeter. Fluid Dynamic Approach. The fluid dynamics analysis of experimental data would be needed to define the methodology to evaluate the range of the mixture Reynolds number and choose the friction factor correlations for laminar and turbulent conditions. Basically, the presence of precipitated waxes in a mixture would lead to non-Newtonian behavior with the presence of many macroscopic effects, such as yield stress, pseudo-plasticity, and time dependency. Among the contributions provided in the literature on the subject, the Pedersen and Ronningsen29 model was used to describe the rheological behavior of the mixtures under investigation. This model describes the non-Newtonian behavior as a consequence of precipitated wax, combining the model by Richardson for the viscosity of oil/water emulsion and a modified Casson equation. Thus, the following formula was given:
Table 1. WAT Measurements of Mixtures and Temperature Range Investigated in the Flow Loop in Cold Flow Conditions
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wax (nominal) (wt %)
wax (real) (wt %)
WAT (°C)
temperature (T2) (°C)
5 10
4.1 8.5
20.4 26.5
13−18 16−23
RESULTS AND DISCUSSION Results of the cold flow experiments are summarized in Figure 7, where the measured steady-state ΔP1 as a function of the mixture velocity and wax concentration are shown.
⎡ Eϕwax Fϕ 4 ⎤ ηws = ηL⎢e Dϕwax + 1/2 + wax ⎥ ⎢⎣ γ ̇ ⎥⎦ γ̇
Figure 7. Experimental steady-state pressure drop in cold flow conditions as a function of the mixture velocity (v) and wax concentration (Ωw).
where ηws is the waxy slurry viscosity (mPa s), ηL is the liquid viscosity (mPa s), φwax is the volume fraction of precipitated waxes, and D, E, and F are three parameters used to fit the experimental curves (D = 37.82, E = 83.96, and F = 8.559 × 106). The model has been tested against 713 points for 15 different paraffinic oils, reporting an average absolute deviation of 48%.29 Using this approach for the experimental data at a lower wax concentration (5%), the model predicted a bulk viscosity ranging from 1.17 to 1.64 mPa s, which poorly agreed with rheological measurements. On the basis of this, a model tuning procedure was established to determine the best fitting against the D, E, and F parameters. The new tuned model fairly agreed with the experimental data, leading to calculated viscosity ranging from 1.6 to 6.1 mPa s. The new fitting parameters resulted in D = −347.89, E = 3091.33, and F = 3.025 × 107 (with an associated correlation coefficient of R2 = 0.9891). At this stage, using the calculated bulk viscosities for a constant wax concentration and temperature, the mixture Reynolds numbers resulted in the range of 1900−20 700. This is the wellknown transition laminar−turbulent region, according to the Moody diagram. It was difficult to correctly estimate the friction factor in this transition zone because, according to the traditional Moody diagram, the error in this area would be in the order of the difference between laminar and turbulent estimates. As a consequence, when the wrong correlation is chosen, errors can be up to 100%. For the purpose of the analysis, the Colebrook− White30 and Haaland28 correlations for full turbulence were implemented.
To better elucidate how the steady-state pressure drop increases in comparison to the cases with waxy slurries or pure solvent (n-decane), a dimensionless parameter e1 is defined as the ratio between waxy slurries and pure n-decane steady-state pressure drop at the same mixture velocity.
( ΔLP )ws e1 = ( ΔLP )solv
(3)
(2)
The analysis elucidated that e1 resulted in the range of 1.2−2.2 for Ωw = 5% and between 1.2 and 6 for Ωw = 10%. In both cases, the highest values calculated correspond to the lowest mixture velocities and temperatures. Because wax particle precipitation and the effect on slurry rheology depend upon the temperature and total wax content in the mixture, the viscosity effects were more pronounced for Ωw = 10%, keeping all of the other parameters constant. Experimental data suggested that, given a certain initial wax concentration, the cold flow transportation system could be optimized, varying the inlet mixture temperature and mass flow rate as well as geometrical characteristics, i.e., D and L, to reach the lowest steady-state pressure drop. Reliable design criteria are then required for determining the most appropriate friction factor correlations to optimize the transportation system. For the following section, two possible interpretations of the collected data are presented. 1813
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The results of such an analysis are reported in Figure 8 (dotted lines; ±15%). It can be seen that, at higher Reynolds numbers
Figure 9. Comparison between experimental and measured pressure gradients (Ωw = 10%), with Hagen−Poiseulle (laminar flow) and Haaland (transition zone) using the Pedersen and Ronningsen tuned viscosity model.
Figure 8. Comparison between the experimental steady-state and modeled pressure gradients (Ωw = 5%).
(>5000) within the turbulent region, 95% of experimental points were well-predicted. Nevertheless, the correlations underestimated the experimental data at lower Reynolds numbers (1900−4000), being within the transition zone. Including experimental points falling into the laminar region, 65% of experimental values seemed reasonably well-predicted. For the flow experiments at Ωw = 10%, the approach was more complicated. The experimental temperature ranged from 16 to 23 °C, and from Figures 4 and 5, the mixtures showed a shearthinning behavior over the entire range of shear rates investigated, which also would explain higher values of the e1 parameter at lower mixture velocities. The formation of a strength gel caused by wax precipitation showed a high value of apparent viscosity and a different rheological behavior for such mixtures. Using the same model as for the Ωw = 5% mixture and repeating the tuning procedure, the estimated model parameters for Ωw = 10% were D = 57, E = 5741.74, and F = 9.592 × 107 (with an associated correlation coefficient of R2 = 0.9267). The Reynolds numbers estimated through the tuned viscosities were found in the range of 315−3300, where only six operating points (at higher mixture velocities and temperatures) were found in the transition region, i.e., 2100 < Re < 3300. For such a reason, Hagen−Poiseulle for laminar flow and Haaland friction factor for turbulent flow were used. Figure 9 shows the final results of this combined model. It is worth noting at this point that the pressure gradient calculated through the relationship tuned on laboratory measurements was almost systematically underestimated. At a first sight, by considering the scale of the plant and the employed instrumentation, this result seems to be acceptable. However, the rheological analyses of the data, which will be presented in the next paragraph, rather indicate that the deviation would be due to a systematic underestimation of the bulk viscosity of the fluid. Rheological Approach. The experimental flow loop was not always able to maintain closely a constant temperature, as previously explained in the Experimental Section. In particular, the thermal excursion between day and night varied with respect
to the temperature set point. For such a reason, a statistical approach was adopted to analyze the flow data. For each run, intervals were identified, characterized by a (i) constant nominal flow rate and (ii) monotonous trend of the temperature over time. It was hypothesized that temperature variations in the intervals were reasonably linear, and the following variables were considered: time (t), temperature (T), flow rate (F), and pressure drop (ΔP). Pearson’s correlation coefficient between each pair of variables (the covariance of the two variables divided by the product of their standard deviations) was evaluated. A high cross-correlation coefficient with time would mean that the measurements were affected by the effect of external temperature changes with time. In this case, by linear regression of the data, it was possible to make a correction by reporting all data to the nominal temperature of 18 °C. At this point, the Mooney−Rabinowitsch method31 allowed for the drawing of a flow curve without any assumption about the rheological constitutive equation. When this analysis was performed on the flow loop data, the graph in Figure 10 was obtained. When this second approach was employed, higher values of shear stresses were obtained, and this had dramatic effects on the physical picture of the phenomenon. On the other hand, this second perspective allows for the explaination of the systematic underestimation obtained by the fluid dynamic approach and was a bit more coherent with the physical picture of viscous wax slurry. From this analysis, the flow is “laminar” for almost all of the experimental campaign, and the rheological behavior of the slurry is described by means of the following power laws: y = 0.0012x1.5501 ,
R2 = 0.9734 (for 5% wax slurry)
y = 0.0066x1.4602 ,
R2 = 0.7295 (for 10% wax slurry) (4)
On the basis of the results described in eq 4, the wax suspensions become shear-thickening as the flow indexes in the power law become higher than 1. 1814
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correlations for full turbulence flow seems to well-predict the experimental pressure gradient. For higher wax concentrations, the models failed as a result of a systematic underestimation of the slurry viscosity only based on rheological laboratory analysis. The experimental pressure drops were then analyzed to determine the flow behavior of waxy slurries (rheological approach). Because of the relatively high viscosity of wax slurries, almost all of the experiments resulted in the laminar regime. The resulting flow curve for both of the wax concentrations was wellinterpolated by means of a power law constitutive equation. Contrary to what reported in the literature, suspensions became shear-thickening; i.e., the flow index became greater than 1. This behavior was very different from the rheological behavior observed by means of laboratory rotational measurements, and this aspect deserves further investigation. The analysis presented in this work allowed for the highlighting of the importance of correctly estimating the bulk viscosity of waxy slurries, showing that rheological characterization should be carefully assessed and suitable procedures for the preparation of slurry waxes should be taken into consideration.
Figure 10. Flow curves from the Mooney−Rabinowitsch method.
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A possible explanation of the discrepancy between the two interpretations can be derived from the fact that the strain rates in the measurements of the rotational viscometer were estimated by assuming a linear velocity profile (i.e., the gap between the two coaxial cylinders is “small”). However, this assumption was not true for the wax slurry, and this entailed a systematic underestimation of the bulk viscosity. General Comments. The comparison between the two approaches for modeling the behavior of waxy slurry in pipes shows that the flow characterization through the laboratory rheometer tests could not be sufficient to correctly determine the rheological behavior of waxy slurries, because it may be difficult to establish whether the flow is laminar or turbulent and find the correct model for estimating the Reynolds number. The implementation of independent measurements through a bench-scale flow loop, in combination with appropriate rheological studies, can aim to better elucidate the flowing conditions of wax slurries in a pipe in cold flow conditions. In addition to this, the experimental work presented in this paper shows that the wax cold flow imposes a higher pressure drop compared to flow conditions at temperatures higher than the WAT. In the case of potential applications in the oil industry for long deepwater tie-back scenarios, the augmented pressure drop could have a great impact on the production and the field management along the field life.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS The authors thank the Exploration and Production Division of Eni for special permission to publish this paper. Fabrizio Podenzani from the Refining and Marketing Division of Eni is acknowledged for fruitful discussion and cooperation in the project.
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REFERENCES
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CONCLUSIONS AND REMARKS This study dealt with the experimental analysis of waxy cold flow in a pipe to determine the rheological and pressure drop behavior. Different waxy mixtures were flowed at isothermal conditions at T < WAT on a large flow loop with rough pipes. The experimental pressure gradient was measured, and the effects of the mixture temperature, wax concentration, and flow rates were investigated. For all waxy mixtures, the larger the wax concentration, the higher the pressure drop at a constant mass flow rate. The effects of a bulk viscosity increase as a result of the formation of a waxy slurry largely affect the experimental pressure drop, showing that the pressure gradient at constant mass flow rates may be up to 6 times the pressure drop with a pure solvent for higher wax concentrations. With the aim to model the experimental results, a fluid dynamic analysis was performed, leading to the conclusion that, at least for lower wax concentrations, the use of friction factor 1815
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