Energy & Fuels 2008, 22, 3293–3298
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Energy-Savings Modeling of Oil Pipelines That Use Drag-Reducing Additives F. Go´mez Cuenca,† M. Go´mez Marı´n,† and M. B. Folgueras Dı´az*,‡ Compan˜´ıa Logı´stica de Hidrocarburos (CLH), Central Laboratory, Mendez A´lVaro 44, 28045 Madrid, Spain, and Department of Energy, UniVersity of OViedo, Independencia 13, 33004 OViedo, Spain ReceiVed May 16, 2008. ReVised Manuscript ReceiVed June 30, 2008
New data are presented for drag reduction in a 307 mm in inner diameter × 84 km in length commercial pipeline using 12-25 vppm of a drag-reducing additive (DRA) gel that induced 36-45% drag reduction (DR) in diesel fuel flowing at Reynolds numbers from 60 000 to 160 000. These data were correlated by Hinkebein’s method for scaling drag reduction onset and slope parameters on Prandtl-Karman coordinates to form a model that simulates oil flow with DRA in pipelines. Also, energy savings from DRA use were obtained in two ways: first by the power reduction at constant fuel flow rate and second from the increase in fuel flow rate at constant power. At conditions corresponding to a fuel flow rate of 320 m3/h, the use of 20 vppm DRA can provide either a 42.6% reduction in energy or a 43.0% increase in flow rate.
1. Introduction Most of the policies and strategies in the field of energy management agree on the outstanding role of four main components: energy efficiency upgrading, diversification, assured supply, and environmental behavior upgrading. For different reasons, crude and fuel transportation is a key activity in the value chain of these products from both a strategic and economic point of view. The transportation can be carried out in different ways, with big vessels and pipelines being these with the lowest cost and the best energy efficiency. Despite the high efficiency of pipelines, a considerable percentage of the total cost of pipeline transportation comes from energy consumption. Because of both economic and energy management reasons, the reduction in energy consumption in pipeline transportation is an initiative of great interest, for both the companies themselves directly involved and the economic and social environment in which they function. Reduction in energy consumption in pipeline transportation can be undertaken in different ways. The way that it is selected in this work is based on “Toms Effect”,1 which consists of drag reduction (DR) when small amounts of a long-chain polymer are added to turbulent fluid flows. These polymers are usually called drag reducing additives (DRAs). In a turbulent pipeline flow system, this phenomenon can be used for reducing energy consumption required to move oil through the pipeline or increasing the flow rate. Polymer effectiveness depends upon their properties, such as molecular weight, solubility, flexibility, and solution relaxation time. Mechanical and thermal effects often degrade DRA, and such degradation can make them unsuitable for transporting systems. However, for oil transport * To whom correspondence should be addressed. Telephone: +34-98510-43-33. Fax: +34-985-10-43-22. E-mail:
[email protected]. † Compan ˜ ´ıa Logı´stica de Hidrocarburos (CLH). ‡ University of Oviedo. (1) Toms, B. A. Some observations on the flow of linear polymer solutions through straight tubes at large Reynolds numbers. Proceedings of the 1st International Congress on Rheology, North Holland, Amsterdam, 1948; Vol. 2, pp 135-141.
through commercial pipelines, degradation of the polymers is also necessary, because if the molecular weight of the polymer remains constant, it could modify the quality of the fuel.2 Horn et al.3 found that the rate of degradation of a DRA in a commercial pipeline is 3 orders of magnitude lower than that of a small line. In oil pipeline transport, the use of an adequate DRA must produce either high flow increases or high energetic saving without changing oil product specifications. Energy savings depends upon (a) the efficacy of the additive and its concentration, which provide a decreasing friction factor, (b) oil characteristics, (c) the diameter of the pipeline, and (d) the bulk fluid velocity. One of the most successful applications of DRAs was carried out in the Trans-Alaska Pipeline in1979. Several papers on the behavior of DRA in large installations and its role in energy savings have been published.3-6 In this work, a series of tests with a gel-type DRA were carried out in a commercial pipeline, and the data were correlated by Hinkebein’s method7 based on the original data (2) Rabecki, F.; Henrist, M.; Wilde´ria, D.; Go´mez-Cuenca, F. Shearing of drag reducing polymers in fuel oil pipelines with ultrasonic methods: A feasibility study. J. Appl. Polym. Sci. 2006, 100, 4723–4728. (3) Horn, A. F.; Motier, J. F.; Munk, W. R. Apparent first order rate constants for degradation of a commercial drag reducing agent. In Drag Reduction in Fluid Flows: Techniques for Friction Control; Sellin, R. H. J., Moses, R. T., Eds.; Ellis Horwood Ltd., Publishers: Chichester, U.K., 1989; pp 255-262. (4) Burger, E. D.; Chorn, L. G.; Perkins, T. K. Studies of drag reduction conducted over a broad range of pipeline conditions when flowing Prudhoe Bay crude oil. J. Rheol. 1980, 24 (5), 603–626. (5) Motier, J. F.; Pritulski, D. J.; Shanti, In.; Kostelnik, R. J. Polymeric drag reduction in petroleum products. Proceedings of the 3rd International Conference on Drag Reduction; Sellin, R. H. J., Moses, R. T., Eds.; University of Bristol: Bristol, U.K., 1984; pp 1-23. (6) Motier, J. F.; Chou, L. C.; Kommareddi, N. Commercial drag reduction: past, present and future. Proc. ASME Fluids Eng. DiV. 1996, 237 (2), 229–234. (7) Hinkebein, T. E. An analysis of drag reducing agents for use at the strategic petroleum reserve site at West Hackrerry, Louisiana. SPR Geothermal Division, Sandia National Laboratories, Albuquerque, NM. Projects SAND85-0045 and SAND85-2027, 1985.
10.1021/ef800364a CCC: $40.75 2008 American Chemical Society Published on Web 08/15/2008
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Table 1. Physical Properties and Flow Conditions for the Fuel and the Fuel with DRA fuel properties density at 15 °C (kg/m3) kinematic viscosity at 40 °C (mm2/s) flow conditions number of tests temperature (°C) flow rate (m3/h) friction factor
12 vppm DRA
834.0 ( 0.4 3.134 ( 0.018
and concepts of Virk8,9 for describing and forecasting the behavior of the oil-containing DRA flowing through the pipeline. Also, the DRA efficiency is determined for both the decrease of energy consumption in the oil transport and the increase of oil transportation capability for the same energy consumption. Previous papers4,5 were mainly focused on friction factor reduction and the evaluation of the percentage of DR, while this work is focused on energy savings and increase in transport capability. The method used in this work allows for the calculation of relative energy savings and relative increase in transport capability as well as their limits depending upon the DRA concentration. This analysis would allow for the estimation of the reduction in CO2 emissions that can be attained using a given DRA concentration. 2. Experimental Section 2.1. DRA and Oil. The DRA used is a polyolefin gel type with isopentane as the solvent, with its active polymer content and average molecular weight being 15 wt % and 6.4 × 106 g/mol, respectively. The oil flowing through pipelines during tests was diesel fuel (fuel). Physical properties of fuel and the DRA solutions used in the tests are shown in Table 1. The fuel properties, density and viscosity, were determined at 15 and 40 °C according to the Standards EN ISO 12185 and EN ISO 3104, respectively (Table 1). At test temperatures, fuel density values were calculated by eqs 1 and 2, while the fuel viscosities were determined by eq 3
dt ) exp[-K2(t - 15)][1 + 0.8K2(t - 15)] d15
(1)
where dt is density at t °C, d15 is density at 15 °C, and K2 is given by eq 2.
K2 )
K0 d15
2
+
K1 d15
(2)
The values of K0 and K1 depend upon the density range. For the range of densities from 779 to 839 kg/m3, K0 and K1 are equal to 594.55 and 0.00000, respectively
()
log log(νT + 0.7) ) log log(νT0 + 0.7) + 4.5 log
T0 T
(3)
where νT and νT0 are kinematic viscosity (centistokes) at temperatures T and T0 (K), respectively. For solutions of the fuel with DRA, kinematic viscosity varies linearly with the concentration of DRA for concentrations lower than 200 vppm, while density only varies slightly with respect to that of the fuel for the concentrations of DRA used in the tests. 2.2. Flow System and Setting up of the Measurement Conditions. All experiments were carried out in a section of the pipeline Tarragona-Barcelona-Gerona (TABAGE) of the Spanish network of oil pipelines of the Compan˜´ıa Logı´stica de Hidrocarburos (CLH). (8) Virk, P. S. Drag reduction in rough pipes. J. Fluid Mech. 1971, 45, 225–246. (9) Virk, P. S. Drag reduction fundamentals. AIChE J. 1975, 21 (4), 625–656.
20 vppm DRA
25 vppm DRA
833.4 ( 0.4 3.183 ( 0.018
833.9 ( 0.4 3.223 ( 0.018
831.8 ( 0.4 3.248 ( 0.018
5 17 ( 2 382.5-532.4 0.01036-0.01201
5 18 ( 2 277.1-475.1 0.00886-0.01135
7 27 ( 2 286.9-604.4 0.00850-0.01197
The characteristics of the pipeline section were the following: length and internal diameter were 84.22 km and 307.1 mm, respectively, with a roughness of 0.016 91 mm. The initial and final elevations were 61.0 and 35.0 m, respectively. In every test carried out in the pipeline, data measured were the following: pressure and temperature at the initial and final points and pumping volumetric flow rate. At the initial point of the pipeline section, an infrastructure to inject the DRA was added. The above equipment consists of the following elements: an accumulating tank for the DRA, an injection pump (volumetric flow rate to be varied by a velocity regulator), a flow meter for measuring the doses of DRA injected, and thermostatic equipment to keep the temperature of DRA above 5 °C. To control the DRA injection, every test in the pipeline began with the maximum volumetric flow rate. In this situation, the volumetric flow rate of DRA injected at the origin was the one needed to reach the target concentration. As the injection of additive progresses (keeping the rest of the operational variables constant), the pumping volumetric flow will increase as a consequence of the friction reduction. To compensate for this effect, the DRA flow volumetric rate will be increased to maintain its concentration constant. When the DRA has been flowing for 3 h with proper DRA concentration, the section for testing was considered suitable for measurement. Thus, the fuel was pumped for more than 3 h through the pipeline section with DRA concentrations of 12, 20, and 25 vppm (parts per million in volume, mL/m3). The number of the tests as well as the flow rate range for each DRA concentration are given in Table 1. 2.3. Working Scenarios and Setting up of Turbulent Regime Equations for Estimating Friction Factors and Bulk Velocities of the Fuel. To evaluate the energetic benefit by using DRA, two different scenarios have been set up. In the first scenario, the volumetric flow rate was kept constant with and without DRA. Thus, the use of DRA leads to an energy savings because of the reduction of frictional losses. In the second scenario, energy consumption was kept constant after the addition of DRA, which produces an increase in the volumetric flow rate through the pipeline and, therefore, in the transport capacity of the pipeline. First Scenario (Estimation of Friction Factors with a Constant Volumetric Flow Rate). In this scenario, frictional losses and friction factors were determined in two different ways for the fuel with and without additive. For the fuel with DRA, they were determined from experimental data measured in the pipeline. Friction factors for the fuel were not determined from experimental data, for economic reasons together with the fact that it is very difficult to reproduce the same volumetric flow rate used in the presence of DRA. They were calculated from equations developed for Newtonian fluids in turbulent regime, which were previously validated with experimental data for diesel fuel flowing in a section of CLH pipelines (BASESECTOR). The above methods for the fuel with DRA and the fuel without DRA are described below. Determination of Frictional Losses and Friction Factors from Experimental Data (Fuel with DRA). The loss of pressure in the fluid is due to the energy required to overcome the viscous or frictional forces exerted by the wall of the pipe on the moving fluid. For a pipeline with a constant diameter, the combination of energy balance and continuity for flow between points 1 and 2 leads to the following expression:
Energy-SaVings Modeling with DRAs
(
) (
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)
P1 P2 + z1 ) + z2 + J Fg Fg
(4)
where P1 and P2 are pressures at points 1 and 2, respectively, F is fuel density, g is acceleration because of gravity, z1 and z2 are elevations above the data at points 1 and 2, respectively, and J is frictional losses. J values were obtained from eq 4, while friction factors (f) were determined from the Darcy-Weisbach equation (eq 5)
J)
fLV2 2gD
(5)
where L is the pipe length, D is the pipe diameter, and V is the cross-sectional bulk fluid velocity. Determination of Friction Factors Using Equations for Newtonian Fluids in Turbulent Regime (Fuel without DRA). Because of the difficulties in measuring friction factors for the fuel alone in TABAGE, the equations found for diesel fuel flowing through other pipelines of CLH3 (BASESECTOR) were used to determine friction factors of the fuel in TABAGE. For the diesel fuel flowing through BASESECTOR, the flow is turbulent with a hydraulically smooth regime, because nondimensional roughness k+ < 5. According to this, friction factors can be determined using the equations of Newtonian fluids given by Prandtl-Karman, with the best fit being obtained by Zaragola’s modification10 (eq 6). The comparison of friction factor values (experimental and calculated) shows that the mean relative error of the estimated values by eq 6 is around 1.1%.
1 ) 1.889 log(Re√f) - 0.358 √f
Figure 1. Modeling parameters on Prandtl-Karman coordinates (adapted from Hinkebein7).
(P in Figure 1) and depends upon the polymer species-solvent pair. Abscissa of the above point will be identified by (Ref/ D)c. The region b shows the characteristic linear behavior of the polymeric solutions. In this region, the reduction of the friction factor as a consequence of the polymer addition can be observed. The increase of the slope of the line (δ) depends upon the type of polymer and its concentration for a given solvent,9 thus permitting us to estimate the polymer efficiency. In the region c, over a certain value of Reynolds number, the friction factor stays approximately constant, independent of the Reynolds values. Abscissa of this point (Q in Figure 1) will be identified by (Ref/D)es. This value can be estimated from eq 7.7
(Re√f/D)es )
(6)
For TABAGE, the regime would also be hydraulically smooth because k+ ) 0.4 < 5, which is why Zaragola’s equation was used to calculate friction factors for the fuel flowing through TABAGE. Second Scenario (Estimation of Bulk Velocities with Constant Energy Consumption). By considering the same energy consumption of the tests with DRA, fuel bulk velocities were estimated from both Darcy (eq 5) and Prandtl-Karman (eq 6) equations. The volumetric flow rates (Q) can be easily obtained by multiplying the area of the cross-section of the pipe by the fluid bulk velocity (V). The procedure for calculating bulk velocities for the fuel alone was validated with data from CLH pipelines (BASESECTOR). For the fuel alone, the difference between experimental and estimated volumetric flow rate was lower than 18 m3/h (relative error < 1.8%).
3. Changes in the Friction Factor in the Presence of DRA (DRA Model) The behavior of the oil with DRA can be analyzed using Prandtl-Karman coordinates according to Hinkebein’s scheme7 based on the original data and concepts of Virk.8,9 In such a graphic, 1/f is represented versus log(Re f/D) (Figure 1). In Figure 1, the differences in the behavior of fluids can be seen. A discontinuous line shows the behavior of the polymeric solutions. The polymeric solutions show three different regions of behavior: (a) the region of Newtonian behavior, (b) the region of polymeric behavior, and (c) the region with conditions of hydraulically rough flow surfaces. In the linear region a, the polymer has no influence on the friction factor. From a certain value of Reynolds number, the DRA begins to be an influence and the behavior of the solution becomes different from that of the oil. This value is usually named as the onset point for the region of polymeric behavior (10) Zaragola, M. V.; Smits, A. J. Mean-flow scaling of turbulent pipe flow. J. Fluid Mech. 1998, 373, 33–79.
+ 2√2kes ε
(7)
+ being the with ε being the roughness of the wall duct and kes maximum dimensionless pipe roughness for the effectively smooth regime, which is approximately 50 for a great variety of conditions.8 Between the limits of the region b, zone of our experiments, the polymeric behavior is characterized by a slope different from that of its Newtonian one. The slope of the polymeric line is usually defined with respect to that of the Newtonian behavior. Thus, by subtracting both linear equations, the following equation is obtained:
( ) ( )
Re√f D ) δ log √f f f Re √ DRA √ fuel D 1
1
(8)
c
where fDRA is the friction factor of the oil with DRA, ffuel is that of the oil without DRA, and δ is the difference between the slopes of the straight lines corresponding to the oil with and without DRA. According to eq 8, the plot of 1/fDRA - 1/ffuel against log(Re f/D) is a straight line with slope δ intercepting the abscissa axis at log(Ref/D)c. The estimation of both the slope δ and the intercept log(Ref/ D)c yields an analytical equation, which shows the influence of DRA addition on the friction factor. It should be noted that polymeric drag reduction only occurs in turbulent flow. 4. Results and Discussion 4.1. Effect of DRA Addition on Friction Factors. To determine the efficacy of DRA addition on energy savings, a series of tests was performed in actual pipelines, with flow conditions being shown in Table 1. In Figure 2, data are plotted in Prandtl-Karman coordinates. In each case (fuel without and
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Figure 2. Relationship between the friction factor and the Reynolds number in Prandtl-Karman coordinates.
Figure 5. Power requirements and energy consumption with and without DRA. Figure 3. Efficiency of DRA with concentration.
Figure 4. Determination of model parameters.
with DRA), plots fit to linear equations, with the slope of the fuel being the lowest one in accordance with the model described in section 3. Moreover, an increase in DRA concentration produces a slight increase of the slope. The DRA efficiency (% DR), expressed as the percentage of friction reduction, is calculated by eq 9 and provides a comparison between frictional losses for fuel and those for fuel with DRA maintaining the same flow rate Q. % DR )
(
)
Jfuel - JDRA 100 Jfuel
(9)
The plot of DRA efficiency against DRA concentration shows that decreasing marginal benefits are obtained with the increase in DRA concentration (see Figure 3), with the maximum mean efficiency (45.3%) being obtained for 20 vppm. As can be seen in Figure 3, DRA efficiency does not vary substantially with bulk velocity for a given DRA concentration. Motier et al.5 obtained similar % DR using FLO Pipeline Booster as DRA in a 210 mm in inner diameter × 82 km in length commercial pipeline. At 240 m3/h and using a concentration of 42 ppm of the cited DRA in diesel fuel, a 44.2% drag reduction was achieved. 4.2. Determination of the DRA Model Parameters. To obtain the model parameters, according to eq 8, the plot of 1/fDRA - 1/ffuel versus log(Ref/D) was made for the sector of pipeline tested (TABAGE) and shown in Figure 4.
For each concentration of DRA, Figure 4 shows that data fit to different straight lines, practically parallel lines (r2 > 0.97), whose slopes increase only slightly with DRA concentration, with the slope values being 4.48, 4.55, and 4.69 for 12, 20, and 25 vppm. The fact that the slope scarcely varies with DRA concentration may be related to the relatively tight range of DRA concentrations used. Moreover, the intercepts of these lines with the x axis (onset) obtained by extrapolation are quite similar, with the abscissa values decreasing slightly with the DRA concentration, so that the values obtained were 4.25 for 12 vppm, 3.97 for 20 vppm, and 3.95 for 25 vppm. Virk9 found that, for solutions of a given polymer, onset corresponds to a single critical wall shear stress and, therefore, is essentially independent of the DRA concentration. However, from this work data, it is not possible to affirm that onset occurs at a single value, because as our data are situated far from it, this produces an error in the extrapolation to determining the said onset. The plot of the onsets (log(Ref/D)c) versus DRA concentration fits to a straight line with a correlation coefficient of 0.8863, with the onset decreasing slightly with the DRA concentration (eq 10). Heinkebein7 found that onset depends upon concentration by using experimental data close to it.
( )
log
Re√f ) -0.0238C + 4.5091 D c
(10)
The variation of the slope (δ) with DRA concentration can be fitted to an equation of the type δ ) aCn for a very small value for n. For n equal to 0.06, the correlation coefficient obtained was 0.9998. 4.3. Energy Savings Using DRA on Pipeline Oil Transportation Systems. Below, the benefit of the use of DRA will be analyzed considering the two different scenarios previously mentioned: (a) reduction of energy consumption (first scenario) and (b) enhancement of transportation capability (second scenario). SaVings in Power Requirements and Energy Consumption (First Scenario). Power requirements to balance frictional losses with DRA against those without DRA are shown in Figure 5a (height differences have not been considered). For each DRA concentration, data fit to straight lines that cross the diagonal
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Energy & Fuels, Vol. 22, No. 5, 2008 3297
Figure 6. Asymptotic function of relative energy savings.
line and whose correlation indexes are higher than 0.99. The power requirements for the intercept of the above lines with the diagonal line are those of the onsets. Analogously, Figure 5b shows energy consumption per unit of mass transported and per unit of distance covered. Also, the intercepts with the diagonal line give us the energy consumptions of the onsets. For each DRA concentration, the slope of the straight line (m) is related to the relative energy savings with respect to the onset, according to the following equation: 1-m)
(Efuel - Eonset) - (EDRA - Eonset) (Efuel - Eonset)
(11)
with Efuel and EDRA being the energy consumptions for the fuel and the fuel with DRA for the same volumetric flow and Eonset being the energy consumption for the onset of the polymeric behavior. From eq 11, relative energy savings can be obtained by eq 12:
(
Eonset Efuel - EDRA ) (1 - m) 1 Efuel Efuel
)
Figure 7. Volumetric flow rate with DRA versus that without DRA for constant energy consumption.
(12)
Thus, for each DRA concentration, relative energy savings is an asymptotic function of the energy consumption for the fuel without DRA, with the asymptote being (1 - m). In Figure 6, both eq 12 and the experimental relative energy savings (ranging from 32 to 38% for 12 vppm, from 40 to 48% for 20 vppm, and from 39 to 50% for 25 vppm) are shown. According to eq 12, the limits of the energy savings are (1 - m), with them being 45, 53, and 54% for 12, 20, and 25 vppm, respectively. Burger et al.4 carried out several tests using Conoco CDR drag-reducing additive in a 343 mm in inner diameter × 8.29 km in length commercial pipeline. The fuel transported was Sadlerochit crude oil, with flow rates ranging from 104 to 244 m3/h and several DRA concentrations. With data from Burger et al. for 20 wppm of DRA and applying the procedure previously described, a limit energy savings of 29% was obtained (Figures 5b and 6). The energy savings is lower than that obtained in this work because of the fact that the polymer-solvent system is different. Not only can the DRA efficiency be different but also the DRA performance depending upon the type of oil flowing along the pipeline. Motier et al.5 indicated that, in general, DRA is more effective in diesel fuel and gasoline than in crude oil. Increase of Transport Capability (Second Scenario). Because the increase of pipeline transport capability can be a matter of a great interest for oil companies, the benefits of using DRA can be evaluated from this perspective. Such an increase can be obtained by determining the increase of oil volumetric flow rate for a constant energy consumption. Without DRA and for the same energy consumption, which implies the same frictional
Figure 8. Asymptotic function of the relative increase of the volumetric flow rate.
losses, the volumetric flow rate is lower than that with DRA because of the existence of higher friction factors. In this scenario, the experimental data for the fuel with 12, 20, and 25 vppm of DRA were also used, although the volumetric flow rate for the fuel was calculated according to the procedure described in the second scenario of section 2.3. For each DRA concentration, the plot of volumetric flow rates with DRA against those without DRA fits to a straight line (r2 > 0.99), whose slope will be named m′ (Figure 7). Also, the volumetric flow rates for the intercepts of the straight lines with the diagonal line are those of the onsets. For each concentration, the relative increment of the transport capability with respect to the onset is given by eq 13 m′ - 1 )
(QDRA - Qonset) - (Qfuel - Qonset) (Qfuel - Qonset)
(13)
with Qfuel and QDRA being the volumetric flow rates for the fuel and the fuel with DRA for the same energy consumption and Qonset being the volumetric flow rate for the onset of the polymeric behavior. From eq 13, a relative increase of transport capability can be obtained by the asymptotic function given by eq 14:
(
Qonset QDRA - Qfuel ) (m′ - 1) 1 Qfuel Qfuel
)
(14)
Thus, for each DRA concentration, a relative increase of transport capability is a function of the volumetric flow rate of the fuel. The asymptote of the above function (m′ - 1) corresponds to the limit of the energy savings, being 50, 61, and 64% for 12, 20, and 25 vppm, respectively. Equation 14 together with the experimental relative increases of volumetric flow rate (ranging from 24 to 30% for 12 vppm, from 33 to 44% for 20 vppm, and from 32 to 47% for 25 vppm) is shown in Figure 8. By applying eq 14, for a volumetric flow rate of
3298 Energy & Fuels, Vol. 22, No. 5, 2008
the fuel of 320 m3/h and using a DRA concentration of 20 vppm, the increase in transport capability would be 43%, which implies a volumetric flow rate of 458 m3/h. The increase in the transporting capability of the pipeline will lead to a reduction in the necessity of using an additional way of oil transporting, such as road transporting. This will produce an energy savings as well as an environmental benefit derived from the reduction of CO2 emissions. 5. Conclusions A series of tests have been carried out in a 307 mm in inner diamater × 84 km in length commercial pipeline to determine the efficiency of a polyolefin gel-type DRA (12, 20, and 25 vppm) on drag reducing when diesel fuel is being transported (60 000 < Re < 160 000). Experimental data fit to the model proposed by Hinkebein satisfactorily, and slopes and onsets were obtained to characterize the polymeric behavior of the diesel with the DRA additive. On one hand, a slight increase of slope with DRA concentration was observed. The variation of the slope versus DRA fits to an equation of the type δ ∝ Cn, with n being very small (around 0.06). On the other hand, a single onset was not seen, because it undergoes a slight decrease with the DRA concentration, with the data fitting to a straight line.
Go´mez Cuenca et al.
The effectiveness of the DRA on energy savings was evaluated by determining both the reduction of energy consumption for a constant volumetric flow and the increase in transport capability for constant energy consumption. The decreases of both power requirements and energy consumption obtained from the decrease of friction factors are proportional to those of the frictional losses. For a given DRA concentration, the relative energy savings fit to an asymptotic function of the energy consumption for the fuel. The asymptotes, which represent the relative energy savings limit, were 45, 53, and 54% for 12, 20, and 25 vppm, respectively. Analogously, the relative increase in transport capability for a given DRA concentration also fits to an asymptotic function of the volumetric flow rate for the fuel. The limits of the relative increase in the volumetric flow rate were 50, 61, and 64% for 12, 20, and 25 vppm, respectively. For a DRA concentration of 20 vppm, power and energy savings achieved values ranging from 40 to 48%. For the same concentration, the increases in transport capability ranged from 33 to 44%. Thus, the use of this type of additive leads to important energy savings and, additionally, an important reduction in CO2 emissions. EF800364A
