Chen Yang
Li Changjun
Southwest Petroleum University
Chengdu, China.
A.M. Nechval
Ufa State Petroleum Technology University
Ufa, Russia
Yang Peng
Southwest Branch Co. of Sinopec
Chengdu
A. Yu. Zhukov
Kazan Federal University
Kazan, Russia
Formulating drag reducing agents' (DRA) average concentration and corresponding drag reduction efficiency can show that mechanical degradation of DRA not only occurs after its dissolution but also while dissolution is underway.
Most studies about polymer degradation in DRA have concentrated on the polymers' molecular construction and their chain scission during shear degradation. These studies, however, have used short pipes. Even field experiments were conducted in a 7.5-km pipe. Polymer degradation is a long process. This article's study was carried out in a 130-km commercial refined products pipeline.
Experimental procedure
All experiments used M-Flowtreat poly alpha olefin (PAO)(Oil & Gas Journal, May 1, 2017, p. 70). Tables 1 and 2 show the physical properties of the diesel and DRA respectively. The 130-km pipeline had 20-in. OD and relative roughness, ε, = 8.92 × 10-5. Experiments used 5.82-15.96 ppm DRA, inducing 28-55% drag reduction.
To exclude the pump's shear action on additives, the field experiment occurred between two stations, adding DRA after the first pump, with pressure measurement done at the beginning and end of pipeline (Fig. 1). Pressure drops on each section of the pipe were measured with absolute-pressure transducers (Fig. 2, Table 3).
The experiment lasted 84 hr in steady-state conditions, with an average flow of Q = 1,231.94 cu m/hr. It took 6 hr to administer the DRA (Figs. 3-4).
Fig. 5 shows pressure head distribution along the pipeline with different additive concentrations and after pressure correction for measuring error and hydraulic slope.
Results
Evaluation of the PAO's frictional resistance coefficient, λ, used Equation 1. With the addition of DRA the value A0 increases. On the basis of experimental data, Equation 2 expresses A0 by empirical equation θ, with R-square = 0.9931.
Fig. 6 compares the slope increment obtained through the predicting model with the experimental measured data, showing an error <0.5%. Therefore, in pipeline transportation, diesel pressure drop dP/dx can be expressed as shown in Equation 3.
Definitions
With constant flow Q = idem, Equation 4 can calculate drag reduction efficiency. Different heights of experimental pipe section in this experiment allow confirmation of drag reduction efficiency via Equation 5.
Equation 6 calculated hydraulic gradient without DRA while diesel was being transported. Average pressure was calculated within 6 hr for a given DRA concentration, θ0, in stationary condition. Equation 7 expresses pressure and elevation head in the point of j-section's pressure transducer, relative to the head at the beginning of the pipeline (M0).
Equation 8 confirms hydraulic gradient while transporting diesel with DRA. Therefore, according to Equation 5, drag reduction efficiency and its asymptote are shown in Fig. 5.
Jouenne considered there was no mechanical degradation for velocities lower than a certain value regardless of the polymer concentration in his experimental range. The field experiment seemed to be incorrect. Jouenne, however, didn't account for degradation due to the short experimental distance (7.5 km).
On a 130-km scale, the drag reduction process can be divided into two parts: dissolution and degradation (Fig. 6). Field experiments, however, indicated that in the process of dissolution polymer additive degradation is also happening. Fig. 7 shows that the curve gradually drops after peak value, allowing the degradation process to be expressed by Equation 9.
Equation 9, therefore, can easily calculate initial drag reduction efficiency, while Equation 10 shows DRA concentration, θ, during diesel oil transport at distance X from the position of adding the DRA.
Fig. 6 shows the change of PAO concentration by transport distance during the field experiment. In the first 20 km of pipe DRA is gradually dissolving and, after the peak value, additive concentration is gradually decreasing, which can be explained by polymer mechanical degradation. Since the field experiment was carried out at normal temperature, temperature's influence on mechanical degradation was not considered.
Equation 11 expresses the material concentration derivative. Ignoring the axial fluctuation of polymeric concentration in the pipe and treating transportation as a steady flow allows treating the whole process as one-dimensional flow. Under these conditions, Equation 12 confirms in-pipe DRA concentration.
Assuming axial fluctuation of polymeric concentration was ignored allows simplifying Equation 12 as Equation 13. Logarithmic non-dimensional form is considered, but the obtained θ(x) fits the experimental data poorly. Applying αθβ to replace Equation 13's dimensional expression lets θ(x) be calculated by Equation 14.
Fig. 6 shows that in the dissolving process additive concentration linearly increases with transport distance. Therefore, in combination with the dissolving process, the whole transport process with DRA can be expressed by Equation 15.
DRA concentration, efficiency
In accordance with Equation 15, the integration of θ(x) in the diesel oil pipeline (L0 = 130 km) can be obtained via Equations 16 and 17. According to Equation 10, DR(ϴ0, x) = ϴ(x)/a1+a2 ϴ(x)2, therefore average drag reduction efficiency could be expressed as Equation 18.
Acknowledgent
We would like to acknowledge support from Mirriko Co. and assistance from the Southwest Branch Co. of Sinopec. This study was financially supported by the subproject of the National Science and Technology Major Project of China (No.2016ZX05028-001-006); the National Natural Science Foundation of China (No.51474184, No.51504026); Research Project of the Education Department of Sichuan Province (No.15ZB0050), and China Scholarship Council.
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The authors
Chen Yang ([email protected]) is a researcher in State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation, Southwest Petroleum University, Chengdu, China. She has also served as a researcher in Ufa State Petroleum Technology University, Ufa, Russia. She holds PhDs from Southwest Petroleum University and Ufa State Petroleum Technology University. She is a member of Society of Petroleum Engineers (SPE).
Li Changjun ([email protected]) is the chief of the Oil-Gas Storage and Transportation Department, Southwest Petroleum University, Chengdu. He holds a PhD from Southwest Petroleum University. He is a member of Chinese Petroleum Society (CPS).
A.M. Nechval ([email protected]) is a PhD supervisor in Ufa State Petroleum Technology University, from which he holds a PhD.
Yang Peng ([email protected]) is a senior engineer of Southwest Branch Co. of Sinopec, Chengdu. He previously served as an engineer of Northwest Branch Co. of Sinopec, Urumqi, China. He holds a PhD from Southwest Petroleum University. He is a member of Society of Petroleum Engineers (SPE).
A. Yu. Zhukov ([email protected]) is a senior researcher in Kazan Federal University, Tartarstan, Russia, from which he holds a PhD.