The Reliability of Thermal Analysis of Cross-Country Gas Pipelines B
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Technical Physics, Vol. 47, No. 4, 2002, pp. 375–379. Translated from Zhurnal TekhnicheskoÏ Fiziki, Vol. 72, No. 4, 2002, pp. 1–5. Original Russian Text Copyright © 2002 by Kudryashov, Litvinenko, Serdyukov. THEORETICAL AND MATHEMATICAL PHYSICS The Reliability of Thermal Analysis of Cross-Country Gas Pipelines B. B. Kudryashov*, V. S. Litvinenko*, and S. G. Serdyukov** * St. Petersburg State Mining Institute (Technical University), Vtoraya liniya 21, St. Petersburg, 199026 Russia ** Lentransgaz Ltd. Received July 26, 2001; in final form, October 10, 2001 Abstract—In the designs of gas pipelines that must be laid on the bottom of north and south seas, the reliability of analytical results for the gas temperature in the pipelines is questionable. The reason is that different authors take into account various factors influencing the temperature conditions in the pipelines. © 2002 MAIK “Nauka/Interperiodica”. Today’s gas pipeline is a very complex and expen- projected to be laid in deep-water layers of the Barents, sive structure that is designed for long-term trouble- Black, and Caspian seas. Therefore, Shukhov’s formula free exploitation. The design and construction of any can no longer adequately describe the temperature dis- gas pipeline is based on extensive engineering work tribution. The authors of handbook [1] suggest the dif- that takes into account multiple factors, such as preset ferential equation capacity; mechanical strength; reliability; stability p – p against technogenic and environmental effects, includ- –kπDt()– t dx = Gc dt+ Gc Dh----------------1 -2dx ing natural calamities; and environmental safety. In r p p l addition, the pipeline material must withstand mechan- (2) ∆z v 2 ical wear and corrosion for a long time, the design must + Gg------dx+ Gd ------ , be accident-proof, etc. l 2 The validity of the available design methods, specif- which, as they argue, includes all the factors influenc- ically, hydraulic (aerodynamic) methods, is beyond ing the gas temperature in the pipeline. Ignoring the gas question in most cases, since it has been repeatedly velocity variation (the last term on the right-hand side) checked during the long-term exploitation of the exten- and integrating Eq. (2), they come to an equation for the sive gas-pipe networks. However, the reliability of the gas temperature at any point of the pipeline: analysis of the gas temperature distribution in pipelines is questionable, because different authors variously tt= + ()t – t e–ax take into account factors influencing the temperature r 0 r conditions in gas pipelines. p – p 1 – e–ax ∆z1 – e–ax (3) – Dh----------------1 -2 ----------------- – g----------------------- ; Over many years, the temperature distribution in gas l a l c pa and oil pipelines has been estimated with well-known kπD Shukhov’s formula a = ---------- , kπD Gcp –-----------x ()Gcp tt= r + t0 – tr e , (1) where Dh is the Joule–Thomson coefficient for natural ° 5 gas, C/10 Pa; p1 and p2 are the gas pressures at the where t and t0 are the instantaneous and initial gas tem- beginning and at the end of the pipeline, Pa; ∆z is a rise ° peratures, respectively, C; tr is the environmental in the level, m; and l is the total length of the pipeline, m. (rock) temperature, °C; k is the coefficient of heat trans- 2 ° However, both initial equation (2) and Eq. (3), fer through the pipeline wall, W/(m C); D is the inner which is used in calculations, lack the term that takes diameter of the pipeline, m; G is the mass flow rate of into account the work of friction of the gas flow. Note the gas, kg/s; cp is the specific heat of the gas at constant ° that the authors of [1] contradict themselves. In the sec- pressure, J/(kg C); and x is the distance from the begin- tion devoted to the Joule–Thomson effect upon throt- ning of the pipeline. tling [1, p. 11], they argue that “…the work spent to Currently, gas pipelines many thousands of kilome- overcome obstacles… is converted to heat and is ters long pass through permafrost, cross huge water received by the substance…adiabatic throttling of obstacles, and have large level drops. New pipelines are gases, vapors, and liquids is an isoenthalpic process, 1063-7842/02/4704-0375 $22.00 © 2002 MAIK “Nauka/Interperiodica” 376 KUDRYASHOV et al. h = idem.” On the other hand [1, p. 16], it is argued that are intended to prevent negative temperatures that are “in the absence of external heat exchange, the tempera- expected at the end of the pipeline. ture of the gas being transported changes due to only “Throttling is a method of expanding a gas at con- the Joule–Thomson effect and a change in the position stant enthalpy when it passes through a throttle (that is, of the center of gravity of the flow.” through a local resistance, such as an aperture, nozzle, While analyzing the throttling of natural gas, Rus- pipe connection, valve, cock, tube constriction, etc.). sian engineers usually take the Joule–Thomson coeffi- The expansion, in this case, is attended by a tempera- cient in the range Dh = 3–5 K/MPa. A particular value ture change because the energy is spent to overcome the depends on the pressure and temperature. The value of internal molecular forces of mutual attraction” [2, p. 87]. Dh can be found by various techniques according to Upon the adiabatic throttling of oil in the near-bottom specific conditions [1–3]. We will find it with the for- region of a well, the oil temperature grows, while the mula for adiabatic expansion, taking the formula for gas temperature drops. This makes it possible to evalu- gas adiabatic expansion as the basis: ate the collecting properties of a pool and determine the k – 1 structure of strata [5]. In industrial condensed gas -------------0 - k T2 p2 0 equipment, the throttling effect is used for cooling nat- ----- = ----- . (4) ural gas in order to separate out water and readily con- T p 1 1 densing hydrocarbons [1]. In all these and similar The parameters of the improved version of the Blue cases, formula (4) for the Joule–Thomson coefficient is Flow project [4] are the following: rate of gas delivery valid and can be applied for calculations under specific simultaneously through two pipelines is 16 billion m3 conditions, since it holds only for sudden adiabatic gas pear year; the length and outer diameter of the pipelines expansion and this effect can by no means be “diffused” are 380 km and 24′′, respectively; the thickness of the throughout the many-kilometer pipeline. pipeline wall is 31.8 mm; the pipelines must be laid on Actually, when gas transport through a horizontal the Black Sea bottom at a depth of 2150 m; the methane pipeline lying deep in a rock is steady, the process is pressure at the beginning and end of the pipeline is similar to the adiabatic gas flow with friction, because 251.5 and 130.8 bar (abs.); the adiabatic exponent for the specific heat of rocks is high and their thermal con- methane (97.5% in natural gas) is k0 = 1.314; the initial ductivity is low. During the transport, the heat from the gas temperature at the Beregovaya station is t = 50°C or gas-heated pipeline wall returns to the gas and the gas T1 = 273 + 50 = 323 K (according to the estimates made in the pipeline cools down by converting the potential by Italian engineers [4]); the compressor discharge energy of pressure to the kinetic energy of the gas pressure is p1 = 251.5 bar; and the pressure at the Turk- (without allowance for external heat exchange). The ish coast is p2 = 130.8 bar. Then, the temperature at the degree of cooling is defined by the difference between end of the pipeline should be the initial and final velocities squared. In this case, the k – 1 gas temperature drop can be found, e.g., from the Ale- -------------0 - 1.314– 1 k ---------------------- ksandrov formula [6] p 0 130.8 1.314 T ==T -----2 323 ------------- =276.28 K. 2 1 2 2 p1 251.5 v v ∆ k0 – 1 2 – 1 ∆ T = ------------- ------------------, (5) The temperature drop will be T = 323–276.28 = k0 2R 46.72 K, and the pressure drop will be ∆p = 251.5– 130.8 = 120.7 bar = 120.7 × 105 Pa. Accordingly, the where v1 and v2 are the cross-section-averaged veloci- Joule–Thomson coefficient in this case is ties of compressible gas at the beginning and end of the pipeline, m/s; k is the adiabatic exponent (for methane, ∆T 46.72 0 Dh ==------- --------------------------- =3.87 K/MPa, k = 1.314); and R is the gas constant (for methane, R = ∆ 5 0 p 120.7× 10 500 J/(kg K)). which virtually coincides with the midpoint of the For the parameters of the Blue Flow version listed range Dh = 3–5 K/MPa. above, v1 = 4.27 m/s and v1 = 6.94 m/s. Then, accord- We do not know the methods of thermal analysis ing to formula (5), the gas temperature drop is less than applied by the Italian engineers in the Blue Flow 0.01°C. This value is convincingly confirmed by expe- project. It is noteworthy, however, that with the calcu- rience of many years in drilling wells with air (gas) lated value Dh = 3.87 K/MPa substituted into Eq. (3), blow and measuring the temperature distribution in which ignores the work of flow friction, we do obtain them [7–10]. Early in the development of this technol- ° the gas temperature at the Turkish coast t2 = –10 C.