PSI - Issue 36

344 S. Hryhorskyi et al. / Procedia Structural Integrity 36 (2022) 342–349 S. Hryhorskyi et al. / Structural Integrity Procedia 00 (2021) 000 – 000 3 using the least squares method for the full range of pump flows); i r is the number of pumps in operation at the oil pump station; n is number of OPS on the pipeline route; 3) checking the conditions for technological pressure limitations: for the minimum permissible operating pressure min і P , to ensure reliable and cavitation-free operation of centrifugal pumps at intermediate pump stations; according to the maximum possible working pressure max і P , to ensure the strength of the linear part of the oil pipeline:

,

і inp P P P P

out     

max

(4)

і

,

min

і

і

where і inp P , і out P are excess oil pressure at the inlet and outlet of the oil pumping station; 4) checking the condition for the absolute difference between the required r f P and actual inlet to the final point of the pipeline to ensure accuracy for the final pressure P  :

a f P pressure at the

(5)

.

f f P P P  − 

r

a

The pipeline capacity is calculated using the successive approximation method and contains the following blocks. First, for the accepted value of the volumetric flow rate in the system Q , the oil velocity is calculated using the flow continuity equation w , then the Reynolds number Re . The coefficient of hydraulic resistance  is determined by the modified Kolbrook's formula taking into account the transitional Reynolds number (Serediuk and Grygorskyi (2015)). These parameters are also determined using iterations with a previously accepted calculation accuracy. The hydraulic calculation of each stretch is carried out according to the formula (1). In the future, hydraulic equations are used that regulate the joint operation of the pump station and the linear part of the oil pipeline. The pressure at the beginning of each of the sections is determined taking into account the value of the throttling of the oil flow at the outlet of the OPS, and the oil pressure at the section end is determined taking into account the actual pressure losses. If there is a limiting section, at the end of which pressure is equal to the minimum allowable operating value at the inlet to the OPS min і P , an additional throttling value is calculated. Iterative calculations are performed until condition (5) is satisfied. After that, the throughput of the pipeline is determined, taking into account oil leaks q . In this case, the ratio between the productivity of the pipeline before Q and after the leak Q  with the value q has the form: . Q Q q  = − (6)

For a small hole in the wall of an oil pipeline, when the difference in head pressure inside the pipeline and outside it is much larger than the linear dimensions of the hole, the oil flow through the hole is expressed by the formula:

2 , х Р 

(7)

q f 

=  

l



where  is the coefficient of oil flow through the hole, determined depending on the Reynolds number for the hole Re l (Table 1); l f is sectional area of the hole, m 2 ; х Р is excess oil pressure in a section located at a distance і x , Pa. With a known volumetric flow rate q of oil through a small hole, using formula (7) and dependencies from table 1, you can calculate the linear dimensions of the hole. For example, determine the equivalent diameter of a round hole in a pipeline e d . The algorithm for calculating the equivalent diameter of a round hole is as follows: 1. We take as a first approximation the coefficient of the flow rate of the hole 0,60  = . 2. Determine the approximate value of the hole area using the formula:

q

Р 

(8)

.

f

 = 

l

2



х