PSI - Issue 36

S. Hryhorskyi et al. / Procedia Structural Integrity 36 (2022) 342–349

345

4

S. Hryhorskyi et al. / Structural Integrity Procedia 00 (2021) 000 – 000

In this case, the oil pressure х Р in the section of the hole can be determined using the Bernoulli equation written for the section at the beginning of the section and the section of the leak taking into account the volumetric flow rate of oil before the leak Q .

Table 1. Dependencies for calculating the flow coefficient of a round through hole (Vasiliev et al. (2002)). Reynolds number Re l < 25 25 …400 400 …10 4 10 4 …3·10 5

> 3·10 5

5.5

6 0.27 0.592 Re o +

Re

Re 1.5 Re 1.4 o o  +

0.592

+

Flow rate coefficient 

o

0.60

Re o

48

3. Calculate the equivalent diameter of a round hole:

4 , м. о f 

(9)

d

=

o



4. Calculate the Reynolds number for the hole:

2 P   

d

Re

,

l = 

x

(10)

l

where  is kinematic viscosity of oil under pumping conditions, m 2 /s. 5. Depending on the value of the Reynolds number Re l , we select the formula (Table 1), according to which the updated value of the hole discharge coefficient is calculated it  . 6. Further, according to the formula (8), the refined value of the cross-sectional area of the hole it l f is determined, and according to the formula (9), the equivalent diameter of the hole it l d is correspondingly refined at the value of the flow coefficient it  . 7. The iterative process of calculations ends when the condition:

,

it l l d d d −  

(11)

where d  is the accuracy of calculating the diameter of the hole is accepted, m. Otherwise, we accept , it l l d d =

(12)

and continue the calculations, starting from point 4. The maximum possible loss of oil from infiltration into the soil can be estimated using the formula (Tugunov et al. (2002)):

   

   

2

   

   

k

m

k

m

  

  

q V   −

f

d p

f

d p

(13)

,

G q V S

=   − − 

+

−

d

c

inf

. .

d

c

o s

 

2

2

S

. .

o s

where d  is duration of oil filtration into the ground, s; c V is volume of oil collected from the soil surface as a result of emergency recovery operations, m 3 ; . . o s S is oil slick area (oil surface), m 2 ; f k and p m are filtration coefficient and soil porosity, respectively. To estimate the area of an oil slick, one of the empirical dependencies can be used (Tugunov et al. (2002)): - on a horizontal ground surface: