## 3 Results and Discussion
### Effect of Varying Crude Oil Grades on Maximum Induced Stresses  
Slug flow occurrence is known to cause serious damage to pipelines. Hence, the effect of slug characteristics on induced stresses in carbon steel pipes is investigated in this work. Figure 15 shows that varying crude oil grades cause significant variation in maximum induced stresses values. The flow of light crude oil records the lowest induced stresses. However, as the crude oil density increases, the induced stresses increase.  
Figure 15 also shows that the flow of light and medium crude oil in carbon steel pipe records a marginal increase in stresses when the liquid and gas velocities change. By contrast, when heavy and extra heavy crude oil flow in pipes, the margin of increase in induced stresses due to changes in gas and liquid velocities is significant.  
Moreover, for very heavy crude oil, the maximum induced stresses decrease by up to 33% when the liquid velocity increases at a constant gas velocity. Meanwhile, decreasing the gas velocity at 0.93 m/s liquid velocity records the lowest induced stresses for all crude oil grades.  
The slug initiation position is a function of the operating conditions and physical properties of flowing media. Slug formation in piping systems subsequently exerts hydrodynamic loads on the piping's inner surface. The perturbation of the slug that moves with a velocity higher than the gas and liquid superficial velocities causes high momentum, which is then transferred to the piping wall where it causes induced stresses.  
Figure 16 illustrates the relation between the slug initiation position and the induced stresses for Case 1. As the slug formation occurs at 64D (D represents the pipe diameter) for the light crude oil, the maximum induced stress observed is 48 MPa at the location of slug formation. When the crude oil density increases, the liquid slug translational velocity increases (Figure 13), thereby causing the slug to move with high momentum. This condition leads to high induced stresses, as seen in the medium crude, heavy and very heavy crude oil grades with maximum recorded induced stresses of 54, 189 and 216 MPa, respectively, as shown in Figure 16.  
Figure 15: Effect of varying crude oil grades on maximum induced stresses.  
Sluq liquid length is one of the main variables that characterise slug flow and could be associated with maximum induced stresses when the liquid impinges on the internal wall of the pipe. Thus, the relationship between slug length and maximum induced stresses for various crude oil grades should be understood.  
Figure 17 shows that for all cases (Cases 1, 2 and 3), when the slug length increases, the recorded maximum induced stresses decrease. For heavy and extra heavy crude oil at a constant gas velocity, increasing the liquid velocity causes a decrease in slug length and consequently leads to high stresses. A possible reason is that the stresses are related to both the magnitude of force and the area. Hence, the induced stresses caused by the slug flow is affected by the fluid density and mass of the slug and the size of the crude oil slug impinged area at the pipe surface.  
Figure 16: Effect of slug hydrodynamics (A) on the maximum induced stresses (B) (‘D’ represents pipe diameter).  
However, decreasing the gas velocity to 0.7 m/s at 0.93 m/s liquid velocity records the lowest induced stresses for all investigated cases. It is important to mention that this research mainly investigates varying the liquid velocity at constant gas velocity.  
The results of the induced stresses indicate the need to carefully perform pipeline designs that handle heavy and extra heavy crude oil because the maximum induced stresses may change significantly after a slight change in liquid superficial velocities. Moreover, when the slug moves at a velocity that is higher than the gas and liquid superficial velocities, the slug moves with higher momentum, resulting in higher maximum induced stresses.