Petroleum and marine technology applications and infrastructures consist of extended pipelines’ networks in order to accommodate fluid transfer needs. The pipelines’ leaks may occur and lead to high energy and working fluid losses, while most of the times these are related to environmental hazards. Additionally, corrosion problems are reported due to this un-desirable flow rate loss. In this paper the rheological behavior of the crude oil flow inside pipes with one or two leakages is numerically analyzed, studied and solved. Un-uniform and adaptive grids to the location of the leakages are generated in order to cover the specific requirements of the pipe domain, while finite volume methodology is followed for the discretization of the flow equations. The type of the oil has been received to be the Arabian light one, while an approach is developed for its properties. The boundary conditions are the corresponded flow rate – pressure flow conditions for all the exits of the pipe due to the better control of the algorithm that they usually provide. Various test cases have been developed for different Reynolds number values, providing robust and accurate results concerning the velocity and pressure distribution. It seems that high pressure variation is depicted near the location of the leaks, and in this way a clear indication is occur for such phenomenon. Petroleum and marine technology applications and infrastructures consist of extended pipelines’ networks in order to accommodate fluid transfer needs. The pipelines’ leaks may occur and lead to high energy and working fluid losses, while most of the times these are related to environmental hazards. Additionally, corrosion problems are reported due to this un-desirable flow rate loss. In this paper the rheological behavior of the crude oil flow inside pipes with one or two leakages is numerically analyzed, studied and solved. Un-uniform and adaptive grids to the location of the leakages are generated in order to cover the specific requirements of the pipe domain, while finite volume methodology is followed for the discretization of the flow equations. The type of the oil has been received to be the Arabian light one, while an approach is developed for its properties. The boundary conditions are the corresponded flow rate – pressure flow conditions for all the exits of the pipe due to the better control of the algorithm that they usually provide. Various test cases have been developed for different Reynolds number values, providing robust and accurate results concerning the velocity and pressure distribution. It seems that high pressure variation is depicted near the location of the leaks, and in this way a clear indication is occur for such phenomenon.