Heavy crude oil (S G=0.925 and ν=1.0 ×10^-4 m^2 / s) is pumped through a pipeline laid on flat

step 1 In this question you have to find the maximum spacing between pump stations and also find the po

Heavy crude oil (S G=0.925 and ν=1.0 ×10^-4 m^2 / s) is...

Heavy crude oil $\left(S G=0.925 \text { and } \nu=1.0 \times 10^{-4} \mathrm{m}^{2} / \mathrm{s}\right)$ is pumped through a pipeline laid on flat ground. The line is made from steel pipe with $600 \mathrm{mm}$ i.d. and has a wall thickness of $12 \mathrm{mm}$. The allowable tensile stress in the pipe wall is limited to $275 \mathrm{MPa}$ by corrosion considerations. It is important to keep the oil under pressure to ensure that gases remain in solution. The minimum recommended pressure is 500 kPa. The pipeline carries a flow of 400,000 barrels (in the petroleum industry, a "barrel" is 42 gal) per day. Determine the maximum spacing between pumping stations. Compute the power added to the oil at each pumping station.

Key Concepts

Pipeline Structural Integrity

Ensuring the structural integrity of a pipeline involves analysis of the stresses induced in the pipe material due to internal pressures and external forces. Key aspects include hoop stress and longitudinal stress, which must be kept below the material’s allowable limits to prevent failure. This concept is crucial when selecting materials and designing pipelines, especially under conditions where corrosion or other environmental factors may limit the allowable stress.

Pumping Power Calculation

The concept of pumping power involves quantifying the energy required to overcome pressure drops and to maintain the necessary flow rate within a pipeline. This calculation is based on the fluid’s properties, the pipeline’s geometry, and the operating conditions. Engineers use relationships between pressure head, flow rate, and mechanical energy to design efficient pumping systems and determine optimal spacing between pumping stations.

Viscosity and Reynolds Number

Viscosity is a measure of a fluid’s resistance to deformation, which is crucial in determining flow characteristics within a pipe. The Reynolds number, a dimensionless parameter, is used to predict whether the flow will be laminar or turbulent. This classification is important because it influences the selection of friction factor correlations and affects pressure loss and pump sizing calculations.

Fluid Flow in Pipes

This concept involves understanding how fluids behave when transported through conduits. It encompasses the relationships between pressure, velocity, viscosity, and frictional forces that affect the movement of the fluid. Engineers use principles like the continuity equation and Bernoulli’s equation alongside empirical correlations (e.g., the Darcy-Weisbach equation) to predict pressure drop, flow rate, and energy loss due to friction.

Pressure Drop and Friction Loss

Pressure drop in a pipeline occurs due to frictional resistance between the fluid and the pipe walls, as well as due to any changes in elevation or fittings. Understanding and calculating pressure drop is critical, as it dictates the required pump head to maintain a prescribed flow rate. The Darcy-Weisbach equation is a common tool used for estimating friction losses in pipe systems.

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