Introduction
Tank overfilling occurs when the liquid stored in a tank exceeds its capacity, causing a spill. This can happen in various scenarios, such as in filling, due to operator errors, equipment malfunction, etc. Tank overfills can cause environmental damage and pose safety risks when the stored liquid is hazardous. Additionally, this can lead to financial losses, as well as damage to the tank and related equipment.
Storage tanks must be equipped with drainage lines to allow the fluid contained to be discharged in a safe and controlled manner. Drain lines should be connected to the tank near the top, at a lower level than the tank feed line. It is critical that the drain line is designed to be ventilated. Otherwise, it can easily happen that the tank drain fails due to the generation of vacuum in the line.
Tank overfill drain lines are usually vertical pipes through which the liquid flows downward by the action of gravity (see Figure 1). These are free surface flows where the liquid flow does not completely fill the diameter of the pipe, therefore coexisting with an air phase. When gas and liquid flow simultaneously in a pipe or duct, various flow regimes can result depending on the pipe geometry, fluid properties, volumetric fractions, and velocities of each phase. [2] In vertical pipes, the most commonly described flow regimes are bubble flow, plug flow, turbulent, and annular flow, as shown in Figure 2.
In bubble flow, the liquid flows downwards, forming the continuous phase, while the gas disperses into the liquid forming dispersed bubbles. These bubbles are distributed throughout the cross-section of the pipe, increasing in number, size, and velocity as the gas flow increases.
In the flow plug, the bubbles fuse together to form elongated gas plugs with a parabolic front edge. The liquid runs down the film surrounding these gas plugs. When the surface velocity of the gas is high, the liquid descending around the gas plugs almost stops, causing instability in these gas plugs and their subsequent rupture. The liquid begins to flow in a turbulent and oscillatory manner in a turbulent flow pattern. Both phases flow like a turbulent mixture, with structural elements in a continuous process of collapse and formation. This phenomenon occurs for a wide range of gas surface velocities.
In annular flow or falling film flow, the liquid flows downward as a film along the inner walls of the pipe, forming a ring, while the gas flows through the center. The gas usually drags a portion of the liquid in the form of small droplets, which flow at the speed of the gas. Finally, in the fog flow, the liquid flows as fine droplets dispersed in the gas, which constitutes the continuous phase.
To prevent air from blocking vertical overfill drain lines, the velocity of the liquid must be kept low enough to allow air to return to the tank. The only method to ensure correct free surface flow is to make the pipe diameter large enough to prevent the formation of unwanted flow patterns and achieve annular flow. [4]
Experimental method
According to Hills’ research [5], gravity flow in self-ventilated drains must meet two simultaneous conditions to ensure lateral outflow without siphoning effect or any unwanted flow pattern other than the annular pattern. This implies a minimum diameter at the inlet limit at the outlet and a maximum Froude number (Equation 1):
The above unevenness ensures that the height of the fluid at the beginning of the drain line is less than half the height of this pipe. As shown in Figure 1, to ensure a ventilated gravity flow, a critical height of static fluid in the central area of the tank (away from the outlet) of less than 0.8 d must be maintained.[1]
The Froude number is a dimensionless number used to indicate the influence of gravity on the motion of a fluid. It is defined as the ratio of the inertial forces acting on a fluid element to the weight of that fluid element and can be calculated with Equation 2.
In addition, maintaining Fr values below 0.3 is a widely accepted criterion in the scientific community to achieve a ventilated line in which the liquid can easily drain from the reservoir.
Case Study
In this article, we want to design an overfill drain pipe that can evacuate the maximum flow of fed water to the tank shown in Figure 3. This tank has 1200 L of storage capacity and can be continuously fed with up to 9 m3/h of water. In addition, the Pipping Class specification states that piping must be constructed with an NPS nominal diameter of 1 to 6 inches, always with Schedule 10S.
By establishing 9 m3/h of water as the maximum flow to be drained, the minimum inner diameter of the drainage pipe can be calculated with Equation 1.
Now, the nominal diameter of the pipe must be selected from the sizes available in the ASME B36.10M standard. As shown in Figure 4, a pipe diameter of NPS 4 in. and Sch. 10S meets the requirements, since its internal diameter would be 0.108 m, and therefore higher than the 0.103 m obtained from the calculation.
Finally, the Froude number is calculated with Equation 2 to verify that this condition is also fulfilled.
In conclusion, an NPS 4 pipe diameter (sch. 10S) is the best choice for the design of this drainage system, as it will allow a vent line to be achieved when water can overflow the tank.
This article has been written by Dr. Javier Sánchez Laínez, Project Director at Sistemiza.
Bibliography
[1] Selecting the Optimum Pipe Size © 2008, 2015 Randall W. Whitesides, CPE, PE.
[2] WU, Benjamin, et al. A critical review of flow maps for gas-liquid flows in vertical pipes and annuli. Chemical Engineering Journal, 2017, vol. 326, p. 350-377.
[3] R.A. Sultan et. al. CFD Simulation Investigation of Natural Gas Components through a Drilling Pipe. ENGI 9120 (Advanced Natural Gas)- Term ProjectAffiliation: Memorial University of Newfoundland. March 2016
[4] Assess the Gravity of the Situation. Chemical Processing. Nov. 2009.
[5] HILLS, P. D. Designing piping for gravity flow. Chem. Eng. (London); (United Kingdom), 1983, vol. 90, no. 18.
6] Thickness of Carbon Steel pipes according to ASME B36.10M. http://www.dnbrida.com/espesor-tuberia-acero-al-carbono-sch-asme-b36.10m.php. Last Access on 03/06/2024.
Download the paper
You can download the article in PDF from here or from the image.
