Theoretical and experimental study of motion and sinking time of Saxon Bowls

This work focuses on investigating the time of sinking of a Saxon bowl proposed by ‘International Young Physicists’ Tournament in 2020. A quasi-static model is built to simulate the motion path of the bowl and predict the sinking time subsequently. The model assumes an open axisymmetric bowl with a hole in its base. The hole is modelled as a pipe for which the flow profile is governed by a modified Bernoulli’s equation which has a Coefficient of Discharge (C_d) added to account for energy losses. The motion of the entire bowl is assumed to be in quasi-static equilibrium for an infinitesimal time interval to calculate the volumetric flow rate through the hole. The model is used to predict the sinking times of various bowls against independent variables - hole radius, bowl dimensions, mass of bowl, mass distribution of bowl, and Coefficient of Discharge - and predict the motion path of bowls of different, axisymmetric geometries. Characterisation of C_d was done by draining a bowl filled with water and measuring the time taken to do so. Experimental verification was completed through measuring sinking times of 3D printed hemispherical bowls of the different variables in water. Motion tracking of bowls with different geometries was done using computational pixel tracking software to verify the model’s predictive power. Data from experiments for sinking time against the variables corroborate with the model to a great degree. The motion path tracked, matched the modelled motion path to a high degree for bowls of different shapes, namely a hemisphere, cylinder, frustum, and a free-form axisymmetric shape. The work is poised for an undergraduate level of readership.

Determination of the Near-Wellbore Pressure Drop for Dual Casing in Hydraulic Fracturing and Refracturing Applications

Due to the increases in completion costs demand for production improvements, fracturing through double casing in upper reservoirs for mature wells and refracturing early stimulated wells to change the completion design, has become more and more popular. One of the most common technologies used to re-stimulate previously fracked wells, is to run a second, smaller casing or tubular inside of the existing and already perforated pipes of the completed well. The new inner and old outer casing are isolated from each other by a cement layer, which prevents any hydraulic communication between the pre-existing and new perforations, as well as between adjacent new perforations. For these smaller inner casing diameters, specially tailored and designed re-fracturing perforation systems are deployed, which can shoot casing entrance holes of very similar size through both casings, nearly independent of the phasing and still capable of creating tunnels reaching beyond the cement layer into the natural rock formation. Although discussing on the API RP-19B section VII test format has recently been initiated and many companies have started to test multiple casing scenarios and charge performance, not much is known about the complex flow through two radially aligned holes in dual casings. In the paper we will look in detail at the parameters which influence the flow, especially the Coefficient of Discharge of such a dual casing setup. We will evaluate how much the near wellbore pressure drop is affected by the hole's sizes in the first and second casing, respectively the difference between them and investigate how the cement layer is influenced by turbulences, which might build up in the annulus. The results will enhance the design and provide a better understanding of fracturing or refracturing through double casings for hydraulic fracturing specialists and both operation and services companies.

Exploring Torricelli's theorem with Arduino

We explore the dynamics of the water in a PVC pipe during the drain using two independent sensors simultaneously. We track the height of the water column and the discharge velocity of the water through the hole made in the lower part of the pipe. The ultrasonic distance sensor and the flow meter used as sensors were controlled by an Arduíno board. The acquired data follows the theoretical models but, with a coefficient of discharge smaller than 1.

EXPERIMENTAL INVESTIGATION INTO FACTORS AFFECTING THE TRANSIENT FLOW OF FLUID THROUGH AN ORIFICE IN REALISTIC CONDITIONS

During operations, damage can occur with a resulting ingress or egress of fluid. The incoming water affects the reserve buoyancy and it can also change stability and hull girder loading. During a flooding event it is vital that the flow through the damaged orifice and the movement of floodwater around the structure can be predicted quickly to avoid further damage and ensure environmental safety. The empirical measure coefficient of discharge is used as a simplified method to quantify the flooding rate. In many internal flow applications the coefficient of discharge is estimated to be 0.6 but recent research shows that it can vary considerably when applied to transient flooding flows. This paper uses an experimental setup to investigate how changes to the orifice edges and position within the structure affect the flow. It is then used to investigate the coefficient in a more realistic scenario, a static compartment in waves.

Comparative study of experimental and CFD analysis for predicting discharge coefficient of compound broad crested weir

Present study highlights the behavior of weir crest head and width parameter on the discharge coefficient of compound broad crested (CBC) weir. Computational fluid dynamics model (CFD) is validated with laboratory experimental investigations. In the discharge analysis through broad crested weirs, the upstream head over the weir crest (h) is crucial, where the result is mainly dependent upon the weir crest length (L) in transverse direction to flow, water depth from channel bed. Currently, minimal investigations are known for CFD validations on compound broad crested weirs. The hydraulic research for measuring discharge numerically is carried out using FLOW 3D software. The model applies renormalized group (RNG) using volume of fluid (VOF) method for improved accuracy in free surface simulations. Structured hexagonal meshes of cubic elements define discretized meshing. The comparative analysis of the numerical simulations and experimental observations confirm the performance of CBC weir for precise measurement of a wide range of discharges. Series of CFD model studies and experimental validation have led to constant range of discharge coefficients for various head over weir crest. The correlation coefficient of discharge predictions is 0.999 with mean error of 0.28%.

EXPERIMENTAL STUDY OF FLOW THROUGH TRAPEZOIDAL WEIR CONTROLLED UNDER A SEMI-CIRCULAR GATE

Different parameters of a weir model have a great effect on the discharge coefficient. In this experimental study the effect of varying angle of a trapezoidal weir coupled with a below semi-circular gate is determined. The result showed that the higher the value of the higher the coefficient of discharge. The respective average discharge coefficient of the block model and the trapezoidal weir models are; 0.48031,0.48880, 0.49565, 0.49647, 0.49892 and 0.49934. As such the trapezoidal weir with has the highest value of average discharge coefficient =0.49934. Hence the most efficient. Linear and nonlinear regression analysis were used to generate mathematical equations that can be used to predict the flow rate Q for the combined weir-gate structure and the discharge coefficient of the most efficient model with respectively. The discharge coefficient for the most efficient weir model was found to be 3.81% more than that of the block model (with rectangular weir). The predicted coefficient of discharge for the most efficient model was also found to be in good agreement with the observed discharge coefficient with a percentage error in the range of 0.4%

Study Investigates Factors Affecting Coefficient of Discharge in Stimulation

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 200612, “The Role of Backpressure and Perforation-Hole Erosion on the Magnitude of the Coefficient of Discharge in Hydraulic Fracturing Stimulation,” by Davood M. Yosefnejad, Bernd Fricke, and Joern Loehken, DynaEnergetics Europe, et al., prepared for the 2020 SPE Virtual Europec Conference, 1–3 December. The paper has not been peer reviewed. One of the important factors affecting the near-wellbore-fluid pressure drop is the coefficient of discharge (Cd). In the complete paper, the authors investigate some of the factors that can affect Cd, such as the erosion of the perforated hole and the backpressure given by the fracture. The paper studies the effect of perforation hole size, geometry, and shape on the Cd value at ambient conditions and with backpressure, before and after sand erosion. Setup Specifications and Materials For this study, a high-pressure, high-flow setup was built for Cd measurements, as well as a second setup in which the holes can be eroded by proppant-laden slurries. The test cell was the same for both setups. The holders of the plates were stainless steel and connected to 7-in. pipes approximately 4 ft long on each side. In all the experiments, the flow rate and inlet and outlet pressure data were recorded simultaneously vs. injection time by high-precision sensors. All experiments were carried out at an ambient temperature of 15–28°C. For these flow-test experiments, only water was used, circulated with different pressure differentials to determine the effect of pressure on Cd magnitude. In addition, backpressure was applied through the needle valve to simulate real reservoir conditions and to compare the Cd value with the tests under ambient conditions. The flow rate range of the pump was 1–7 bbl/min at maximum pressures of approximately 2,000 psi. Erosion tests have been performed for 30 minutes with a near-constant flow rate (approximately 1 bbl/min), constant pressure (approximately 200 psi), and constant sand concentration. For the erosion test, a viscosity of approximately 10 cp was used. The sand concentration was kept at 1 to 2 lbm/gal to keep the erosion rate low, which would allow distinguishing between shape-driven changes in Cd and changes caused by an increase of the hole size. The study used machined holes and holes created by differently shaped charges, which also differed in size and geometry. A description of these holes, and associated shaped-charge tests, is provided in the complete paper. Experimental Results and Discussion Generic Holes. In the first sets of experiments, generic holes with different entrance-hole diameters were used. The experiment began with the lowest inlet pressure, which gradually was increased to the maximum pressure. The outlet pressure was kept constant at an ambient pressure. The flow rate increased because of the increase in differential pressure. After reaching the maximum pressure, the inlet pressure was kept constant and the choke on the outlet side was closed step by step to establish a backpressure, which led to a decrease in differential pressure. Surprisingly, the flow rate stayed constant until the differential pressure surpassed 700 psi.