A new relationship describing dynamic multiphase orifice pressure drops and fluid flow capacities has been derived and tested with field data. The mathematical model relates dynamic orifice behavior in both critical and noncritical flow regions. Correlations are presented for predicting the ultimate (critical) capacity of an presented for predicting the ultimate (critical) capacity of an orifice for any given set of dynamic conditions. Introduction A new relationship describing dynamic, multiphase orifice pressure drops and fluid flow capacities has been derived and tested with actual field data. The mathematical model relates dynamic orifice behavior in both critical and noncritical flow regimes. Orifice pressure drops and capacities are related to pertinent fluid properties and choke dimensions. Graphical pertinent fluid properties and choke dimensions. Graphical correlations are also presented to predict the ultimate (critical) capacity of an orifice for any given set of dynamic conditions. To verify the model, a field test was designed and carried out in a flowing oil well. Both orifice pressure drops and fluid flow rates were measured in the well and the information was compared with analogous data predicted by the model. Comparable information was then predicted by the model. Comparable information was then used to compute an "orifice discharge coefficient" that enables calculation of actual orifice capacities from theoretical ones. The discharge coefficients are presented for 14/64-, 16/64- and 20/64-in. orifice diameters. The collected data reflect the behavior of an Otis Engineering Corp. J-type 22J037 safety valve. However, the model may be used to estimate multiphase pressure drops through restrictive beans in safety valves of other internal geometrical configurations. Discussion The increased need for more accurate settings on downhole, self-contained, flowing safety devices (storm chokes) has prompted efforts by many oil-producing companies to develop new multiphase orifice flow relationships. Interest in antipollution devices, especially in offshore oil-producing areas, has also encouraged the major oil companies to re-evaluate old, established procedures for the design of oil- and gas-well safety procedures for the design of oil- and gas-well safety valves. A review of the existing orifice flow literature and analysis of standard safety-valve design procedures yielded the following facts concerning noncritical multiphase orifice flow.Most orifice flow models do not adequately reflect the compressible nature of actual oilwell multiphase orifice flow. Consequently, models now in use do not adequately describe the dynamic behavior of orifice flow.The existing orifice flow relationships become less exact as the dynamic conditions approach the critical value; that is, at a given upstream pressure, no further flow-rate increase occurs through the orifice, regardless of the pressure drop across the orifice. Those who are involved in manufacturing down-hole, pressure-drop-operated safety valves are aware of the pressure-drop-operated safety valves are aware of the problems associated with accurate prediction of orifice problems associated with accurate prediction of orifice flow behavior. Most agree that a more rigorous mathematical model is needed to describe the mechanics of orifice flow under all oilfield conditions. The orifice relationships used by design engineers, though acceptable under certain flow conditions, are questionable for applications falling outside these specifications. A more rigorous procedure applicable to oilfield JPT P. 1145
American Institute of Mining, Metallurgical, and Petroleum Engineers, Inc. Abstract Flow closing coefficients and a function for prediction of orifice size, given the pressure drop and flow rate, were derived from pressure drop and flow rate, were derived from an analysis of water flow tests made on subsurface controlled safety valves. A pressure-drop function, the mass flux function, and four pressure-drop function, the mass flux function, and four Buckingham pi-number functions, were investigated, using the test data, as possible equivalents to the Bernoulli flow equation. The Euler function gave the highest probability of minimum error in prediction of the flow closing coefficients and orifice size. Introduction Subsurface controlled safety valves (SSCSV) are installed down hole in the tubing by wireline. They are frequently referred to as velocity closing valves or Storm Chokes. When they are installed in oil or gas wells, their purpose is to shut the well in when a disaster purpose is to shut the well in when a disaster occurs at the surface causing the wellhead to be partially or completely removed. The sudden partially or completely removed. The sudden increase in production rate resulting from such an event causes the safety valves to close because of an increased pressure drop across the bean or choke. This increased pressure drop acting against a differential area formed by the bean diameter and a sealing element diameter produces a force that overcomes a spring force produces a force that overcomes a spring force acting to keep the valve open during normal production. production. Fig. 1 shows a common type of SSCSV usually referred to as a "poppet type". The valve is shown in both open and closed positions. It is in the open position during normal production and is closed immediately after a disaster production rate occurs. production rate occurs. Fig. 2 shows a ball-type SSCSV in both the open and closed position, and Fig. 3 illustrates a third type called a "flapper valve" in both positions. The operating principle is the same positions. The operating principle is the same for all three valves; that is, a pressure drop acting against a differential area causes a force greater than a preset spring force tending to keep the valve open, therefore the valve closes. Fig. 4 shows the derivation of the force-balance equation. This is a general derivation and is assumed to apply to all types of safety valves although a ball type is shown in the schematic. Fig. 5 shows the position of the pressure taps used to measure the effective or valve-closing pressure drop across the valve.
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