Determining Multiphase Pressure Drops and Flow Capacities in Down-Hole Safety Valves
Authors: Ashford F.E. , Pierce P.E. 
Published: December 2007

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.
1. 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.
2. 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.
JPT
P. 1145