Two-phase flow through wellhead chokes, including both critical and subcritical flow and the boundary between them, was studied. Data were gathered for air-water and air-kerosene flows through five choke diameters from 1/4 in. (6.35 mm) to 1/2 in. (12.7 mm), and results were compared to published correlations. A new theoretical model for predicting flow rates and the critical-subcritical flow boundary was tested against these data, as well as data from two published studies. The new model substantially improves the existing methods for predicting choke behavior in two-phase flow. Introduction Chokes are widely used in the petroleum industry to protect surface processing equipment from slugging, to protect surface processing equipment from slugging, to control flow rates from wells, to provide the necessary backpressure to a reservoir to avoid formation damage from excessive drawdown, to maintain stable pressure downstream from the choke and dampen large pressure fluctuations. Either critical or subcritical flow may exist. Since different methods apply for predicting choke behavior in these regimes, the prediction of the critical-subcritical flow boundary is also important. The majority of correlations available apply to critical flow only. Pressure drops through chokes can be substantial. For example, in critical flow the pressure downstream from the choke may be as low as pressure downstream from the choke may be as low as 50% or even 5% of the upstream pressure. Modern techniques, like Nodal* Analysis, of analyzing the entire production system require two-phase models of production system require two-phase models of comparable accuracy for each system component. Thus, to optimize the performance of the entire production system, an improved two-phase choke model is required. THEORY For the purpose of modeling, a wellhead choke can be treated as a restriction in a pipe. Two types of two-phase flow can exist in a choke: critical and subcritical flow. During critical flow, the flow rate through the choke reaches a maximum value with respect to the prevailing upstream conditions. The velocity of the fluids flowing through the restriction reaches the sonic or pressure wave propagation velocity for the two-phase fluid. This implies that the flow "choked" because downstream disturbances cannot propgate upstream. Therefore, decreasing the downstream propgate upstream. Therefore, decreasing the downstream pressure does not increase the flow rate. If the pressure does not increase the flow rate. If the downstream pressure is gradually increased, there Will be no change in either the flow rate or the upstream pressure until the critical-subcritical flow boundary pressure until the critical-subcritical flow boundary is reached. If the downstream pressure is increased slightly beyond the boundary conditions, both flow rate and upstream pressure are affected. The velocities of fluids passing through the choke drop below the sonic velocity of the upstream fluids. Here, the flow rate depends on the pressure differential and changes in the downstream pressure affect the upstream pressure. This behavior characterizes subcritical pressure. This behavior characterizes subcritical flow. Although it is often desirable to operate wells under critical flow conditions with uniform flow rate and downstream pressure, Fortunate' reports that a majority of wells in the field operate under subcritical conditions. However, most of the correlations available to petroleum industry are for critical flow. Existing Methods A complete model for two-phase flow through chokes should define the boundary between the critical and subcritical flow regimes and predict the functional relationships of flow rate through the choke and the pressure differential across the choke for a given set of fluid properties and flow conditions. Most existing methods model critical flow only and a few even attempt to define the criticalsubcritical flow boundary. These models are surveyed.
Summary Hydraulic jet pumping of gas/liquid mixtures was studied experimentally, and a mathematical model is proposed to extend the standard single-phase model for predicting efficiency and pressure recovery to suction fluids with gas/liquid ratios up to 2,200 pressure recovery to suction fluids with gas/liquid ratios up to 2,200 scf/STB. The experimental program comprises 616 low-pressure tests in a plastic model pump designed for flow visualization and measurement of plastic model pump designed for flow visualization and measurement of pressure profile along the throat and diffuser, and 373 high-pressure tests pressure profile along the throat and diffuser, and 373 high-pressure tests on a stock pump. For the high-pressure tests, power fluid was supplied at 200 to 3,000 psi and at 200 to 860 B/D; air was supplied from 0 to 185 Mscf/D. Discharge pressures ranged from 800 to 2,000 psi. The mathematical model extends a previous model that describes single-phase performance from mass and energy conservation. The empirical loss coefficients for the nozzle and throat/diffuser are replaced by a nondimensional expression that varies as three dimensionless parameters: nozzle-to-throat area ratio, discharge-to-power-fluid pressure ratio, and air/water ratio (which usually is in conventional units of cubic feet per stock-tank barrel but is, of course, basically dimensionless). The loss coefficient for the nozzle is constant, but for the throat/diffuser it is a constant plus a product of a constant times the three parameters, each to a power. power. Compared with the standard model, which always overpredicts pressure recovery and thus efficiency, the new model reduces the standard error of the estimate to 18% of its former value. Introduction The accepted theory of jet-pump operation is derived from single-phase assumptions. Power fluid and suction fluid are assumed to be similar liquids. Since Rankine developed the basic theory of operation in 1870, using concepts of mass and energy conservation, most investigators have grappled with realistically assessing frictional losses, not with addressing operation when suction fluid is a multiphase mixture. Notable among these early studies are those of Gosline and O'Brien and Cunningham. Petrie et al.'s standard installation design model cautions users to apply Petrie et al.'s standard installation design model cautions users to apply it only when free gas is limited to less than 10 scf/STB. Corteville et al. recently published results of a study on two-phase performance using kerosene and N2 at power-fluid pressures up to 1,160 psi. The two-phase model reported here is based on experiments con-ducted with water as a power fluid and with water and air as the suction fluid in a surface test loop operated at field-scale pressures and flow rates. This model extends the applicability of the standard design model by adjusting an empirical loss coefficient for the throat and diffuser. Rather than being a dimensionless constant, this coefficient becomes a function of three dimensionless parameters - one describing pump geometry; another, the operating pressures; and a third, the gas/liquid ratio. Because all tests were conducted with air and water, no empirical adjustment for physical properties of the suction or power fluid is attempted. The work reported properties of the suction or power fluid is attempted. The work reported here is drawn from Refs. 6 and 7, which provide more detailed information. Theory and Definitions The principal component of a jet pump (Fig. 1) is a nozzle fitted to a throat/diffuser section. Power fluid, usually clean crude from a surface pump, is injected into the nozzle under high pressure, from which it issues pump, is injected into the nozzle under high pressure, from which it issues at high speed. The resulting high-speed jet is at low pressure by Bernoulli's principle. Thus, it entrains suction fluid, and the combined mixtured is allowed to decelerate in a cylindrical throat and then passes through an expanding, conical diffuser. Pressure is recovered as the slowing fluid swaps kinetic energy for pressure. The quantitative theory of jet-pump performance is based on mass and energy conservation. Cunningham gives a complete derivation, and Petrie et al. provide an abridged form. This steady-state model assumes uniform properties of a single-phase, incompressible discharge fluid resulting from properties of a single-phase, incompressible discharge fluid resulting from complete mixing of power and suction fluids in an axially symmetric, simplified pump geometry.
Casing heading, an unsteady flow in oil wells completed without packers, occurs when both gas and liquid superficial velocities are low. A hydrodynamic model is presented that simulates laboratory data for the cases considered. Results confirm that heading occurs for low superficial gas and liquid velocities and that choking re-establishes stability.
Summary The flow performance of two nitrogen-loaded gas-lift valves and one combination gas-lift valve was tested under simulated downhole conditions. Set pressures up to 1,500 psig and injection pressures up to 1,650 psig yielded a maximum observed gas flow rate of 3.6 MMscf/D. Pressure-operated valve performance depends on injection pressure for specific production and domepressures, valve geometry, and other factors. Two performance pressures, valvegeometry, and other factors. Two performance characteristics, separated by the test-rack opening pressure, are observed: throttling and orifice flows. Semimechanistic models predict throttling and orifice flow performance. Experimental predict throttling and orifice flow performance. Experimental performance characteristics tune the model for any port size used performance characteristics tune the model for any port size used in the Camco R-20valve. Introduction Ninety percent of domestic wells use artificial lift. Continuous-flow gaslift is popular in wells determined suitable by a feasibility study. This presupposes that the performance of each system component is predictable. This study proposes more reliable empirically based methods of predicting gas flow than are available currently. Most manufacturers recommend treating the gas-lift valve as an orifice; only a few provide empirical evidence. Since its inception in May, 1983, Tulsa U. Artificial Lift Projects (TUALP), an industrially funded research consortium, gave Projects (TUALP), an industrially funded research consortium, gave the study of gas-passage performance of nitrogen-loaded gas-lift valves the highest priority. TUALP studied the performance of two 1.5-in.-OD nitrogen-loaded and one combination gas-lift valve under simulated downhole conditions. This paper summarizes the observed gas-lift valve flow performance characteristics, presents two semi-mechanistic models that predict throttling and orifice flow performance, and defines a procedure for incorporating the models performance, and defines a procedure for incorporating the models into gas-lift designs. Test Facilities. Ref. 1 gives details on the TUALP test facility. Air supplied at a working pressure up to 2,500 psi and a flow rate up to 3.6MMscf/D was used. Operating limits were 2,000 psia and 2.0 MMscf/D. To use the dynamic test facility, one closes the downstream flow-control valves and admits gas to the flow loop by opening the upstream flow-control valves. Once sufficient pressure is applied for the test valve to open and both upstream and downstream pressures equilibrate, the downstream flow-control valves are opened slowly to reduce the downstream pressure and to initiate flow through the test valve. Throughout the test, the upstream flow-control valves are adjusted to maintain constant injection pressure while the downstream pressure is reduced in 25- to 100-psig decrements until either the valve closes or the downstream pressure falls to atmospheric. For each decrement in downstream pressure falls to atmospheric. For each decrement in downstream pressure, flowing conditions are stabilized with the flow-control pressure, flowing conditions are stabilized with the flow-control valves and the data acquisition system is manually prompted to sample and store all the pressure and temperature transducer responses. Note that one can hold either downstream tubing orupstream injection pressure constant during a test. Careful experiments show that results of tests done either way mathematically transform so that either experimental procedure is acceptable. Gas Flow Rate Calculation. The American Gas Assn. calculation procedures is used to compute gas flow rates. Base temperature and procedures is used to compute gas flow rates. Base temperature and pressure are assumed to be 60F and14.73 psia. For natural gas pressure are assumed to be 60F and 14.73 psia. For natural gas calculations, the ratio of specific heats and gas specific gravity must be known to compute the gas expansion factor, Y. Hall and Yarborough and Lee et al. give gas compressibility factors and viscosities. For air flow rate calculations, the ratio of specific heats is assumed to be 1.4 and the specific gravity is 1.0; standard references give viscosities and compressibility factors for dry air. Experimental Data The experimental data were taken for two nitrogen valves, the Camco R-20 and the McMurry-Hughes VR-STD, and one combination valve, the Teledyne MerlaLN-20R. Most tests were conducted with air as the flowing gas, but a few tests were conducted on the R-20 and VR-STD valves with natural gas. Stem displacement tests were performed on the R-20 valve to define the load rate of the bellows performed on the R-20 valve to define the load rate of the bellowsassembly. Test Conditions. LN-20R Valve. This is a wireline-retrievable, 1.5-in.-ODvalve with a combination nitrogen-spring-loading element. For constant upstream or injection pressure, the spring-nitrogen-loading element and the large port causes the flow performance of the LN-20R valve to be sensitive to downstream pressure. Because of its high flow rate capacity, this valve was tested only with the smallest 0.582-in.-ID port. The valve closing pressure was set at 685psig and the test-rack opening pressure at 1,060 psig at 64F. Only 12 dynamic tests were conducted, with pressure at 1,060 psig at 64F. Only 12 dynamic tests were conducted, with injection pressures ranging from 880 to 1,050 psig, because of insufficient capacity of the air supply at the time. R-20 Valve. TheR-20 valve is a wireline-retrievable, 1.5-in.-OD, nitrogen-loaded valve capable of passing and regulating both low and high gas flow rates with small and large ports. Measuring this valve with all available port sizes required I year of flow performance testing. Each port size was tested at valve closing performance testing. Each port size was tested at valve closing pressures set at about 500, 600, 700, 800, 900, 1,000, 1,250, and pressures set at about 500,600, 700, 800, 900, 1,000, 1,250, and 1,500 psig. At least six flow performance tests were performed at each valve closing pressure, with injection pressures that generate a family of three throttling and three orifice flow performance curves. Table 1 summarizes the data acquired from the 476 air flow performance tests on the R-20 valve. performance tests on the R-20 valve. Natural Gas Tests. We tried to test the R-20 valve with natural gas to evaluate the validity of Biglarbigi's theoretical air-to-natural-gas flow rate conversion equation. To conduct the natural gas flow tests, the dynamic test facility was connected between a high-pressure gas well and a low-pressure gas pipeline. Agas well at the ONG Depew Storage Facility in Depew, OK, was selected for tests on the R-20 and VR-STD valves. Two R-20 valves, with a 0. 187- and a 0.3750-in.-ID port, were used. For comparison, the VR-STD valve with a 0. 1875-in.-IDport was chosen because it is similar to the R-20 valve in geometry and construction. Table 2 shows data for 11 flow performance tests. Because a minimal amount of data on natural gas flow performance was obtained on the R-20valves, the air-to-natural-gas conversion equation could not be evaluated effectively with the R-20 valve data. The flow rate conversion equation was evaluated after 11 air flow performance tests on the VR-STD valve to duplicate the natural gas tests at the same test conditions. Valve Performance Characteristics Fig. 1 is a typical family of flow performance curves for the R-20 and VR-STD valves. The separate curves differ by the upstream or injection pressure, which is the intercept on the horizontal axis at the high-pressure end of a curve. SPEPF P. 203
TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractThis paper presents the modeling of a sucker rod pumping system for both vertical and deviated wells. It focuses on the derivation and applicaton of a new set of comprehensive equations that incorporate both the dynamic rod motion as well as the fluid flow through the annulus between the rod and tubing. The mathematical model for a deviated well is developed using the principles of virtual work. Partial differential equations, and their associate boundary conditions, have been derived to describe the dynamic performance of the system in great generality. The model incorporates all system components and most downhole pump inflow conditions. The effect of lateral rod deformation between the couplings is evaluated by introducing effective longitudinal stiffness and by the Garlakin method. The model for deviated wells incorporates not only viscous friction, but also Coulomb friction. The model' results are validated against actual measured data. Numerous examples are presented to demonstrate the application of the new technique for the design, analysis and optimization of sucker-rod pumped wells, specially deviated wells.
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