Steady Adiabatic, Two-Phase Flow of Steam and Water Through Porous Media
- J. Michael Sanchez (U. of Texas) | Robert S. Schechter (U. of Texas)
- Document ID
- Society of Petroleum Engineers
- SPE Reservoir Engineering
- Publication Date
- August 1990
- Document Type
- Journal Paper
- 293 - 300
- 1990. Society of Petroleum Engineers
- 2.4.3 Sand/Solids Control, 5.9.2 Geothermal Resources, 5.4.6 Thermal Methods, 4.1.2 Separation and Treating, 5.6.5 Tracers, 5.2.1 Phase Behavior and PVT Measurements, 5.5.2 Core Analysis, 1.6.9 Coring, Fishing, 5.5 Reservoir Simulation, 4.2.3 Materials and Corrosion, 4.1.5 Processing Equipment
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Summary. Reliable steam/water relative permeability curves that have not been previously reported were obtained under conditions of near-adiabatic, two-phase, steady flow in an unconsolidated Ottawa sandpack. Comparison of higher-temperature steam/water relative permeability curves to those for nitrogen/water at room temperature indicate that the two types of flows are essentially identical.
Reservoir steam simulators are relied on as tools for the prediction of reservoir and production performance. 1-12 Recent advances in steam simulation allow mechanistic studies that were not previously possible. All reported steam simulators, however, have assumed, with little or even contradictory evidence, that steam/water flow can accurately be represented as gas/water flow. To the best of our knowledge, no prior experimental data support this assumption.
Steam/water relative permeability data for synthetic sandstones were previously reported by Arihara and Chen, who assumed adiabatic conditions in their calculations even though no provision was made to insulate or to control heat loss. In addition, Arihara did not measure the liquid saturation. Trimble and Menzie used insulation and heating tapes to ensure adiabatic conditions, but they assumed that liquid saturation was equal to the mass fraction of water multiplied by the specific volumes of liquid to the total specific volume.
Monsalve et al. measured steam/water permeability curves in Berea sandstone under conditions of adiabatic flow. Quantitative comparison with gas flow was limited, however, by the relatively small quantity of data presented.
Counsel and Ramey measured steam/water and gas/water relative permeabilities in synthetic sandstones. Their data indicate large differences between the two flow types. In their studies, however, steam was generated by introduction of liquid water at the core face at just above its saturation vapor pressure. As the pressure decreased along the core's length, vaporization occurred. Counsil and Ramey estimated the heat input along the core with an experimentally obtained heat-transfer coefficient and assumed that no radial saturation distribution existed. With this method of generating steam, however, radial saturation gradients are inevitable. In addition, assessing the vapor and liquid flow rates to be used with measured pressure drops is difficult in this type of flow because significant vaporization occurs with increasing axial distance from the inlet. The use of one heat-transfer coefficient to estimate heat input as a function of axial distance for all data has merit only if that heat-transfer coefficient remains unchanged. Counsil and Ramey did not measure the effects of flow rate and saturation changes on the overall heat-transfer coefficient used. Hence, it is difficult to assess whether the coefficient was constant under all the operating conditions of the experiment. These difficulties, combined with the larger pressure gradients (and corresponding axial saturation gradients) in consolidated cores, may have contributed to the differences between gas/water and steam/water relative permeabilities they observed.
Miller reported similar experimental work. He sought to characterize hydrocarbon vaporization under an applied pressure gradient. Propane was used as the test fluid. Experiments were performed under conditions of steady mass flow. Liquid propane was injected into the inlet face of a sandpack, and a mixture of vapor and liquid was produced. Miller matched his experimental pressure profiles with a theoretical description of the flow and found excellent agreement. Note that no attempt was made to measure relative permeability data. Indeed, to match theory with experiment, a set of relative permeability curves was generated from data for a sand different from that used in the experiments.
This paper presents a reliable description of steam/water flow through porous media and compares this description with that for nitrogen/water flow, This comparison serves to support the contention that steam/water relative permeability functions are nearly identical to those for nitrogen/water. Details of the flow apparatus and the design of a novel, adiabatic steam generator are presented. The thermodynamics of a single-component, two-phase system under the influence of capillary pressure has been presented previously. We use those analyses together with the capillary pressure to show that the lowering of vapor pressure is negligible for the experimental system considered here. The capillary pressure is significant, but does not cause a deviation of the liquid pressure gradient from that in the steam.
Thermodynamics of Steam/Water Flow
If we assume local equilibrium along a radial cross section of a porous medium undergoing two-phase flow of steam and water, then (1)
Because the temperature is constant in the radial direction,
where i represents the molar volume of either vapor or liquid. For water, VL is essentially constant and
where is the chemical potential of liquid water at temperature T and pressure pL. For steam over the range of experimental operating temperatures,
and from Eq. 2, we have
Equating Eqs. 4 and 6, we obtain
Note that for equilibrium across a flat interface, which has been chosen here as the initial state,
Eq. 7 reduces to
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