Modeling Nonisothermal Rapid Multiphase Flow in Wells Under Nonequilibrium Conditions
- Guillermo Michel (U. of Oklahoma) | Faruk Civan (U. of Oklahoma)
- Document ID
- Society of Petroleum Engineers
- SPE Production & Operations
- Publication Date
- May 2008
- Document Type
- Journal Paper
- 125 - 134
- 2008. Society of Petroleum Engineers
- 7.4.4 Energy Policy and Regulation, 5.5 Reservoir Simulation, 5.2.1 Phase Behavior and PVT Measurements, 4.1.2 Separation and Treating, 1.8 Formation Damage, 1.10 Drilling Equipment, 5.2 Reservoir Fluid Dynamics, 5.3.2 Multiphase Flow, 4.2 Pipelines, Flowlines and Risers, 4.6 Natural Gas, 5.1.5 Geologic Modeling, 4.1.5 Processing Equipment, 5.9.2 Geothermal Resources
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An improved nonisothermal mathematical model considering the nonequilibrium effects involved during rapid multiphase flow in wells is presented. The extent of the nonequilibrium effect on deviation from the equilibrium-model predictions is delineated at various flow rates, fluid saturations, and temperatures. Applications for two-phase (oil/gas) and three-phase (oil/water/gas) systems are presented. The model presented here can be coupled with reservoir simulation for accurate representation of the well-fluid hydraulics under non-equilibrium- and nonisothermal-flow conditions.
In general, reservoir fluids consist of three phases, referred to as the gas, oil, and water phases. Each of these phases has different physical behaviors, and each phase interacts differently with the others as the reservoir fluid travels along the production pipe or a pipeline from the inlet to the outlet. At atmospheric or standard conditions, the pipe fluid stream can be separated physically into three parts, known as the pseudocomponents. These are the gas, oil, and water pseudo-components, and they are different substances from the gas, oil, and water phases. The pseudocomponents have been widely studied so that the physical properties of the phases can be estimated from the pseudocomponent's properties.
Multiphase flow in pipes is a phenomenon yet to be modeled accurately. When of two or more phases flow in a mixture in a closed environment they flow at different volumetric flow rates. The densities of the phases differ greatly in oil and gas wells; thus, the gas phases and liquid phases flow at different velocities in a pipe with constant cross-sectional area. This causes a slippage of the gas phases past the liquid phases.
Under no-slip conditions, the volume fraction for each phase is the volumetric flow ratio (Sg , So , and Sw ). This is the ratio of the volumetric flow rate of that phase to the volumetric flow rate of the mixture. Because the phases flow at different velocities, these two quantities are not equal. It has been observed that for wells, the volumetric fraction of the liquid phases (HL ) is larger than its volumetric flow rate (SL ). This characteristic is called liquid holdup.
The density of the mixture at any point can be calculated by taking the weighted average of each phase density with the volumetric fraction of each phase as the weighting factor. It is the main property that predicts the pressure drop in a well. Therefore, the estimation of the liquid holdup is of paramount importance to the pressure drop prediction. However, for all models proposed so far the accuracy of predicting liquid holdup is not acceptable.
Several procedures and techniques have been developed to describe the liquid holdup in multiphase flow. In describing this flow, some dimensionless parameters have been defined to assert its nature. Multiphase flow has been was observed experimentally to occur in various modes, such as bubble flow, plug flow, slug flow, froth flow, and mist flow, depending on the way the liquid and gas phases distribute in a representative elemental volume.
Apparently, each kind of flow has a characteristic physical behavior. These behaviors may indicate that the laws governing the liquid holdup are different for each kind of flow. This assumption has been accepted widely by the most recent and accurate techniques available today. For instance, such analysis for predicting the liquid holdup was carried out by Ros (1961).
Each kind of flow has a different model to predict liquid holdup in every proposed technique. This makes the liquid-holdup prediction become discontinuous when the flow changes from one kind to another. There is no smooth adjustment for transition between different kinds of flow. Therefore, the liquid-holdup prediction is extremely sensitive to the prediction of the changing point.
The assumption that each kind of flow is governed by different laws might not be an accurate representation of the slippage phenomenon. Assuming a general law for all kinds of flows would yield a continuous curve for the liquid-holdup prediction. Then, the change from one kind of flow to another would be smooth and continuous, and liquid holdup would be insensitive to the changing point. The current study makes the assumption that the governing equations for the liquid holdup are the same regardless of the kind of flow occurring inside the well.
The mass fraction of the liquid phases and the gas phase for a mixture can be determined by empirical correlations that have been accepted widely for gas and oil wells. Of course, these correlations predict the mass fraction of the phases once the mixture has reached an equilibrium state. Because of the liquid holdup, the mass fraction of the phases in a fluid in motion differs from the equilibrium state. This suggests that the liquid holdup is characteristic for flow under a nonequilibrium condition.
As a multiphase-fluid system, the reservoir fluid flow can be described by means of the fundamental equations governing the flow of fluids in conduits. These equations represent the mass, momentum, and energy conservation laws for the multiphase-fluid system. In addition to these previous laws of conservation, the mass conservation for the gas phase is considered to find a relationship between the dryness at the equilibrium state and at the nonequilibrium state.
A pressure drop occurs along the well during the motion of the multiphase fluid from the bottom of the hole to the surface. The gas-phase generation occurs when the pressure of the system falls below the bubblepoint pressure of the liquid phases (oil and water). At this condition, a mass transfer takes place between the gas phase and the liquid phases (oil and water) across the interface between the gas phase and the liquid phases. Generally, this interface mass-transfer is assumed to happen instantaneously. However, in reality, the mass transfer process requires a finite period of time to be completed. This phenomenon is referred to as relaxation. The multiphase-fluid system is said to be at an equilibrium state when the gas mass transfer across the gas/liquid interface has been completed; otherwise, the multi-phase-fluid system is said to be at a nonequilibrium state or undergoing a flashing phenomenon.
The interface mass transfer is bidirectional (i.e., reversible, involving the separation and dissolution of the gas phase). In this study, a cumulative separation is assumed to describe the bidirectional gas mass transfer. In addition to consideration of the flashing phenomenon, the energy losses by heat exchange with the surroundings and the temperature change by the multiphase-fluid expansion are also taken into account in the formulation of the wellbore hydraulics. The pressure drop, caused by friction between the flowing fluid and pipewall, causes the multiphase-fluid to expand. This expansion spreads the internal energy into a greater volume thus causing a temperature drop. This process is known as the Joule-Thompson effect, and it can be modeled by the fundamentals of thermodynamics. The heat exchange can be estimated by knowing the temperature of the surroundings. Usually, it is assumed that the temperature of the surroundings or external temperature, varies with a constant slope, referred to as the thermal gradient. For wells, this gradient is called the geothermal gradient. The rate of the heat exchange is set mainly by the completion technique for wells and by the coating technique for pipelines.
Several studies have been carried out to simulate and predict the flow conditions in oil and gas wells. Ayala and Adewumi (2003) successfully simulated the fluid transmission in pipelines with liquid holdup. Cazaraez-Candia and Vásquez-Cruz (2005) simulated the flow in vertical wells under the transient-flow regime. However, the heat loss to the ambient medium was ignored in both studies. Hagoort (2005) considered the heat losses in vertical wells for a single-phase fluid (gas). Yoshioka et al. (2005) described multiphase flow in horizontal wells with heat losses. However, these studies ignored the effect of gas flashing from the liquid phases to the gas phase in the mass-transfer model and considered constant-inclination wells. Civan (2006) included the effect of gas flashing and demonstrated its significance.
The primary objective of this paper is the consideration of the thermal effects and nonequilibrium gas separation from the liquid phases in the description of the hydraulics for wells. The model presented in this paper is an improvement over the model presented by Civan (2006). The flow of the multiphase fluid is described with the differential versions of the previously mentioned conservation laws. A numerical solution for the set of differential equations is obtained for the steady-state case. The procedure for solving the system of equations for any particular set of data is explained. A number of scenarios are presented to demonstrate the importance of a new relationship provided in the new modeling of the liquid holdup.
|File Size||1 MB||Number of Pages||10|
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