NO20140079A1 - Method for Determining Flow Parameters for a Multiphase Flow in a Pipeline Section - Google Patents

Description

Field of the invention

This invention relates to a method for transient quasi-three-dimensional simulation of multiphase fluid flow in pipelines which enables much faster simulation of multiphase fluid flows and which is less dependent on empirically developed correlations, which has increased reliability, improved ability to simulate multiphase flows at high pressures, and improved handling of the water phase than currently available fully three-dimensional simulators.

Background

Multiphase flows occur when more or less separate phases of gases, liquids and/or solid particles flow simultaneously as a mixture. Multiphase flows can involve complex irregular interactions between the flowing phases and induce pressure drops, fluid accumulations and unsteady flows. These phenomena can occur in a wide range of applications, varying from large-scale industrial processes in, for example, the pharmaceutical industry, paper industry, food industry, metallurgical industry, to small-scale applications such as cooling systems, combustion engines, etc.

One particular area where the understanding and management of multiphase flows is particularly important is the transport of hydrocarbons in pipelines from the production site to processing facilities. Fluid flows in pipelines from oil and gas fields will typically involve simultaneous flows of water, oil and gas, and may also contain entrained solids. The flow patterns can occupy many different regimes, such as, for example, turbulent flow, bubble flow, stratified flow, annular flow, and/or vortex flow.

Developments in today's oil and gas extraction are moving towards more marginal fields, and in remote and technically challenging areas. It has therefore become more important to understand and predict possible multiphase behavior and complex fluid-related effects that may occur in the pipelines during the planning and operation of the oil and gas transport pipelines. The main objective for operators is optimized production under optimized safety conditions, which results in the need to be able to control the flow rates, pressure variations and fluid temperatures in the pipelines.

The irregular and complex behavior of multiphase flows necessitates the use of numerical simulations, often assisted by extensive experimentally determined flow parameters, to estimate and/or gain an understanding of the behavior of the multiphase flow and the complex fluid-related effects that can be expected to occur in a particular pipeline .

Known technique

Numerical models for the simulation of fluid flows will typically use an Euler-based framework to solve the continuous phases of the multiphase flows, and they can roughly be considered to consist of two model classes; models for separate flows and models for dispersed flows.

Separate flow models usually treat the different fluid phases as completely separated by a sharp interface between the fluid phases. Among such models, so-called free-surface models are known, which keep track of the boundary surface by means of a reference field that moves together with the boundary surface. An example of such models is given in US 2007/0045344. However, such models cannot process flows where the interface folds, breaks up or merges.

Another approach is the volume of fluid method (VOF) where each fluid phase is modeled by formulating local conservation equations for mass, momentum and energy and replacing the jump conditions at the interface with uniformly varying volumetric forces. This enables the complicated motion and folding of the interface to be accounted for indirectly by tracking the motion of each individual fluid phase and then determining the position of the interface as a function of time from the volumetric fluid fractions resulting from the motion of all the fluid phases. The VOF approach is thus able to treat flows where the interface folds, breaks and or merges. An example of such a model is described in US 7,379,852, which discloses a model for keeping track of a number of N fluid materials and their associated interfaces during a simulated fluid flow by using a micro-lattice cell method embedded on a regular macrolattice for to partition and then label the fluid materials in a computer system, preferably using a prime number algorithm. The motion of the microlattice cells is accounted for using local velocity conditions, and rectifies small anomalies by coupled evaluation of local volume fraction fields and global mass conservation. Volume fractions can be calculated at each time step via an evaluation of first localizations so that average cell densities and viscosity values can be updated regularly.

The numerical workload increases significantly for each fluid phase whose interface must be kept track of and determined. Models for separate flows can therefore only treat a relatively low number of fluid phases. It is therefore necessary to use a different approach to treat dispersed flows where there may be very high numbers of relatively small and locally varying distributions of fluid phases carried with a continuous main fluid phase. A non-exhaustive list of examples of dispersed flows include bubble flow where a gas phase is distributed in the form of bubbles in a liquid phase, mist flow where small droplets of a liquid phase are distributed in a gas phase, emulsions where small droplets of a liquid phase are distributed in a main liquid phase, sievings where small solid particles are distributed in a liquid phase, and any combination of these.

In order to handle large numbers of relatively small phases distributed in a continuous main phase, dispersed flow models abandon the concept of keeping track of the interfaces separating the fluid phases and instead treat the different fluid phases as an interpenetrating continuum connected by discrete entrained particles, bubbles or drops. Thus, in this approach, the discrete characteristic of the multiphase flow will be averaged out so that small-scale fluid motions around individual particles, bubbles or droplets are ignored. The concentration fields in these models will typically vary evenly in space. Dispersed flow models are unable to treat flows that are appreciably affected by effects originating from the interfaces that separate the fluid phases.

However, in many industrial applications, multiphase flows can simultaneously involve both large-scale phenomena and dispersed particles/bubbles or droplets. Such situations require that one can simulate both separated flow situations and dispersed flow situations.

From US 5 550 761 a modeling procedure is known which distinguishes between these two types of flow situations: Separate flow situations (layered or annular) and dispersed flow patterns and which treats intermittent flow patterns (dusty flow, eddy flow) as a combination of these. This is achieved by characterizing the flow regimes by a parameter p representing the fraction of the flow in the separate state, where the parameter has a continuous range from 0 for dispersed flow regimes to 1 for separate flow regimes and then applying a transition algorithm to determine whether the flow should be treated as separate, intermittent or dispersed.

Another approach is known from Laux et al. (2005) [1]. This document introduces a hybrid approach for two-phase flows in pipelines, where a multilevel approach is used to avoid being limited by the direct simulation technique to solve all interfaces. The two-phase flow is divided into a set of fields which are usually: A continuous liquid layer, a continuous gas layer, bubbles suspended in the continuous liquid layer and droplets suspended in the continuous gas layer. A set of Euler-based volume and ensemble-averaged turbulent transport equations are then derived for each field. That is that each field is treated as an interpenetrating continuum according to the dispersed flow approach with the exception of the two main continuous fluid phases (liquid and gas). These two phases are treated as two distinct separate phases according to the fluid volume approximation. The interface that separates these two main phases is also the main interface of the flow and is therefore often referred to as the large-scale interface (LSI) in the literature.

The approach in [1] is thus a hybrid approach that simultaneously uses both the dispersed flow approach to treat suspended droplets, particles and/or bubbles, and the separated flow approach to account for the interface that separates the continuous main fluid phases. According to conventional VOF models, the hybrid approach in [1] uses local model descriptions to represent smoothly varying volumetric forces across the large-scale interface and determines the position of the interface indirectly. The shear force across the interface is, for example, approximated using wall functions for rough walls [3]. The large-scale interface is also made responsible for delivering droplets and bubbles to the respective continuous main fluid phases. Laux et al.

(2007) [2] uses a similar approach as presented in [1], but now for multiphase flows in pipelines.

Purpose of the invention

The main purpose of the invention is to provide a robust method for transient quasi-three-dimensional simulation of multiphase fluid flow in pipelines.

Another purpose of the invention is to provide a robust method for transient quasi-three-dimensional simulation of multiphase fluid flow in pipelines which enables much faster simulation of multiphase fluid flows than currently available simulators.

A further object is to provide a robust method for transient quasi-three-dimensional simulation of multiphase fluid flow in pipelines that is less dependent on empirically developed correlations, which has increased reliability, improved ability to simulate multiphase flows at high pressures, and improved handling of the water phase.

Description of the invention

The present invention is based on the recognition that a robust but simple and cost-effective method for determining multiphase flows in pipelines by transient three-dimensional simulations is achieved by using a hybrid model that treats different continuous fluid phases as separate phases connected together with local boundary conditions on large-scale interfaces and that treats dispersed phases within the continuous phases as dispersed fluids in accordance with the drift flux concept.

In a first aspect, the present invention relates to a method for determining flow parameters for a multiphase flow in a pipeline section, where

- the multiphase flow comprises a plurality of layered, continuous fluid phases separated by large-scale interfaces, and - each continuous fluid phase may include one or more dispersed fluid fields, where the method comprises the following steps: a) providing estimated or measured input values that describe the three-dimensional, physical geometry of the pipeline section , b) formulate a three-dimensional virtual grid representing the three-dimensional physical geometry of the pipeline section as defined

at the input values from a),

there

i) the grid is made up of a set of virtual discs that together

forms the virtual pipeline section, and

ii) each virtual slice is made up of a set of discrete volumes or cells arranged in a set of columns and rows that line up the cross-sectional area of the actual virtual slice of the pipeline, c) providing estimated and measured input values characterizing the multiphase flow, where the input values include at least the following:

i) starting position for the large-scale border fleets,

ii) the physical properties of the fluid,

iii) which continuous fluid phases are present in

the multiphase flow, and

iv) the flow volume for each continuous phase;

d) define a set of fluid fields representing all continuous and dispersed phases in the multiphase flow,

e) use a numerical model that includes:

el) describe the conservation of mass, turbulence, fields, energy,

fluid composition and size of the dispersed phase fields for each fluid field in the set of fluid fields by volume- and ensemble-averaged Euler-formulated transport equations over a vertical cross-section of the pipeline,

e2) describe the conservation of momentum for each fluid field representing a continuous phase of the multiphase flow with a set of algebra relationships derived by using the drift flux concept to describe the relative velocities between the continuous fluid field and local mixing velocities,

e3) use the initial position of the large-scale boundary rafts and the pipeline wall as boundary values for each fluid field representing a continuous fluid phase to determine the mass flow rates for each fluid field,

e4) use conventional sharp-front techniques and the above determined mass flow rates for the fluid fields to determine the local boundary conditions at the large-scale interfaces, and then

f) solve the numerical model with the transport equations in step el) and e2) with the boundary conditions in step e4) over all slices defined in step b) to

determine the flow parameters in the multiphase flow.

The physical properties that characterize the multiphase flow may include one or more of the following properties: Specific density, viscosity, enthalpy, thermal conductivity, component diffusivity, equilibrium phase fractions, activity coefficients, and interfacial tensions. One or more of the physical properties listed above can advantageously be provided to the numerical model in the form of algebraic functions that describe how they depend on temperature, pressure and fluid composition. The above list is not exhaustive and other physical characteristics may also be included when appropriate.

The flow parameters may be sent to a display device for visual representation, sent to a computer data storage device for later use, or sent to a computer memory device for use as input values for other numerical models for determining multiphase fluid flows. The flow parameters for multiphase flow which may be determined by the first aspect of the invention may include one or more of the following characteristic fluid flow parameters; fluid volume fractions, velocities, compositions, pressures, heat and mass transfer coefficients, average particle or bubble sizes, wall shear stresses, phase and field velocity profiles, phase and field volume fraction profiles, field droplet and field bubble size profiles, and phase and field superficial velocities . The list of specified flow parameters is not exhaustive, and any known or conceivable flow parameter that can be extracted from numerical determination of fluid flows with models based on Euler-formulated transport equations can also be included.

The invention according to the first aspect is, as mentioned above, a hybrid approach which enables simultaneous handling of dispersed and separated fluid fields. Conventional separated multiphase flow models cannot resolve large flow domains with large numbers of small droplets or bubbles. However, such flow regimes can be described and modeled with dispersed Euler-Euler multi-fluid equations, but which cannot handle continuous fluid fields. By introducing the large-scale boundary surface concept, as known from Laux et al., 2007 [2], where the large-scale boundary surface is considered an internal, dynamic boundary that has different, continuous fluid fields on either side of the boundary that are constructed and followed in time, however, the model is capable of simultaneously treating two or more continuous, separated fluid fields having from zero to more dispersed fluid fields in them.

Operating flux

By using the concept of drift flux, i.e. assuming that the droplets or bubbles in the dispersed phase behave as during uniform sedimentation, it becomes possible to estimate the sedimentation velocities for droplets and bubbles in the continuous phases by known, analytical fluid-dynamic relations, and further using the impulse measurements to derive algebraic expressions describing the relative velocity between the continuous fluid and the dispersed fields for all spatial directions. Without the uniform sedimentation assumption, it is necessary to use the significantly more complex and computationally challenging Euler-Euler multi-fluid descriptions that are usually used in fluid flow models in the known technique for dispersed flows.

The determined sedimentation velocities and the relative velocity between the continuous fluid and the dispersed fields for all spatial directions can then be used to determine the local mixing velocity inside each continuous fluid. As a result, we obtain the local slip velocity between each fluid field and the local mixture. Then, the momentum equations belonging to one continuous layer (ie, continuous water, gas bubbles in water, and oil droplets in water) can be added together to form a local mixture momentum equation.

The derived slip velocities are used to close the local mixing momentum equation. All fields belonging to this local, continuous fluid layer are now fully described, both in terms of mass and momentum. The mass and momentum equations for each continuous fluid zone can then be used to determine the exchange of mass, momentum and energy at the large-scale interfaces.

The feature of assuming steady-state sedimentation to determine the local mixing rate of the dispersed fluid fields inside each continuous fluid field constitutes a significant simplification and reduction of the necessary computing power to solve the transport equations for each continuous fluid field having one or more dispersed fluid fields compared to models in the known technique that uses Euler-Euler multi-fluid descriptions.

Disc mediation

A further simplification of the numerical effort to solve the numerical model used in the method according to the invention can be achieved by averaging the derived flow conservation equations in the transverse direction, by allowing discrete model equations to be formulated on the disks. By using this concept, gradients of the resolved field variables are allowed in both the axial direction and in the transverse direction of gravity (with respect to the pipeline). This feature has the effect of transforming the three-dimensional description of the multiphase flow into a so-called two-dimensional description that will hereafter be termed "quasi-three-dimensional", and which can be solved in dramatically less computational time compared to the full three-dimensional models without lose pipe geometry-related effects and many of the critical fluid flow parameters.

The result of disc averaging is primarily a two-dimensional set of transport equations where additional sets of closure expressions are derived to model the fluxes acting on the sidewall of the tube. These fluxes, such as wall shear loading, wall heat flux and production of turbulent kinetic energy, can be derived and calculated locally at each grid cell over the pipe, from the bottom to the top wall. Compared to the purely two-dimensional model equations, the Q3D concept includes more detailed physics, and solving the Q3D model equations becomes much more computationally efficient compared to solving the full 3D model equations.

With this so-called two-dimensional approach, it is possible to simulate sufficiently long sections of pipelines containing multiphase flows within the application of reasonable computer resources to analyze or determine flow development and flow regime transitions in the pipeline.

Treatment of large-scale interfaces

According to the first aspect, the invention can be provided with an extended treatment of the transport phenomena on the large-scale boundary rafts and/or the determination and monitoring of the progression of the large-scale boundary surfaces.

This can e.g. be achieved by treating the large-scale boundary surfaces as dynamic boundaries that are allowed to cut through the numerical grid of the numerical model in any possible way, except for grid cells that define the boundary against the pipeline edge. The exception ensures that the model will always include a very small film of continuous fluid on the inner wall of the pipeline to ensure the establishment of a new continuous fluid field when the physical conditions permit. By using a numerical method that includes this feature, the method according to the invention achieves an improved determination and tracking of the large-scale boundary surfaces in the multiphase flow compared to models in the known technique (Laux et al., 2007 [2]), which were limited to defining the large-scale boundary surfaces on the lattice cell boundaries.

A further improvement can e.g. be achieved by modeling the transport of mass, momentum and energy on and/or across the large-scale interfaces with a set of sub-models. E.g. the turbulent shear stress can be calculated with wall functions that include the effect of interface waves, by using the wall functions and interface wave roughness [4] from both sides of the interface. Examples of wall functions for mass and heat transfer are e.g. found in [5]. Furthermore, the entrainment and deposition rates of dispersed fluid fields such as e.g. bubbles or droplets suspended in a continuous fluid phase be determined by specific models, which enable the description of the reduction or growth of the size of the continuous fluid fields. This treatment provides the advantage that the model is independent of the concept of phase inversion to describe the movement and progression of the large-scale interfaces, because the application of the large-scale interface concept allows the phase inversion to be predicted directly from the model and the model provides a specific continuous zone that will gradually disappear when the entrainment flux is greater than the deposition flux , i.e., in the case of liquid flow with entrained bubbles and a very small film of continuous gas, it is possible for the gas bubbles to separate to form two distinct, continuous layers—a continuous gas phase and the liquid zone of dispersed bubbles. With a local change in the flow conditions (typically increased velocities), liquid droplets can also start to be entrained into the continuous gas phase, where the entire continuous liquid phase is slowly eroded. Finally, you have a continuous gas with a high concentration of droplets, and a very small film of continuous liquid.

The deposition rates for dispersed fluid fields are, as a first approximation, handled directly with the drift flux model itself. The relative velocity between the continuous fluid and the dispersed fields, and the local concentration of dispersed fields, represent this first approximation depositional flux. If more accuracy is required, more refined models can be used ([5]-[7]), and it has been shown that these models can be made to represent easily applicable wall functions for the deposition rate [8].

The entrainment flux of droplets and bubbles from the large-scale interface can be represented by semi-empirical models such as Pan & Hanratty [9]. An alternative approach is to provide a physically based concentration of dispersed phases on the large-scale interface and calculate the entrainment flux based on an efficient, turbulent dispersion mechanism. Examples of this approach are found in [10] and [11].

Phases and fields

A multiphase flow in a pipe contains several fluids, such as oil, water and gas which may exist as continuous bulk phases of the fluids and/or mixtures thereof. In the method according to the first aspect of the invention, each fluid is thus further divided into several fields, which makes it possible to distinguish between the different physical appearances of one fluid.

An example of such a division can be shown in Figure 1, which represents a fluid mixture consisting of three different fluids: water, gas and oil. The flow is therefore characterized by 12 fields; three continuous fields (water, oil, gas), dispersed water in gas, dispersed oil in gas, dispersed gas in water, dispersed gas in oil, dispersed oil in water and dispersed water in oil. In addition, in this example we have the liquid oil and water films on the pipe wall in the continuous gas zone and a gas film on the pipe wall in the continuous liquid zones.

The invention according to the first aspect can be used for the determination of multiphase flows in pipelines with a pipe geometry that can be bent in any bend, and the flow equations can be solved by using an extended, local gravity vector which has the property that correct hydrostatic pressure is produced at shutdown. Furthermore, according to the first aspect, the invention can easily be extended to full 3D models by dividing a 3D geometry and discretizing the model equations on the resulting 3D grid. All methods described above can be used discretely on this full 3D approach. In this case, the simplifications introduced by the disc averaging are not necessary and the invention represents a complete 3D method for computer-assisted determination of the multiphase flows.

Figure list

Figure 1 is a schematic representation showing an example of the distribution of phases and fluid fields in a multiphase flow containing gas, oil and water. Each zone consists of the continuous phase and dispersed fields formed by the remaining, present phases. Figure 2 is a schematic representation of a quasi-3D network for pipe geometry, Figure 2 a) shows the grid in the pipe cross-section, and Figure 2 b) from the longitudinal direction. Figure 3 a) is a graphical representation showing a snapshot of a predicted 2-phase flow oil fraction and the oil velocity vectors for hydrodynamic slug flow, the color scale denotes local oil fraction. Figure 3 b) is a graphical representation showing a snapshot of a two-phase flow where the gray band represents the LSF, which separates gas (above) and oil (below), the vectors represent the liquid velocities and the colors show the spatial distribution of the locally averaged droplet sizes. Figure 4 is a graphical representation showing the assumed change in flow regime in the two-phase oil-gas flow in complex pipe geometry. Figure 5 is a graphical representation of simulation results for 2-phase, viscous oil-gas flows for varying superficial gas velocities and fixed superficial velocity. Figure 6 is a graphical representation showing a snapshot from a representative simulation of incipient water accumulation in a 10° inclined pipe. Figure 7 is a graphical representation showing a snapshot of predicted methyl ethylene glycol (MEG) injection into a pipe containing water. Figure 8 is a graphical representation showing a 3-phase flow in a pipe separator.

Verification of the invention

The invention will be described in greater detail by means of an exemplary embodiment.

Anticipate multiphase flow in an oil and gas pipeline

The example embodiment applies the large-scale interface, disc-averaging and drift flux concept to a multiphase flow in a section of a pipeline containing the fluid fields as shown in Figure 1.1 this example embodiment, the multiphase flow consists of a three-phase oil-water-gas flow, and the fluid fields are continuous gas , continuous water, continuous oil, dispersed water in gas, dispersed oil in gas, dispersed gas in water, dispersed gas in oil, dispersed oil in water and dispersed water in oil. In addition, we have the liquid film on the pipe wall in the continuous gas zone and a gas film on the pipe wall in the continuous liquid zones. The numerical model used in the example embodiment is designed by the following steps: 1) the pipe is divided into discrete volumes or computational cells by dividing the cross-section of the pipeline into several slices in one spatial direction, where the discrete sliced areas, as shown in Fig. 2, fills the entire pipe cross-section. In the axial direction, as indicated in figure 2b, any number of corresponding cross-sectional discs can be placed (in this example there are 22 discs), which constitute 3-dimensional volumes on which flow equations can be solved. 2) Next, the multiphase flow for all phases and fields is described by Euler-formulated transport equations which are the average over the width of the discs. For each continuous phase of the multiphase flow, the dispersed fields are assumed to have locally uniform sedimentation and the full Euler-formulated momentum equations are used to derive a set of algebraic relationships for the local sedimentation rates. In this approach, the sedimentation can be driven by many effects, including streamline curvature (centrifugal and Coriolis forces), body forces, turbulent dispersion, and internal migration forces. From the known sedimentation rates, a local mixing impulse equation can then be established. The derived algebra relationships for the relative velocities between dispersed fields and continuous fields are then reworked to form velocities between the fluid fields and the local mixture. The flow inside a continuous region in a given phase of the multiphase flow is now completely described by the local mixing momentum equation and the local sedimentation rates that relate field and local mixing rates, and the mass conservation equations for all fluid fields in the actual continuous phase can be solved by use these speeds. 3) Each continuous phase is treated as bound by the large-scale interfaces (LSI) to handle the physical processes that take place at the interfaces between continuous phases (such as the major gas-oil, oil-water, or water-solid interfaces in the case of four-phase currents). This is achieved by initially assuming or calculating the position of the LSFs independently of the configuration of the calculation cells. That is, the LSI positions can cut through space in any possible configuration with the constraint that continuous phases below the computational grid size cannot be resolved. This can be achieved by determining the LSI positions on the calculation grid from the calculation of the mass equations for each of the mixtures. Since these local mixtures can be considered as individually separated flows, the exemplary embodiment determines the movements of the fronts using the mass-conserving, standard "sharp front" techniques from the literature (volume of fluid or leveling methods). Based on these techniques, the LSI positions at both the start and end of a time step are determined. Based on this geometric information and local field information, the exchange of field mass, zonal mass, zonal impulse, field energy and finally composition can also be determined. Furthermore, the entrainment and deposition of dispersed fields on the large-scale interfaces is calculated from specific and locally based models. The imbalance between deposition and entrainment will affect the development of each continuous zone and control which phase will become the dominant continuous phase. Thus, the exemplary embodiment is capable of calculating multiphase flows that include phase inversion phenomena. 4) The zonal mixing equations described in 2) are now closed by using wall functions to represent the given physical boundary conditions for the walls, due to the disc averaging, and using similar wall functions to represent the local boundary conditions for the LSF, as described in 3). 5) The general models in 2), the treatment of the LSI exchange processes in 3) and the wall treatment in 4) provide a complete set of model equations describing the flow development. In this example embodiment, there will be 9 mass equations, one for each of the 6 dispersed fields and one each for the 3 local continuous phase mixtures, the momentum equations for the three local mixtures (gas with dispersed oil and water droplets, oil with dispersed water and gas, and water with dispersed gas and oil) with 6 algebra relations for the relative velocity between dispersed fields and the local mixtures, 9 field-specific energy equations and 9 field-specific composition equations. In addition to this, conservation equations for all field-turbulence fields and the evolution of the magnitude of each dispersed field can be added to determine turbulence fields in the multiphase flow. The last transport equation in 5), which is solved in the lattice described in 1), includes conservation of mass, momentum, turbulence fields, energy, fluid composition and size of the dispersed phases. 6) The equations representing the full set of conservation equations are then solved in time and space, where the new LSI locations at the beginning of a new time step are determined from the local mixing rates at the previous time step. Then linearized coefficients for the exchange of mass, impulse and energy are calculated in the LSI cells. Then all three mixing impulse equations are solved simultaneously. After this we solve the dispersed field mass equations and the local mass equations, the composition equations, the energy equations and the pressure correction equation. Here the velocities are corrected due to the pressure changes, so that mass is conserved for all fields. Due to the non-linearities in the conservation equations, the complete set of conservation equations cannot be fully satisfied after the equations have been solved once for a new time step. Thus, the solution can be repeated within each time step to reduce solution errors (residuals). For each iteration, the LSI localization is updated as the local mixture mass conservation equations are solved.

Examples of application of the exemplary embodiment according to the invention The invention is tailored for pipeline-type flows in the oil and gas industry. Applications are generally local analyzes of transient flow phenomena in shorter sections of a pipeline segment, including phase separation. Specifically, the invention can be used to interpret 1D transient model results and provide more details about the flow structures. In this way, the invention can be used as a magnifying glass into the flow predicted by an 1D multiphase flow model.

Example 1

Application of embodiment to predict slug flow comprising 2 or 3 phases.

In Figure 3a), a representative snapshot of a 2-phase flow provided by the example embodiment is shown. The colors denote gas (blue) and oil (red). The gray band on the figure is the LSF, which separates the gas- and oil-dominated regions. The green areas inside the oil-dominated region are due to the reduction in the oil fraction, which is caused by entrained gas bubbles. At increased gas flow rates, the exemplary embodiment produces more complex flow patterns (regimes) as shown in figure 3b). The gray band in the figure represents the LSF, and the colors represent the distribution of the droplet sizes. Behind the wave (slug element) the droplet sizes are large. The figure illustrated that the droplet size varies significantly with the local conditions.

Example 2

Application of the example embodiment to predict multiphase flows in pipelines with complex geometries such as curved pipes and intelligent wells, T-splitters and manifolds.

Figure 4 shows the anticipated change in flow regime in two-phase oil-gas flow in complex pipe geometry. The flow enters from the left, and is basically stratified in the horizontal section. In the first inclined section, the flow forms large waves and slugs. After the bend, the flow develops rolling waves. In the bend before the riser, liquid accumulates, and pattern flow structures form in the riser.

Example 3

Application of the example embodiment to predict multiphase viscous oil flows in pipelines.

Figure 5 shows simulation results for 2-phase, viscous oil-gas flows for varying superficial gas velocities (Usg [m/s] and fixed superficial velocity. The liquid viscosity is 0.181 Pa.s. The figure shows the change in flow configuration (flow regime) with regard to the variation on gas-oil flow ratio.

Example 4

Application of the exemplary embodiment to predict water accumulation in oil-dominated multiphase flows in inclined pipes.

Figure 6 shows a snapshot from a representative simulation of incipient water accumulation in a 10° inclined pipe. Water droplets are deposited on the bottom of the pipe and form continuous water and an accompanying, strong backflow, which drives further water accumulation. The thin black line represents the oil-water LSF.

Example 5

Application of the example embodiment to predict displacement of fluids in drill strings during pipeline shut-in to prevent freezing.

Figure 7 shows a snapshot of predicted methyl ethylene glycol (MEG) injection into a pipe containing water. By injecting MEG, water can be displaced and local freezing can be avoided. ME is seen coming from the left, in the lower left corner. The curved band is the LSF that separates MEG and water (upper right side of the LSI).

Example 6

Application of the example embodiment to predict 2- and 3-phase gravity separators in a multiphase pipeline flow.

Figure 8 shows a 3-phase flow in a pipeline separator. Flow enters from the left. The colors represent phase fraction, where red is phase fraction=1.0 and blue is 0.0. The upper figure shows the gas distribution and the gas-oil LSF. In the lower figure you can see the water distribution and the oil-water LSF. Yellow represents large fractions of dispersed oil droplets.

Definition of expressions used in the application

As used herein, the meanings of the following expressions are defined to be:

- "axial" means in a direction parallel to the central axis of the pipeline (the direction of the fluid flow), - "continuous fluid phase" is a phase in which droplets, bubbles and particles are dispersed. In a multiphase flow of water, oil and natural gas, each of these will form a layered, continuous phase separated by a large-scale boundary surface, - "Euler transport equation" is a partial differential equation that expresses the conservation law for a given variable in a fixed coordinate system, - "explicit coupling » means that the outflow from one pipe is injected into another pipe, only by sequentially updating the inflow values for pipe 2 with the outflow values for pipe 1. The inflow pressure for pipe 2 is connected directly to the outflow pressure for pipe 1, - "field" is used for to describe the physical appearance of a phase. The water may be present in the multiphase as the following fields: water droplet in gas, water droplet in oil, continuous water phase, water condensate film on pipe wall, etc., - "flow geometry values" means the values that represent the physical distribution and properties of the fluid phases in the pipeline, and usually include at least the localization of the large-scale boundary surfaces, - "horizontal" is used in connection with the Earth's gravity field, so that a horizontal plane is oriented normally to the direction of the Earth's gravity field, - "large-scale boundary surface" means the boundary surface between two continuous phase regions in the multiphase flow, - "quasi-3-dimensional model » (Q3D) means a full three-dimensional multiphase flow model averaged over one transverse direction to simulate transient multiphase flows in pipelines on a two-dimensional computational grid, - "stratified layers in the continuous fluid phases" means that the fluid phases in the multiphase flow are assumed to be superimposed on each other in the pipeline in ho horizontally oriented layers, - "zone" means a three-dimensional region that has a common fluid as the continuous phase and in which all other phases within the region are dispersed.

References

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Soc, 81, 639-640. 5. S.T. Johansen, "On the modeling of turbulent two phase flows", Dr.Techn. thesis, The Norwegian Institute of Technology, Trondheim, 1990 6. S.T. Johansen, On the deposition of particles to vertical walls, Int. Journal Multiphase Flow, 17, 1991, pp.355 376 7. S.T. Johansen: Thermal inertial deposition of particles, Proceedings of the International Conference of Multiphase Flows '91 Tsukuba, Sept.24 29, Japan, 1991, Vol. 1, pp. 415 421 8. Johnsen Sverre Gullikstad, Stein Tore Johansen (2009). Development of a Boundary Condition Wall Function for Particulate Fouling CFD Modelling, Proceedings of the Seventh International Conference on CFD in the Minerals and Process Industries, CSIRO Australia. 9. Pan L., Hanratty T.J. (2002) Correlation of entrainment for annular flow in horizontal pipes, Int. J. Multiphase Flow 28 385-408 10. S.T. Johansen, S. Graadahl, and T.F. Hagelien, "Entrainment of Inclusions From the Dross in Stirred Reactors for Melt Treatment", Applied Mathematical Modelling, 28, 2004, pp. 63-77 11. Kjølaas, Jørn, Johansen, Stein Tore, Ladam, Yves, Belt, Roel, Danielson , Tom and Stinessen, Marit, Modeling of the droplet field in near-horizontal low liquid loading flows, Proceedings of the 15th International Conference on Multiphase Production Technology, Cannes, France, BHR Group, 2011

Claims (13)

1. Method method for determining flow parameters for a multiphase flow in a pipeline section, where - the multiphase flow comprises a plurality of layered, continuous fluid phases separated by large-scale boundary surfaces, and - each continuous fluid phase may include one or more dispersed fluid fields, where the method comprises the following steps: a) provide estimated or measured input values that describe the three-dimensional physical geometry of the pipeline section, b) formulate a three-dimensional virtual grid representing the three-dimensional physical geometry of the pipeline section as defined by the input values from a), where i) the grid is made up of a set of virtual slices that together form the virtual pipeline section, and ii) each virtual slice is made up of a set of discrete volumes or cells arranged in a set of columns and rows that line up the cross-sectional area of the actual virtual slice of the pipeline, c) provide estimated and measured input values that characterize i) the multiphase flow, where the input values include at least the following: initial position of the large-scale interfaces, ii) the physical properties of the fluid, iii) which continuous fluid phases are present in the multiphase flow, and iv ) the flow volume for each continuous phase, d) define a set of fluid fields that represent all continuous and dispersed phases in the multiphase flow, e) use a numerical model that includes: el) describe the conservation of mass, turbulence, fields, energy, fluid composition and size of the dispersed phase fields for each fluid field in the set of fluid fields is by volume- and ensemble-averaged Euler-formulated transport equations over a vertical cross-section of the pipeline, e2) describe the conservation of momentum for each fluid field representing a continuous phase of the multiphase flow with a set of algebraic relations derived by using the drift flux concept to describe the relative velocities between the continuous fluid field and local mixing velocities, e3) use the initial position of the large-scale boundary surfaces and the pipeline wall as boundary values for each fluid field representing a continuous fluid phase to determine the mass flow rates for each fluid field, e4) use conventional "sharp-front" techniques and the above determined mass flow rates for the fluid fields to determine the local boundary conditions on the large-scale interfaces, and then f) solve the numerical model with the transport equations in steps el) and e2) with the boundary conditions in step e4) over all slices defined in step b) to determine the flow ing parameters in the multiphase flow. 2. Method according to claim 1, where the algebra relationships describing the relative velocities between the continuous fluid field and local mixing velocities are derived by, in successive order: - assuming that the droplets or bubbles in the dispersed phases behave as during uniform sedimentation and estimating sedimentation rates for drops and bubbles in the continuous phases using known, analytical fluid-dynamic relationships, - use the impulse equations to derive algebra expressions that describe the relative speed between the continuous fluid and the dispersed fields for all spatial directions, and - use the determined the sedimentation velocities and the relative velocity between the continuous fluid and the dispersed fields for all spatial directions to determine the local mixing velocity within each continuous fluid, to describe the relative velocities between each continuous fluid field and the local mixing velocities. 3. Method according to claim 1, where the method further comprises: - adding together the momentum equations belonging to one continuous layer to form a local mixing momentum equation, - using the derived algebra relationships that describe the relative velocities to close the local mixing momentum equation, and - using the mass and momentum equations for each continuous fluid zone to determine the exchange of mass, momentum, and energy at the large-scale interfaces. 4. Method according to one of claims 1, 2 or 3, where the large-scale boundary surfaces are treated as dynamic boundaries which are allowed to cut through the numerical grid in the numerical model in any possible way, except for grid cells that define the boundary against the pipeline wall. 5. Method according to claim 4, where the modeling the transport of mass, impulse and energy on and/or across the large-scale boundary surfaces with a set of sub-models. 6. Method according to claim 5, where: the turbulent shear stress is calculated with wall functions that include the effect of interface waves, by using the wall functions and interface wave roughness from both sides of the interface. 7. Method according to any of the preceding claims, wherein the physical properties of the fluid include one or more of the following properties: specific density, viscosity, enthalpy, thermal conductivity, component diffusivity, equilibrium phase fractions, activity coefficients and interfacial tensions. 8. Method according to claim 7, where one or more of the physical properties are provided to the numerical model as algebraic functions that describe how they depend on temperature, pressure and fluid composition. 9. A method according to any one of the preceding claims, wherein the flow parameters include one or more of the following characteristic fluid flow parameters; fluid volume fractions, velocities, compositions, pressures, heat and mass transfer coefficients, average particle or bubble size, wall shear stresses, phase and field velocity profiles, phase and field volume fraction profiles, field droplet and bubble size profiles, and phase and field superficial speeds. 10. A method according to any of the preceding claims, wherein the flow parameters are sent to a display device for visual representation, sent to a data storage device for later use and/or sent to a computer memory device for use as input values for other numerical models for determining multiphase fluid flows. 11. A method according to any one of the preceding claims, wherein the modeling of the transport of mass, momentum and energy on and/or across the large-scale interfaces is carried out with a set of sub-models that include calculation of the turbulent shear stress with wall functions that include the effect of interface waves, by using the wall functions and the interface wave roughness from both sides of the interface. 12. Computer program, comprising processing instructions that cause a computer to carry out the method according to any one of claims 1-11 when instructions are executed by a processing device in the computer. 13. Computer, comprising a processing device and a computer memory, where the computer memory stores a computer program according to claim 12.