WO2015110599A1

WO2015110599A1 - Method for transient quasi three-dimensional simulation of multiphase fluid flow in pipelines

Info

Publication number: WO2015110599A1
Application number: PCT/EP2015/051393
Authority: WO
Inventors: Stein Tore Johansen
Original assignee: Ledaflow Technologies Da
Priority date: 2014-01-24
Filing date: 2015-01-23
Publication date: 2015-07-30
Also published as: AU2015208052C1; DK179330B1; GB201612524D0; BR112016016918A8; AU2015208052B2; GB2539117A; AU2015208052A1; AP2016009390A0; DK201670491A1; NO337063B1; NO20140079A1

Abstract

This invention relates to a method for transient quasi three-dimensional simulation of multiphase fluid flow in pipelines by employing a hybrid numerical model which treats different continuous fluid phases as separate phases coupled together by local boundary conditions at large scale interfaces and which treats dispersed phases within the continuous phases as dispersed fluids according to the drift flux concept.

Description

Method for transient quasi three-dimensional simulation of multiphase fluid flow in pipelines

Field of invention

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

Multiphase flow occurs when more or less separate phases of gases, liquids and/or solid particles flows simultaneously as a mixture. Multiphase flow may involve complex irregular interactions between the flowing phases inducing many different types of interface instabilities, including interface break-up, formation of emulsions and foams, particle precipitation and wall deposition. All these phenomena impact important flow parameters such as pressure drops, fluid temperatures and liquid accumulation. These phenomena may occur in a wide range of applications ranging from large scale industrial processes such as i.e. pharmaceutical industry, paper industry, food industry, metallurgical industry, to small scale applications such as i.e. cooling systems, combustion engines etc.

One particular area where understanding and managing multiphase flow is of vital importance is transportation of hydrocarbons in pipelines from the production sites to treating plants. Fluid flow in pipelines from oil- and gas fields typically involves simultaneous flow of water, oil, and gas, and may also contain entrained solids. The flow patterns may take many different regimes, such as slug flow, bubbly flow, stratified flow, annular flow, and/or churn flow.

The present development of oil- and gas extraction is towards more marginal fields, and in remote and technically challenging areas. It has thus become more important to understand and predict possible multiphase behaviour and complex fluid-related effects which may occur in the pipelines during design and operation of oil- and gas

transportation lines. The basic objective for operators is to maximize hydrocarbon recovery, obtaining optimized production operations under optimized safety - conditions, resulting in a need for controlling the flow velocities, pressure variations and fluid temperatures in the pipelines. The irregular and complex behaviour of multiphase flow makes it necessary to use numerical simulations, often assisted by extensive experimentally determined flow parameters, to predict and/or to obtain an understanding of the multiphase behaviour and complex fluid-related effects that may be expected to occur in a specific pipeline.

Prior art

Numerical models for simulating fluid flows typically employ an Eulerian framework for solving the conservation equations characterizing phases of multiphase flow, and they may grossly be considered as two classes of models; separate flow models and models for dispersed flow.

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

Another approach is the volume of fluid method (VOF) where each fluid phase is modelled by formulating local conservation equations for mass, momentum and energy and replacing the jump conditions at the interface by smoothly varying volumetric forces. This allow tracking of the complicated movement and folding of the interface indirectly by tracking the motion of each of the fluid phases and then determine the interface position as a function of time from the volumetric fluid fractions resulting from the movement of all fluid phases. The VOF approach is thus able to handle flows where the interface folds, breaks or merges. An example of such models is described in US 7 379 852, which discloses a method for tracking a number N of fluid materials and their associated interfaces during simulated fluid flow by use of a microgrid cell methodology which is embedded on a regular macrogrid to subdivide and then tag fluid materials in a computational system preferably using a prime numbering algorithm. The motion of microgrid cells is tracked based on local velocity conditions, rectifying small anomalies by a coupled evaluation of local volume fraction fields and global mass conservation. Volume fractions can be calculated at any time step via an evaluation of the prime locations so that average cellular density and viscosity values can be regularly updated.

The numerical workload enhances considerably for each fluid phase of which the interface needs to be tracked and determined. Thus, separate flow models may handle only a relatively low number of fluid phases such that there is necessary to employ another approach for handling dispersed flow where there may be a very large number of relatively small and locally varying distribution of fluid phases entrained in a continuous main fluid phase. A non-exhaustive list of examples of dispersed flows include bubble flow where a gas phase is distributed as 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 is distributed in a main liquid phase, slurries where small solid particles are distributed in a liquid phase, and any conceivable mixture of these.

In order to handle large number of relatively small phases distributed in a major continuous phase, the models for dispersed flow abandon the concept of tracking the interfaces separating the fluid phases and instead treat the different fluid phases as an interpenetrating continuum associated with discrete entrained particles, bubbles or droplets. Thus, in this approach, the discrete character of the multiphase flow is averaged out such that the small scale fluid movements around individual particles, bubbles, or droplets, or the trajectory of these individual particles, bubbles, or droplet are ignored. The concentration fields in these models will typically vary smoothly in space. Dispersed flow models are incapable of handling flows with large scale interfaces separating the fluid phases.

However, multiphase flows in many industrial applications involve large scale features co-existing with dispersed particles/bubbles or droplets. These multiphase flow situations require the capability of simulating both separated flow situations and dispersed flow situations.

US 5 550 761 discloses a modelling method which differentiates these two types of flow patterns: separated flow patterns (stratified or annular) and dispersed flow patterns, and which treats intermittent flow patterns (slug, churn flow) as a combination of them. This is obtained by characterising the flow regimes by a parameter β representing the fraction of a flow in a separated state, the parameter ranges continuously from 0 for dispersed flow regimes to 1 for separated flow regimes and then apply a transition algorithm for determining whether the flow should be treated as separated, intermittent or dispersed. Another approach is presented in Laux et al. (2005) [1] . This document discloses a hybrid approach for a two-phase flow in pipes, where a multi-level approach is employed to avoid being limited by the direct simulation technique of resolving all interfaces. The two-phase flow is divided into a set of fields which usually are: a continuous liquid layer, a continuous gaseous layer, bubbles suspended in the continuous liquid layer, and droplets suspended in the continuous gas layer. A set of Eulerian volume and ensemble averaged turbulent transport equations are then derived for each field. That is, each field is treated as an interpenetrating continuum in accordance with the dispersed flow approach except for the two major continuous fluid phases (liquid and gas). These two phases are treated as two distinctly separated phases in accordance with the volume of fluid approach. The interface separating these two major phases is also the major interface of the flow, and is thus often denoted the large-scale interface (LSI) in the literature.

The approach of [1] is thus a hybrid approach simultaneously employing both the dispersed flow approach to handle suspended droplets, particles and/or bubbles, and the separated flow approach for keeping track of the interface separating the continuous major fluid phases. In accordance with conventional VOF models, the hybrid approach of [1] employs local model descriptions to represent smoothly varying volumetric forces across the large-scale interface and indirectly determines the position of the interface. The shear forces across the interface are i.e.

approximated by using wall functions for rough walls [3] . The large-scale interface is also made responsible for delivering droplets and bubbles to the respective continuous major fluid phases. Laux et al. (2007) [2] uses a similar approach as [1], but now for multiphase flows in pipelines. Objective of the invention

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

Another objective 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 present commercially available simulators.

A further objective is to provide a robust method for transient quasi three- dimensional simulation of multiphase fluid flow in pipelines which is less dependent upon empirically-developed correlations, having 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 realisation that a robust but simple and cost effective method for determining multiphase flows in pipelines by transient three- dimensional simulations, is obtained by employing a hybrid model which treats different continuous fluid phases as separate phases coupled together by local boundary conditions at large scale interfaces and which treats dispersed phases within the continuous phases as dispersed fluids according to the drift flux concept.

Thus in a first aspect, the present invention relates to a method for determination of flow parameters of a multiphase flow in a pipeline section, where

- the multiphase flow comprises a plurality of stratified continuous fluid phases separated by large scale interfaces, where

- each continuous fluid phase may include one or more dispersed fluid fields, and

- the fluid comprises one or more fluid zones which are three dimensional regions where one common fluid is the continuous phase and where all other phases inside this region are dispersed,

wherein the method comprises the following steps:

a) providing estimated or measured input values describing the three-dimensional physical geometry of the pipeline section,

b) formulating 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 which together form a virtual pipeline section, and

ii) each virtual slice is made up of a set of discrete volumes or cells arranged into a set of columns and rows which tessellate the cross-sectional area of the actual virtual slice of the pipeline,

c) providing estimated or measured input values characterising the multiphase flow, where the input values at least comprises the following:

i) initial position of the large scale interfaces,

ii) the physical properties of the fluid,

iii) which fluid zones being present in the multiphase flow, and

iv) the flow volume of each continuous zone, as well as the volume of the dispersed fields in the zone,

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

e) employing a numerical model which comprises:

el) volume averaged and ensemble averaged 3 dimensional equations, describing the conservation of mass, turbulence fields, energy, fluid composition and size of the dispersed phase fields for each fluid field of the set of fluid fields by volume, and finally a second layer of ensemble averaging in order to obtain Eulerian formulated transport equations over a vertical cross-section of the pipeline

e2) a description of the conservation of mixture momentum of each fluid zone, comprising the sum of the zone's continuous field and dispersed field momentum equations, and where the field velocities are obtained by a set of algebraic relations which can be derived from the individual field momentum equations by using the drift flux concept for describing the relative velocities between the continuous fluid field and local mixture velocities, and where the numerical model:

e3) uses the initial position of the large scale interfaces and the

pipeline wall as boundary values for each fluid field representing a continuous fluid phase to determine the mass flow rates of each fluid field, and

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

and then

f) solving the numerical model with the transport equations of step el) and e2) with the boundary conditions of step e4) over all slices defined in step b) to determine the flow parameters of the multiphase flow.

The physical properties characterising 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 interface tensions. One or more of the above listed physical properties may advantageously be provided to the numerical model in the form of algebraic functions describing how they depend on temperature, pressure and fluid composition. The above list is not exhaustive; other physical properties may also be included whenever appropriate.

The flow parameters may be transmitted to a displaying device for visual representation, transmitted to a computer data storage device for later use, or transmitted to a computer memory device for use as input values for other numerical models for determination of multiphase fluid flows. The flow parameters of 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, pressure, heat- and mass transfer coefficients, averaged particle or bubble sizes, walls shear stresses, profiles of phase- and field velocities, profiles of phase- and field volume fractions, profiles of field droplet- and bubble sizes, and phase- and field superficial velocities. The list of specified flow parameters is not exhaustive; any other known or conceivable flow parameter which may be extracted from numerical determination of fluid flows by models based on Eulerian formulated transport equations may also be included.

The invention according to the first aspect is as mentioned above a hybrid approach enabling simultaneously handling dispersed and separated fluid fields. Conventional separated multiphase flow models cannot resolve large flow domains with large number of small droplets or bubbles. Such flow regimes may however be described and modelled by dispersed Eulerian-Eulerian multi fluid equations, but which cannot handle continuous fluid fields. However, by introducing the large scale interface concept, as known from i.e. Laux et al. 2007 [2], where the large scale interface is considered as an internal dynamic boundary having different continuous fluid fields on each side of the boundary which is constructed and tracked in time, the model is able to simultaneously treat two or more continuous separated fluid fields having from zero to several dispersed fluid fields in them. Drift flux

By employing the concept of drift flux, i.e. assuming the droplets or bubbles in the dispersed phases to behave as under steady sedimentation, it becomes possible to estimate the sedimentation velocities of droplets and bubbles in the continuous phases by known analytic fluid dynamic relations, and further to employ the momentum equations to derive algebraic relations describing the relative velocity between the continuous fluid and the dispersed fields for all spatial directions. Without the steady sedimentation assumption it is necessary to employ the considerably more complex and computationally demanding Eulerian-Eulerian multi-fluid descriptions usually employed in prior art fluid flow models for dispersed flows.

The determined sedimentation velocities and the relative velocity between the continuous fluid and the dispersed fields for all spatial directions may then be applied to determine the local mixture velocity inside each continuous fluid. As a result we get the local slip velocity between each fluid field and the local mixture. Then, the momentum equations that belong to one continuous layer (i.e. continuous water, gas bubbles in water and oil droplets in water) may be added together to form a local mixture momentum equation.

The derived slip velocities are used to close the local mixture momentum equation. All fields that belong to this local fluid continuous layer are now fully described, both when it comes to mass and momentum. The mass and momentum equations for each continuous fluid zone may then be employed 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 mixture velocity of the dispersed fluid fields inside each continuous fluid field constitutes a significant simplification and reduction of required computer power to solve the transport equations for each continuous fluid field having one or more dispersed fluid fields as compared to prior art models applying Eulerian-Eulerian multi-fluid descriptions. Slice averaging

A further simplification of the numerical effort for solving the numerical model being applied in the method according to the invention may be obtained by averaging the derived flow conservation equations in the transversal direction, allowing discrete model equations to be formulated on the slices. Using this concept, gradients of the solved field variables are allowed in both in the axial and in the transversal direction of gravity (with respect to the pipeline). This feature has the effect of transforming the three-dimensional description of the multi-phase flow into a basically two-dimensional description, which hereinafter will be termed as "quasi-three dimensional", and which may be solved at dramatically less computational time as compared to full three-dimensional models without loosing pipe geometry related effects and much of the fluid flow critical parameters.

The outcome of the slice averaging is primarily a two-dimensional set of transport equations in which additional set of closure terms are derived to model the fluxes acting on the side wall of the pipe. These fluxes, such as wall shear stress, wall heat flux and production of turbulent kinetic energy, may be derived and calculated locally at each grid cell across 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 the solution of the Q3D model equations becomes much more computationally efficient compared to solving the full 3D model equations.

By this basically two-dimensional approach, it is possible to simulate sufficiently long sections of pipelines containing multiphase flows within use of reasonable computer resources to analyse or determine flow development and flow regime transitions in the pipeline.

Treatment of the large scale interfaces

The invention according to the first aspect may be provided with an extended treatment of the transport phenomena at the large scale interfaces and/or the determination and tracking of the progression of the large scale interfaces. This may be obtained by i.e. treating the large scale interfaces as dynamic boundaries which are allowed to cut through the numerical grid of the numerical model in any possible manner, except for grid cells defining the boundary towards the pipeline wall. The exception ensures that the model will always include a tiny film of continuous fluid at the inner wall of the pipeline to ensure establishing a new continuous fluid field when the physical conditions allow it. By employing a numerical method including this feature, the method according to the invention obtains an improved determination and tracking of the large scale interfaces in the multi-phase flow as compared to prior art models ( Laux et al. 2007 [2]), which was confined to define the large scale interfaces at the grid cell boundaries. A further enhancement may be obtained by i.e. modelling the transport of mass, momentum and energy at and/or across the large scale interfaces by a set of submodels. For example, the turbulent shear stress may be calculated by wall functions including the effect of interfacial waves, using the wall functions and interface wave roughness [4] from both sides of the interface. Examples of wall functions for mass- and heat transfer is i.e. found in [5] . Further, the entrainment and deposition rates of dispersed fluid fields such as i.e. bubbles or droplets suspended in a continuous fluid phase may be determined by specific models, enabling describing the reduction or growth of the size of the continuous fluid fields. This treatment provides the advantage of the model being independent of the concept of phase inversion to describe the locomotion and progress of the large scale interfaces, since using the large scale interface concept allows predicting the phase inversion directly from the model and the model provides a specific continuous zone which will gradually disappear when the entrainment flux is larger than the deposition flux, i.e. in the case of liquid flow with entrained bubbles and a tiny film of continuous gas it is possible that the gas bubbles separate to form two distinct continuous layers - a continuous gas phase and the liquid zone with dispersed bubbles. Also, with local change in flow conditions (typically increased velocities) liquid droplets may start to be entrained into the continuous gas phase, slowly eroding all the continuous liquid phase. At the end, we have continuous gas with a large concentration of droplets, and a tiny film of continuous liquid.

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

The entrainment flux of droplets and bubbles out 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 at the large scale interface and calculate the entrainment flux based on an effective turbulent dispersion mechanism. Examples of this approach are found in [10] and [11] . Phases and fields

A multiphase flow within a pipe contains several fluids, such as i.e. oil, water and gas which may exist as continuous bulk phases of the fluids and/or mixtures of them. Thus in the method according to the first aspect of the invention, each fluid is subdivided into several fields, making it possible to distinguish the different physical appearances of one fluid.

An example of such division may be as shown in Figure 1, which represents a fluid mixture consisting of three different fluids: water, gas, and oil. The flow is, therefore, characterised 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, we have in this example the liquid oil and water films on the pipe wall in the gas continuous zone and a gas film on pipe wall in the liquid continuous zones.

The invention according to the first aspect may be applied for determination of multiphase flows in pipelines with pipe geometry that can be bent to any

inclination, and the flow equations can be solved using an extended local gravity vector that has the feature that a correct hydrostatic pressure is produced at shut down. Further, the invention according to the first aspect may easily be extended to full 3D-models by partitioning of a 3D-geometry and discretizing the model equations on the resulting 3D-grid. All methods described above can be applied directly to this full 3D-approach. In this case, the simplifications introduced by the slice averages are not necessary and the invention represents a complete 3D-method for computer assisted determinations of multiphase flows. List of Figures

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 made up of the remaining present phases. Figure 2 is a schematic representation of a quasi-3D mesh for the 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 snap shot of a predicted 2-phase flow oil fraction and the oil velocity vectors for hydrodynamic slug flow, the colour scale denotes local oil fraction.

Figure 3 b) is a graphical representation showing a snap shot of a two-phase flow where the grey band represents the LSI, separating gas (above) and oil (below), the vectors represent the liquid velocities and the colours show the spatial distribution of the locally averaged droplet sizes. Figure 4 is a graphical representation showing predicted change in flow regime in 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 snap shot from a representative simulation of beginning water accumulation in a 10° inclined pipe.

Figure 7 is a graphical representation showing a snap shot 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 in the next be described in greater detail by way of an example embodiment.

Predicting multiphase flow in an oil and gas pipeline

The example embodiment is employing the large scale interface, slice averaging, and drift flux concepts on a multiphase flow within a section of a pipeline containing the fluid fields as shown in Figure 1. In this example embodiment the multiphase flow consist 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 gas continuous zone and a gas film on pipe wall in liquid continuous zones. The numerical model employed in the example embodiment is formed 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, in which the discrete slice areas, as demonstrated in Figure 2a fill the entire pipe cross section. In the axial direction, as indicated by Figure 2b, any number of similar cross-section slices can be placed (in this example there are 22 slices), making up 3-dimensional volumes on which the flow equations can be solved.

2) Then the multiphase flow of all phases and fields is described by Eulerian formulated transport equations which are averaged over the width of the slices. For each continuous phase of the multiphase flow, the dispersed fields are assumed to have locally steady sedimentation and the complete Eulerian formulated momentum equations are employed to derive a set of algebraic relations for the local

sedimentation velocities. In this approach, the sedimentation can be driven by numerous effects, including streamline curvature (centrifugal and Coriolis forces), body forces, turbulent dispersion and internal migration forces. Then, from the known sedimentation velocities, a local mixture momentum equation is established. The derived algebraic relations for the relative velocities between dispersed fields and continuous fields are then recast to form relative 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 mixture momentum equation and the local sedimentation velocities relating field and local mixture velocities, and the mass conservations equations for all fluid fields of the actual continuous phase may be solved using these velocities.

3) Each continuous phase is treated as bounded by large scale interfaces (LSI) in order to handle the physical processes taking place at the interfaces between continuous phases (such as the main gas-oil, oil-water or water-solids interfaces in the case of four phase flows). This is obtained by initially assuming or estimating the position of the LSIs regardless of the configuration of the computational cells. That is, the LSI positions can cut through the space in any possible configuration with the limitation that continuous phases below the computational grid size cannot be resolved. This may be obtained by determining the LSI positions on the computational grid from the computation of the mass equations for each of the mixtures. As these local mixtures can be regarded as individual separated flows the example embodiment determine the movements of the fronts using mass conserving standard sharp front techniques from the literature (Volume of Fluid or Level Set methods). Based on these techniques the interface (LSI) positions both at start and end of a time step are determined. Based on this geometrical information and local field information, the exchange of field mass, zone mass, zone momentum, field energy and finally field composition may also be determined. Furthermore, the entrainment and deposition of dispersed fields at the large scale interfaces are computed from specific and locally based models. The imbalance between deposition and entrainment will impact the evolution of each continuous zone and control which phase is going to be the dominating continuous phase. Hence, the example embodiment is capable of computing multiphase flows which include phase inversion phenomena.

4) The zone mixture equations described in 2) are now closed by applying wall functions to represent the given physical boundary conditions for the walls, due to the slice averaging, and applying similar wall functions to represent the local boundary conditions for the LSI, as described in 3).

5) The generic models in 2), the treatment of the LSI exchange processes in 3) and the wall treatment in 4), provides a complete set of model equations which describe the flow evolution. In this example embodiment there will be 9 mass equations, one for each of the 6 dispersed fields and one for each of the 3 local continuous phase mixtures, 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 algebraic 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, it may be added conservation equations for all the field turbulence fields and the evolution of the size for each dispersed field in order to determine turbulence fields of the multiphase flow. The final transport equations in 5), solved on the mesh described in 1), comprise conservation of mass, momentum, turbulence fields, energy, fluid composition and size of the dispersed phase phases.

6) The equations representing the complete 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 mixture velocities at the previous time step. Then linearized coefficients for exchange of mass, momentum and energy are computed in the LSI cells. Next all three mixture momentum equations are solved simultaneously. After that we solve the dispersed field mass equations and the local mixture mass equations, the composition equations, the energy equations and the pressure correction equation. Here the velocities are corrected due to the pressure changes, such that mass is conserved for all fields. Due to non-linearities in the conservation equations, the complete set of conservation equations may not be satisfied fully after the equations have been solved once for a new time step. Hence, the solution may be iterated within each time step in order to reduce the solution error (residuals). For each iteration, the LSI location is updated when the local mixture mass conservation equations are solved.

Examples of application of the example embodiment of the invention

The invention is tailored for pipeline type flows in the oil and gas industry.

Applications are in general local analyses of transient flow phenomena in shorter section of a pipeline segment, including phase separation. In particular the invention can be used to interpret ID-transient model results and give more details of the flow structures. In this way the invention can be used as a magnifying glass into the flow predicted by a ID-multiphase flow model.

Example 1

Use of the example embodiment for predicting slug flow, comprising 2 or 3 phases. In Figure 3 a), a representative snap shot of a 2-phase flow predicted by the example embodiment is shown. The colours denote gas (blue) and oil (red). The grey band in the figure is the LSI, separating the gas and oil dominated regions. The green areas inside the oil dominated region are due to reduction in the oil fraction, caused by entrained gas bubbles. At increased gas flow rates the example

embodiment gives more complex flow patterns (regimes) as seen in Figure 3 b). The grey band in the figure represents the LSI, and the colours represent the distribution of the droplet sizes. Behind the wave (slug body) the droplet sizes are large. The figure illustrated that the droplet size varies significantly with the local conditions.

Example 2

Use of the example embodiment for predicting multiphase flows in pipelines with complex geometries such as i.e. curved pipes and intelligent wells, T-splits and manifolds. Figure 4 shows the predicted change in flow regime in two phase oil-gas flow in complex pipe geometry. The flow enters from the left, being initially stratified in the horizontal section. In the first inclined section the flow forms large waves and slugs. After the bend, the flow develops roll waves. In the bend before the riser liquid accumulates, and churn flow structures form in the riser.

Example 3

Use of the example embodiment for predicting 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 respect to the variation on the gas-oil flow ratio. Example 4

Use of the example embodiment for predicting water accumulation in oil dominated multiphase flows in inclined pipes

Figure 6 shows a snap shot from a representative simulation of beginning water accumulation in a 10 ⁰ inclined pipe. Water droplets deposit at the bottom of the pipe and forms continuous water and a resulting strong backflow, driving further water accumulation. The thin black line represents the oil-water LSI.

Example 5

Use of the example embodiment for predicting displacement of fluids in jumpers during pipeline shut-in for preventing freezing.

Figure 7 shows a snap shot of predicted Methyl Ethylene Glycol (MEG) injection into a pipe containing water. By injecting the MEG water can be displaced and local freezing can be avoided. MEG is seen coming from the left, in lower left corner. The curved band is the LSI separating MEG and water (upper right side of the LSI). Example 6

Use of the example embodiment for predicting 2-and 3-phase gravity separators in a multiphase pipeline flow.

Figure 8 shows a 3-phase flow in a pipe separator. Flow enters from the left. The colours represent phase fraction, red being phase fraction = 1.0 and blue is 0.0. Upper figure show the gas distribution and the gas-oil LSI. In the lower figure we see the water distribution and the oil-water LSI. Yellow represents large fractions of dispersed oil droplets.

Definition of terms used in the application

As used herein, the meaning of the following terms are defined to be:

- "axial" means in a direction parallel with the centre axis of the pipeline (direction of the fluid flow),

- "continuous fluid phase" is a phase in which droplets, bubbles, and particles are dispersed. In i.e. a multiphase flow of water, oil, and natural gas, each of these will form a stratified continuous phase separated by a large scale interface,

- "Eulerian transport equation" is a partial differential equation expressing 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 coupled directly to the outflow pressure for pipe 1,

- "field" is used to describe the physical appearance of a phase. The water may i.e. be present in the multiphase as the following fields; water droplet in gas, water droplet in oil, continuous water phase, water condensate film at pipe wall etc., - "flow geometry values" means the values representing the physical distribution and properties of the fluid phases in the pipeline, and usually includes at least the location of the large scale interfaces,

- "horizontal" is used in relation to the earth gravity field, such that a horizontal plane is oriented normal to the direction of the earth gravity field,

- "large scale interface" means the interface between two continuous phase regions in the multiphase flow,

- "quasi 3-dimensional model" (Q3D) means a full three-dimensional multiphase flow model which is averaged over one transverse direction to simulate transient multiphase flows in pipelines on a two-dimensional computational mesh,

- "stratified layers of the continuous fluid phases" means that the fluid phases of the multiphase flow are assumed overlaid each other in the pipeline in horizontally oriented layers,

- "zone" or "fluid zone" means a three-dimensional region which has a common fluid as the continuous phase and where all other phases inside the region is dispersed. Thus "inside each continuous fluid" is the same as and employed interchangeably as "inside each zone".

References

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A. Goldszal, and J. I. Monsen (2005), Multi-dimensional simulations of slug and slug-like flows in inclined pipes and channels, 6th North American BHRG Conference on Multiphase Technology, June 12th 2005, Banff, pp. 21-36

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Claims

1. A method for determination of flow parameters of a multiphase flow in a pipeline section, where

wherein the method comprises the following steps:

i) initial position of the large scale interfaces,

ii) the physical properties of the fluid,

iii) which fluid zones being present in the multiphase flow, and

e) employing a numerical model which comprises:

e3) uses the initial position of the large scale interfaces and the

and then

2. A method according to claim 1 , wherein the algebraic relations describing the relative velocities between the continuous fluid field and the local mixture velocities are derived by, in successive order:

- assuming the droplets or bubbles in the dispersed phases behaves as under steady sedimentation and estimating sedimentation velocities of droplets and bubbles in the continuous phases by known analytic fluid dynamic relations,

- employing the momentum equations to derive algebraic relations describing the relative velocity between the continuous fluid and the dispersed fields for all spatial directions, and

- employing the determined sedimentation velocities and the relative velocity between the continuous fluid and the dispersed fields for all spatial directions to determine the local mixture velocity inside each continuous fluid to describe the relative velocities between each continuous fluid field and the local mixture velocities.

3. A method according to claim 1 , wherein the method further comprises:

- adding the momentum equations that belong to one continuous layer together to form a local mixture momentum equation,

- employing the derived algebraic relations describing the relative velocities to close the local mixture momentum equation, and

- employing 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. A method according to one of claim 1 , 2 or 3, wherein the large scale interfaces are treated as dynamic boundaries which are allowed to cut through the numerical grid of the numerical model in any possible manner, except for grid cells defining the boundary towards the pipeline wall.

5. A method according to claim 4, wherein the modelling of the transport of mass, momentum and energy at and/or across the large scale interfaces is performed by a set of sub-models.

6. A method according to claim 5, wherein:

- the turbulent shear stress is calculated by wall functions including the effect of interfacial waves, using the wall functions and interface wave roughness from both sides of the interface.

7. A method according to any preceding claim, 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 interface tensions.

8. A method according to claim 7, wherein one or more of the physical properties are provided to the numerical model as algebraic functions describing how they depend on temperature, pressure and fluid composition.

9. A method according to any preceding claim, wherein the flow parameters includes one or more of the following characteristic fluid flow parameters; fluid volume fractions, velocities, compositions, pressure, heat- and mass transfer coefficients, averaged particle or bubble sizes, walls shear stresses, profiles of phase- and field velocities, profiles of phase- and field volume fractions, profiles of field droplet- and bubble sizes, and phase- and field superficial velocities.

10. A method according to any preceding claim, wherein the flow parameters are transmitted to a displaying device for visual representation, transmitted to a computer data storage device for later use, and/or transmitted to a computer memory device for use as input values for other numerical models for determination of multiphase fluid flows.

11. A method according to any preceding claim, wherein the modelling of the transport of mass, momentum and energy at and/or across the large scale interfaces is made by a set of sub-models which includes calculating the turbulent shear stress by wall functions including the effect of interfacial waves, using the wall functions and interface wave roughness from both sides of the interface.

12. A computer program, comprising processing instructions which causes a computer to perform the method according to any of claims 1 - 11 when the instructions are executed by a processing device in the computer.

13. A computer, comprising a processing device and a computer memory, the computer memory is storing a computer program as set forth in claim 12.