SPE-169328-MS

Evaluation of Multiphase Flow Models To Predict Pressure Gradient inVertical Pipes With Highly Viscous Liquids

R. Ruiz, A. Brito, and J. Marquez, PDVSA Intevep

Copyright 2014, Society of Petroleum Engineers

This paper was prepared for presentation at the SPE Latin American and Caribbean Petroleum Engineering Conference held in Maracaibo, Venezuela, 21–23 May2014.

This paper was selected for presentation by an SPE program committee following review of information contained in an abstract submitted by the author(s). Contentsof the paper have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material does not necessarily reflectany position of the Society of Petroleum Engineers, its officers, or members. Electronic reproduction, distribution, or storage of any part of this paper without the writtenconsent of the Society of Petroleum Engineers is prohibited. Permission to reproduce in print is restricted to an abstract of not more than 300 words; illustrations maynot be copied. The abstract must contain conspicuous acknowledgment of SPE copyright.

Abstract

The prediction of pressure drop in multiphase flow for risers is of particular interest for the oil industryand also a critical variable for the right design of surface facilities in offshore fields. Empirical steady statecorrelations, mechanistic models and dynamic models are available to calculate the multiphase flowpressure drop, holdup and phases distribution.

The main purpose of this paper is to evaluate the accuracy of several steady state pressure drop predictionmodels with two phase flow laboratory data conformed by 108 point using air as gas phase and liquids withviscosity up to 310cP. The models considered in this study, for predicting pressure drop are Beggs and Brill,Duns and Ros, Govier and Aziz, Hagedorn and Brown, Mukherjee and Brill, Orkiszewski, Ansari and OLGASmodel, using PIPESIM simulator. The evaluation was based on the comparison between the predicted and themeasured pressure drops, demonstrating the performance of each model for highly viscous liquids. Statisticalparameters as average absolute percent error and standard deviation have been calculated to find the mostacceptable one. The statistical analysis showed that among the evaluated Hagedorn and Brown model has thebest performance to predict pressure drop in risers with highly viscous liquids.

IntroductionThe multiphase flow is a common condition to transport the production fluids from the well to the surfacefacilities of the oil and gas industry. Typically the production streams are composed by water, crude oiland gas. Nowadays the production environment in the oil industry is complex and hostile. That is thereason why the multiphase flow transportation has many considerations that need to be taken into accountfor designing the surface facilities. Once of this consideration is the prediction of pressure drop, liquidholdup and flow pattern. In this sense, it is very important to evaluate the performance of models availablein commercial simulators, for estimating the pressure drop.

A more obvious consequence of a proper pipeline sizing is the impact over the CAPEX of a newdevelopment project. The piping cost could be 25% of the total project cost or even higher for offshoretieback projects [1] and up to 60% for gas condensate developments [2]. A new trunk line for an onshoreheavy oil development could cost around 2.25 MMUSD per km. With such heavy investment, the wrongpipeline size selection could jeopardize the profitable exploitation of the new heavy oil fields.

Knowing the level of accuracy of each model will increase the confidence of the designer and providea very useful tool to select the most suited method for a particular heavy or extra heavy oil fielddevelopment. This paper presents an evaluation of the most common steady state pressure drop methodsfor gas – liquid flow in vertical pipelines with air and mineral oil up to 310cp.

BackgroundMost of models available to predict pressure drop in vertical pipelines have been developed and validatedby using low pressure, small diameter and air/water laboratory data. In addition, oil & gas applicationsranges are limited and only few of them are valid for heavy oils below to 22° API.

The high viscosity of the oils imposes technical challenges for their profitable, reliable, long termproduction. The transport of the production streams from the wellbore to the processing facilities is oneof those challenges as the friction pressure drop in the multiphase pipelines could become a severeconstrain. The multiphase pipeline operational envelope is bounded by the pressure drop constrains linkedto the flowing wellhead pressures, and the production – water cut combinations which promote sluggingoccurrence. Therefore, the proper pressure drop prediction is of great importance for a reliable pipelinedesign in order to define these boundaries, minimizing the possibility of slug flow occurrence. There isstill a lack of published evidence over the accuracy of these methods regarding the prediction of themultiphase flow behavior with highly viscous liquids. In 2008 PDVSA Intevep with the objective toestimate the magnitude of the errors, in the prediction of pressure drop with horizontal pipe, developeda work using a database of heavy and extra heavy oil, the results were that the Oliemans (1976)correlations best predict the pressure gradient with an error of 20% follow by the Beggs and Brill (1973)models which got an error in the estimation of pressure drop of 22% [3].

Pressure Drop Models in Vertical PipeThe models considered in this study for predicting pressure drop are as follows: Beggs & Brill original(1973), Duns & Ros (1963), Govier & Aziz (1972), Hagedorn & Brown (1965), Mukherjee & Brill(1985), Orkiszewski (1967), Ansari (1994) and OLGAS (2006).

Beggs & Brill (1973) Model [4]This model considers pipe inclination angle between –90° and 90°. The correlation was developed usingair/water data base and pipe diameter between 1 and 1.5 inches. They consider four flow patterns:segregated, intermittent, and distributed. It is important to mention that the flow pattern is used as acorrelating parameter and does not represent the flow pattern unless the pipe is horizontal. The holdup iscalculated for horizontal pipeline and then corrected for the pipe inclination angle. The flow pattern mapis represented as a function of two non-dimensional numbers, the Froude number and the no-slip liquidholdup (equations 1 and 2). Also it is necessary to calculate a friction factor that is not dependent on theflow pattern in the pipe. The pressure drop in this model considers the friction losses, elevation of the pipeand the acceleration term.

(1)

(2)

The Beggs & Brill model estimates the friction pressure drop as in the Dukler et al (1964) model.

(3)

The two phase friction factor fTP is calculated from the liquid slip holdup in horizontal pipe HL (0)and depends on the flow pattern in the pipe.

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The gravitational pressure losses are determined from equation (4).

(4)

Duns & Ros (1961) Model [5]Duns and Ros model was developed for two phase flow in vertical wells taking into account the flowpatterns in the well. They considered three flow patterns: bubble, slug and mist flow. The model is basedon four non-dimensional numbers: the liquid and gas velocities number NLV and NGV, the diameternumber (ND) and the liquid viscosity number (NL), see equations (5) to (8). They validated the modelagainst a data base of 4000 test runs with 20.000 data points, with pipeline diameter between 1.25 and 5.6inches and the liquid and gas superficial velocities up to 3.2 m/s and 100 m/s, respectively. The fluids usedwere gas and several types of oil and water.

(5)

(6)

(7)

(8)

Once the flow pattern in the pipe is known, the superficial fluids velocities, densities and liquid holdupare calculated using the proper equations. For the slug and bubble flow pattern, the friction pressure dropequation (9) is the same, the elevation term is calculated with equation (11) and the acceleration term isnot considered.

(9)

(10)

Govier & Aziz (1972) Model [6]The Govier, Aziz and Fogarasi correlation is used for pressure loss, holdup and flow regime. It wasdeveloped following a study of pressure drop in wells producing gas and condensate, 102 wells with gasliquid ratios from 3900 to 1170000 Scf/bbl were analyzed in detail. The authors developed their own flowpattern map for identify four flow regimes: bubble, slug, mist and transition zone.

Govier and Aziz give the mechanical energy equation for vertical flow of a single or multi-phasemixture written for a small elevation change, dz as follows:

(11)

Where:D � inside diameter pipe, ftf � friction factor dimensionlessg � acceleration gravity, ft/sec2

gc � dimensional conversion factor, lbm ft/lbf sec2

V � cross sectional average velocity, ft/sec� � velocity profile correction term� � density, lbm/ft3

SPE-169328-MS 3

After the estimation of the flow regime the corresponding model is used to calculate liquid holdup andfrictional pressure losses. Govier and Aziz developed equations for the estimation of pressure drop in slugand Bubble flow, for the estimation of the pressure gradient in mist and forth flow the Duns & Ros modelis used.

Hagedorn & Brown (1965) Model [7]The Hagedorn and Brown method was developed for multiphase wellbore pressure loss calculations usingdata from a 1500 ft deep producing test well with nominal tubing sizes of 1, 1/4 and 1 1/2 inches. Testswere conducted for widely varying liquid flowrates, gas liquid ratios and liquid viscosities. The liquidholdup was not directly measured; instead, it was inferred from the measured pressure losses. The originalHagedorn and Brown method is independent of flow regime. The revised version determines if bubbleflow exists according to the Griffith and Wallis criteria. If bubble flow exists, the Griffith and Wallisequations to compute liquid holdup and friction loss are used, otherwise the original Hagedorn and Brownprocedure is followed. The original correlation utilizes the same dimensionless groups developed by Dunsand Ros which also used by the Eaton (1967) liquid holdup correlation.

Mukherjee & Brill (1985) Model [8]The correlation of Mukherjee & Brill was developed for pipe with different inclination angles. It was thefirst correlation that considered the change of the flow pattern due to the inclination angle of the pipe. Inaddition to the patterns observed invertical pipe:bubble, slug and mist flow, the stratified flow pattern inhorizontal and downward pipes is included (�90 � � � 0°). For the estimation of liquid holdup more than1500 measurments of holdup were considered with a pipe inclination angle between –90° and 90°. Thefriction factor is calculated according to the flow pattern identified. Different equations have beenproposed for each flow pattern, for bubble and slug flow the moody diagram is used and for mist flow acorrelation proposed by Mukherjee & Brill is used, where the slippage between phases is not considered.

Orkiszewski (1967) Model [9]The orkiszewski correlation is used for pressure losses, holdup, and flow regime. The Orkiszewskicorrelation was developed for the prediction of two phase pressure drops in vertical pipe. Four flowregimes were considered, bubble, slug, annular-slug transition, annular mist. The method can accuratelypredict, to within 10%, the two phase pressure drops in naturally flowing and gas lifted production wellsover a wide range of well conditions. The precision of the method was verified when its predicted valueswere compared against 148 measured pressure drops. Unlike most others methods, liquid holdup arederived from observed physical phenomena, and is adjusted for angle of deviation.

Ansari (1994) Model [10]The Ansari model was developed as part of the Tulsa University Fluid Flow Projects (TUFFP) researchprogram. A comprehensive model was formulated to predict flow patterns characteristics and the flowcharacteristics of the predicted flow patterns for upward two phase flow. The comprehensive mechanisticmodel is composed of a model for flow pattern prediction and a set of independent models for predictingholdup and pressure drop in bubble, slug and annular flows. The model was evaluated by using TUFFPwell databank that is composed of 1775 well cases.

OLGAS (2006) Model [11]OLGAS is a model for steady state flow. This model is able to predict the pressure drop in pipelines, liquidholdup and flow pattern for each pipe section [8]. The model considers continuity and momentumequations for each phase. The total mixture composition is assumed to be constant with time along thepipeline, while the composition of gas and liquid changes with pressure and temperature due to interphasemass transfer [9]. As some correlations used in the model depend on the flow pattern in the pipe, this hasto be determined as the first step. OLGAS considers four flow patterns: stratified, annular, bubble and slugflow.

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The most commonly used correlation models topredict pressure drop in a vertical pipeline are Hage-dorn and Brown (1965) and Beggs and Brill (1973).(See Table 1.)

Experimental DataThe gas liquid experimental database used in thisstudy corresponds to 108 points of upward verticalflow with a mineral oil viscosity up to 310 cP andair, with an operation pressure up to 103 Psia, inpipe diameters of 1 and 1 ½ inches. The range ofoperation conditions and fluids properties of data-base are summarized in Table 2.

Methodology

The pressure drop prediction was carried out using the PIPESIM commercial simulator and differentempirical models such as Beggs and Brill original (1963), Duns and Ros (1963), Hagedorn and Brown(1965), Mukherjee and Brill (1985), Orkiszewski (1967), and Govier and Aziz (1972), Ansari (1994) andOLGAS (2006) mechanistic models. The variables of interest that will be obtained from the simulator are:the pressure drop gradient (Pa/m), flow pattern and liquid viscosity (cp).

The statistical parameters used in this study are: the average error (Ei) and the average absolute error(EA). These parameters will be calculated to compare the performance of the different models evaluated.The average error is related to the agreement between predicted value (Vp) and measured value (Vm), theaverage absolute error EA, considered one of the most important statistical parameters because thenegative and positive values do not cancel out.

(3)

(4)

Experimental ResultsFlow PatternThe flow pattern prediction is an important parameter used in most of the mechanistic pressure drop andholdup models as there are many closure relationships that depend on the flow pattern prediction.

Beggs & Brill (1973) model considers four flow patterns in pipeline: segregated, intermittent,distributed and a transition region. In the case of Mukherjee & Brill (1985) model, it considers three flow

Table 1—Pressure drop prediction models

Pressure drop models Type of model Application

Beggs and Brill Empirical For horizontal and inclined pipes

Duns and Ros Empirical For vertical flow

Orkiszewski Empirical For vertical flow

Hagedorn and Brown Empirical For vertical flow

Mukherjee and Brill Empirical For vertical flow

Govier and Aziz Mechanistic Two phase flow model in vertical pipe

Ansari Mechanistic Two phase flow model in vertical pipe

OLGAS Mechanistic Two phase flow model

Table 2—Experimental database

Variable Minimum Maximum

Usl (m/s) 0.03 3.3

Usg (m/s) 0.17 26.5

� l (PaS) 0.001 0.311

dp/dz (Pa/m) 408 29664

Holdup 0.020 0.97

0.2 2111

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patterns: Slug, bubble and mist. Hagedorn & Brown (1965) does not consider the existence of flowpattern. This correlation was developed for two phase vertical flow as was the case for Duns & Ros (1961)correlation which considers three flow patterns: Intermittent, bubble and mist.

Orkiszewski (1967) and Govier and Aziz (1972) models considers four flow patterns: bubble, slug,mist and a transition region. Orkiszewski predicted the flow pattern in the pipe through the Griffith andWallis limits for slug and bubble flow, for the other cases the Duns and Ros limits are used. For Govier& Aziz model a dimensional numbers have to be estimated, and also the properties of the fluids asdensities, superficial stress and superficial velocities.

Ansari model for upward two phase flow in wellbores is composed by flow pattern prediction and aset of independent mechanistic models for predicting holdup and pressure drop in bubble, slug and annularflow. This model predicts the flow pattern in the pipe through the well known Taitel & Barnea equations(1980). For OLGAS model, it is necessary to determine a flow pattern for each segment of pipe, gettingthe flow pattern in the pipe as an average of the flow pattern obtained through all of the pipe length. Theflow pattern transition in this model is based on the minimum phases slip concept.

The best flow pattern prediction was made by Beggs and Brill and Ansari with a 43% and 40% ofsuccess, respectively. The worst flow pattern prediction were obtained by Govier and Aziz model andMukherjee y Brill with a 12% and 3% of correct pattern predictions, respectively. (Figure 1).

Pressure drop predictionThe pressure drop prediction was carried out using the PIPESIM commercial simulators for verticalpipeline, using different empirical models as Beggs and Brill original (1963), Duns and Ros (1963),Govier and Aziz (1972), Hagedorn and Brown (1965), Mukherjee and Brill (1985), Orkiszewski (1967),Ansari (1994) and OLGAS (2006). The pressure drop obtained from the models was compared against theexperimental data base. Figure 2 shows the performance obtained from the different pressure drop modelsrepresented by the absolute average error. The best prediction was achieved with the Hagendorn andBrown empirical model showing a 19% average absolute error. The second best prediction was obtainedwith Beggs & Brill displaying a 27% average absolute error. The best performance obtained by theHagedorn and Brown correlation can be explained only by the extensive data used in its development andmodifications made to the correlation.

Figure 1—Flow Pattern Prediction using PIPESIM

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Conclusions

1. The best flow pattern prediction was obtained by Beggs and Brill model, with 43% of success.2. The lower average errors for the pressure drop prediction were obtained with the Hagedorn and

Brown and Beggs and Brill models with 19% and 27% of error, respectively.

Nomenclature

� Density (kg/m3)� Viscosity (cp)V Fluid velocity (m/s)gc Gravity acceleration (m/s2)d Pipe diameter (m)NRe Reynolds numberf Wall friction factorf/fn Normalized friction factor� Surface tension (N/m)NFR Froude numberNLV Liquid velocity numberNGV Gas velocity numberND Diameter numberNG Gas viscosity numberNL Liquid viscosity numberH Slip holdup� No-slip holdupEi Average error (%)EA Average absolute error (%)Vp Predicted valueVm Measurement valuedP/dX Pressure gradient (Pa/m)

Figure 2—Pressure gradient model’s absolute error

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Subscripts and superscripts

g Gas phaseL Liquid phasesl Liquid superficialsg Gas superficialm mixture

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