Comparison between analytical and

numerical solutions for pressure drop in

gas-liquid intermittent flow pattern

Renato Pacheco Silva

Sinésio Domingues Franco

Juliano Oséias de Moraes

PRESENTATION TOPICS

• Lab Overview

• Problem Description;

• Goals;

• Methodology;

• Results;

• Conclusion and next steps.

LAB OVERVIEW

• Laboratory of Friction and Wear Technology (LTAD);

• Our work:

– Subjects related to friction and wear in mining, oil and gas;

– Formation of human resources;

– Development of research projects and technical services in

exploitation, productions and transportation of oil;

LAB OVERVIEW

• Personnel:

– Professors with good knowledge in tribology, mechanical projects,

instrumentation and control;

– Secretary;

– Mechanical and electrical engineers;

– Technicians in metallography, mechanical and electro-electronics;

– Phd, master and graduate students;

LAB OVERVIEW

• Structure:

LAB OVERVIEW

• Structure:

– Cupons preparation;

– Metallographic and topographic characterization;

– Tribologic characterization;

– Corrosion/erosion;

– Friction welding;

– In situ mechanical properties;

– Intrumentation.

LAB OVERVIEW

• Structure:

– Cupons preparation;

– Metallographic and topographic characterization;

– Tribologic characterization;

– Corrosion/erosion;

– Friction welding;

– In situ mechanical properties;

– Intrumentation.

LAB OVERVIEW

• Facilities:

Machine Shop

LAB OVERVIEW

• Facilities:

Metallographic

preparation

LAB OVERVIEW

• Facilities:

Scanning Electon Microscopy

LAB OVERVIEW

• Facilities:

Objectives

Topography

AnalysisSample

Holder

Microindentation and

Microscratching

LAB OVERVIEW

• Facilities:

Interferometer and rugosimeter

LAB OVERVIEW

• Facilities:

Tribometer

LAB OVERVIEW

• Facilities:

Impinging Jet

LAB OVERVIEW

• Facilities:

Erosion/Corrosion Loop

PROBLEM DESCRIPTION

• Pressure loss in two-phase gas-liquid flow;

• Equipment selection;

• Empirical-analytical calculus vs computer simulation.

PROBLEM DESCRIPTION

• Intermittent Flow Pattern:

PROBLEM DESCRIPTION

• Taitel & Dukler (1976) flow pattern map, compared to

Mandhane (1973) flow pattern map:

GOALS

• Calculate pressure loss;

• Use the results for equipment dimensioning.

METHODOLOGY

• First method:

– Analytical calculus;

• Second method:

– Computer simulation;

Air water

Superficial Velocity (m/s) 2 1

Viscosity (kg/(m*s) 1,7894e-5 0,001003

Density (kg/m3) 1,225 998,2

METHODOLOGY

• Analytical calculus:

– Based on literature (Oliemans, 2006);

– One method for each flow pattern involved;

• Computer simulation:

– RANS simulation;

– k-ω-sst model;

METHODOLOGY

• Analytical calculus:

METHODOLOGY

• Analytical equationing:

– Calculate the distribution parameter CO;

– Determine bubble rise velocity ub;

– Calculate shedding parameter C;

– Determine liquid holdup in slug cylinder αLs;

– Calculate liquid holdup of slug unit αL;

– Determine slug cylinder–slug unit length ratio ls/lu;

– Calculate average liquid holdup in film;

– Calculate actual gas and liquid velocities in the film region;

– Calculate perimeters and shear stresses in film region with either

stratified or annular flow model;

– Calculate frictional pressure gradient (dp/dx)F;

– Calculate total pressure gradient.

METHODOLOGY

• Analytical equationing for pressure loss:

• Where things like tension, perimeters, áreas, friction factor,

mean velocities ans length ratios were previously calculated.

RESULTS

• Comparing this case to the literature:

RESULTS

• Comparing this case to the literature:

RESULTS

• Pressure loss in slug flow:

RESULTS

• Computer simulation of slug formation:

RESULTS

• Pressure field:

RESULTS

• Measurement place:

Cauda 1Cauda 2

RESULTS

• Pressure report:

"Surface Integral Report"

mixture

Area-Weighted Average

Total Pressure (pascal)

-------------------------------- --------------------

cauda1 1001905.1

"Surface Integral Report"

mixture

Area-Weighted Average

Total Pressure (pascal)

-------------------------------- --------------------

cauda2 1001480.6

RESULTS

• KSLA model pressure loss obtained: 558 [Pa/m];

• Fluent simulation pressure loss obtained: 380 [Pa/m].

CONCLUSIONS

• Analytical model represents a higher pressure drop than

calculated from Fluent;

• 32% higher;

• From literature, holdup for intermittent in this case is 30 to

50% higher than no-slip holdup;

• This analytical form is called KSLA and uses liquid holdup for

pressure loss calculation;

• As the main objective is to domensioning a positive

displacement blower, one shall use KSLA model

CONCLUSIONS

• From the literature:

NEXT STEPS

• Discover if this error is associated to the liquid holdup

calculation;

• Use the loop experimental equipment for pressure loss

measurement.

END

THANKS!