A Combined Experimental & Numerical Research Program to ... · A Combined Experimental & Numerical Research Program to Develop a Computer Simulator for Intermittent Gas-lift Bordalo,

Feb. 3 - 7, 2014 2014 Gas-Lift Workshop 1

A Combined Experimental &

Numerical Research Program

to Develop a Computer Simulator

for Intermittent Gas-lift

Bordalo, S.(1), Barreto, M.(2),

Pestana, T.(1), Ochoa Lara, I.(1)

(1) UNICAMP, (2) PETROBRAS

37th Gas-Lift Workshop Houston, Texas, USA February 3 – 7, 2014

Motivation

• Hundreds of petroleum wells, mainly in the northeast

region of Brazil, are equipped with Intermittent Gas-Lift

systems (IGL), due to the high number of mature fields

with low reservoir static pressure.

• Desire for a rational tool to evaluate the IGL’s

performance and to compare artificial lift methods

Slide 3

Objective

Slide 4

To develop a computer simulator, employing a model

based on the fundamental equations of fluid dynamics.

1991 – Liao: laid out most of the general equations.

1997 – Santos: applied the equations to 4 IGL methods (conventional

IGL, IGL with plunger, IGL with chamber, Pig-lift).

1997 – Bordalo et al.: established the foundation for the IGL simulator.

2004 – Carvalho: wrote the first full simulator (with variants for the

conventional IGL, IGL with plunger, inverted IGL).

Intermittent Gas Lift

Slide 5

IGL Cycle

Pestana’s work:

Based on the simulator developed by Carvalho (2004)

Introduction of specific formulations for topics such as:

•the throttling flow regime of the gas-lift valve

•the behavior of the pressure upstream of the motor valve

•the behavior of the bottom-hole pressure when the standing valve closes

•the gas velocity during the decompression stage

•the two-phase flow in the production line

Slide 6

Mathematical Modeling


Pressure Upstream of the Motor Valve:

Slide 7

Mass Conservation

applied to the gas

injection line

Pressure Upstream of the Motor Valve is estimated

New gas flow is estimated

Weymouth’s

Correlation

Pressure Upstream of

the Motor Valve

Thornhil-Craver’s

equation


Gas-Lift Valve – Throttling flow

• Force balance determines the valve stem’s position.

• Stem’s position determines the equivalent port size

(Hepguler model, 1993).

• Flow is estimated using the equivalent port size

(Thornhill-Craver’s equation).

Slide 8


Bottom-Hole Pressure (BHP)

• Depends on the state of the standing valve (open / close)

• Valve closes immediately when the injection gas raises the pressure

downstream of the standing valve to a value higher than what prevails

upstream of the valve.

• While closed, as suggested by Brown (1984), the BHP remains

increasing as if the reservoir fluid is accumulating in a “virtual”

hydrostatic column.

Slide 9


The well is divided into several subsystems (the control

volumes) and, for each of these systems, mass and

momentum balance equations are applied, as well as

specific correlations for fluid properties (gas compressibility),

flow through valves and friction factors.

Subsystems:

• Casing

• Gas Core

• Liquid Slug

• Liquid Film

• Liquid Load

Slide 10

Nonlinear system

of 23 equations:

7 OTDE + 16 Algebraic

Extension to other Variants

Slide 11

Motor Valve

Ga

s

Ga

s

Ga

s

Reservoir

Gas-Lift Valve

Line

Production

Packer

Slu

g

Ga

s

Reservoir

ProductionLine

Packer

Motor Valve

Slu

g

Slu

g

Motor Valve

Slu

g

Ga

s

Ga

s

Gas

Ga

s

Reservoir

Gas-Lift Valve

LineProduction

Packer

Plunger

Gas-Lift with Plunger Gas-Lift with Chamber Inverted Gas-Lift

Numerical Solution

Slide 12

Nonlinear System

ODE + Algebraic

Solution

?

Numerical Solution

Slide 13

Nonlinear System

ODE + Algebraic

System of Nonlinear

Algebraic Equations

System of Linear

Equations

Solution based on a

Convergence Criteria

LU Decomposition

Newton-Raphson

Method

Crank-Nicolson

Method

For each time-step


Bottom-Hole Pressure (Pbh) and Tubing Pressure (Pt)

Slide 14

Pbh

Pt - glv

Computational Code / Graphical User Interface

• Codes were implemented using FORTRAN 90

• Each gas-lift method was implemented independently and has it’s own

executable code.

• The Graphical User Interface was developed using Python and the

PySide library (freeware).

Slide 15

Numerical Output Graphical Output

Volume of produced liquid Bottom-Hole Pressure

Fallback Wellhead Pressure

Volume of Injected Gas Tubing & Casing Pressure

Graphical User Interface

Slide 16


Slide 17


Slide 18


Slide 19

1.5

2

2.5

3

3.5

4

4.5

5

5.5

0 500 1000 1500 2000 2500 3000

Bo

ttom

Ho

le P

ressure

(M

Pa

)

Time (s)

Graphical Output

Bottom-hole Pressure

Slide 20

2

3

4

5

6

7

0 500 1000 1500 2000 2500 3000

Tub

ing P

ressu

re (

MP

a)

Time (s)

Tubing Pressure


Graphical Output

Slide 21

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

0 500 1000 1500 2000 2500 3000

We

llhea

d P

ressu

re (

MP

a)

Time (s)

Wellhead Pressure


Graphical Output

Slide 22

5.6

5.8

6

6.2

6.4

6.6

6.8

7

0 500 1000 1500 2000 2500 3000

Ca

sin

g P

ressu

re (

MP

a)

Time (s)

Casing Pressure


Graphical Output

Intermittent Gas-Lift & Zadson pneumatic pump

Slide 23

Similar to the IGL, the ZPP lifts of oil through

cycles of compression and decompression of

gas.

The gas injection occurs at regular time

intervals synchronized with the feeding of

oil from the reservoir to the well.

T-1

2'’

2'’

2'’

S-1

V-3 V-1V-2

1'’1.5'’

2'’

1.5'’

V-5V-6

V-7

I-17

T-2

T-3

VE-1

VE-2

VE-3

F-1

F-2

F-3

S-3

T-4

F-4 C-1

V-4

SV-4

2'’

S-6

S-5

S-4

V-8

P-2

P-1

M-1

M-2M-3M-4

M-5

M-6M-

7

S-2

1.5'’

1.5'’

2'’

M-8M-9M-10M-11

Globe valve

Ball valve

Solenoid valve

Check valve

Pressure Transducers and

Manometers

Pressure regulator

Y Filter

Centrifugal pump

Compressor

Compressed air vessel

(Horizontal)

Compressed air vessel

(Vertical)

M-13M-12

V-IP

SV-1SV-2SV-3

Diagram of physical simulator for IGL and ZPP

Slide 24

Reservoir

Injection of Compressed Gas

Columns of Production

Elements of the physical simulator for IGL and ZPP

Slide 25

Motor valve

Gas-Lift valve

Cycles Stability for GLI

Slide 26

•Operation map for the IGL in

which stable cycles are found.

•Tests were performed with

different timings ( tc , tinj )

The parameters used were: Pinj = 1.5 bar, Pto = 0.29 bar, and the gas-lift valve

was calibrated with Pd = 0.5 bar and R = 0.71

Stable cycles

Slide 27

Stability is identified by…

•Synchronizing of gas-lift valve with motor

valve

•Stability of fallback over the cycles

Short cycle time

Slide 28

Instability is presented by the mismatch of

the gas-lift valve and motor valve

Long cycle time

Slide 29

Tubing pressure at the moment of the

injection increases with the number of

cycles; greater fallback at each cycle; gas

cannot adequately lift the liquid load fed into

the tubing.

Influence of dome pressure on stability

Slide 30

• Increasing the dome pressure shifts the stable area to the “right”

• Higher cycle times are required to acchieve stable cycles

Dynamic behavior of ZPP for first mode

Slide 31

• Behavior of key pressures, featuring a

ZPP cycle in Mode 1.

• During the second pressurization, part

of the accumulated gas in the

intermediate annular is transferred to

the internal annular, passing through the

V2 valve.

• The moment when the liquid reaches

the surface is identified by increasing

wellhead pressure (Pwh).

Dynamic behavior of ZPP for second mode

Slide 32

• Feeding and first pressurization

happens similarly to Mode 1.

• This mode is used when injection

pressure in the first mode doesn’t

provide an efficient lifting, but it

demands higher gas volumes.

Dynamic behavior of ZPP for third mode

Slide 33

• The principle of lifting in the third mode

is similar to a Sucker Rod Pump (SRP),

in which the tubing is totally filled and

the volume fed into the tubing is

produced at the surface

• Figure shows the behavior of the Pam

and Pwf vs time, as well as the

actuation of V1 and V3 valves following

compression and decompression

Conclusions

• a working computer simulator was developed for the dynamics of IGL systems,

using a rational mechanistic approach.

• results are qualitatively consistent.

• a GUI was created to operate the simulator.

• the IGLsim may be improved using lab or field data.

• the IGLsim may be expanded with new features.

• a laboratory apparatus was built for the study of the Intermittent Gas-lift and

Zadson Pneumatic Pump.

• a map was draw as a function of tc and tinj indicating the region where the

cycles are stable.

• increasing dome pressure requires higher cycle times for stable cycles

• the dynamics of the stages of a ZPP cycle can be observed, for all the three

modes of operation, by monitoring key pressures.

• produced volumes and fallback can be determined.

The authors wish to acknowledge the support of Petrobras and

the Gas-lift Lab of the Dept. of Petroleum Engineering at UNICAMP.

[email protected]

[email protected]

[email protected]

[email protected]

Feb. 3 – 7, 2014

2014 Gas-Lift Workshop 36

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Feb. 3 – 7, 2014 2014 Gas-Lift Workshop 37

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A Combined Experimental & Numerical Research Program to ... · A Combined Experimental & Numerical Research Program to Develop a Computer Simulator for Intermittent Gas-lift Bordalo,

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