optimal sensor placement for multi-phase flow rate estimation

Optimal Sensor Placement for Multi-Phase Flow

Rate Estimation Using

Pressure and Temperature Measurements

1

SPE Aberdeen Summit Series Seminar

Inwell flow surveillance and control: new frontiers

October 22, 2013, Aberdeen, UK

K. Kawaguchi1, SPE, M. Takekawa1, SPE, M. Ali2, H. Wada1, and T. Ohtani1

Yokogawa Electric Corporation1

Yokogawa Saudi Arabia Company2

Agenda

1. Introduction

2. Methodology

3. Example Analysis

4. Summary & Future Work

2




Optimal Sensor Placement for Multi-Phase Flow Rate Estimation Using P&T Measurements

K. Kawaguchi, M. Takekawa, M. Ali, H. Wada, and T. Ohtani

Introduction

For improved oil recovery, multi-lateral wells are becoming major in oil fields

Knowing the oil, gas & water (Multi-phase) flow rate from each well and lateral is crucial to optimize the production

3






??

?

?

?

Multi-Phase Flow Meter(MPFM)

Multi-phase flow is known to show complex behavior

Combination of sophisticated sensors are used in MPFM to measure gas, oil and water flow rates

Wide deployment of MPFMs to downhole condition is hard due to cost, reliability, and maintenance problems

4






Homogenizer

Electric

Capacitance

Meter

dPC1 C2

Cross Correlation

Velocity Meter

Venturi

Densitometer

Flow patterns in pipe Example Configuration of MPFM

Flow

Pressure & Temperature Measurements

Available pressure and temperature measurements are increasing both in time and space

Point pressure/temperature measurements

Permanent Down Hole Gauges(PDHG)(Quartz gauge, Fiber Bragg Grating)

Distributed temperature measurementsz z

Well head

5






Distributed temperature measurements

Distributed Temperature Sensor(DTS)(Raman Optical Time Domain Reflectmeter)

Distributed pressure measurements

Distributed Pressure Sensor(DPS)(Brillouan Optical Time Domain Reflectmeter)

DPS DTS

PDHG

P T

P

T

t

t

Optical Fiber

Interest is growing to estimate multi-phase flow by means of soft-sensing

Naevdal et al. (2001)indicated the importance of P&T measurements

de Kruif et al. (2008) found difficulty estimating 3 phase flow using down hole P&T measurement only, but was able to estimate 2 phase flow using 6P&6T measurements

Lorentzen et al. (2010) found difficulty to estimate 2 phase flow using only BHP and BHT

Even for the 2 phase unilateral case, number and placement of required measurements are not clear

Soft-Sensing of Multi-Phase Flow

AuthorsNo. of

phases

Model Estimation

method

Well

setup

Sensor

Placement

Measurements

usedResult

covariance 3 inflow Yes 3 F, 21T, 6P, 4WC OK

6






Naevdal et

al. 20013 phase

3 fluid

model

covariance

matrix

analysis

3 inflow Yes 3 F, 21T, 6P, 4WC OK

5 lateral Yes 3 F, 9T, 24P OK

de Kruif et

al. 2008

2 phase

3 phase

Drift-

flux

model

Extended

Kalman Filter

Uni-lateral No 6 P, 6T

2 phase

OK

3 phase

NG

Bi-lateral No 6 P, 6T

2 phase

OK

3 phase

NG

Lorentzen et

al. 20102 phase

2 fluid

model

Ensemble

Kalman Filter

Uni-lateral No 1 BHP, 1 BHT NG

Bi-lateral No 2 T OK

Objective of the Study

Questions to be studied

How many P&T measurements are required to estimate the multiphase flow rates?

What combination of P&T measurements gives the best estimation while sensors are having uncertainty?

Analysis method

7






Analysis method

Simulation study using wellbore model capturing essential physics

Evaluation of estimation uncertainty through uncertainty propagation

Comparison of estimation uncertainty between different measurement combination to search for optimal placement of sensors

Example simulation

Uni-lateral, two-phase well as a start point

Model capturing essential physics of multiphase flow

Conservation equations for mixture fluid:

Phase behavior: Black oil model (Whitson & Brule 2000)

Wellbore Model

Qgzv

hvdx

d

dx

vdgvv

d

f

dx

dp

dx

vd

mmmm

mmmmm

m

mm

=

++

−−−=

=

2 :Energy

sin2

:Momentum

0 :Mass

2

2

ρ

ρθρ

ρ

ρ

outgoutooutout vvTp ,, ,,,

8






Phase behavior: Black oil model (Whitson & Brule 2000)

Velocity slip: Drift-flux model(Shi et al. 2005)

Friction factor: Moody friction factor

Heat transfer: Overall heat transfer modelinginoinin vvTp ,, ,,,

( ) ( ) ( ) ( )TphhTphhTpTp ggooggoo ,,,,,,, ==== ρρρρ θ

M

Mdmg vvCv += 0

( ),2000for 64

Re

Re

<= NN

f ( )3000for 7.18

2log274.11

Re

Re

10 >

+−= N

fNfε

( )geoTTdUQ −−= π

Linear Approximation

Wellbore model is linearized to derive the relation between uncertainty of measurements and multi-phase flow rates

Input condition vector(n Dim.):

Measurement vector(m Dim.):

Nonlinear model equation(m eq.): ( )vfw =

[ ]scgscofwfw qqTp ,, ,,,=v

[ ]1002110021 ,,,,,,, TTTppp LL=w

( )100100 ,Tp

M

9






Linear simultaneous equation:

Sensitivity Matrix:

wMv =

[ ]

∂

∂⋅==

= 00,

0,

vv

M

j

i

i

j

ijv

w

w

vM

( )11,Tp

( )22 ,Tp

M

M

( )scgscofwfw qqTp ,, ,,,

M

M

Linearization through Taylor expansion

Estimation Uncertainty Evaluation

Estimation

Estimation of vvvv (n dimension) are given by solving the inverse problem of Mv=wMv=wMv=wMv=w, given the measurement wwww(m dimension)

● m=n case:

● m>n case(least square solution):

Estimation Uncertainty

wMv1−=

( ) wMMMvT1T −

=

10






Standard deviation of estimations are evaluated given the measurement with sigma = 1% Gaussian noise.

● Measurement noise:

● Average estimations*:

● Standard deviations of estimations*:

(*evaluated with N=3,000 samples)

( )

−−=

2

0,

2

1exp

2

1

iiw

ii

w

i

wwwp

σπσ

∑=

=N

k

kii vN

v1

,

1

( )2

1

,

2

1

1∑

=

−−

=N

k

ikiv vvNi

σ

Example Well Setup

Typical gas/oil 2-phase vertical well as an example

Parameters obtained from a literature* Depth: 5,151 ft (1,570 m)

Diameter: 3 in (0.0762 m)

Oil density: 23 ˚API (915 kg/m3)

Oil production rate: 1,140 stb/d (181.2 m3/d)

Gas density: 0.80 SG (0.984 kg/m3)

Producing gas-oil ratio: 450 scf/stb(80.1 m3/m3)

11






Producing gas-oil ratio: 450 scf/stb(80.1 m3/m3)

Bottom Hole Pressure: 2,105 psig (14,614 kPa)

Bottom Hole Temperature**: 110 ˚F (43.3 ˚C)

Geothermal temperature gradient**: 6.79 ˚F/1,000 ft (1.23 ˚C/100 m)

Overall Heat Transfer Coefficient**: 100 W/m2 ˚F(180 W/m2 ˚C)

* Hasan, A.R. & Kabir, C.S., “Fluid flow and heat transfer in wellbores,” SPE, 2002

**Thermal parameters not described in Hasan & Kabir 2002 are assumed with reasonable value

5,1

51

ft

Simulated Profiles for the Example Well

0 500 1000 1500 2000 2500-6000

-5000

-4000

-3000

-2000

-1000

0

Pressure, psig

Dep

th,

ft

simulated data

field data

60 70 80 90 100 110 120-6000

-5000

-4000

-3000

-2000

-1000

0

Temperature, oF

Dep

th,

ft

fluid temperature

geothermal temperature

12






0 0.2 0.4 0.6 0.8 1-6000

-5000

-4000

-3000

-2000

-1000

0

Liquid holdup

Dep

th,

ft

0 1 2 3 4 5 6 7-6000

-5000

-4000

-3000

-2000

-1000

0

Velocity, ft/s

Dep

th,

ft

gas

liquid

Pressure, psig Temperature, oF

Case Studies

13






Case 1: Multiple P/T Gauges

0.05

0.1

0.15

0.2

σq

o,s

c

2PT

3PT

4PT

0.05

0.1

0.15

0.2

σq

g,s

c

2PT

3PT

4PT

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

te

14






Adding a 2nd P/T gauge at the bottom hole gives the lowest uncertainty

Adding a 3rd P/T gauge adjacent to bottom hole gives the lower uncertainty

Adding a 4th P/T gauge gives only a slightly better result

-5000 -4000 -3000 -2000 -1000 00

location of added measurement, ft

-5000 -4000 -3000 -2000 -1000 00


Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

te

Case 2: DTS Base

0.02

0.04

0.06

0.08

0.1

σq o

,sc

DTS+P

DTS+2P

DTS+3P

0.02

0.04

0.06

0.08

0.1

σq

g,s

c

DTS+P

DTS+2P

DTS+3PDTS only: 0.064

DTS only: 0.034

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

te

15






DTS alone gives a fairly good result

Adding a P measurement at tubing head gives lowest uncertainty

Adding a 2nd P measurement has only a slight improvement

-5000 -4000 -3000 -2000 -1000 00

0.02


-5000 -4000 -3000 -2000 -1000 00

0.02


Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

te

Case 3: DPS Base

0.1

0.15

0.2

0.25

σq

o,s

c

DPS+T

DPS+2T

DPS+3T

0.1

0.15

0.2

0.25

σq

g,s

c

DPS+T

DPS+2T

DPS+3T

DPS only: 0.377DPS only: 0.299

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

te

16






-5000 -4000 -3000 -2000 -1000 00

0.05


-5000 -4000 -3000 -2000 -1000 00

0.05


Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d o

il flo

w r

ate

Sta

nd

ard

de

via

tio

n o

f e

stim

ate

d g

as f

low

ra

teDPS alone gives high uncertainty

Adding a T measurement at bottom hole reduces the uncertainty

Adding a 2nd T measurement improves the result

Adding a 3rd T measurement has only a slight improvement

Summary of Case Studies & Perspectives

17






Ideally, DTS&DPS gives the best estimation

If DTS is available, 1 or more additional P gauge is favorable.

If only P/T gauges are available, 3 or more P/T gauges are favorable

Summary & Future Work

Summary

Methodology for evaluating the estimation uncertainty were shown

Uncertainty of multi-phase flow rate estimation using P&T measurements are evaluated for example 2 phase well

Perspectives from an example analysis

● Ideally, DTS&DPS gives the best estimation

18






●

● If DTS is available, 1 or more additional P gauge is favorable.

● If only P/T gauges are available, 3 or more gauges are favorable

Future Work

Consideration of actual measurement uncertainty

Another well example to derive general perspective

Extension to 3 phase analysis

Acknowledgements

To Dr. Sami El-Ferik and Dr. Abdelsalam Al-Sarkhi of King Fahd University of Petroleum & Minerals for discussions and suggestions

19






To organizing committee of “SPE Aberdeen Summit Series Seminar Inwell flow surveillance and control: new frontier” for opportunity to make the presentation

Thank You

Slide 20

20






Thank You

optimal sensor placement for multi-phase flow rate estimation

Documents