Optimal Sensor Placement for Multi-Phase Flow Rate Estimation Using Pressure and Temperature Measurements

Transcription

1 Optimal Sensor Placement for Multi-Phase Flow Rate Estimation Using Pressure and Temperature K. Kawaguchi 1, SPE, M. Takekawa 1, SPE, M. Ali 2, H. Wada 1, and T. Ohtani 1 Yokogawa Electric Corporation 1 Yokogawa Saudi Arabia Company 2 1

2 Agenda 1. Introduction 2. Methodology 3. Example Analysis 4. Summary & Future Work 2

3 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

4 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 Homogenizer Electric Capacitance Meter Flow C1 C2 dp Flow patterns in pipe Cross Correlation Velocity Meter Venturi Densitometer Example Configuration of MPFM 4

5 Pressure & Temperature 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 measurements Distributed Temperature Sensor(DTS) (Raman Optical Time Domain Reflectmeter) z P Well head DPS DTS z T Distributed pressure measurements Distributed Pressure Sensor(DPS) (Brillouan Optical Time Domain Reflectmeter) P T t Optical Fiber t PDHG 5

6 Soft-Sensing of Multi-Phase Flow Interest is growing to estimate multi-phase flow by means of soft-sensing Naevdal et al. (2001)indicated the importance of measurements de Kruif et al. (2008) found difficulty estimating 3 phase flow using down hole 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 No. ofare Model not clear Estimation Authors Naevdal et al de Kruif et al phases 3 phase 2 phase 3 phase 3 fluid model Driftflux model method Well setup Sensor Placement used covariance 3 inflow Yes 3 F, 21T, 6P, 4WC OK matrix analysis 5 lateral Yes 3 F, 9T, 24P OK Extended Kalman Filter Uni-lateral No 6 P, 6T Bi-lateral No 6 P, 6T Result 2 phase OK 3 phase NG 2 phase OK 3 phase NG Lorentzen et al phase 2 fluid model Ensemble Kalman Filter Uni-lateral No 1 BHP, 1 BHT NG Bi-lateral No 2 T OK 6

7 Questions to be studied Objective of the Study How many measurements are required to estimate the multiphase flow rates? What combination of measurements gives the best estimation while sensors are having uncertainty? 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 7

8 Wellbore Model Model capturing essential physics of multiphase flow Conservation equations for mixture fluid: dρmvm Mass : = 0 dx Momentum : Energy : dp dx d ρ mv dx fρ m = 2d m h m v m v m vm dρmv ρm g sinθ dx + gz = Q Phase behavior: Black oil model (Whitson & Brule 2000) ρ ( p, T ), ρ = ( p, T ), h = h ( p, T ), h = h ( p T ) o = ρ o g ρ g o o g g, Velocity slip: Drift-flux model(shi et al. 2005) v C v + v g = 0 m d Friction factor: Moody friction factor = ( for N Re < 2000), = log 2ε + for N N Re f N Re f Heat transfer: Overall heat transfer model f ( 3000) Q = πdu T ( ) T geo 2 m 10 Re > p out, Tout, vo, out, vg, out θ p in, Tin, vo, in, vg, in M M 8

9 Linear Approximation Wellbore model is linearized to derive the relation between uncertainty of measurements and multi-phase flow rates v = Input condition vector(n Dim.): w = Measurement vector(m Dim.): Nonlinear model equation(m eq.): Linearization through Taylor expansion Linear simultaneous equation: v j M = [ M ] = ij Sensitivity Matrix: wi [, T, q q ] p fw fw o, sc, g, sc [ p, p, L, p, T, T, L T ] , w = f Mv = w,0,0 w v i j v = v 0 ( v) 100 (, T, q q ) p fw fw o, sc, g, sc M M ( ) p 100,T 100 M M ( p,t 2 2 ) ( p,t 1 1) 9

10 Estimation Uncertainty Evaluation Estimation Estimation of v (n dimension) are given by solving the inverse problem of Mv=w, given the measurement w(m dimension) 1 v = M w m=n case: m>n case(least square solution): Estimation Uncertainty v = T 1 T ( M M) M w Standard deviation of estimations are evaluated given the measurement with sigma = 1% Gaussian noise. 2 Measurement noise: Average estimations*: ( w ) Standard deviations of estimations*: p i v = = 1 1 2πσ N w i v i, k N k = 1 1 w i w exp 2 σ i w i σ 2 v i 1 = N 1 i,0 N ( ) 2 vi, k vi k = 1 (*evaluated with N=3,000 samples) 10

11 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 ( m) Oil density: 23 API (915 kg/m 3 ) Oil production rate: 1,140 stb/d (181.2 m 3 /d) Gas density: 0.80 SG (0.984 kg/m 3 ) Producing gas-oil ratio: 450 scf/stb(80.1 m 3 /m 3 ) 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) 5,151ft * 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 11

12 Simulated Profiles for the Example Well Depth, ft simulated data field data Depth, ft Pressure, psig fluid temperature geothermal temperature Temperature, o F Depth, ft Depth, ft Liquid holdup gas liquid Velocity, ft/s 12

13 Case Studies 13

14 Case 1: Multiple P/T Gauges σ qo,sc Standard deviation of estimated oil flow rate PT 3PT 4PT location of added measurement, ft Standard deviation of estimated gas flow rate σ qg,sc PT 3PT 4PT location of added measurement, ft 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 14

15 Case 2: DTS Base Standard deviation of estimated oil flow rate σ qo,sc DTS only: DTS+P DTS+2P DTS+3P location of added measurement, ft σ qg,sc Standard deviation of estimated gas flow rate DTS only: DTS+P DTS+2P DTS+3P location of added measurement, ft 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 15

16 Case 3: DPS Base Standard deviation of estimated oil flow rate σ qo,sc DPS only: DPS+T DPS+2T DPS+3T location of added measurement, ft DPS alone gives high uncertainty Standard deviation of estimated gas flow rate σ qg,sc DPS only: DPS+T DPS+2T DPS+3T location of added measurement, ft 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 16

17 Summary of Case Studies & Perspectives 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 17

18 Summary Summary & Future Work Methodology for evaluating the estimation uncertainty were shown Uncertainty of multi-phase flow rate estimation using measurements are evaluated for example 2 phase well Perspectives from an example analysis 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 gauges are favorable Future Work Consideration of actual measurement uncertainty Another well example to derive general perspective Extension to 3 phase analysis 18

19 Acknowledgements To Dr. Sami El-Ferik and Dr. Abdelsalam Al-Sarkhi of King Fahd University of Petroleum & Minerals for discussions and suggestions To organizing committee of SPE Aberdeen Summit Series Seminar Inwell flow surveillance and control: new frontier for opportunity to make the presentation 19

20 Slide 20 Thank You 20