A Physics-Based Data-Driven Model for History Matching, Prediction and Characterization of Unconventional Reservoirs*

Transcription

1 A Physics-Based Data-Driven Model for History Matching, Prediction and Characterization of Unconventional Reservoirs* Yanbin Zhang *This work has been submitted to SPEJ and under review for publication

2 Motivation

3 Reservoir Characterization with Play-Doh

4 Reservoir Characterization with Play-Doh Reservoir 4

5 Reservoir Characterization with Play-Doh Reservoir Wellbore 5

6 Reservoir Characterization with Play-Doh Reservoir Wellbore 6

7 Reservoir Characterization with Play-Doh Reservoir Wellbore 7

8 Reservoir Characterization with Play-Doh Reservoir Wellbore 8

9 Reservoir Characterization with Play-Doh y Wellbore x 9

10 Reservoir Characterization with Play-Doh Fractures y fracture x 0

11 Diffusive Diagnostic Function (DDF) D D Set of contours of the pressure solution in D well well PV PV PV PV 4 PV 5 PV PV PV PV 4 T 0 T T T T 4 Each ring is represented as a single cell PV 5 From Darcy s Law Qቚ = ර Σ Σ Tቚ = ර Σ Σ vds = ර Σ k ds dl ds ȁ Σ P dl A contour surface of the pressure solution in D ȁ Σ P+dP k dp dl ds = Tቚ dp Σ dpvቚ = ර Σ Σ φ dl ds In physical space, we need two functions PV x and T(x) PV = σδξ ቐ T = σ Δξ dξቚ Σ dpvȁ Σ = Σ Tȁ Σ Σ φ dl ds k ds dl = φdl Σ k dl Σ Σ ξȁ Σ = Σ0 dξ where Σ0 is the completion sand face σ(ξ) In dimensionless ξ space, we only need one function σ ξ which is called the DDF σቚ Σ dpvቚ Tቚ = Σ Σ ර Σ φ dl ds ර Σ k ds dl k = Sቚ φdl Σ Σ dl Σ

12 The D Simulation Model with DDF y 6 5 well unit: ft md / σ -Dimension N Grid blocks PV i = σ i + σ i (ξ i ξ i ) 4 σ 4 T i = σ i (ξ i+ ξ i )/ x Well P wf σ 0 σ σ σ ξ ξ ξ ξ 4 σ N ξ N ξ N J = σ 0 ξ / ξ unit: ft/md / We are doing the same, old, regular reservoir simulation except that we replace the D grid with DDF Complex fluid and rock model Changing well constraints Capillary pressure Adsorption Coupled with wellbore flow modeling and surface network Caveat Remember we reduce D reservoir into a D model and that is an approximation However, as we will show later, it is quite a good approximation in many cases

13 All this is good, but... How do I know if I should cut my reservoir this way or that way? y 6 y x x

14 All this is good, but... How do I know if I should cut my reservoir this way or that way? The bad news: we don t know in general 4 y 6 y x x 4

15 All this is good, but... How do I know if I should cut my reservoir this way or that way? y y 4 σ The bad news: we don t know in general The good news: () We can guess and we ll make a lot of guesses () We can adjust our guesses by history matching DDFs forward modeling ξ history matching q Production Data History Matching using ESMDA t x x Ensemble Smoother with Multiple Data Assimilation 5

16 We don t do wild guesses; we guess based on DDF Characteristics x f radial flow linear flow d f r w r x f L w d N f σ slope:πkh infinite acting σ σ 0 = 4x f h kφ infinite acting σ 0 ~4x f N f h kφ σ σ 0 = πr w h kφ boundary boundary SRV p slope~αkh boundary r w = r w e s 0 ξ = r φ/k ξ 0 ξ = d φ/k ξ σ~(4x f + L w + 4d f )h 0 kφ ξ SRV ~ d f φ/k ξ Take out your Play-Doh and construct this DDF! 6

17 DDF Characteristics - Summary Characteristics of the DDF Diagnostic Properties Approximate Equations Comments σ level Flow area and Reservoir quality σ~a kφ Fractures cause sharp increase in σ level. Interferences or boundaries cause drop in σ level. σ level keeps constant for linear flow Slope of linearly increasing σ ξ Reservoir permeability Δσ Δξ ~αkh α depends on flow pattern. α = π for radial flow. Generally, α > π for irregular flow pattern. Area under the DDF curve Pore volume Area = V p interferences. For unconventional reservoirs, SRV may A dramatic drop in σ level signifies boundary effect or be identified in this way. ξ at which σ behavior changes Distance ξ~d φ k The estimation of distance is difficult to be precise because the transition of σ behavior is usually not clear-cut and may span a wide range. 7

18 Synthetic Example: Vertical Well D Cartesian grid 0 0 DX = DY = 9.9 ft DZ = 00 ft Before HM r w = 0.ft r e = 500ft k = 0.00md φ = 0.05md h = 00ft After HM ξ (ft/md / ) (a) Time (days) (b) Black oil fluid model (P b = 800 psia) Initial reservoir pressure P i = 5000 psia Initial water saturation S wi = S wir = 0.5 Well producing at constant BHP = 000 psia ξ (ft/md / ) (c) Time (days) (d) 8

19 Synthetic Example: Multiple Fractures Before HM After HM ξ (ft/md / ) (a) Time (days) (b) 0 Infinite conductivity fractures Other parameters are the same as previous slide ξ (ft/md / ) (c) Time (days) (d) 9

20 Applications Physics Based Complex fluid, multi-phase flow Data Driven Extremely fast history match Reservoir Characterization Total fracture area and SRV Integrated Workflow Coupled with surface network Optimization / uncertainty analysis History matching and forecasting for a Gas Well Oil Well Examples 0

21 Summary. Physics-Based: DDF provides a general D simulation framework to approximate D reservoir. Data-Driven: DDF is probabilistically conditioned to production data Future Research First-principle-based computation Machine learning and big data DDF?

22 Acknowledgement ETC/RPP Jincong He Jiang Xie Xian-huan Wen ETC/RPS Robert Fitzmorris Shusei Tanaka ETC/PEWP Jorge Acuna ETC/TRU Reza Banki MCBU Baosheng Liang Hannah Luk AMBU James Wing Richin Chhajlani Please reach out to me for any questions or to connect with me. You may contact me at:

23 Backup Slides

24 History Matching using ESMDA with DDF Ensemble Smoother with Multiple Data Assimilation Diffusive Diagnostic Function σ model update DDFs m i+ = m i + Δm forward modeling ξ history matching q Production Data data mismatch Δm = C MD C DD + α i C D (d obs d pred ) perturbed observations / d obs = d obs + α i C D zd where z d ~N(0, I Nd ) t Workflow. Come up with initial ensemble of DDFs. Perform forward modeling to obtain data prediction a) predictions way off, go back to b) if predictions follow the trend and cover the range of observed data, go to. Randomize the model to avoid ensemble collapse 4. For the ith (out of n) iteration, use α i = /n in the equation to update the ensemble of models considering the mismatch of all data points simultaneously 5. Model regularization by smoothing the DDF curves and eliminate negative values (set to 0) 6. Go to 4 for next iteration 4

25 Synthetic Example: Single Fracture Infinite Conductivity vs. Finite Conductivity Infinite conductivity fracture k f = 0 6 md σ starts at a much larger value σ 0 = 4x f h kφ = 5 ft md / ξ (ft/md / ) Finite conductivity fracture k f = md σ starts at a smaller value, but increases rapidly near ξ = 0 Infinite or finite conductivity single fracture Other parameters are the same as previous slide ξ (ft/md / ) T 5

26 Synthetic Example: Multiple Fractures DDF Diagnostics σ ~500 ft md / x f L w hφ = 6.5x0 5 ft SRV p ~ 6x0 5 ft x f d f σ ~000 ft md / Slope ~ ft md L w ξ i ~40 ft/md / N f L w = 450 ft N f = 0 d f = 50 ft σ σ ~.5 ξ (ft/md / ) ξ (ft/md / ) (a) (b) x f ~ 0 ft φ = 0.05 σ ~ 500 ft md / k ~ 0.00 md σ ~4x f N f h kφ σ ~(4x f + L w + 4d f )h σ 0 SRV p kφ slope~αkh ξ SRV ~ d f φ/k boundary ξ 6

27 Normalized Gas Potential (psi/cp/mscfd) Bottomhole Pressure (psia) Gas production Rate (MMSCF/D) Well length (L w ) 0 ft Number of hydraulic fractures (N f ) Reservoir thickness (h) 50 ft Reservoir porosity (φ) Initial reservoir pressure (P i ) psia Reservoir temperature (T) 60 F Connate water saturation (S wc ) 0.9 Rock compressibility (c f ) 0-6 psi - Gas specific gravity (γ) 0.57 Square Root Time Plot Field Example: Marcellus Gas Well E+07 HM prediction Log-Log Plot Time (days) Integral of Normalized Gas Potential Bourdet Derivative E+06 A straight line can be used to fit the data even though it is not linear flow Not half slope E Material Balance Time (hr) 7

28 Field Example: HM and prediction with DDF Before HM ξ (ft/md / ) After HM ξ (ft/md / ) (a) Time (days) (b) ξ (ft/md / ) (c) Time (days) (d) 8

29 Field Example: DDF Diagnostics Characteristic of finite conductivity fractures x f d f L w N f ξ (ft/md / ) σ SRV p ~ ft σ ~4x f N f h kφ A total kφ~ 0 4 ft md / φ = A total k~4 0 4 ft md / SRV p slope~αkh boundary Total fracture sandface area σ ~(4x f + L w + 4d f )h 0 kφ ξ SRV ~ d f φ/k ξ 9

30 Field Example: Probabilistic Nature of the DDF Method HM P50 SRV p decreases ξ (ft/md / ) Time (days) SRV p uncertainty range decreases HM ξ (ft/md / ) Time (days) 0