Abstract
Production data analysis (PDA) is a subject to determine reservoir properties and predict future performance of single wells. It is normally conducted with either analytical methods or numerical history-matching methods. However, the analytical models normally have limited accuracy due to simplifying assumptions, while the history-match based on numerical simulations sacrifices computation load to increased accuracy. Therefore, in this study, the authors incorporated Ensemble Kalman Filter (EnKF) to improve PDA considering its superior efficiency in predicting system state and uncertainties. In this work, we applied the EnKF algorithm to single-well reservoir models to estimate permeability, skin factor, and drainage area. First, we tested the model accuracy after comparing the EnKF estimates to known reservoir properties. Next, we evaluated the cases with large estimation error and then adjusted the initial uncertainties and covariance of the static parameters. With confirmed improvements of property estimation in synthetic cases, the model is finally applied in a field study for further verifications. The results from this study confirmed that EnKF method could be an efficient solution for the modern PDA. They also indicate that accuracy issues are sometimes present when estimating skin factor and reservoir permeability simultaneously: large error exists in the property estimates, their uncertainties are overly reduced, and thus analysis and predicts are affected. By increasing the initial uncertainty bounds and adding minimum threshold values for the covariance, the property estimates could be improved, and reasonable uncertainty bounds are preserved. The methodology from this study is applicable for full-field evaluations.
Copyright 2019, IPPTC Organizing Committee.
This paper was prepared for presentation at the 2019 International Petroleum and Petrochemical Technology Conference in Beijing, China, 27–29, March, 2019.
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Abbreviations
- \( A_{x} \) :
-
Cross-sectional area normal to x direction, ft2
- \( A_{y} \) :
-
Cross-sectional area normal to y direction, ft2
- \( B_{g} \) :
-
Gas formation volume factor, RB/scf
- \( B_{o} \) :
-
Oil formation volume factor, RB/stb
- \( B_{w} \) :
-
Water formation volume factor, RB/stb
- c :
-
Component
- B:
-
Formation volume factor, reservoir volume/volume at standard conditions
- \( \varvec{C}_{D} \) :
-
Covariance matrix of the measured data
- \( \varvec{C}_{Y}^{f} \) :
-
The prior covariance matrix for the state variables
- \( \varvec{d}_{m}^{o} \) :
-
Measurement data used for assimilation
- \( \varvec{d}_{m} \) :
-
Simulation model output at each assimilation time step
- k:
-
Reservoir permeability, md (in the context of governing equation)
- \( k_{r} \) :
-
Relative permeability, fraction
- \( k_{rl} \) :
-
Relative permeability to phase l, dimensionless
- \( k_{rg} \) :
-
Relative permeability to gas, dimensionless
- \( k_{ro} \) :
-
Relative permeability to oil, dimensionless
- \( k_{rw} \) :
-
Relative permeability to water, dimensionless
- \( k_{s} \) :
-
Permeability of the damaged/stimulated area, md
- \( k_{x} \) :
-
Permeability in the direction of the x axis, md
- \( k_{y} \) :
-
Permeability in the direction of the y axis, md
- \( \varvec{K} \) :
-
Kalman Gain
- \( \overrightarrow {{\dot{m}}}_{c} \) :
-
Mass flux for component c, lbm/(D-ft2)
- \( \dot{m}_{cx} \) :
-
c component of mass flux in x direction, lbm/(D-ft2)
- \( \dot{m}_{cy} \) :
-
c component of mass flux in y direction, lbm/(D-ft2)
- \( m_{{V_{c} }} \) :
-
Mass of component c per unit volume of rock, lbm/ft3
- \( N_{d} \) :
-
Number of observations
- \( N_{k} \) :
-
Ensemble size
- \( N_{x} \) :
-
The number of the state variables
- \( N_{y} \) :
-
\( N_{y} = N_{\theta } + N_{x} + N_{d} \)
- \( N_{\theta } \) :
-
The number of poorly known parameters
- \( \varvec{O} \) :
-
\( N_{d} \times \left( {N_{\theta } + N_{x} } \right) \) null matrix
- \( P_{cgo} \) :
-
Gas/oil capillary pressure, psi
- \( P_{cow} \) :
-
Oil/water capillary pressure, psi
- \( P_{g} \) :
-
Gas pressure, psi
- \( P_{o} \) :
-
Oil pressure, psi
- \( P_{w} \) :
-
Water pressure, psi
- \( q_{gsc} \) :
-
Gas production rate at standard conditions, scf/D
- \( q_{{m_{c} }} \) :
-
Rate of mass depletion for component \( c \) through wells/lbm/D
- \( q_{{mt_{c} }} \) :
-
Rate of mass depletion for component c between phases, lbm/D
- \( q_{osc} \) :
-
Oil production rate at standard conditions, STB/D
- \( q_{wsc} \) :
-
Water production rate at standard conditions, STB/D
- \( r_{s} \) :
-
Radius of the damage/stimulated area around a wellbore, ft
- \( {\text{r}}_{\text{w}} \) :
-
Well radius, ft
- \( R_{s} \) :
-
Solution gas oil ratio, scf/STB
- \( S_{g} \) :
-
Gas saturation, fraction
- \( S_{o} \) :
-
Oil saturation, fraction
- \( S_{w} \) :
-
Water saturation, fraction
- t :
-
Simulation time, days
- \( \Delta t \) :
-
Simulation time step, days
- u :
-
Superficial velocity, RB/(D-ft2)
- \( \overrightarrow {{u_{c} }} \) :
-
Component c superficial velocity vector, RB/(D-ft2)
- \( u_{cx} \) :
-
x component of component c superficial velocity, RB/(D-ft2)
- \( u_{cy} \) :
-
y component of component c superficial velocity, RB/(D-ft2)
- \( V_{b} \) :
-
Gridblock bulk volume, ft
- \( \varvec{x} \) :
-
Reservoir state vector (including reservoir pressures and phase saturations), \( x = x\left( t \right) \in {\mathbb{R}}^{{N_{x} }} \)
- \( \varvec{y}_{m}^{k} \) :
-
State vector of ensemble number k at time m
- \( \varvec{Y}_{m} \) :
-
State vectors of the entire ensembles at time m
- \( \overline{{\varvec{Y}_{m} }} \) :
-
Matrix containing ensemble mean in each column at time m
- \( \overline{{y_{m}^{1} }} \) :
-
Ensemble mean of each member at time m
- \( \varepsilon_{m}^{o} \) :
-
Measurement error, which is a zero-mean Gaussian noise \( \varepsilon_{m}^{o} \sim \mathcal{N}\left( {0,R} \right) \)
- \( \alpha_{c} \) :
-
Volumetric conversion factor, 5.614583
- \( \beta_{c} \) :
-
Transmissibility conversion factor, 1.127
- \( \gamma_{g} \) :
-
Gas gravity, psi/ft
- \( \gamma_{l} \) :
-
Gravity of phase l, psi/ft
- \( \gamma_{o} \) :
-
Oil gravity, psi/ft
- \( \gamma_{w} \) :
-
Water gravity, psi/ft
- \( \varepsilon_{m} \) :
-
Model error
- \( \varvec{\theta} \) :
-
Static reservoir parameters, \( \theta \in {\mathbb{R}}^{{N_{\theta } }} \)
- \( \Delta \) :
-
Difference, difference operator
- \( \mu_{g} \) :
-
Gas viscosity, cp
- \( \mu_{o} \) :
-
Oil viscosity, cp
- \( \mu_{w} \) :
-
Water viscosity, cp
- \( \rho_{c} \) :
-
Density of component \( c \), lbm/ft3
- \( \rho_{g} \) :
-
Gas phase density, lbm/ft3
- \( \rho_{gsc} \) :
-
Gas phase density at standard condition, lbm/ft3
- \( \rho_{w} \) :
-
Water phase density, lbm/ft3
- \( \phi \) :
-
Porosity, fraction
- \( \Delta {\text{x}} \) :
-
Difference along x direction, ft
- \( \Delta {\text{y}} \) :
-
Difference along y direction, ft
- b :
-
Grid bulk
- c :
-
Component
- fg :
-
Free gas
- g :
-
Gas
- k :
-
Ensemble member, \( k = 1,2,3 \ldots N_{k} \)
- l :
-
Phase l or component l
- m :
-
Assimilation time, \( m = 1, 2, \ldots , N_{m} \)
- mt :
-
Mass transfer
- o :
-
Oil
- sc :
-
Standard condition
- sg :
-
Solution gas
- t :
-
Simulation time
- w :
-
Water
- f :
-
Forecasted
- o:
-
Observed or measured
- u :
-
Updated
- T :
-
Transpose of
- →:
-
Vector
References
Al Haddad, S., Mancini, E.A.: Reservoir characterization, modeling, and evaluation of Upper Jurassic Smackover microbial carbonate and associated facies in Little Cedar Creek field, southwest Alabama, eastern Gulf coastal plain of the United States. AAPG Bull. 97(11), 2059–2083 (2013). https://doi.org/10.1306/07081312187
Ampomah, W., Balch, R., Cather, M., Rose-Coss, D., Dai, Z., Heath, J., Mozley, P.: Evaluation of CO2 storage mechanisms in CO2 enhanced oil recovery sites: application to Morrow Sandstone reservoir. Energy Fuels 30(10), 8545–8555 (2016). https://doi.org/10.1021/acs.energyfuels.6b01888
Arps, J.J.: Analysis of decline curves. Trans. AIME 160(01), 228–247 (1945). https://doi.org/10.2118/945228-G
Bhattacharya, S., Nikolaou, M.: Analysis of production history for unconventional gas reservoirs with statistical methods. SPE J. 18(5), 878–896 (2013). https://doi.org/10.2118/147658-PA
Blasingame, T.A.: “Skin Factor” Concept (2007)
Burgers, G., Jan van Leeuwen, P., Evensen, G.: Analysis scheme in the Ensemble Kalman Filter. Mon. Weather Rev. 126(6), 1719–1724 (1998). https://doi.org/10.1175/1520-0493(1998)126%3c1719:ASITEK%3e2.0.CO;2
Cai, Y., Liu, D., Pan, Z.: Partial coal pyrolysis and its implication to enhance coalbed methane recovery: a simulation study. Energy Fuels 31(5), 4895–4903 (2017). https://doi.org/10.1021/acs.energyfuels.7b00219
Cao, P., Liu, J., Leong, Y.-K.: A fully coupled multiscale shale deformation-gas transport model for the evaluation of shale gas extraction. Fuel 178, 103–117 (2016). https://doi.org/10.1016/J.FUEL.2016.03.055
Cokar, M., Ford, B., Gieg, L.M., Kallos, M.S., Gates, I.D.: Reactive reservoir simulation of biogenic shallow shale gas systems enabled by experimentally determined methane generation rates. Energy Fuels 27(5), 2413–2421 (2013). https://doi.org/10.1021/ef400616k
Ertekin, T., Abou-Kassem, J.H., King, G.R.: Basic applied reservoir simulation. In: Doherty, H.L. (eds.) Memorial Fund of AIME. Society of Petroleum Engineers (2001). Retrieved from http://books.google.com/books?id=M41dAQAACAAJ&pgis=1
Evensen, G.: Inverse methods and data assimilation in nonlinear ocean models. Physica D 77(1–3), 108–129 (1994a). https://doi.org/10.1016/0167-2789(94)90130-9
Evensen, G.: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res. (1994b). https://doi.org/10.1029/94JC00572
Evensen, G.: The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dyn. (2003). https://doi.org/10.1007/s10236-003-0036-9
Evensen, G.: Data Assimilation: The Ensemble Kalman Filter. Springer, New York, Inc. (2006). Retrieved from http://dl.acm.org/citation.cfm?id=1206873
Fan, D., Ettehadtavakkol, A.: Semi-analytical modeling of shale gas flow through fractal induced fracture networks with microseismic data. Fuel 193, 444–459 (2017). https://doi.org/10.1016/J.FUEL.2016.12.059
Geir, Æ., Trond, M., Vefring, E.: Near-well reservoir monitoring through Ensemble Kalman Filter. In: Proceedings of SPE/DOE Improved Oil Recovery Symposium. Society of Petroleum Engineers (2002). https://doi.org/10.2118/75235-MS
Han, M., Li, G., Chen, J.: Assimilating microseismic and well-test data by use of EnKF for accurate reservoir characterization. SPE J. (2014). https://doi.org/10.2118/171554-PA
Haugen, V.E., Natvik, L.-J., Evensen, G., Berg, A., Flornes, K., Naevdal, G.: History matching using the Ensemble Kalman Filter on a North Sea field case. In: Proceedings of SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. (2006). https://doi.org/10.2118/102430-MS
Haugen, V.E., Naevdal, G., Natvik, L.-J., Evensen, G., Berg, A., Flornes, K.: History matching using the Ensemble Kalman Filter on a North Sea field case. SPE J. 13(4), 382–391 (2008). https://doi.org/10.2118/102430-PA
Heydari, E., Baria, L.R.: A microbial Smackover Formation and the dual reservoir-seal system at the Little Cedar Creek Field in Conecuh County of Alabama. GCAGS Trans. 55, 294–320 (2006)
Houtekamer, P.L., Mitchell, H.L.: Data assimilation using an Ensemble Kalman Filter technique. Mon. Weather Rev. 126(3), 796–811 (1998). https://doi.org/10.1175/1520-0493(1998)126%3c0796:DAUAEK%3e2.0.CO;2
Li, G., Han, M., Banerjee, R., Reynolds, A.C.: Integration of well-test pressure data into heterogeneous geological reservoir models. SPE Reservoir Eval. Eng. 13(03), 496–508 (2010). https://doi.org/10.2118/124055-PA
Liang, B.: An Ensemble Kalman Filter Module for Automatic. The University of Texas at Austin (2007)
Mancini, E.A., Parcell, W.C., Ahr, W.M., Ramirez, V.O., Llinás, J.C., Cameron, M.: Upper Jurassic updip stratigraphic trap and associated Smackover microbial and nearshore carbonate facies, eastern Gulf coastal plain. AAPG Bull. 92(4), 417–442 (2008). https://doi.org/10.1306/11140707076
Mandel, J.: A Brief Tutorial on the Ensemble Kalman Filter, 7. Atmospheric and Oceanic Physics (2009). Retrieved from http://arxiv.org/abs/0901.3725
Mullins, O.C., Zuo, J.Y., Pomerantz, A.E., Forsythe, J.C., Peters, K.: Reservoir fluid geodynamics: the chemistry and physics of oilfield reservoir fluids after trap filling. Energy Fuels 31(12), 13088–13119 (2017). https://doi.org/10.1021/acs.energyfuels.7b02945
Naevdal, G., Johnsen, L., Aanonsen, S., Vefring, E.: Reservoir monitoring and continuous model updating using Ensemble Kalman Filter. SPE J. 10(1), 66–74 (2005). https://doi.org/10.2118/84372-PA
Poston, S.W., Poe Jr., B.D.: Analysis of Production Decline Curves. Society of Petroleum Engineers (2008). Retrieved from http://books.google.com/books?id=rHxOPgAACAAJ&pgis=1
Wu, Y., Cheng, L., Huang, S., Jia, P., Zhang, J., Lan, X., Huang, H.: A practical method for production data analysis from multistage fractured horizontal wells in shale gas reservoirs. Fuel 186, 821–829 (2016). https://doi.org/10.1016/J.FUEL.2016.09.029
Yue, W., Wang, J.Y.: Feasibility of waterflooding for a carbonate oil field through whole-field simulation studies. J. Energy Res. Technol. 137(6), 064501 (2015). https://doi.org/10.1115/1.4030401
Zhang, Y., Song, C., Yang, D.: A damped iterative EnKF method to estimate relative permeability and capillary pressure for tight formations from displacement experiments. Fuel 167, 306–315 (2016). https://doi.org/10.1016/J.FUEL.2015.11.040
Zhao, X., Liao, X.: Evaluation method of CO2 sequestration and enhanced oil recovery in an oil reservoir, as applied to the Changqing Oilfields, China. Energy Fuels 26(8), 5350–5354 (2012). https://doi.org/10.1021/ef300783c
Zheng, J., Ju, Y., Liu, H.-H., Zheng, L., Wang, M.: Numerical prediction of the decline of the shale gas production rate with considering the geomechanical effects based on the two-part Hooke’s model. Fuel 185, 362–369 (2016). https://doi.org/10.1016/J.FUEL.2016.07.112
Acknowledgements
The authors would like to acknowledge Computer Modeling Group Ltd. for providing the CMG software for this study.
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Yue, Wt., Wang, J.Y. (2020). Application and Improvement of Ensemble Kalman Filter Method in Production Data Analysis. In: Lin, J. (eds) Proceedings of the International Petroleum and Petrochemical Technology Conference 2019. IPPTC 2019. Springer, Singapore. https://doi.org/10.1007/978-981-15-0860-8_36
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