A New Probabilistic Approach for Uncertainty Quantification in Well Performance of Shale Gas Reservoirs

[1]  M. Dentz,et al.  Modeling non‐Fickian transport in geological formations as a continuous time random walk , 2006 .

[2]  R. Raghavan Fractional diffusion: Performance of fractured wells , 2012 .

[3]  Ashish Sharma,et al.  A comparative study of Markov chain Monte Carlo methods for conceptual rainfall‐runoff modeling , 2004 .

[4]  William Rundell,et al.  Uniqueness and reconstruction of an unknown semilinear term in a time-fractional reaction–diffusion equation , 2013 .

[5]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[6]  L. Tierney Markov Chains for Exploring Posterior Distributions , 1994 .

[7]  Scott W. Tinker,et al.  Fayetteville shale-production outlook , 2014 .

[8]  Peter P. Valko,et al.  A Better Way To Forecast Production From Unconventional Gas Wells , 2010 .

[9]  Kan Wu,et al.  A fractional decline curve analysis model for shale gas reservoirs , 2016 .

[10]  N. Yoshida,et al.  Dynamic Modeling of Hydraulic Fractures Using Multisegment Wells , 2015 .

[11]  W. K. Hastings,et al.  Monte Carlo Sampling Methods Using Markov Chains and Their Applications , 1970 .

[12]  R. Raghavan,et al.  Fractured-Well Performance Under Anomalous Diffusion , 2013 .

[13]  Jeroen C. Vink,et al.  Bayesian Style History Matching: Another Way to Under-Estimate Forecast Uncertainty? , 2015 .

[14]  Kamy Sepehrnoori,et al.  Modeling Gas Adsorption in Marcellus Shale With Langmuir and BET Isotherms , 2016 .

[15]  Christopher R. Clarkson,et al.  A Semi-Analytical Forecasting Method for Unconventional Gas and Light Oil Wells: A Hybrid Approach for Addressing the Limitations of Existing Empirical and Analytical Methods , 2014 .

[16]  J. Klafter,et al.  The random walk's guide to anomalous diffusion: a fractional dynamics approach , 2000 .

[17]  J. Olson,et al.  Mechanisms of Simultaneous Hydraulic-Fracture Propagation From Multiple Perforation Clusters in Horizontal Wells , 2016 .

[18]  Long D. Nghiem,et al.  An Efficient and Practical Workflow for Probabilistic Forecasting of Brown Fields Constrained by Historical Data , 2015 .

[19]  Yueming Cheng,et al.  Practical Application of Probabilistic Approach To Estimate Reserves Using Production-Decline Data , 2005 .

[20]  David S. Schechter,et al.  Optimization-Based Unstructured Meshing Algorithms for Simulation of Hydraulically and Naturally Fractured Reservoirs With Variable Distribution of Fracture Aperture, Spacing, Length, and Strike , 2015 .

[21]  Michael Thambynayagam,et al.  Semianalytical Production Simulation of Complex Hydraulic-Fracture Networks , 2013 .

[22]  David S. Fulford,et al.  Machine Learning as a Reliable Technology for Evaluating Time/Rate Performance of Unconventional Wells , 2015 .

[23]  R. Aguilera,et al.  Analysis of Decline Curves on the Basis of Beta-Derivative , 2015 .

[24]  Yalchin Efendiev,et al.  Bayesian uncertainty quantification for flows in heterogeneous porous media using reversible jump Markov chain Monte Carlo methods , 2010 .

[25]  Bangti Jin,et al.  Multilevel Markov Chain Monte Carlo Method for High-Contrast Single-Phase Flow Problems , 2014, 1402.5068.

[26]  Dilhan Ilk,et al.  Exponential vs. Hyperbolic Decline in Tight Gas Sands: Understanding the Origin and Implications for Reserve Estimates Using Arps' Decline Curves , 2008 .

[27]  Xiaosi Tan Multilevel Uncertainty Quantification Techniques Using Multiscale Methods , 2015 .

[28]  Masahiro Yamamoto,et al.  Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems , 2011 .

[29]  Rudolf Hilfer,et al.  Numerical Algorithm for Calculating the Generalized Mittag-Leffler Function , 2008, SIAM J. Numer. Anal..

[30]  N. Goodwin,et al.  Bridging the Gap Between Deterministic and Probabilistic Uncertainty Quantification Using Advanced Proxy Based Methods , 2015, ANSS 2015.

[31]  Dennis Denney Fayetteville-Shale Production: Seismic-to- Simulation Reservoir Characterization , 2012 .

[32]  Masahiro Yamamoto,et al.  Overview to mathematical analysis for fractional diffusion equations - new mathematical aspects motivated by industrial collaboration , 2010 .

[33]  H. Haario,et al.  An adaptive Metropolis algorithm , 2001 .

[34]  J. J. Arps Analysis of Decline Curves , 1945 .

[35]  A. Chaves,et al.  A fractional diffusion equation to describe Lévy flights , 1998 .

[36]  Andrew Gelman,et al.  The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo , 2011, J. Mach. Learn. Res..

[37]  Wei Yu,et al.  A Comprehensive Model for Simulation of Gas Transport in Shale Formation with Complex Hydraulic Fracture Geometry , 2015 .

[38]  M. Caputo Linear Models of Dissipation whose Q is almost Frequency Independent-II , 1967 .

[39]  R. Raghavan,et al.  Anomalous Subdiffusion to a Horizontal Well by a Subordinator , 2015, Transport in Porous Media.

[40]  William John Lee,et al.  Gas Reserves Estimation in Resource Plays , 2010 .

[41]  David B. Dunson,et al.  Bayesian data analysis, third edition , 2013 .

[42]  L. Mattar Production Analysis and Forecasting of Shale Gas Reservoirs: Case History-Based Approach , 2008 .

[43]  Rajagopal Raghavan,et al.  Practical Solutions for Pressure-Transient Responses of Fractured Horizontal Wells in Unconventional Shale Reservoirs , 2011 .

[44]  D. W. Peaceman Interpretation of well-block pressures in numerical reservoir simulation with nonsquare grid blocks and anisotropic permeability , 1983 .

[45]  Duane A. McVay,et al.  Bayesian Probabilistic Decline-Curve Analysis Reliably Quantifies Uncertainty in Shale-Well-Production Forecasts , 2014 .

[46]  Anh N. Duong,et al.  Rate-Decline Analysis for Fracture-Dominated Shale Reservoirs , 2011 .

[47]  Kamy Sepehrnoori,et al.  A Semianalytical Model for Production Simulation From Nonplanar Hydraulic-Fracture Geometry in Tight Oil Reservoirs , 2016 .