Title: Parallel tempered trans-dimensional Bayesian inference for the inversion of ultra-deep directional logging-while-drilling resistivity measurements

Journal Article · · Journal of Petroleum Science and Engineering
 [1];  [2];  [2];  [2];  [3]
  1. University of Houston, TX (United States); Cyentech Consulting LLC
  2. University of Houston, TX (United States)
  3. Cyentech Consulting LLC, Cypress, TX (United States)

As one of the most important downhole technology, directional Electromagnetic (EM) logging-while-drilling (LWD) has been developing over the decades. The new generation of resistivity logging service expands the depth of investigation (DoI) to over 100 ft from the wellbore. As a result, more geological features are within the scope of the logging tool, which increases the complexity of logging measurements dramatically. Reservoir imaging relies on the inversion of the logging measurements, whereas most conventional inversion approaches depend on the deterministic optimization which oftentimes suffers from local minima. Many efforts were focused on the improvement of data processing workflow by using prior knowledge of the formation structure to constrain the optimizer from stepping into local minima although the prior can be inaccurate. As such, to reduce the negative impact of inaccurate prior assumptions, we propose to infer the model parameters via the trans-dimensional Markov chain Monte Carlo (tMCMC) method. Governed by the Bayesian theorem, the trans-dimensional inference addresses the complexity of the model by allowing the number of layers of the target model to be a free parameter. Driven by the measurements, the joint posterior distribution of model parameters is sampled accordingly, which provides a probability solution of a potential answer. Bayesian sampling is computationally expensive with a slow convergence rate. In this paper, we propose a meta-technique called parallel tempering (PT) combining with tMCMC to improve the sampling performance. PT is also known as replica Bayesian sampling where multiple Markov chains are constructed to explore the posterior distribution simultaneously with periodic information exchange between chains. Verified by our experiments, combining tMCMC and PT builds an efficient and reliable framework for interpreting ultra-deep LWD resistivity measurements. The inversion results from a series of benchmark models demonstrate that the proposed data-driven framework is robust and can be used to infer a reservoir-scale earth model.

Research Organization:
University of Houston, TX (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
Grant/Contract Number:
SC0017033
OSTI ID:
1593840
Journal Information:
Journal of Petroleum Science and Engineering, Journal Name: Journal of Petroleum Science and Engineering Journal Issue: C Vol. 188; ISSN 0920-4105
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English

References (19)

Markov chain Monte Carlo (MCMC) sampling methods to determine optimal models, model resolution and model choice for Earth Science problems journal April 2009
Solving geosteering inverse problems by stochastic Hybrid Monte Carlo method journal February 2018
Parallel multiple-chain DRAM MCMC for large-scale geosteering inversion and uncertainty quantification journal March 2019
Transdimensional inversion of receiver functions and surface wave dispersion: TRANSDIMENSIONAL INVERSION OF RF AND SWD journal February 2012
Monte Carlo sampling of solutions to inverse problems journal July 1995
Parsimonious Bayesian Markov chain Monte Carlo inversion in a nonlinear geophysical problem journal December 2002
Parametric Empirical Bayes Inference: Theory and Applications journal March 1983
Reversible jump Markov chain Monte Carlo computation and Bayesian model determination journal January 1995
A Parallel Tempering algorithm for probabilistic sampling and multimodal optimization journal October 2013
Seismic tomography with the reversible jump algorithm journal September 2009
Trans-dimensional geoacoustic inversion journal December 2010
A Stochastic Newton MCMC Method for Large-Scale Statistical Inverse Problems with Application to Seismic Inversion journal January 2012
Occam’s inversion: A practical algorithm for generating smooth models from electromagnetic sounding data journal March 1987
1D inversion of multicomponent, multifrequency marine CSEM data: Methodology and synthetic studies for resolving thin resistive layers journal March 2009
components?an alternative to reversible jump methods journal February 2000
Inference from Iterative Simulation Using Multiple Sequences journal November 1992
Mapping-While-Drilling System Improves Well Placement and Field Development journal August 2014
A New Azimuthal Deep-Reading Resistivity Tool for Geosteering and Advanced Formation Evaluation journal April 2009
Electromagnetic Wave Resistivity MWD Tool journal October 1986