Rock physics based facies classification from seismic inversion results in unconventional

reservoirs Zakir Hossain* and Stefano Volterrani, ION

Summary

The objective of this study is to demonstrate the power of

integrating rock physics theory, measurement and

simulation to improve facies prediction in an

unconventional limestone and shale reservoir. Reliable

facies prediction is a challenge in unconventional reservoir

characterization because of complex geological

heterogeneities. Both deterministic and probabilistic

approaches are commonly used in facies classifications that

use well and seismic data. Bayes’ theory with

uninformative priors is often used for probabilistic facies

classification. We provide a case study that uses Bayes’

theory with informative priors for facies classification from

pre-stack simultaneous elastic inversion results in an

unconventional reservoir. In the proposed methodology, we

integrate rock physics based theory, measurements and

simulation with Bayesian statistical techniques where the

prior probability represents our knowledge about rock

properties, and is consistent with our geological

knowledge, rock physics theory and measured data. We

evaluate four facies classification methodologies:

deterministic method, probabilistic method with

uninformative priors, probabilistic method with

uninformative priors and training facies defined from

simulation, and probabilistic method with informative

priors and training facies defined from simulation. This

study indicates that, in probabilistic facies classification

(Method 2), if uninformative priors are used, results are

sub-optimal compared to deterministic methods involving a

Rock Physics Template (RPT) workflow (Method 1).

Additionally, probabilistic facies classification can be

further improved if we use uninformative priors and

training facies defined from Monte Carlo simulation

(Method 3). Probabilistic facies prediction improves if we

use informative priors and training facies defined from

Monte Carlo simulation (Method 4).

Introduction

Reliable facies prediction is an essential problem in

reservoir characterization. Predicted facies properties are

important engineering inputs for drilling and production.

For reservoir facies characterization, two different methods

are commonly used: deterministic approach (Doyen, 1988;

Loertzer and Berkhout, 1992; Avseth et al., 2005; Hossain

et al. 2015) and probabilistic approach (Gastaldi, et al.

1998; Gouveia, 1996; Takashashi, 2000; Mukerji et al.,

2001; Hossain and Mukerji, 2011; Bachrach et al., 2004;

Bachrach, and Dutta, 2004; Grana et al., 2012; Hossain et

al. 2015). For deterministic facies classification we use an

RPT workflow, while for probabilistic facies prediction, we

can use Bayes’ theory:

n

i

ii

iii

cpcxp

cpcxpxcp

1

|

|| (1)

where, p(ci) is the prior probability,

p(ci|x) is the posterior probability of our observation,

p(x|ci) is the likelihood of obtaining our particular

observation ci, under the supposition that any of the

possible states of the variable x was actually the case.

For seismic based facies prediction, the above expression

can be written as:

priorfaciestrainingseismicp

seismicfaciespredictedp

)_|(

)|_( (2)

From this expression, we observe that the training facies

influence the predicted facies, but the prior probabilities are

more heavily influenced by the predicted facies. Hossain et

al. (2015) demonstrated the role of prior belief of Bayesian

statistics by using three types of priors: uninformative

priors, informative priors, and continuous priors and found

that for uninformative prior, the posterior remains

unchanged, while for informative priors, the posterior is

increased.

For uninformative priors, equation (1) becomes:

Figure 1: The relationship between rock physics theory, rock

physics measurement and rock physics based simulation for facies

prediction.

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Rock physics based facies classification

ii cxpxcp || or

liklihoodposterior (3)

The objective of this study is to demonstrate the power of

integrating rock physics theory, measurement and

simulation to improve facies prediction for reservoir

characterization.

Theory and/or Method

The real nature is too difficult to understand because of the

large number of properties. The scientist’s goal is to create

an understanding of physical properties and processes of

nature that are as complete as possible, making use of the

perfect control of experimental conditions in the simulation

experiment and of the possibility to examine every aspect

of system configurations in detail (Landau and Binder,

2000). Only theory or only experiment or only simulation is

not good enough to create an understanding of physical

properties and the processes of nature. Landau and Binder

(2000) presented the relationship between theory,

experiment, and simulation as being similar to those of the

vertices of a triangle, as shown in Figure 1: each is distinct,

but each is strongly connected to the other two. In this

paper, our objective is to define the facies from seismic

data by integrating rock physics theory, rock physics

measurement and rock physics based simulation for

Figure 2: ( a) Petrophysical analysis of studied well George 1-23 from Pink limestone to Wilcox, (b) Petrophysical analysis for zone of interest

(ZOI) from Mississippi Lime to Woodford shale, (c) Defiined facies from rock physics template (RPT): silica-rich limestone (cyan), clay-rich

limestone (black), lower kerogen-rich shale (magenta) and higher kerogen-rich shale (red), (d) ) 2D PDFs for each facies using attributes P-

impedance and Vp/Vs,

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Rock physics based facies classification

reservoir characterization of an unconventional limestone

and shale reservoir in the Mississippi Lime Play, north-

central Oklahoma.

We used well log measurement results of well George 1-23

from the studied region. We performed petrophysical

analysis calibrated with available laboratory measurement

results (Figure 2b). The zone of interest (ZOI) in this study

is from the top of the Mississippi Lime to the bottom of the

Woodford shale (Figure 2b). We used elastic attribute

volumes (P-Impedance, S-Impedance) obtained from the

pre-stack seismic inversion. We defined four facies based

on petrophysics and rock physics analysis. Defined facies

are: silica-rich limestone, clay-rich limestone, lower

kerogen-rich shale and higher kerogen-rich shale (Figure

2b). We used an RPT (Figure 2a after Hossain et al. 2015)

for deterministic facies prediction. Furthermore, for seismic

reservoir characterization, well data along with RPT are

used to define the prior probability. For seismic

applications, one of the central issues for stochastic

simulation is to use a statistical model rather than a rock

physics model:

yuncertaintmodel) lstatistica( Model

simulation Carlo Monte

We replaced the statistical model by a rock physics model,

addressed the uncertainly defined from rock physics

analysis, and included rock physics based upper bound and

lower bound to constrain the simulation results:

boundupper

boundlower yuncertaint

model) physicsRock ( Model

simulation Carlo Monte

Results and discussions

Figure 4a shows the deterministic facies predictions

involving an RPT workflow. Overall facies predictions are

moderate, but there are many under predicted and over

predicted intervals. To improve these predictions we

performed probabilistic facies predictions. It is commonly

assumed that probabilistic predictions are always better

than deterministic predictions. Unfortunately, this is not

always true if uninformative priors are used and training

facies are defined from well log data (Figure 4b). Defined

training facies from well log data are not good enough to

capture the seismic data away from the well (Figure 2c).

Therefore, under-predicted facies, away from well,are

mainly due to the training facies defined from the well log.

To make a better match for the entire seismic data,

including areas away from the well, we used defined

training facies from Monte Carlo simulation (Figure 3).

Hence, probabilistic facies classification can be further

improved if we use uninformative priors and training facies

defined from Monte Carlo simulation (Figure 4c).

However, better probabilistic facies prediction can be

obtained if we use informative priors and training facies

defined from Monte Carlo Simulation (Figure 4d).

Conclusions

For seismic reservoir characterization, we provided a case

study for facies predictions from pre-stack simultaneous

elastic inversion results in an unconventional reservoir.

This study indicates that, in probabilistic facies

classification, if uninformative priors are used, results are

sub-optimal compared to deterministic methods involving a

Rock Physics Template (RPT) workflow. Additionally,

probabilistic facies classification can be further improved if

we use uninformative priors and training facies defined

from Monte Carlo simulation. Probabilistic facies

prediction improves if we use informative priors and

training facies defined from Monte Carlo simulation.

Acknowledgments

The authors thank EnerVest for allowing this work to be

published. There are a number of individuals at ION that

contributed to this work, including Howard Rael, who did

the petrophysical analysis and Shihong Chi did inversion.

Tanya L. Inks from IS Interpretation Services, Inc and Paul

Brettwood from ION acknowledged for edits.

Figure 3: Simulated results for silica-rich limestone (cyan), clay-

rich limestone (black), lower kerogen-rich shale (magenta), higer

kerogen-rich shale (magenta) and seismic inversion results (red).

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Rock physics based facies classification

Figure 4: (a) Deterministic facies predictions involving an RPT workflow. Probabilistic facies prediction using Bayes theory: (b) if

uninformative priors are used, (c) if uninformative priors and training facies defined from Monte Carlo simulation are used, and (d) if

informative priors and training facies defined from Monte Carlo simulation are used.

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EDITED REFERENCES Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2016

SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web.

REFERENCES Avseth, P., T. Mukerji, and G. Mavko, 2005, Quantitative seismic interpretation: Applying rock physics

tools to reduce interpretation risk: Cambridge University, http://dx.doi.org/10.1017/CBO9780511600074.

Bachrach, R., and N. Dutta, 2004, Joint estimation of porosity and saturation using stochastic rock physics modeling: 66th Annual International Conference and Exhibition, EAGE, Extended Abstracts, http://dx.doi.org/10.2118/89991-MS.

Bachrach, R., M. Beller, C. Liu, J. Perdomo, D. Shelander, and N. Dutta, 2004, Combining rock physics analysis, full wave form prestack inversion and high resolution seismic interpretation to map lithology units in deep water: A Gulf of Mexico case study: The Leading Edge, 23, 378–383, http://dx.doi.org/10.1190/1.1729224.

Doyen, P. M., 1988, Porosity from seismic data: A geostatistical approach: Geophysics, 53, 1263–1275, http://dx.doi.org/10.1190/1.1442404.

Gastaldi, C., D. Roy, P. Doyen, and L. Den Boer, 1998, Using Bayesian simulations to predict reservoir thickness under tuning conditions: The Leading Edge, 17, 539–543, http://dx.doi.org/10.1190/1.1438008.

Gouveia, W., 1996, Bayesian seismic waveform data inversion: Parameter estimation and uncertainty analysis: Ph.D. thesis, Colorado School of Mines.

Grana, D., M. Pirrone, and T. Mukerji, 2012, Quantitative log interpretation and uncertainty propagation of petrophysical properties and facies classification from rock physics modeling and formation evaluation analysis: Geophysics, 77, no. 3, WA45–WA63, http://dx.doi.org/10.1190/geo2011-0272.1.

Hossain, Z., and T. Mukerji, 2011, Statistical rock physics and Monte Carlo Simulation of seismic attributes for greensand: 73rd Annual International Conference and Exhibition, EAGE, Extended Abstracts, http://dx.doi.org/10.3997/2214-4609.20149674.

Hossain, Z., S. Volterrani, and F. Diaz, 2015, Integration of rock physics template to improve Bayes’ facies classification: 85th Annual International Meeting, SEG, Expanded Abstracts, 2760–2764, http://dx.doi.org/10.1190/segam2015-5900545.1.

Landau, D. P., and K. Binder, 2000, A Guide to Monte Carlo Simulations in Statistical Physics: Cambridge University Press.

Lörtzer, G. J. M., and A. J. Berkhout, 1992, An integrated approach to lithologic inversion: Part 1, Theory: Geophysics, 57, 233–244, http://dx.doi.org/10.1190/1.1443236.

Takahashi, I., 2000, Quantifying information and uncertainty of rock property estimation from seismic data: Ph.D. thesis, Stanford University.

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