Linking for Rate of Penetration to Seismic Attributes and Mechanical Properties in the Mississippi Lime, OK
Xuan Qi, Joseph Snyder, Kurt Marfurt, and Matthew J. Pranter, University of Oklahoma
Summary
The Mississippian Limestone is a heterogeneous formation. This heterogeneity impacts the rate of penetration (ROP). ROP is a function of bit size,
weight on bit, drilling mud, and lithology, where lithology can be statistically correlated to surface seismic attributes. Because the bit actually destroys the rock, we expect correlations to be nonlinear; however, if even a soft correlation can be found, the economic impact on drilling could be significant, allowing
the drilling engineer to prepare for and, if necessary, avoid problems associated with the drilling process.
This study explores if a correlation can be found between seismic attributes, seismically derived mechanical properties and ROP. The seismic
survey of this study is located in the Anadarko Shelf of Northern Oklahoma. Seismic attributes that may be indirectly related to the depositional and tectonic history are extracted from seismic data along wellbores in the depth domain. Seismic estimates of mechanical parameters are derived from seismic inversion and AVAz
analysis. We show the results of several correlation techniques including multi-linear regression, neural networks, and alternating conditional expectation (ACE) algorithms.
Introduction
Drilling and completions of horizontal wells are the largest expenses in unconventional reservoir plays, where the cost of drilling a well is proportional to the time it takes to reach the
target objective. Accordingly, the faster the desired penetration depth is achieved, the lower the cost of the drilling process. ROP is measured in all wells, but rarely examined by geophysicists. ROP depends on many factors, but the primary factors are weight on the bit, the speed of rotation of the drill bit, the rate of flow
of drilling fluid and characteristics of the formation being drilled. In this study, we will
mainly focus on influence of the geological formation on ROP.
A “drill off test” method is primarily used to determine an optimum ROP of a particular set of
conditions; however, one problem with using a drill off test is that this process produces a static weight only valid for limited conditions during the test. It does not work well under more complex geological conditions (King and Pinckard, 2000).
Seismic attributes have been widely used in predicting lithological and petrophysical properties of a reservoir. Seismic inversion results (e.g. impedance) have been used to predict fault zones, potential fractures and lithology in the Mississippian Limestone play (Dowdell et al., 2013; Roy et al., 2013; Verma et
al., 2013).
Here we propose to use a geostatistical approach to correlate seismic attributes and mechanical properties with ROP to predict ROP on a larger scale. Several correlation techniques will be
applied in our study, including multi-linear regression, neural networks and alternating conditional expectation algorithms.
This study is conducted in a relatively heterogeneous reservoir located in north-central Oklahoma. Hydrocarbon exploration and
development has been present in this area for more than 50 years (Rogers, 2001).
Figure 1 Major geologic provinces of Oklahoma with the area of interest outlined in crimson (Modified from Johnson and Luza (2008); Northcutt and Campbell (1996))
Geological Settings
The Mississippian interval within the mid-continent is characterized by four distinct stages of deposition. From oldest to youngest these stages include: Kinderhookian, Osagean,
Meramecian, and Chesterian. However, within the specific study area, only Kinderhookian, Osagean, and Meramecian intervals are preserved. In some areas, the Meramecian interval is not present. “Mississippi Lime” is a broad informal term that refers to dominantly carbonate deposits of the mid-continent (Parham
and Northcutt, 1993).
Three main depositional environments represented in the Mississippian include inner, main, and outer ramp settings (Parham and Northcutt, 1993), representing a basinward trend from shallow water, structurally updip areas in
the north to deeper, downdip areas in the south. These environments have resulted in commonly acknowledged facies within the Mississippian carbonates, ranging from basal argillaceous mudstones, to spiculitic packstones with nodular or bedded chert, to autoclastic chert, to an overlying bioclastic grainstone (Mazzullo et al.,
2009; Watney et al., 2001). The lower Mississippian, Osagean rocks which were deposited across much of the mid-continent were subsequently eroded in places by tectonic activity during the late Mississippian (Parham and Northcutt, 1993). Regional uplift during the Pennsylvanian not only removed large sections of rock but caused alteration at the top of the
Mississippian section and created detrital deposits of reworked Mississippian-aged rocks. These altered sections of rock are comprised of highly porous tripolitic chert and very dense glass-like chert. The leaching due to meteoric waters during uplift has led to karsting, locally contained caverns and solution-channel features
(Parham and Northcutt, 1993).
Data Available
A 3D survey was acquired in Woods County, Oklahoma by Chesapeake Energy. The seismic processing workflow included refraction statics, velocity analysis, residual statics, NMO, CDP stack, finite difference migration, fxy prediction noise rejection, and a 6-12-80-90 Ormsby filter.
The overall data quality is excellent. The signal/noise is relatively high and the wavelet amplitude seems continuous throughout the same horizon. Data for 83 wells have been provided by Chesapeake Energy, consisting of 52 horizontal wells and 31 vertical wells.
Figure 2 Stratigraphic column showing the sequence of units in the area of interest (Modified from Mazzullo (2011)).
Method
Artificial Neural networks (ANN)
ANNs are a family of statistical learning algorithms inspired by biological neural
networks. The mathematical neuron proceeds in a similar way. ANN has been widely used in pattern recognition, curve fitting, and clustering.
In fitting problems, ANN algorithms are used to map relationships between a set of numeric inputs and a set of numeric targets. In pattern classification, given a set of patterns and the corresponding class label, the objective is to capture the implicate relation among the patterns of the same class, so that when a test pattern is
given, the corresponding output class label is retrieved (Fig. 3). We use MATLAB’s Neural Network Toolbox for data analysis.
Figure 1 A Flow chart describing the ANN algorithm. The neural networks are trained so that a particular input leads to a specific target output (modified from Demuth and Beale (1993)).
Alternating Expectation Algorithms (ACE)
In regression analysis, the response variable Y and the predictor variables are often
replaced by the functions ( ) and ( ) ( ). Breiman and Friedman
(1985) created a new approach for estimating the functions and that minimize
{[ ( ) ∑ ( )
] }
, ( )-, given only a
sample *( ) + and
making minimal assumptions concerning the
data distribution or the form of the solution function. Our codes are built upon MATLAB ACE file (Voss and Kurths, 1997).
Workflow
To accomplish the objectives of this study, the following workflow is proposed:
1) Target the production zones in seismic data and conduct a time-depth conversion for the seismic survey.
2) Extract rock-physics related parameters from the seismic inversion results in the
following manner:
Vertical wells:
Horizontal wells:
3) Conduct a multi-linear regression
analysis with all of the attributes and find the three dominant factors that relate to ROP.
4) Import the data from step 3) into a
Neural Network. Train the Neural Network using representative zones over the study area. This ANN model is trained to find a fit for ROP from the imported data.
5) Repeat step 4) using ACE. 6) Apply the obtained relationship from
step 4) and 5) to a subset of wells that were not used in the creation of the transform in order to sustain the validity of this workflow.
7) Compare the results from step 6) and employ the better analysis.
8) Upscale the data close to the well into whole seismic volume.
Figure 4 A schematic graph demonstrating the work flow. The input X variables (left frame) include the seismic inversion and the derived parameters from well data; the Y variable is ROP (right frame). We use ANN and ACE to explore statistical relationships between the two sides.
Preliminary Results
Gridded volume has been created for porosity and ROP (Fig. 5). The volume spans the Mississippian Limestone section of the survey and a general well position can be seen.
Figure 5 3D petrophysical modeling covered formation from top of Mississippian to top of Woodford Shale zone in this study area. a) Porosity and b) ROP modeling scaled up from well logs
Conclusion
Rate of penetration is a major factor in the drilling process. The faster the well can be drilled, the cheaper the overall cost is. We introduce a workflow consisting of two
statistical analyses in an effort to predict ROP in our survey. Seismic attributes and mechanical properties will be compared with ROP through the use of Artificial Neural Networks and Alternating Expectation Algorithms. Ultimately, a 3D grid model honoring the correlations will be created with the intention of making the
drilling process a smoother and more economical endeavor.
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