Jeffrey Marc Yarus

Stochastic Modeling and Geostatistics

This publication is dedicated in part to understanding qualitative and deterministic geologic models in terms of statistics. The book is precisely concerned with the fact that given the same set of data, different geologists will generate different results, all of which may be valid interpretations. Consisting of 25 individually authored chapters, it is the premise of all authors that understanding the interpretive variations is far more important than identifying any one particular model as truth. This publication contains sections on getting started, principles, methods and case studies, and public domain software for stochastic modeling.

Practical Geostatistics - An Armchair Overview for Petroleum Reservoir Engineers

JPT • NOVEMBER 2006 Abstract Some engineers are skeptical of statistical, let alone geostatistical, methods. Geostatistical analysis in reservoir characterization necessitates an understanding of a new and often unintuitive vocabulary. Statistical approaches for measuring uncertainty in reservoirs is indeed a rapidly growing part of the best-practice set of methodologies for many companies. For those already familiar with the basic concepts of geostatistics, it is hoped that this overview will be a useful refresher and perhaps clarify some concepts. For others, this overview is intended to provide a basic understanding and a new level of comfort with a technology that may be useful to them in the very near future.

Petroleum geostatistics for nongeostatisticians Part 1

For more than a decade, stochastic, or geostatistical, modeling methods have been increasingly used to “map” spatially correlated data. Recall that kriging is a deterministic method whose function has a unique solution and that does not attempt to represent actual variability of the studied attribute. Thus, the smoothing property of kriging dismisses local detail in place of a good average. However, often the geoscientist or reservoir engineer is more interested in fine-scale details captured by the estimation variance than a map of local estimates of the mean.

Causal Analysis and Data Mining of Well Stimulation Data Using Classification and Regression Tree with Enhancements

In the well-treatment program certain variables, like Job Pause Time (JPT) and fracture screen-out, can affect its efficiency. JPT is the time during which pumping is paused in-between subsequent treatments and screen-out occurs when the fluid flow is restricted inside the fracture. We investigate whether it is possible to identify characteristic patterns in existing data that affect the extreme values of JPT as well as the most critical variables causing fracture screen-out. We apply Classification and Regression Tree (CART) analysis, validate the approach with well-stimulation case studies and enhance predictive capability by implementing normal score transform and data clustering.

Optimizing Lateral Lengths in Horizontal Wells for a Heterogeneous Shale Play

A successful evaluation and development program in oil- and gas-bearing shales requires considerable analysis and investment, not to mention optimization to help ensure a profitable outcome. Accelerating optimization, reducing capital expenditures, and improving lifecycle net present value (NPV) for the asset are reasonable goals. Seven shale properties are key drivers to help achieve successful play economics. However, the heterogeneity of shales makes well location selection difficult without appraisal well logs and geostatistical mapping of shale property quality. The analysis method allows operators to quickly high-grade areas within a large, heterogeneous shale play using logging suites from a limited number of wellbores in the play. Further, the methodology has been extended to quantify the play’s potential reward versus risk distribution for in-fill drilling investments. This study extends the method to optimizing lateral lengths of horizontal wells. Geostatistics provides a means to determine correlation lengths of aggregate shale properties known to be critical to successful economics. The correlation length is used to determine the appropriate length of the horizontal well lateral, restricting it within the highest rock quality for stimulation effectiveness and production rates. Because optimal lateral lengths can be predicted using this approach, it is now possible to pinpoint the best wellhead location, the best landing point for the horizontal portion of the well, and set the optimal length of the lateral. This reduces the drilling of unproductive lateral lengths and targets stimulations. By shortening the “trial-and-error” evaluation lifecycle stage using this methodology, an operator can develop an asset more quickly and at less cost than with previous approaches.

Modeling Distribution of Geological Properties Using Local Continuity Directions

Summary We present an innovative technology for 3D volumetric modeling of geological properties, using a Maximum Continuity Field. The method provides the user unique opportunity to a) directly control the local continuity directions, b) interactively operate with “geologically intuitive” datasets and c) retain the maximum fidelity of geological model by postponing the creation of grid/mesh until the final stage of static model building. We validate the method by modeling a permeability distribution in a fluvial system of complex synthetic field-case.

Stochastic modeling and geostatistics; principles, methods and case studies; Volume II

Since publication of the first volume of Stochastic Modeling and Geostatistics in 1994, there has been an explosion of interest and activity in geostatistical methods and spatial stochastic modeling techniques. Many of the computational algorithms and methodological approaches that were available then have greatly matured, and new, even better ones have come to the forefront. Advances in computing and increased focus on software commercialization have resulted in improved access to, and usability of, the available tools and techniques. Against this backdrop, Stochastic Modeling and Geostatistics Volume II provides a much-needed update on this important technology. As in the case of the first volume, it largely focuses on applications and case studies from the petroleum and related fields, but it also contains an appropriate mix of the theory and methods developed throughout the past decade. Geologists, petroleum engineers, and other individuals working in the earth and environmental sciences will find Stochastic Modeling and Geostatistics Volume II to be an important addition to their technical information resources.

Using Spatial Constraints in Clustering for Electrofacies Calculation

Petroleum reservoir geological models are usually built in two steps. First, a 3-D model of geological bodies is computed, within which rock properties are expected to be stationary and to have low variability. Such geological domains are referred to as “facies” and are often “electrofacies” obtained by clustering petrophysical log curves and calibrating the results with core data. It can happen that log responses of different types of rock are too similar to enable satisfactory estimation of the facies. In such situations, taking into account the spatial aspect of the data might help the discriminative process. Since the clustering algorithms that are used in this context usually fail to do so, we propose a method to overcome such limitations. It consists in post-calibrating the estimated probabilities of the presence of each facies in the samples, using geological trends determined by experts. The final facies probability is estimated by a simple kriging of the initial ones. Measurement errors reflecting the confidence in the clustering algorithms are added to the model, and the target mean is taken as the aforementioned geological trend. Assets and liabilities of this approach are reviewed; in particular, theoretical and practical issues about stationarity, neighborhood choice, and possible generalizations are discussed. The estimation of the variance to be assigned to each data point is also analyzed. As the class probabilities sum up to one, the classes are not independent; solutions are proposed in each context. This approach can be applied for extending class probabilities in 3-D.

Simulation-to-seismic: rock type definitions used to characterise flow units in the reservoir model

The earth modelling workflow involves the construction of petrophysical models, which can be spatially constrained by depositional facies. The authors recommend a novel petrofacies approach to reconcile disparities in the petrophysical model that lack the aforementioned constraint. Here, permeability is used to assign rock types in petrofacies, which spatially dictate the multiphase flow behaviour in the simulation model, petro-elastic rock properties can be used in tuning unconstrained petrophysical models for flow simulation. The conclusion is that the veracity of the petrofacies definitions in flow simulation are applicable for selected models depending upon the existing hydraulic rock types and petrofacies assemblages.

Multivariate Analysis of Job Pause Time Data Using Classification and Regression Tree and Kernel Clustering

The well treatment program is an important part of the field development plan, and certain variables, such as job pause time (JPT), can affect its efficiency. JPT is the time during which pumping is paused between subsequent treatments of a job. The objectives of this work are to investigate whether, from existing data, it is possible to find patterns in significant variables that affect the extreme values of JPT in a particular region. The answers are sought by applying a classification and regression tree (CART) to both categorical and continuous variables in the database. The practical application of CART is presented using case studies first using classical CART analysis, then using CART analysis with enhancement tools such as the normal score transform (NST), and then dividing the large dataset into smaller groups using clustering. Significant variables are found that affect the response variables, and predictor variables are ranked in order of their importance. Such information can be used to control predictor variables that cause high JPT. The results are outlined in an intuitive way, including categorical, continuous, and missing values. Because CART is a data driven, deterministic model, we cannot calculate the confidence interval of the predicted response. Confidence in the results is purely based on the historical values, and the accuracy of the result produced by a tree model depends on the quality of the recorded data measured in terms of volume, reliability, and consistency. The prediction capability of CART is enhanced by the use of NST and clustering techniques. The approach presented in this paper analyzes a dataset with limited information and high uncertainty and should lead to developing a method for generating proxy models to find future success indices (e.g., for drilling efficiency or production from a fracture). This could standardize stimulation and generate decision ‘best practices’ to save costs in field development and the optimization process.