Olena Babak

An intrinsic model of coregionalization that solves variance inflation in collocated cokriging

Sequential Gaussian simulation (SGS) is a widely used geostatistical simulation approach for continuous variables. A variant of SGS that employs collocated cokriging under a Markov model is commonly applied to integrate seismic data and to cosimulate multiple variables. This approach is popular because it is simple; the correlation coefficient between the primary variable being modeled and secondary data is the sole additional statistic required to integrate the secondary data. Collocated cokriging, however, has a longstanding problem with variance inflation that leads to a systematic bias in the mean and variance of the simulated realizations. An alternative approach is presented here that is equally simple, with no additional parameters needed. An intrinsic model of coregionalization is adopted for cokriging using secondary data at the location being considered and at the locations of the primary data. The resulting technique can be referred to as intrinsic collocated cokriging (ICCK). The resulting estimates are checked carefully and no variance inflation is observed. This implementation should systematically replace all versions of the Markov model and collocated cokriging.

Estimation of the Length Distribution of Marine Populations in the Gaussian-multinomial Setting using the Method of Moments

Abstract In this paper, the problem of estimation of the length distribution of marine populations in the Gaussian-multinomial model is considered. For the purpose of the mean and covariance parameter estimation, the method of moments estimators are developed. That is, minimum variance linear unbiased estimator for the mean frequency vector is derived and a consistent estimator for the covariance matrix of the length observations is presented. The usefulness of the proposed estimators is illustrated with an analysis of real cod length measurement data.

Accounting for non-exclusivity in sequential indicator simulation of categorical variables

Facies models are used to better capture heterogeneity in mineral deposits and petroleum reservoirs. Facies are often considered as mutually exclusive and exhaustive at the scale of the geological model. These two assumptions are needed for sequential indicator simulation and most other facies modeling techniques; however, the assumption that an entire grid block consists of one facies type becomes unreasonable as the scale increases. Most geological models are built at a scale that is larger than the scale of variation of facies. Mixing of multiple facies types within a grid cell is common, especially in zones of transition between different facies. This paper develops a new technique to address the issue of non-exclusivity of facies within grid cells. The approach quantifies the uncertainty resulting from majority-vote upscaling of facies from core or well log scale to the grid cell scale and utilizes this uncertainty to build better models of continuous reservoir properties such as bitumen grade. Uncertainty is quantified using a measure of entropy that is capable of handling situations where there may be similarity between different facies types. A methodology to implement entropy in geo-modeling is introduced and demonstrated with several small examples. An example involving real data from the McMurray formation of Totals Joslyn lease is used to demonstrate the improvement in accuracy compared with traditional modeling workflows.

Inverse distance interpolation for facies modeling

Inverse distance weighted interpolation is a robust and widely used estimation technique. In practical applications, inverse distance interpolation is oftentimes favored over kriging-based techniques when there is a problem of making meaningful estimates of the field spatial structure. Nowadays application of inverse distance interpolation is limited to continuous random variable modeling. There is a need to extend the approach to categorical/discrete random variables. In this paper we propose such an extension using indicator formalism. The applicability of inverse distance interpolation for categorical modeling is then illustrated using Total’s Joslyn Lease facies data.

Estimating barrier shale extent and optimizing well placement in heavy oil reservoirs

Shale barriers within the bituminous oil sand deposits of the McMurray Formation have a detrimental effect on the steam-assisted gravity-drainage chamber growth and oil recovery. Typically, the non-net shale barrier lateral extents are too small to be detected with a few widely spaced delineation wells. The information on net reservoir and shale interval thicknesses collected from wells, along with a vertical indicator variogram, provide limited information about the horizontal extent and connectivity of these intervals. In this paper, a novel quantitative approach for predicting the lateral extents of the barriers, using thickness information provided by well log data, is proposed. The proposed approach is based on moments of inertia (MOI) applied to the shale objects to determine their effective size. The MOI calculation is aimed to simplify the almost infinite complexity of shale bodies into summary size parameters that can be readily understood and calibrated to production parameters. A case study is presented for optimal well placement accounting for uncertainty in the shale barrier sizes.

A workflow for vertical and horizontal near-wellbore permeability modelling in the McMurray Formation

The McMurray Formation is the most volumetrically important source of bitumen in the Canadian oil sands. While there are many parameters that affect prediction of bitumen recovery in commercial in situ oil sand projects, absolute permeability is the most important geological parameter. In this paper, we describe a customized near-wellbore modelling workflow for the estimation of vertical and horizontal permeability in the McMurray Formation using high-resolution microresistivity images. All steps required to calculate permeability logs calibrated to core plug measurements are documented and detailed. To show a general applicability of the method, a case study of several wells from the Cenovus Energy Inc. (Cenovus) Foster Creek project is presented. The wells are specifically selected to be different in terms of facies, their characteristics and interval lengths.