Petroleum Geostatistics 2015

A statistical analysis of different faults' attributes and relation between them is presented. The new method for correction of statistical analysis results for probability distribution of faults and fractures lengths sampled under truncation and censoring effects and their intensity is developed. A series of test calculations confirm the accuracy and computational efficiency of the method.

High demand for hydrocarbons incentivizes the industry to look for new exploration opportunities in unexplored areas with high risk where new potential discoveries of importance might be located. Frontier locations are unexplored or underexplored basins, in which geological and geophysical information might be unavailable, or sparse. In this paper we present a new methodology based on the Global Stochastic Inversion (GSI) algorithm (Soares et al., 2007; Caetano, 2009), which uses Direct Sequential Simulation (Soares, 2001) as a global perturbation method to generate equi-probable models of acoustic impedance, and follows a iterative process to optimize a previously defined objective function. The convergence of the inverse process is evaluated by the local and global correlation coefficient between real seismic and synthetic seismogram. This new method can be useful for preliminary assessment of different scenarios in unexplored areas, where no well log information exists to be used as a constrain to an inverse problem. The method follows the GSI workflow, but without using any well data in the study area. Instead of that, our proposal is to use analogs information (outcrops, modern analogs, and wells logs data from nearby fields) to condition the generation of acoustic impedance models. In this procedure, the geometry and position of the “analog-well” is ignored and the analog information is only used in the form of spatial dispersion and spatial patterns of acoustic impedances (histograms and variograms) for each lithology/facies expected in the geological model, as defined by an expert.

The paper considers the problem occurring in geological modelling of the oil field – the problem of well data interpolation and further reconstruction of the rock properties of the reservoir in the space between the wells. We introduce a new method based on the spectral theory for analysis and modelling of the reservoir rock properties. In the method for well log data representation the Fourier decomposition is used and then each harmonic is interpolated independently. The method allows to obtain more realistic geological models in case of complex and low-permeability reservoirs in comparison with conventional geostatistical methods. An application of this methodology to the real field data is presented which shows encouraging results. We expect this approach to make real improvement in quality and predictive value of the geological models.

esearch Center (EERC) and Plains CO₂ Reduction Partnership Program, in collaboration with the U.S. Department of Energy, have constructed 3-D geocellular models for the purpose of studying CO₂ storage and CO₂ enhanced oil recovery (EOR). These efforts are gaining importance as we continue to investigate methods in climate change mitigation and greenhouse gas reduction. The models created in these efforts range in size from small-scale pinnacle reefs up to formation- and basin-scale, spanning various reservoir types and lithologies, and many have utilized the multiple point statistical (MPS) method in the facies modeling process. This method allows the incorporation of geologic understanding, in the form of a training image, to better capture reservoir heterogeneity. Some complex reservoirs may be divided into multiple ‘geobody’ regions for the MPS process, with each region having a unique training image and facies distribution. The various facies models constructed in these CO₂ storage and CO₂ EOR investigations are used to constrain petrophysical property distributions, which are then used to analyze total and effective pore volumes and viability for CO₂ injection. Dynamic simulations are run to assess CO₂ storage capacity, efficiency, utilization, and consideration of potential as a CO₂ storage resource.

Channelized reservoirs consist of sinusoid patterns for sandstone. It is the most important for decision making to characterize connectivities because they significantly affect reservoir performances. Ensemble Kalman filter (EnKF) and ensemble smoother (ES) modify reservoir models using dynamic data. However, it is difficult for them to apply to channelized reservoirs because they assume that model parameters follow Gaussian distribution. The purpose of this research is to characterize 3D channel connectivities using ensemble-based methods. We use the concept of multiple Kalman gains for improved inverse modeling and it is applied to ES for fast history matching. Multiple Kalman gains are calculated by distance-based method such as hausdorff distance and kernel kmeans clustering. The proposed method, ES with multiple Kalman gains, is compared to EnKF and ES for 3D synthetic case. It solves overshooting problem in ES and describes better channel connectivities and bimodal distribution than EnKF. Furthermore, it requires only 6.4% simulation time of EnKF. When oil production rates and water cuts are predicted by updated ensembles, only the proposed method gives reliable uncertainty quantifications while EnKF and ES deviate from the true productions. Therefore, the proposed method can be utilized for fast decision making tool for 3D channelized reservoirs.

History matching has traditionally been an important element of forecasting, but, due to computational, as well as modeling complexities in real reservoir systems, many ideas have remained academic. In this work we propose a new paradigm to side-step the iterative history matching process and to aim instead to directly establish a statistical relationship between forecast variables (future water & oil rates) and historical production data variables (past water & oil rates). A novel statistical method is developed for this purpose: canonical function principal component analysis (CFCA). A real field case study is presented with complex model variability that includes depositional, geostatistical, structural geological as well as fluid property uncertainty. Forecast are shown to be the same as full history matching with a fraction of computational cost.

The ensemble Kalman based methods have seen numerous successful application over the past 10 years in fields such as numerical weather predictions, oceanography, and reservoir history matching. However, it is well-known that the standard implementation of the ensemble Kalman update equation can lead unphysical model updates and the problem known as filter divergence (or ensemble collapse). In this paper, we will re-visit recent theoretical results which highlights the issues of the standard ensemble Kalman update equations and identifies how you can potentially fix them. We use the data from the Brugge field to demonstrate the link between the theoretical results and practical applications in reservoir history matching.

Mathematical physics is based on the fundamental assumption that physical predictions must be the same, independently of the parameterization of the system. This principle even constitutes the very foundation of certain physical theories, of which the theory of relativity is perhaps the most notable. The importance of the principle is that it seeks to maintain objectivity: When two different analysts predict the evolution of the same physical system, but use different parameterizations (reference systems), their predictions must agree physically. Otherwise the theory would give results that depend on the individual analysts's preferences, and hence be subjective. Our question here is the following: What would happen if we impose the same constraints on modeling and data inversion? What if we required that our procedures for modeling and inversion should be designed such that no conflicts between analysts would appear? We will look into this problem by focusing on three different problem areas where possible inconsistencies may occur.