The year 2008 has witnessed unprecedented fluctuations in the oil prices. During the first three-quarters, the oil price abruptly increased to $140/bbl, a level that has never been reached before; then because of the global economic crisis, the price dramatically plunged to less than $50/bbl by the end of the year losing more than 64% of the maximum price in less than three months period. The supply of crude oil to the international market oscillated to follow suite according to the law of supply and demand. This behavior affected oil production in all exporting countries. Nonetheless, the demand for crude oil in some developing countries, such as China and India, has increased in the past few years because of the rapid growth in the transportation sector in addition to the absence of viable economic alternatives for fossil fuel. The rapid growth in fuel demand has forced the policy makers worldwide to include uninterrupted crude oil supply as a vital priority in their economic and strategic planning. Even though forecasting should be handled with extreme caution, it is always desirable to look ahead as far as possible to make an intellectual judgment on the future supplies of crude oil. Over the years, accurate prediction of oil production was confronted by fluctuating ecological, economical, and political factors, which imposed many restrictions on its exploration, transportation, and supply and demand. The objective of this study is to develop a forecasting model to predict world crude oil supply with better accuracy than the existing models. Even though our approach originates from Hubbert model, it overcomes the limitations and restrictions associated with the original Hubbert model. As opposed to Hubbert single-cycle model, our model has more than one cycle depending on the historical oil production trend and known oil reserves. The presented method is a viable tool to predict the peak oil production rate and time. The model is simple, accurate, and totally data driven, which allows a continuous updating once new data are available. The analysis of 47 major oil producing countries estimates the world's ultimate crude oil reserve by 2140 BSTB and the remaining recoverable oil by 1161 BSTB. The world production is estimated to peak in 2014 at a rate of 79 MMSTB/D. OPEC has remaining reserve of 909 BSTB, which is about 78% of the world reserves. OPEC production is expected to peak in 2026 at a rate of 53 MMSTB/D. On the basis of 2005 world crude oil production and current recovery techniques, the world oil reserves are being depleted at an annual rate of 2.1%.

TX 75083-3836, U.S.A., fax 01-972-952-9435. AbstractWe propose a multiscale approach to data integration that accounts for the varying resolving power of different data types from the very outset. Starting with a very coarse description, we match the production response at the wells by recursively refining the reservoir grid. A multiphase streamline simulator is utilized for modeling fluid flow in the reservoir. The well data is then integrated using conventional geostatistics, for example sequential simulation methods. There are several advantages to our proposed approach. First, we explicitly account for the resolution of the production response by refining the grid only up to a level sufficient to match the data, avoiding over-parameterization and incorporation of artificial regularization constraints. Second, production data is integrated at a coarse-scale with fewer parameters, which makes the method significantly faster compared to direct fine-scale inversion of the production data. Third, decomposition of the inverse problem by scale greatly facilitates the convergence of iterative descent techniques to the global solution, particularly in the presence of multiple local minima. Finally, the streamline approach allows for parameter sensitivities to be computed analytically using a single simulation run and thus, further enhancing the computational speed.The proposed approach has been applied to synthetic as well as field examples. The synthetic examples illustrate the validity of the approach and also address several key issues such as convergence of the algorithm, computational efficiency, and advantages of the multiscale approach compared to conventional methods. The field example is from the Goldsmith San Andres Unit (GSAU) in West Texas and includes multiple patterns consisting of 11 injectors and 31 producers. Using well log data and water-cut history from producing wells, we characterize the permeability distribution, thus demonstrating the feasibility of the proposed approach for large-scale field applications.

Summary We propose a hierarchical approach to spatial modeling based on Markov Random Fields (MRF) and multiresolution algorithms in image analysis. Unlike their geostatistical counterparts, which simultaneously specify distributions across the entire field, MRFs are based on a collection of full conditional distributions that rely on the local neighborhoods of each element. This critical focus on local specification provides several advantages:MRFs are computationally tractable and are ideally suited to simulation based computation, such as Markov Chain Monte Carlo (MCMC) methods, andmodel extensions to account for nonstationarity, discontinuity, and varying spatial properties at various scales of resolution are easily accessible in the MRF framework. Our proposed method is computationally efficient and well suited to reconstruct fine-scale spatial fields from coarser, multiscale samples (based on seismic and production data) and sparse fine-scale conditioning data (e.g., well data). It is easy to implement, and it can account for the complex, nonlinear interactions between different scales, as well as the precision of the data at various scales, in a consistent fashion. We illustrate our method with a variety of examples that demonstrate the power and versatility of the proposed approach. Finally, a comparison with Sequential Gaussian Simulation with Block Kriging (SGSBK) indicates similar performance with less restrictive assumptions. Introduction A persistent problem in petroleum reservoir characterization is to build a model for flow simulations based on incomplete information. Because of the limited spatial information, any conceptual reservoir model used to describe heterogeneities will, necessarily, have large uncertainty. Such uncertainties can be significantly reduced by integrating multiple data sources into the reservoir model.1 In general, we have hard data, such as well logs and cores, and soft data, such as seismic traces, production history, conceptual depositional models, and regional geological analyses. Integrating information from this wide variety of sources into the reservoir model is not a trivial task. This is because different data sources scan different length scales of heterogeneity and can have different degrees of precision.2 Reconciling multiscale data for spatial modeling of reservoir properties is important because different data types provide different information about the reservoir architecture and heterogeneity. It is essential that reservoir models preserve small-scale property variations observed in well logs and core measurements and capture the large-scale structure and continuity observed in global measures such as seismic and production data. A hierarchical model is particularly well suited to address the multiscaled nature of spatial fields, match available data at various levels of resolution, and account for uncertainties inherent in the information.1–3 Several methods to combine multiscale data have been introduced in the literature, with a primary focus on integrating seismic and well data.3–9 These include conventional techniques such as cokriging and its variations,3–6 SGSBK,7 and Bayesian updating of point kriging.8,9 Most kriging-based methods are restricted to multi-Gaussian and stationary random fields.3–9 Therefore, they require data transformation and variogram construction. In practice, variogram modeling with a limited data set can be difficult and strongly user-dependent. Improper variograms can lead to errors and inaccuracies in the estimation. Thus, one might also need to consider the uncertainty in variogram models during estimation. 10 However, conventional geostatistical methods do not provide an effective framework to account for the uncertainty of the variogram. Furthermore, most of the multiscale integration algorithms assume a linear relationship between the scales. The objective of this paper is to introduce a novel multiscale data-integration technique that provides a flexible and sound mathematical framework to overcome some of the limitations of conventional geostatistical techniques. Our approach is based on multiscale MRFs11–14 that can effectively integrate multiple data sources into high-resolution reservoir models for reliable reservoir forecasting. This proposed approach is also ideally suited to simulation- based computations, such as MCMC.15,16 Methodology Our problem of interest is to generate fine-scale random fields based on sparse fine-scale samples and coarse-scale data. Such situations arise when we have limited point measurements, such as well data, and coarse-scale information based on seismic and/or production data. Our proposed method is a Bayesian approach to spatial modeling based on MRF and multiresolution algorithms in image analysis. Broadly, the method consists of two major parts:construction of a posterior distribution for multiscale data integration using a hierarchical model andimplementing MCMC to explore the posterior distribution. Construction of a Posterior Distribution for Multiscale Data Integration. A multiresolution MRF provides an efficient framework to integrate different scales of data hierarchically, provided that the coarse-scale resolution is dependent on the next finescale resolution.11 In general, a hierarchical conditional model over scales 1,. . ., N (from fine to coarse) can be expressed in terms of the product of conditional distributions,Equation 1 where p(xn), n=1, . . ., N, are MRF models at each scale, and the terms p(xn|xn-1) express the statistical interactions between different scales. This approach links the various scales stochastically in a direct Bayesian hierarchical modeling framework (Fig. 1). Knowing the fine-scale field xn does not completely determine the field at a coarser scale xn+1, but depending on the extent of the dependence structure modeled and estimated, it influences the distribution at the coarser scales to a greater or lesser extent. This enables us to address multiscale problems accounting for the scale and precision of the data at various levels. For clarity of exposition, a hierarchical model for reconciling two different scales of data will be considered below.Equation 2 From this equation, the posterior distribution of the fine-scale random field indexed by 1 given a coarse-scale random field indexed by 2 can be derived as follows.

The accurate determination of the pressure, volume, and temperature (PVT) properties such as bubble-point pressure and oil formation volume factor is important in the primary and subsequent development of an oil field. These two parameters are essential for all petroleum engineering calculations such as reservoir simulations, recovery estimates, material balance calculations, well completion, facility design decisions, and production optimization strategies. In this study, a new approach is presented for predicting bubble-point pressure and oil formation volume factor for crude oil samples collected from different regions around the world. The regions include major oil-producing fields in North and South America, the North Sea, Southeast Asia, the Middle East, and Africa. The new approach, which is based on nonparametric optimal transformations, is called alternating conditional expectation (ACE). The transformations are totally data-driven and do not assume any a priori functional form. The data set used in the study consists of 5200 points that represent worldwide crude. An additional 200 PVT data sets were used to investigate the effectiveness of the new proposed method to predict outputs from inputs that were not used during the training process. The ACE model is able to predict the bubble-point pressure and oil formation volume factor as a function of the solution gas-oil ratio, the gas relative density, the oil specific gravity, and the reservoir temperature. The excellent results obtained from the proposed model establish a new simple tool for calculation of the two properties. The accuracy of the models developed in this study was compared in detail with several published correlations.