We propose a methodology to propagate uncertainties in seismic pore pressure prediction using a 3-D Probabilistic Mechanical Earth Model (P-MEM). An extended form of Bowers formula is used to link pore pressure to seismic velocity, overburden stress, porosity and clay volume. Probability Distribution Functions (PDFs) for all input variables are stored as attributes in the 3-D MEM. An output PDF for pore pressure is then calculated point by point in the 3-D model, using either a linearized Gaussian approximation or a sequential stochastic simulation approach that fully accounts for nonlinearities in the velocity to pore pressure transform and spatial correlation between the different input variables. The linearized and stochastic approaches are compared in the context of a seismic pore pressure prediction study involving overpressured reservoir sands.
Subsurface mocfels of Iithology are often poorly constrained due to the lack of dense well control. AIthough limited in vertical resohrtion, high quality 3-D seismic data usually provide vahtable information regsrdmg the lateral variations of Iithology. The Bayesian Sequential Indicator Simulation (BSISIM) technique is a new stochastic method to generate seismically constrained models of Iithology. Unlike cokriging-based simulation methods, BSISM does not-rely on a generalized linear regression rriodel, which is inadequate when combining fithology indicator variables and continuous seismic attributes. Instead, BSLSIIvluses a Bayesian updating rule to construct a posterior probability distribution of lithoclasses at each location. The posterior dkr-ibution combines a local prior distribution obtained by~dicator kriging wftb a function representing the ieismic likelihood of the different Iithofaties. The local posterior dk,tributions are sampled sequentially at all points irr space to generate realizations from the joint posterior dktribution. The realizations define alternative, gquiprobabIe Iithologic models, representing a comprortiise between fidelity to the seismic data, as measured by the likelihood functions, and consistency with spatial continuity information, as expressed by the lithology indicator correlation functions. The simulation technique References and figures at end of paper.is aodied to uredict the lateral distribution of channel ssn& in the N'ms Formation of the Oseberg Field. Channel sand maps are simulated using Lithologic observations in fourteen weIls, and seismic amplitude and channel orientation data extracted from a 3-D survey. Sand probability maps, generated by summarizing a large number of simulations, aIlow de~meation of the probable lateral extent of the channel deposits. Comparison of seismically derived lithologic models to well-derived models demonstrates the improved definition of channel geometry achieved by integrating the geophysical information.
Three-dimensional seismic data, with their dense lateral coverage, provide a valuable source of information for constraining earth models. One drawback is the inherent lower vertical resolution of seismic measurements compared to well logs. This means that the use of seismic attributes is often limited to the areal mapping of zone average reservoir properties. A novel stochastic simulation method is introduced to constrain 3-D earth models with seismic attribute maps. The method accounts explicitly for the difference in vertical scale between seismic and wireline log measurements. Each vertical column of cells in a simulated 3-D model may be constrained to reproduce approximately a seismic-derived average value. The sequential simulation procedure is based on a Bayesian updating of point kriging estimates with a seismic average likelihood function and does not require solving block kriging systems. Three-dimensional porosity simulations are generated for a chalk reservoir layer of the Ekofisk Field, Norwegian North Sea. Vertical average constraints are imposed using a seismic impedance map representative of the gross average porosity across the reservoir interval. Introduction In the last several years, considerable attention has been given to the problem of integrating seismic attribute information in subsurface mapping applications. One complication arises because the vertical resolution of seismic data is much lower than that of well logs. Seismic attributes are therefore typically correlated with petrophysical data averaged vertically across reservoir zones which may be several tens of feet thick, depending on seismic resolution. The seismic attributes are then used to guide the areal interpolation of the well-derived zone average data. Areal reservoir models are useful in many applications such as optimum well siting and volumetric calculations. However, when performing dynamic flow simulation, three-dimensional models with grid-block thicknesses much finer than vertical seismic resolution are usually required to adequately describe the heterogeneities controlling flow. Several authors have recently proposed techniques for constraining 3-D reservoir models with 2-D seismic attribute maps. Gorell and Burns et al. proposed an empirical technique where each vertical column of cells in a 3-D porosity model is linearly re-scaled to reproduce a seismic-derived average porosity map. The technique has the advantage of being straightforward to implement but the re-scaled 3-D model will not tie at deviated wells. Furthermore, the re-scaling process may distort the data histogram. Deutsch et al. introduced an heuristic procedure based on simulated annealing. They built an objective function which includes a term measuring the degree of misfit between vertical average data and average values computed from the 3-D model. Simulated annealing is used to perturb the 3-D model until the degree of misfit is reduced to a value below a user-specified tolerance. One advantage of this method is that it is possible to account for the precision of the seismic average information. P. 465^
Recent advances in data science and machine learning (ML) have brought the benefits of these technologies closer to the mainstream of petrophysics. ML systems, where decisions and self-checks are made by carefully designed algorithms, in addition to executing typical tasks such as classification and regression, offer efficient and liberating solutions to the modern petrophysicist. The outline of such a system and its application in the form of a multilevel workflow to a 59-well multifield study are presented in this paper. The main objective of the workflow is to identify outliers in bulk density and compressional slowness logs and to reconstruct them using data-driven predictive models. A secondary objective of the project is to predict shear slowness in zones where such data do not exist. The system is fully automated, designed to optimize the use of all available data, and provide uncertainty estimates. It integrates modern concepts for outlier detection, predictive classification, and regression, as well as multidimensional scaling based on inter-well similarity. Benchmarking of ML results against those created by experienced petrophysicists shows that the ML workflow can provide high-quality answers that compare favorably to those produced by human experts. A second validation exercise, that compares acoustic impedance logs computed from ML answers to actual seismic data, provides further evidence for the accuracy of the ML-generated results. The ML system supports the petrophysicist by easing the burden on repetitive and burdensome quality control tasks. The efficiency gains and time savings created can be used for enhanced effective cross-discipline integration, collaboration, and further innovation.
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