A New Method for Facies Simulation Using Non-Linear Geostatistics with Directional and Order Asymmetry

In practical operational studies, facies stochastic modelling is often performed with traditional geostatistical algorithms such as Sequential Indicator Simulation or Truncated Gaussian Simulation. In this presentation, we will focus on recent improvements of geostatistical techniques used to improve geological realism, and we will stress on the key points for their use in operational context. As a basis of discussion for the workshop, we will briefly address: the use and improvements of Multiple Point Statistics; the generalization of Truncated Gaussian Simulation with efficient Pluri- Gaussian Truncation; and the Boolean models with flexible objects.

Relay ramps may considerably control fluid flow across otherwise sealing fault zones and, therefore, they are subjected to fluid flow simulation studies in relation with groundwater extraction and petroleum production. However, these studies used mainly deterministic modelling approach based on field observations. In this paper, we extend this approach by incorporating a conditional simulation technique, i.e. truncated Gaussian simulation (TGS), to provide stochastic elements in the modeling work and to improve the representation of detailed relay ramp structure. TGS attributes (facies proportions and variogram ranges of the Gaussian field) are defined based on field observations of the Delicate Arches Ramp, Utah, which is characterized by the presence of three structural sets. Groups of facies defined based on the structural sets are modelled independently using TGS, and the final model is generated by merging the TGS realizations. The relay ramp facies model is used to generate upscaled models. The upscaling procedure use petrophysical values and coarse grid used in a recent flow simulation study of the Delicate Arches Ramp deterministic model. Flow simulation results show that the role of relay ramp as conduits for fluid flow is more pronounced in models built using TGS than that in deterministic models.

Simulated annealing optimization technique was used to simulate geological models. After comparing one-point perturbation scheme with two-point swapping scheme, and the Metropolis algorithm with the greedy algorithm, an optimized combination of simulated annealing schedule is presented. The two-dimensional correlation coefficient matrix is introduced to determine a unit configuration which can represent essential features of a geological model. The proposed simulated annealing technique can be used to reproduce the characteristics of a geological model based on multipoint histogram which can be obtained by using a unit configuration. Various geological vertical cross sections and horizontal slices based on field data are used to validate this new technique. Simulated results confirm that one-point perturbation scheme with the Metropolis algorithm provides the best combination to capture the essential features of a geological model. Further, the two-dimensional correlation coefficient matrix provides a technique to choose a priori unit configuration for multipoint histogram, which captures the geological characteristics adequately.

This paper describes a workflow implemented for the geological model infilling of turbiditic channel complexes driven by lithoseismic Pseudo-VClay (PVClay) to constrain the facies modeling. The key challenge is to conciliate seismic resolution and required geological resolution to represent heterogeneities that allow an accurate prediction of fluid flows. For this purpose, facies modelling has been achieved by using two successive steps. The first one is based on a geostatistical proprietary method named Truncated Geophysical Estimation (TGE) using the PVClay attribute to guide the initial Lithofacies Associated Facies (LAF) positioning. The second step of the facies modelling sequence corresponds to a Truncated Gaussian Simulation (TGS). It distributes AF in a stochastic way within each LAF defined at the previous step. Thanks to this second step of facies modelling it becomes possible to introduce geological heterogeneities at the fine scale required by the vertical resolution of the reservoir model. The advantage of this workflow is that the geological model infilling is conditioned by seismic data and accurately ties the well information. In addition, it can be updated easily in order to integrate new well data. It is also interesting to point-out that the preliminary dynamic simulation delivered by this model allows obtaining a good match with early production data.

Geostatistical simulation aims at reproducing the variability of the real underlying phenomena. When nonlinear features or large-range connectivity is present, the traditional variogram-based simulation approaches do not provide good reproduction of those features. Connectivity of high and low values is often critical for grades in a mineral deposit. Multiple-point statistics can help to characterize these features. The use of multiple-point statistics in geostatistical simulation was proposed more than 10 years ago, on the basis of the use of training images to extract the statistics. This paper proposes the use of multiple-point statistics extracted from actual data. A method is developed to simulate continuous variables. The indicator kriging probabilities used in sequential indicator simulation are modified by probabilities extracted from multiple-point configurations. The correction is done under the assumption of conditional independence. The practical implementation of the method is illustrated with data from a porphyry copper mine.

Multiple techniques are available to construct three-dimensional reservoir models. This study uses comparative analysis to test the impact of applying four commonly used stochastic modeling techniques to capture geologic heterogeneity and fluid-flow behavior in fluvial-dominated deltaic reservoirs of complex facies architecture: (1) sequential indicator simulation; (2) object-based modeling; (3) multiple-point statistics (MPS); and (4) spectral component geologic modeling. A reference for comparison is provided by a high-resolution model of an outcrop analog that captures facies architecture at the scale of parasequences, delta lobes, and facies-association belts. A sparse, pseudosubsurface data set extracted from the reference model is used to condition models constructed using each stochastic reservoir modeling technique. Models constructed using all four algorithms fail to match the facies-association proportions of the reference model because they are conditioned to well data that sample a small, unrepresentative volume of the reservoir. Simulated sweep efficiency is determined by the degree to which the modeling algorithms reproduce two aspects of facies architecture that control sand-body connectivity: (1) the abundance, continuity, and orientation of channelized fluvial sand bodies; and (2) the lateral continuity of barriers to vertical flow associated with flooding surfaces. The MPS algorithm performs best in this regard. However, the static and dynamic performance of the models (as measured against facies-association proportions, facies architecture, and recovery factor of the reference model) is more dependent on the quality and quantity of conditioning data and on the interpreted geologic scenario(s) implicit in the models than on the choice of modeling technique.

Flow simulation studies require an accurate model of the reservoir in terms of its sedimentological architecture. Pixel-based reservoir modeling techniques are often used to model this architecture. There are, however, two problem areas with such techniques. First, several statistical parameters have to be provided whose influence on the resulting model is not readily inferable. Second, conditioning the models to relevant geological data that carry great uncertainty on their own adds to the difficulty of obtaining reliable models and assessing model reliability. The Sequential Indicator Simulation (SIS) method has been used to examine the impact of such uncertainties on the final reservoir model. The effects of varying variogram types, frequencies of lithology occurrence, and the gridblock model orientation with respect to the sedimentological trends are illustrated using different reservoir modeling studies. Results indicate, for example, that the choice of variogram type can have a significant impact on the facies model. Also, reproduction of sedimentological trends and large geometries requires careful parameter selection. By choosing the appropriate modeling strategy, sedimentological principles can be translated into the numerical model. Solutions for dealing with such issues and the geological uncertainties are presented. In conclusion, each reservoir modeling study should begin by developing a thorough quantitative sedimentological understanding of the reservoir under study, followed by detailed sensitivity analyses of relevant statistical and geological parameters.

Geological prior information is one of the ways of bringing geological realism into reservoir facies models. Models based on geologically realistic priors are more accurate and provide more robust predictions under uncertainty. Commonly geological prior information is captured from modern depositional environments or outcrops of ancient deposits. The aim of this work was to demonstrate how use of prior information improves the models of fluvial facies and reduces the uncertainty associated with the estimation of channel geometry. Geological priors are built using intelligent techniques like Artificial Neural Networks and Support Vector Regression. The data driven methods reveal the hidden relationships among the variables that form the priors and also allow handling the associated uncertainty. Furthermore, we used the intelligent prior models to predict realistic parameter combinations which may not have been observed in the available data but are still plausible and may exist in nature. The intelligent prior models were combined with multiple point statistics (MPS) simulation for a test synthetic reservoir case study. Multiple point statistics (MPS) was chosen to model channel facies because of its capability of modelling realistic geobodies and adaptability to well and seismic data. The study shows improvement in controlling simulated channel geometry and highlighting the impact on volume estimation and oil production.

Because facies are nominal variables, their modeling methods are different from the modeling methods for continuous variables. Kriging and stochastic simulation methods presented in Chaps. 16 and 17 cannot be directly used for construction of a facies model; they can be modified for facies modeling, or totally different methods are used. Although facies are often modeled before modeling petrophysical variables, modeling methods for continuous variables were presented in the earlier chapters because it is easier to understand facies modeling methods after understanding kriging and stochastic simulation for continuous variables. This chapter presents several facies modeling methods, including indicator kriging, sequential indicator simulation and its variations, object-based modeling, truncated Gaussian and plurigaussian simulations, and simulation using multipoint statistics.

The Gunsan Basin is located between the eastern Chinese coast and the Korean Peninsula. The basin originated during the Cretaceous due to tectonic activity. After several rifting events, the final rift occurred during the Oligocene. Since the Miocene, the postrift phase has been ongoing to the present day. This study focuses on the interval of the final rifting event of the Cenozoic. The Gunsan Basin remains a frontier basin for hydrocarbon exploration, with only five wells drilled between 1975 and 1991. The study area is located in the eastern sag, known as the East Subbasin, approximately 26 km from the nearest well. Typically, more than 10 wells are needed near a reservoir to predict sand bodies effectively. In this study, we employed geostatistics to generate facies models. The Sequential Indicator Simulation (SIS), one of the stochastic methods, is particularly effective for modeling facies in areas with sparse well data. The pixel-based SIS approach is using trend maps, especially when lateral information is unavailable. These trend maps, derived from the RMS (Root Mean Square) attribute, are based on amplitude and help delineate facies. During the Miocene, the paleoenvironments in the depocenter and margin were lacustrine and littoral, respectively, and the lithology was interpreted as mudstone and sandstone. The transition from littoral to lacustrine environments is attributed to thermal subsidence. Through attribute analysis, we indirectly infer the rift system and the associated facies changes.

Sedimentary facies is a key control on petrophysical properties within subsurface reservoirs and facies modelling is a critical aspect of reservoir modelling. Several modelling methods exist and selecting the best approach for a specific case is challenging and time-consuming. Outcrop analogues provide detailed information on architecture, geometry and facies connectivity that is not directly available in the subsurface. By modelling outcrop data it is possible to test and compare different modelling strategies systematically in a case where the geology is well constrained. The Eocene aged, Sant Llorenc del Munt fan-delta complex (NE Spain) is a well exposed, transgressive–regressive fan-delta. Outcrop data were used to test a variety of modelling strategies in which the density of conditioning wells, stratigraphic subdivision, modelling algorithm and trends were all varied. The results of these modelling exercises were compared against themselves and against a close-to-deterministically built Base Case reconstruction using a series of static measures including the distribution of fan-delta front reservoir facies, directional connectivity and reservoir-to-well connectivity. The results highlight the following: (a) the impact of the conditioning well density on improving the stratigraphic architecture reproduction in the different modelling approaches; (b) that surface-based modelling subdivisions including the maximum flooding surface to separate independent grids for modelling the transgressive and regressive sequence sets can be detrimental when compared to using only the top and base of the composite sequence unless additional constraints are included; (c) that an algorithm combining a linear trend and a Gaussian field is the most suitable algorithm for reproducing this type of architecture, but requires defining a 3D trend; and (d) the need for using trends to reproduce the architecture when well data are sparse. These results provide guidelines for modelling analogue fan-delta reservoirs in the subsurface.

Construction of predictive subsurface flow models involves subjective interpretation and interpolation of spatially limited data, often using imperfect modeling assumptions. Hence, the process can introduce significant uncertainty and bias in predicting the flow and transport behavior of these systems. In particular, the uncertainty in the facies distribution in complex geologic environments, such as alluvial/fluvial channels, can be consequential for forecasting the dynamic response of these systems to perturbations due to pumping and development activities. Conventional model calibration techniques that are designed to update continuous model parameters cannot be used to estimate discrete parameters from flow and pressure data. We present a distance transform approach for converting discrete facies models to continuous parameters that can be updated using continuous model calibration methods. Distance transforms are widely used in discrete image processing, where the discrete values in each pixel are replaced with their distance (i.e., a continuous variable) to the nearest boundary cell. After updating the continuous distance maps during model calibration, a back transformation is applied to retrieve the updated facies maps. To preserve large‐scale facies connectivity, truncated singular value decomposition (SVD) parametrization may be used to represent the distance maps with low‐rank parameters. A variant of the ensemble smoother, ES‐MDA is used to update the continuous parameters of the inversion (either distance maps or their SVD coefficients if used). The distance transform method addresses an important problem in facies model calibration where model updating can result in losing facies connectivity and discreteness.

This paper presents a novel methodology for inverse modeling of groundwater flow and transport problems in a Monte Carlo framework, i.e., multiple solutions to the inverse problem are generated. The methodology is based on the concept of random mixing of spatial random fields. The conditional target hydraulic transmissivity field is obtained as a linear combination of unconditional spatial random fields. The corresponding weights of the linear combination are selected such that the spatial variability of the hydraulic transmissivities as well as the actual observed transmissivity values are reproduced. The constraints related to the hydraulic head and contaminant concentration observations are nonlinear. In order to fulfill these constraints, a specific property of the presented approach is used. A connected domain of fields fulfilling all linear constraints is identified. This domain includes an infinite number of realizations, and in this domain, the head and concentration deviations are minimized using standard continuous optimization techniques. The methodology uses spatial copulas to describe the spatial dependence structure. A combination with multiple point statistics allows inversion under specific structural constraints.

Assessing paleo channel probability for offshore wind farm ground modeling - comparison of multiple-point statistics and sequential indicator simulation

Identifying oil-saturated versus water-saturated sands in shallow, unconsolidated, viscous-oil-bearing terrigenous-clastic reservoirs of Kuwait field is challenging. Field appraisal was based upon seismic, core and wireline-log data from 19 wells. Static and dynamic models incorporating all subsurface data were built to estimate oil-in-place and forecast production. Estimating and modeling fluid saturations in reservoir zones was accomplished by integrating core, dielectric-resistivity, Nuclear Magnetic Resonance (NMR) and Wireline Formation Tester (WFT) data. Wells were drilled along a northwest/southeast-trend, thus geologic and reservoir-property variability in east and west parts of the field are uncertain. Stratigraphy and lithologic properties in these Miocene-age fluvial to shallow-marine strata impart a complex 3–D fluid distribution in the field. Repeated shoreline progradations and retrogradations deposited a stratigraphic succession defined by five facies-associations (i.e., shoal, tidal flat, tidal channel, lagoon, sabkha). Five lithofacies (i.e., shale, shaly sandstone, sandstone, carbonate-cemented sandstone, evaporite) were identified from core, elemental spectroscopy logs, and X-ray diffraction (XRD) data. Facies associations and lithofacies models were built using a combination of multiple-point statistics and sequential-indicator simulation. Lithofacies distribution in the static model was constrained by the facies-association distribution; reservoir-property distribution (e.g., porosity, permeability) was conditioned by lithofacies. Discrete reservoir zones were defined to separate oil-saturated versus water-saturated sands. The volume and position of oil-bearing sands are controlled by the defined zones and permeability distribution. The oil-filling process in these viscous oil-bearing reservoirs is typically controlled by the pore throat distribution with the migrating oil taking the path of least resistance. Due to the presence of stratigraphic-flow baffles, fluid contacts vary from sand-to-sand vertically and laterally. Log data, core descriptions, ultraviolet photographs, WFT and pressure volume temperature (PVT) data guided the interpretation of lowest known oil and highest known water levels, thus reducing fluid saturation uncertainty in the field.