Optimising production from heterogeneous and anisotropic reservoirs challenges the modern hydrocarbon industry because such reservoirs exhibit extreme inter-well variability making them very hard to model. Reasonable reservoir models can be obtained using modern geostatistical techniques, but all of them rely on significant variability in the reservoir only occurring at a scale at or larger than the inter-well spacing. In this paper we take a different, generic approach. We have developed a method for constructing realistic synthetic heterogeneous and anisotropic reservoirs which can be made to represent the reservoir under test. The main physical properties of these synthetic reservoirs are distributed fractally. The models are fully controlled and reproducible and can be extended to model multiple facies reservoir types. This paper shows how the models can be constructed and how they have been tested. Reservoir simulation results of a number of generated 3-D heterogeneous and anisotropic models show that heterogeneity, in terms of only the geometric distribution of reservoir properties, has a little effect on oil production from high and moderate quality reservoirs. However, if the effect of heterogeneity on capillary pressure is taken into account, the effect becomes striking, where varying the heterogeneity of reservoirs properties can lead to a 70 % change in the predicted oil production rate and a significant early shift of water breakthrough time. Hence, it is the heterogeneity consequences that are really substantial if not taken into account. These are very significant uncertainties for a hydrocarbon company if the heterogeneity of their reservoir is not well defined.

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Synthetic Fractal Modelling of Heterogeneous and Anisotropic Reservoirs for Use in Simulation Studies: Implications on Their Hydrocarbon Recovery Prediction

Establishment of sequence limits in a stratigraphic column (i.e., related to depositional environments) re-presents in particular a great contribution to the analysis and characterization of oil reservoirs. In this context, we applied the continuous as well as the discrete wavelet transforms, to data from geophysical well logs from an oil producing area in the Gulf of Mexico, in order to bring about periodicities or cycles and correlate them with lithologic and stratigraphic characteristics of the associated environments. A multiscale analysis of geophysical well loggings (gamma ray, resistivity, and spontaneous potential) was done based in the wavelet transform. In particular the wavelet coefficients were determined. Analysis of the obtained spectrograms-scalograms enabled to establish characteristic pseudowavelengths for each scale (frequencies). Pseudo wavelengths were associated with possible periodicities in deposition (Milankovitch’s climatic cycles) of the study area. This case history shows that the wavelet analysis is a helpful complementary technique for reservoir characterization, specifically in the location of stratigraphic sequences and associated facies.

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Multi-scale analysis of well-logging data in petrophysical and stratigraphic correlation

Multi-scale analysis of well-logging data in petrophysical and stratigraphic correlation ; Multi-scale analysis of well-logging data in petrophysical and stratigraphic correlation

It has been observed that the sources of geophysical anomalies, such as density, susceptibility, conductivity, reflectivity, etc. may be conveniently defined according to a scaling/fractal distribution. Acquisition, processing and interpretation (collectively known as API) are the three main steps in any geophysical investigation. The proper design of acquisition of data can enhance the signal to noise ratio of geophysical response. Fractal theory has been applied and found to be worthwhile in deciding a geophysical survey network. Similarly, the second step, geophysical data processing for interpolation of missing data is key to reduce spurious anomaly due to aliased-interpolated data, and fractal or multi-fractal concepts have been applied to improve data processing significantly. Finally, interpretation is the main step which depends on the nature of the source. This lead to the development of new interpretation methods such as scaling spectral method and modified centroid method to accommodate scaling/fractal distribution of source for scaling geology for improved results. In the present paper, in-depth review of the application of fractal/multi-fractal approach in geophysical API for better geophysical understanding, is presented. Also, the advancement in geophysical API for filling the gaps in our understanding of sub-surface source characterization with recent examples in seismology and heat flow is highlighted, which can be further helpful in conducting future research of scaling geology.

Fractal Theory and its Implication for Acquisition, Processing and Interpretation (API) of Geophysical Investigation: A Review

Facies Heterogeneities and 3d Porosity Modelling in AN Oligocene (upper Chattian) Carbonate Ramp, Salento Peninsula, Southern Italy

. The sandy-clayey hydrocarbon reservoirs of the Upper Paleocene and Lower Eocene located to the north of Veracruz State, Mexico, present highly complex geological and petrophysical characteristics. These reservoirs, which consist of sandstone and shale bodies within a depth interval ranging from 500 to 2000 m, were characterized statistically by means of fractal modeling and geostatistical tools. For 14 wells within an area of study of approximately 6 km2, various geophysical well logs were initially edited and further analyzed to establish a correlation between logs and core data. The fractal modeling based on the R/S (rescaled range) methodology and the interpolation method by successive random additions were used to generate pseudo-well logs between observed wells. The application of geostatistical tools, sequential Gaussian simulation and exponential model variograms contributed to estimate the spatial distribution of petrophysical properties such as effective porosity (PHIE), permeability (K) and shale volume (VSH). From the analysis and correlation of the information generated in the present study, it can be said, from a general point of view, that the results not only are correlated with already reported information but also provide significant characterization elements that would be hardly obtained by means of conventional techniques.

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Distribution of petrophysical properties for sandy-clayey reservoirs by fractal interpolation

Identifying Reservoir Fluids In Sandy Clay And Carbonate Reservoir Using The Wavelet Transform With Well Logs

Multiresolution analysis, based on the discrete wavelet transform, is here incorporated in seismic signal processing. This analysis technique enables decomposing a seismic signal, in different frequency bands, and thus to analyze the information contained in these frequency bands. Multiresolution analysis allows visualizing in the time domain the information contained in the frequency bands. Wavelets commonly used in the discrete wavelet transform present an overlay between scales, this constitutes an aliasing effect that gives rise to spurious effects. Vaidyanathan wavelet minimizes the overlay between scales. We applied this wavelet to synthetic data and to a 3D seismic cube. Accordingly, spurious effects from aliasing generated by overlay between scales are minimized with the Vaidyanathan wavelet.

http://www.scielo.org.mx/pdf/geoint/v55n3/0016-7169-geoint-55-03-189.pdf

David Ernesto Rivera-Recillas

Papers

Distribution of petrophysical properties for sandy-clayey reservoirs by fractal interpolation

Identifying Reservoir Fluids In Sandy Clay And Carbonate Reservoir Using The Wavelet Transform With Well Logs

Eliminated aliasing effect on wavelet transform based multiresolution analysis

Shallow structure of the Chalco and Xochimilco sub-basins (southern Mexico basin) based on wave propagation modelling and seismic data