Classifications

• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
  • G01V11/00—Prospecting or detecting by methods combining techniques covered by two or more of main groups G01V1/00 - G01V9/00
• • G—PHYSICS
  • G01—MEASURING; TESTING
  • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
  • G01V2210/00—Details of seismic processing or analysis
  • G01V2210/60—Analysis
  • G01V2210/66—Subsurface modeling
  • G01V2210/665—Subsurface modeling using geostatistical modeling

Definitions

• the present invention relates generally to characterization of spatial data, and more particularly to use of lacunarity analysis in characterization of geological data.
• An aspect of an embodiment of the present invention includes a computer implemented method for analysis of data representative of subsurface properties of a subsurface region.
• the method includes transforming the data representative of subsurface properties of the subsurface region into transformed data in accordance with a selected criterion.
• a three dimensional window geometry to be applied to the transformed data is selected, based, at least in part, on expected feature sizes present, data sampling density and a size of the subsurface region.
• a plurality of values for a three dimensional lacunarity statistic are calculated by applying the selected three dimensional window geometry to randomly selected regions of the subsurface region, and correlating the calculated values to the subsurface properties of the subsurface region.
• Figure 1 is a flowchart illustrating a method or workflow in accordance with an embodiment of the present invention
• Figure 2a-2d illustrate four possible moving windows that may be used to evaluate lacunarity in a data set in accordance with embodiments of the present invention
• Figure 3 is an example of a three dimensional reservoir heterogeneity architecture that may be evaluated using lacunarity characterizations in accordance with embodiments of the present invention
• Figure 4 is a log- log plot of a lacunarity statistic for the reservoir heterogeneity architecture using an isotropic window, using a window longer along a dip direction and a window longer along a strike direction;
• Figure 5 is a log- log plot of a lacunarity statistic for the reservoir heterogeneity architecture, sampled varying numbers of times indicating the increasing solution accuracy with increasing number of samples;
• Figure 6 is a conceptual illustration of a region of interest showing an intermediate region and a moving window within the intermediate region;
• Figure 7 is a log-log plot illustrating a classification system for lacunarity statistics.
• Figure 8 is a schematic illustration of an embodiment of a system for performing methods in accordance with embodiments of the present invention.
• Figure 1 schematically illustrates a workflow for evaluation of lacunarity of a geological region of interest.
• the workflow accepts as inputs data representative of physical characteristics of the region of interest.
• subsurface properties of interest may include, for example, geophysical, geologic, stratigraphic, lithologic and reservoir properties.
• Particular data types may include well data 102, seismic data 104 and analog data 106, and combinations thereof.
• other data types relating to subsurface properties may be analyzed using similar techniques.
• the data under examination is transformed 108 in order to emphasize the structures of interest.
• this may mean that a threshold is applied in order to transform quantitative data into binary data.
• a binary transform may include, for example, a static threshold, or may allow for a fuzzy or space or time varying threshold.
• the data may be transformed to a discrete or continuous distribution with a spatial and/or temporal filter that emphasizes specific spatial features, or features on a specific scale.
• the threshold may be selected to account for this by allowing for increasing threshold values as depth increases.
• the property may be transformed to a continuous distribution such as a parametric or nonparametric reference distribution or a discrete distribution that is selected in order to emphasize specific data value ranges, manage outliers or other selected results.
• the transformation step may be omitted entirely and the data analyzed directly.
• a visualization of the transformed data may be generated 110, for example on a display of a computer system, for review by an operator.
• This visualization provides a cross-check on the data, to ensure that the transformation has not so altered the data that analysis will not provide accurate or useful results.
• the operator may choose to use a different transformation on the original data before proceeding with the lacunarity analysis.
• This step may also be aided or conducted independently in an automated manner by an optimization engine with optimization criteria that refer to statistics of the transformed data that may indicate the discrimination of heterogeneity architecture not limited to global cumulative density functions, covariance functions, and transition probabilities.
• a window geometry where geometry includes range of orientations, range of sizes, and shape of windows, is selected 112 for use in the lacunarity analysis.
• the geometry may be selected based on one or more factors including an expectation of feature sizes in the region of interest, resolution of the available data, and known or predicted anisotropies of the structures in the regions of interest.
• the shape of the window may be selected based on the expected feature shape.
• Figure 2a illustrates a cuboid isotropic window that may be used for determining lacunarity in accordance with the prior art.
• Figures 2b-2d illustrate a variety of examples of anisotropic moving windows with variable orientation which may be used to evaluate lacunarity for the spatial data in embodiments of the present invention.
• Use of such variably oriented anisotropic windows may allow for characterization of spatial phenomena that themselves have anisotropies.
• various directional lacunarity measurements may be made by altering the orientation. Once such lacunarities have been determined, they may be interpolated to characterize lacunarity over all directions and distance scales (see Figure 2).
• the use of flexible size, orientation and geometry may allow for the ability to iteratively evaluate lacunarity using changing moving window parameters to maximize the information content (as measured by smoothness and uniqueness of the experimental results) of the statistic.
• the three dimensional lacunarity is calculated 1 14 using a moving window or "gliding box" algorithm.
• a box of length r x having height equal to r 2 and width of r 3 is placed at the origin of the data set.
• the number of occupied sites (window mass, s) within the window is determined, then the window is moved along the set and the mass is measured again. This process is repeated over the set, producing a frequency distribution of window masses n(s, n, r 2 , r 3 ). The process is then iterated over a number of window sizes.
• the moving window may be similar to that shown in Figure 2b, and in each iteration the size of the box is changed, but the ratio between r ⁇ and r 2 is kept constant.
• Figures 2c and 2d illustrate alternate window geometries, specifically a spheroid isotropic window and a spheroid anisotropic window respectively.
• the results of the calculated lacunarity are interpreted 116 and an analytical model for all, or some, distances and/or directions is created.
• such models may include, for example, a predictive model to extrapolate or interpolate the data into unobservable scales 118, a classification model for identification of analogs 120, a spatial statistic for geostatistical models 122, and/or a spatial statistic for data-model and model-model comparisons 124.
• the calculated values may be correlated to subsurface parameters or properties including, but not limited to: net-to-gross, univariate and spatial distributions of porosity, permeability, shale barriers, reservoir elements and associated stratigraphic geometries and lithologies.
• an additional step may be included to check for local changes in lacunarity 130.
• identified local changes may be used to identify and/or classify 132 local changes in heterogeneity in the region of interest.
• the transform and window parameters may be adjusted, either according to a predetermined schedule, or in response to operator input based on analysis of the models, and the process iterated 134 using the adjusted parameters.
• Figure 4 is a log-log plot illustrating results for three different approaches to lacunarity analysis.
• an isotropic window was used, resulting in the topmost line.
• a rectangular cuboid anisotropic window (as illustrated in Figure 2b) having a length to width ratio of 5:2 along a dip direction was used, resulting in the middle line.
• a rectangular cuboid anisotropic window having a length to width ratio of 5:2 along a strike direction was used, resulting in the lowermost line.
• the lacunarity statistic for the strike oriented window shows relatively more clustering than do the other two lines.
• moving window statistics rely on the exhaustive sampling of the spatial heterogeneity by visiting all possible moving window locations. In large models, this leads to very high numbers of calculations, especially where a large number of window orientations, geometries and sizes are used.
• the inventors have determined that a reasonable approximation to lacunarity may be calculated by randomly sampling a small subset of possible moving window locations. For each sampled location, the lacunarity statistics are calculated by applying the selected three dimensional window geometry with a range of sizes and orientations. For each window configuration the results from the limited number of randomly sampled locations are applied as an approximation for the more computationally expensive exhaustive gliding box sampling scheme. This results in the lacunarity measure for a single window size and orientation.
• a 1,000,000 cell model with dimensions 100 x 100 x 100 cells would have 753,571 possible window positions for a 10 x 10 x 10 window size.
• the lacunarity statistic appears to show stability by 5000 samples. While not illustrated, the inventors have found that as few as 1,000 random windows can provide stable statistics, resulting in an increase in computational efficiency of over 750 times over the worst case (assuming an inefficient gliding box method).
• stratified sampling methods may be applied. That is, a set of sub-regions may be defined, and some number of the random samples are taken from each sub-region. This approach may prevent a random selection of a large run of samples within a particular, non-representative portion of the region of interest, as might occur as a result of a truly random selection.
• local lacunarity statistics may be used to characterize trends and changes in heterogeneity over an exploration or reservoir area of interest 140, as illustrated in Figure 6.
• a local lacunarity measure may be generated by calculation of lacunarity over an intermediate window 142, having a size smaller than the entire model and larger than the moving window 146. Once calculated, the local lacunarity is assigned to the centroid 144 of the intermediate window.
• the intermediate window size should be chosen to be large enough that there is a reasonable number of possible moving window positions for statistical inference of local lacunarity and not so large as to smooth out local features.
• This method may be directly applied to detect, segment and/or characterize features and/or to assign reservoir potential in any dataset (e.g., well logs or seismic information).
• this local lacunarity measure may be applied as a transform to emphasis specific heterogeneity features as discussed above.
• lacunarity measures may be parameterized or summarized to aid in classification and prediction.
• Figure 7 is a log- log plot illustrating three typical forms of experimental lacunarity and their respective interpretations.
• the downward concave curve 150 at the top of the oval represents lacunarity statistics for a clustered data set.
• the upward concave curve 152 at the bottom represents a data set that has fractal characteristics.
• the middle straight line 154 represents lacunarity of a random data set.
• a lacunarity index may be defined that summarizes the experimentally determined lacunarity statistics in a single value that spans from fractal to random to clustered form based on the proximity of the experimental results to each form. This index is represented in Figure 7 by the line 156 extending perpendicular to the line representing random statistics 154.
• This approach provides a simple statistic for summarizing results, visualizing local lacunarity and for use in model comparison.
• the index value may be assigned to the centroid of each local region, allowing for simple indication of variation within the large region without requiring separate graphical depictions of lacunarity curves for each region.
• a full three dimensional model of lacunarity may be generated that allows for characterization of lacunarity over all directions and distances.
• Such a model may be based on calculation of experimental lacunarity in primary directions of continuity (horizontal major, minor and vertical) then, based on the calculated values, interpolation and extrapolation for all other possible directions.
• numerical analog models are used to define realistic lacunarity forms over all possible directions and distances. These forms are then used to constrain interpolation and extrapolation of lacunarity measures to ensure plausible or geometrically consistent results and to define associated uncertainty.
• the full 3D model of lacunarity may be applied to generate lacunarity -based stochastic realizations of heterogeneity or to constrain / post-process traditional geostatistical methods for improved reservoir architecture prediction and modeling.
• a system 200 for performing the method is schematically illustrated in Figure 8.
• a system includes a data storage device or memory 202.
• the stored data may be made available to a processor 204, such as a programmable general purpose computer.
• the processor 204 may include interface components such as a display 206 and a graphical user interface 208.
• the graphical user interface may be used both to display data and processed data products and to allow the user to select among options for implementing aspects of the method.
• Data may be transferred to the system 200 via a bus 210 either directly from a data acquisition device, or from an intermediate storage or processing facility (not shown).

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• 2009
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