Thursday, November 1, 2018

Inversion for Reservoir Characterization

Fundamental to reservoir characterization is assigning physical property values everywhere within the reservoir volume. The challenge of using all available data to choose the best assignment is being addressed by a group of scientist. Available data could include seismic data, log data, well test results, knowledge of the of the statistical distributions of the sizes and orientations of sedimentary bodies, and even spesific information about reservoir geometry. 

To incorporate all these diverse sources of information, the scientists use an inversion method that begins by considering all possible assignments. Each assignment is represented by a single point in a multidimensional space that has as many dimensions as there are cells in the reservoir model. In assigning acoustic impedance in a reservoir model comprising 10 x 10 x 10 discrete cell, for example, each assignment would be represented by a unique point in a 1000 dimensional space. 

 The available data are then used to determine which of these points are acceptable. This is achieved by representing each available data set -3D surface seismic data, well data, or whatever -by a cloud of points corresponding to assignments that fit that particular data set. Finding an acceptable assignment then reduces to finding a point that lies at the intersection of all such clouds of points.

As the solution is always nonunique ( more than one assignment satifies all the available information), this intersection set will not be a single point but have some volume in the multidimensional space. A procedure to choose a single, best assignment is therefore required. The current method starts with an initial guess and then modifies it as little as possible until the intersection set is reached.

A synthetic example illustrates the method. First, a reservoir model is constructed 21 x 21 horizontal cells and 201 vertical cells, with an acoustic impedance value assigned to each cell. This synthetic model is equivalent to a volume of about 1 km x 1 km horizontally and 100 milliseconds. From this are generated two data sets that would be measured if the reservoir were real: first, a log of acoustic impedance in a well through the center of the model; second, the surface seismic response, which displays a lower spatial resolution than the original model. 

The challenge is to reconstruct the original acoustic impedance model using the log and seismic data only. A reasonable starting model can be obtained from a simple extrapolation of the well log data. This clearly fails to reproduce structural variations away from the well that appear in the original model. However, modifications to this first guess using in addition the surface seismic data produces a reconstruction that is much closer. 

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