Accuracy and Relevance of Digital Rock Physics: Successes and Failures
 
Abstract
 

To quality control the absolute permeability, electrical formation factor, and elastic moduli produced by digital rock physics algorithms on 3D CT-scans of mm-sized rock fragments, we contrast these computational results to physical laboratory data and theoretical rock physics models.  We find that in many cases a mismatch between digital and physical measurement results does not mean that either of the two is flawed.  This mismatch arises from the fact that in heterogeneous natural rock, the measured effective properties of an inch-sized sample do not have to be the same as those computed on a mm-sized test.

To QC digital rock results and, most importantly, make them relevant to practical filed tasks, we revisit the concept of a trend formed by multiple pairs of datapoints (such as between porosity and permeability).  We show that such trends can be computationally derived from a very small fragment of rock.  We argue that if a trend thus produced is close to that formed by physical data, well measurements, and/or theoretical rock physics transforms, the digital rock results are correct and usable at a field scale.  Using this concept, we provide several examples that validate our computational rock physics data.

Are rock properties (porosity, permeability, electrical resistivity and elastic properties) computed in digital rock physics lab and accurate?
 
Several concerns contribute to the significance of this question:  
(a) whether the rock is imaged properly in 3D
(b) whether this 3D gray-scale image is segmented properly
(c) whether the computational procedures that compute the named properties are correct and
(d) whether the properties computed on millimeter-sized rock fragments match those measured in the physical laboratory, in the well, and/or in the field via seismic and EM techniques.

Addressing the first three questions is straightforward: the tomographic 3D images and their segmented versions can be (and have been) compared to SEM and thin section images to verify the quality of the former. Also, the computational engines can be (and have been) tested on idealized porous composites for which theoretical solutions exist. The fourth question is (arguably) posed incorrectly: because rock is heterogeneous at all scales, it is often invalid to assign a single porosity, permeability, resistivity, or an elastic constant to a sample.

Well data demonstrate that these properties can vary appreciably between two points just a foot apart. In Figure 1.1 (top) we display well-log data for the gamma-ray, porosity, and the P- and S-wave velocity versus depth in a high-porosity oil reservoir (sand). Even within this seemingly homogeneous interval, we observe porosity variation between approximately 0.25 and 0.35. The corresponding P- and S-wave wave velocity variation ranges are about 0.5 and 0.3 km/s, respectively.The velocity-porosity cross-plots showing these noticeable variations are displayed in Figure 1.1 (bottom).