Digital rock modeling to quantify scale dependence of petrophysical measurements in burrowed reservoir rocks: An example using Thalassinoides

Abstract

Recent evaluations of burrow connectivity have shown that burrow morphology, abundance, and size impact the sampling scheme required for faithfully representing permeability in the laboratory. Quantifying these controls to design appropriate sampling is essential. This study illustrates a new approach using multipoint statistics modeling and applies it to Thalassinoides, to simulate a range of burrow abundances and sizes, and then interrogates the outcome to develop a statistical model that allows sampling strategies to be designed. Our workflow started with digital models that were known to have open or permeable Thalassinoides that connected one side of the model volume to another, (i.e., high permeability). We cut the model volumes into 540 digital samples with a range of burrow abundance, burrow size and sample cross section. The Thalassinoides showed no cross-sample connectivity in 173 (32%) samples; the remaining 367 (68%) showed cross-sample Thalassinoides connectivity. The data on burrow abundance, burrow size, and sample dimensions (as independent variables) and the result of samples representing Thalassinoides connectivity or not (as a dependent variable), was analyzed using logistic regression modeling. An important outcome from the logistic regression model is an equation that provides a probability of Thalassinoides connectivity across samples, given burrow abundance, burrow size, and sample dimension inputs. This equation has practical applications in determining the minimum sample cross-sections and sample lengths needed for samples to adequately represent the permeability. As examples, for samples with cross sections similar to core plugs and full diameter core, given various burrow percentages and sizes, only 37% yield burrow connectivity across any and all sample lengths. For the rest, our data on the largest connected burrow length allows for calculation of the probabilities of samples of typical lengths being representative of the burrow connectivity. Thus, researchers can assess the likelihood of their samples representing Thalassinoides connectivity given a range of burrow abundance, burrow size, sample cross section and sample length. The spreadsheet to make these calculations and lookup tables are provided as digital accessory files. The example using Thalassinoides provides proof-of-concept of a methodology that should be broadly applicable to any given burrow morphology. An algorithm and lookup table that can be modeled for each given burrow morphology with an appropriate training image.