Linking Acoustic, Electrical, and Hydraulic Tortuosity to Predict Permeability and Formation Factor

Abstract

Different studies have attempted to relate Acoustic velocities, Permeability, and Archie Cementation factor to envisage petrophysical properties. The macro-micro pore properties and mineralogy are known to influence hydraulic flow, electrical flow, and acoustic wave travel. Different grain size, porosity, pore types, and distributions generate the flow path's tortuosity for these independent flow regimes, affecting related measurements and parameters. The present study attempts to integrate the tortuosity concept to achieve practical solutions for Permeability and Archie's electrical parameter. The present work reviews the current understanding of hydraulic and electrical tortuosity. The study then attempts to define acoustic tortuosity on generalized principles. It tries to understand the conceptual interdependence of different tortuosity and studies its variability on other petrophysical properties. The study leverages the published six hundred core measurements on synthetic samples, clean sand, shaly sand, clean carbonates, and shaly carbonates selected from different reservoirs. The analysis of this database establishes the plausible correlative link of electrical, acoustic, and hydraulic tortuosity with porosity, permeability, and formation factor. The extensive and varied dataset helps explain the parametric variability and establish practical relations that are key in predicting permeability and FF. It is concluded that the dry frame acoustic tortuosity defines a path length complementary to the electrical or hydraulic path. An increasing acoustic tortuosity is thus closely related to decreasing electric and hydraulic tortuosity. The shear tortuosity is found to have a useful relationship with permeability, both for clastics and carbonates, showing dependence on flow zone indicator and mineralogy. Electrical and hydraulic tortuosity are seen to be interrelated through power laws in clastics. It is noted that the electrical tortuosity computed from path length simulation can be much less than the tortuosity computed from the formation factor. The electrical tortuosity and mean grain size are closely linked through power functions. The permeability can be computed through electrical tortuosity in clean and shaly sands using its relation with grain size and hydraulic tortuosity. Using the percolation model in clastic formation, the cementation exponent is found to vary from 1.57 (unconsolidated sand) and 1.58 (clean sand) to 1.88 (shaly sand). In carbonates, the cementation exponent varies from 1.65 to 3.0 and is a function of micro-macro pore distribution, pore size, and permeability. The study provides a fresh tool for petrophysical evaluation and reservoir characterization. It proposes novel solutions for estimating electrical properties and permeability using acoustic velocities and vice-versa in clastics and carbonates.