Dual Porosity Effective Medium and Velocity Deviation Modeling for Quantitative Evaluation of Microporosity and Permeability in Micritic Carbonate
Authors: Saxena Vimal 
Published: November 2024

Abstract
Understanding the intricacies of carbonate pore space, particularly microporosity, is crucial for quantitative reservoir characterization. Acoustic velocities are known to be strongly controlled by pore geometry alongside stress and porosity. The velocity behavior is extensively studied in carbonates exhibiting inter-crystalline microporosity, where digital image analysis is utilized to distinguish and measure both macro and micropores. In rock physics, complex pore systems are often conceptualized using varied pore aspect ratios, highlighting the need for acoustic models to quantify bimodal porosity distributions independently of image analysis. Such modeling has significant application for permeability evaluation in micritic carbonates.
An extensive study on rock physics properties is conducted using a substantial database of clean limestone core samples from global reservoirs, with microporosities ranging from 0-30%. The differential effective medium (DEM) approach models the velocities and determines the effective pore aspect ratio (EPAR). Analysis reveals that pores primarily exhibit microporosity below a specific EPAR threshold, whereas pores above a certain EPAR are predominantly macroporous. Porosities within intermediate EPAR display a blend of micro and macro characteristics. Utilizing these thresholds, a Dual-DEM workflow is devised to quantify macro/microporosity from velocities iteratively. The study also notes that the fractional deviation from time-average velocity (termed PFD) exhibits a significant dependency on porosity, which aligns closely with variations in EPAR. This correlation is utilized to establish a generalized regression trend that delineates the micritic porosity domain, above which porosity is considered macroporous. Integrating Dual-DEM and PFD methodologies enables the effective segregation of porosity into micro and macro categories, paving the way for permeability prediction.
The study integrates data from the Middle East, Europe, Asia, and Australia, examining EPAR as a key discriminator among porosity types. EPAR ranges from 0.05 to 0.2, with values below 0.09 typically indicating no macropores and values above 0.6 showing scant microporosity. An EPAR between 0.09-0.6 indicates a mix of macro-microporosity. Utilizing a dual-porosity DEM workflow, observed velocities are modeled, and macro/microporosity components are quantified. Ultrasonic dry velocity measurements are employed to mitigate dispersion effects. The PFD varies from 0-0.8 and has a strong power relationship with porosity that moves with EPAR, defining a microporosity PFD trend. Porosities above this trend are quantified as macroporosity. The Dual-DEM and PFD models are validated through microporosity evaluation by digital image analysis, showing predictions are within 5% accuracy for microporosity levels of 5-30%. Additionally, a Timur-Coats permeability model is employed to estimate permeability from the modeled micro-macro porosities, and core measurements provide robust validation of the permeability evaluations.