A Model to Correlate Permeability With Efficient Porosity and Irreducible Water Saturation

Abstract

This paper introduces a new permeability estimation method using the equivalent rock element model which consists of two pore components, one parallel and the other perpendicular to the potential gradient. Both formation resistivity factor and permeability are related to porosity and pore structure, but permeability also depends on pore scale and internal specific pore area. In water wet rocks, irreducible water saturation is a parameter closely related to pore size or scale and internal specific area. Irreducible water occupies space in both parallel and perpendicular pore components and hinders fluid passage. The relative volume occupied in each component varies with many factors such as pore scale and interconnection, fluid properties, mineralogy and wetting characteristics of the mineral/fluid system. This non-uniform occupancy is approximated by a simple power function. An efficient flow porosity is defined by modifying efficient electrical porosity using irreducible water saturation to account for scale and specific pore area. The correlation between efficient flow porosity and permeability is much greater than those in many of the commonly used methods. This method has been applied to several sets of cores from different parts of the world. Better correlations between measured and estimated permeability have been obtained in all datasets compared with other published approaches, such as porosity versus logarithm of permeability, Kozeny-Carman, Wyllie-Rose, and Timur methods. Introduction Permeability is one of the most critical reservoir properties and is probably one of the most difficult to accurately obtain for reservoir description. Permeability can be directly measured in core analysis or computed from well tests. Core analysis measures properties on a scale of centimeters. Well tests cover an area orders of magnitude larger, but its vertical resolution is much lower than desired. A possible linkage between core and well test analyses is to estimate permeability from properties measurable by well logs. For decades, many efforts have been made to estimate permeability using indirect measurements. Some follow statistical approaches1,2 such as neural networks to find correlations between permeability and various measurements. Others attempt to relate permeability with different properties through a physical model.3 These two approaches are sometimes integrated.4,5 Kozeny6 and Carman7 related permeability with porosity and surface area of grains exposed to fluid flow. They proposed a simple relationship that states permeability is directly proportional to the cube of porosity and inversely proportional to the square of pore surface area per unit volume of rock. For randomly packed spheres, permeability is estimated as:Equation 1 where k is permeability; f is porosity; and Ag is surface area of grains exposed to fluid flow per unit volume of solid material. The specific surface area is difficult to measure directly by conventional methods and is often determined from core sample analysis. Mavko and Nur8 suggested that Kozeny-Carman equation needs to be modified for porosity below percolation threshold. Wyllie and Rose9 proposed a modification to the Carman-Kozeny equation and substituted irreducible water saturation for specific surface area. They conjectured that grain surface area is approximately related to irreducible water saturation, Swir. Their work could be expressed as:Equation 2 where B is a coefficient related to hydrocarbon type and gravity; B' is a correction factor for data fitting. A more generalized Wyllie-Rose relationship is sometimes written as:Equation 3 where P, Q, and R are tuning parameters to be calibrated from the fit to core measurements.

Integrating seismic and log data for improved petroleum reservoir properties estimation using non-linear feature-selection based hybrid computational intelligence models

“…Some of the popular correlations are based on the Darcy's equation that considers the fluid properties namely flow rate, viscosity, crosssectional area and pressure difference (Shang et al, 2003) and the Kozeny-Carman equation that considers other properties such as the shape factor, tortuosity and the surface area per unit grain volume (Carman, 1937;Kozeny, 1927). From the latter, several extensions were proposed.…”

Quantitative Prediction Model for the Water–Oil Relative Permeability Curve and Its Application in Reservoir Numerical Simulation. Part 1: Modeling

“…There are three most widely used models in well logging: Tixier model, Timur model, and Coates model. 22,23 These models adopt the following equations:…”

Mesoscopic approach to fluid-solid interaction: Apparent liquid slippage and its effect on permeability estimation

“…The irreducible water saturation formed when water molecules are adsorbed on solid surfaces is difficult to be mobilized at a lower driving pressure, and its amount is a function of the driving pressure gradient [43]. The improved permeability estimation methods, such as the equivalent rock element model [44], the model for predicting petrophysical properties [45], and the fractal geometry theory [46,47], considered the irreducible water saturation. The adsorbed water layer may account for the following phenomena: (1) the pre-Darcy effect [48][49][50], in which the Darcy flux increases nonlinearly (more than proportionally) with the pressure gradient, and (2) threshold pressure gradient [51][52][53], below which the fluid does not flow.…”

“…Differently from phenomenological investigations of liquid slippage [2][3][4][5][6][7][37][38][39][40][41][42][43][44][45][46][47], the hydrodynamic force measurements using the surface force apparatus [8][9][10] and the numerical simulations based on MD simulation [11][12][13] and mesoscopic LBM approach [14][15][16] considered the physical origin of liquid slippage: the F-S interaction force. Compared with MD simulation based on the Lennard-Jones interactions, the mesoscopic LBM approach is advantageous in describing the mechanism of molecular interactions and allowing the simulation of microfluidic flow experiments.…”