We present this research in two parts.

1,  Evaluation of wettability based on a single pair of relative permeability curves

Craig's rules of thumb have been widely used for qualitative wettability interpretation from relative permeability curves. According to Craig's first rule, in water-wet rocks the relative permeability to water at residual oil saturation is generally less than 30%, whereas in oil-wet systems this is greater than 50%. The second rule considers a system as water-wet, if saturation at the crossover point of relative permeability curves is greater than water saturation of 50%, otherwise oil-wet. The third rule states that in a water-wet rock the value of interstitial water saturation is usually greater than 20 to 25%, whereas this is generally less than 15% (frequently less than 10%) for an oil-wet porous medium.
We investigated the validity of Craig's rules of thumb and showed that while the third rule is generally unreliable, the first rule is suitable. Moreover, we showed that the second rule needed modification. We pointed out that using 50% water saturation as a reference value in Craig's second rule is unrealistic. We defined a reference crossover saturation (RCS). According to the modified second rule, the crossover point of relative permeability curves lies to the right of RCS in water-wet rocks, whereas for oil-wet systems, the crossover point is expected to be located at the left of the RCS. We have also extended the modified second rule to wettability analysis of gas–liquid systems.


Fig. 1. A schematic representation of the concept of RCS.


Fig. 2. Schematic demonstration of relative permeability curves in two systems with different wetting conditions.

A new wettability index (named Lak wettability index) was developed based on a combination of Craig's first rule and modified second rule.


Modified Lak wettability index, also developed by us, exists which is based on the areas below water and oil relative permeability curves.



Fig. 3. Schematic demonstration of the modified Lak wettability index.

2. Converting relative permeability data to fluid flow indicators and dynamic rock typing

We have shown that rock quality assessment and rock typing in two-phase flow applications can be performed by converting relative permeability measurements into new curves called TEM (or true effective mobility). TEM is a function of relative permeability, porosity, absolute permeability and fluid viscosity, and can be determined for each fluid phase separately. Rocks with better fluid dynamics (i.e., experiencing a lower pressure drop in conducting a fluid phase) have higher TEM versus saturation curves. Rocks with lower TEM versus saturation curves resemble low quality systems.


Also, TEM-function can be used for averaging relative permeability curves.


A high-quality reservoir rock is expected to be associated with a high rate of hydrocarbon recovery and high recoverable hydrocarbon saturation. By accounting for these two factors, a new approach called dynamic reservoir quality index (DRQI) was proposed. A modified true effective mobility (TEM) function was developed representing displacement rate of oil by an injected fluid (e.g., water or CO2). DRQI was defined as the area under modified TEM curve of oil and includes the well-known reservoir quality index (RQI) as its special case.



Fig. 4. Modified oil TEM against movable oil saturation. The area below the curve represents the DRQI.


• Abouzar Mirzaei-Paiaman, “New methods for qualitative and quantitative determination of wettability from relative permeability curves: Revisiting Craig’s rules of thumb and introducing Lak wettability index”, Fuel, 288, 2021, 119623,
• Abouzar Mirzaei-Paiaman, et al, “A new approach to measure wettability by relative permeability measurements”, Journal of Petroleum Science and Engineering, 208, Part B, 2022, 109191, 
• Abouzar Mirzaei-Paiaman, et al, “Wettability of Carbonate Reservoir Rocks: A Comparative Analysis”, Appl. Sci. 2022, 12(1), 131; 
• Abouzar Mirzaei-Paiaman, “Analysis of the bounded and unbounded forms of USBM wettability index”, Energy Geoscience, 3, 1, 2022, 94-102, 
• Abouzar Mirzaei-Paiaman, et al. “New technique of True Effective Mobility (TEM-Function) in dynamic rock typing: Reduction of uncertainties in relative permeability data for reservoir simulation”, Journal of Petroleum Science and Engineering, 179, 2019, 210-227,
.• Abouzar Mirzaei-Paiaman, et al. “A note on dynamic rock typing and TEM-function for grouping, averaging and assigning relative permeability data to reservoir simulation models”, Journal of Natural Gas Science and Engineering, 87, 2021, 103789, 
• Abouzar Mirzaei-Paiaman, et al. “A new method for characterizing dynamic reservoir quality: Implications for quality maps in reservoir simulation and rock type classification”, Journal of Petroleum Science and Engineering, 218, 2022, 111049, 
• Abouzar Mirzaei-Paiaman, et al., “A new approach in petrophysical rock typing”, Journal of Petroleum Science and Engineering, 166, 2018, 445-464, 
• Abouzar Mirzaei-Paiaman, et al. “Identifying two-phase flow rock types in CO2-brine systems using TEM-function”, Journal of Petroleum Science and Engineering, 205, 2021, 108818, 
• Abouzar Mirzaei-Paiaman, et al. “Investigating dynamic rock quality in two-phase flow systems using TEM-function: A comparative study of different rock typing indices”, Petroleum Research, 6, 1, 2021, 16-25, 
• Abouzar Mirzaei-Paiaman, et al. “A new framework for selection of representative samples for special core analysis”, Petroleum Research, 5, 3, 2020, 210-226,