# Wettability of Carbonate Reservoir Rocks:
## 2 Wettability Measurement Methods  
The Amott method [33] evaluates the impact of wettability based on the microscopic displacement efficiency. The Amott oil index is given by  
\[I_{\text{O}}=\frac{V_{\text{t}\text{w}\text{i}}}{V_{\text{t}\text{w}}} \tag{1}\]  
where \(V_{\text{t}\text{w}\text{i}}\) is the volume of water displaced by free imbibition of oil and \(V_{\text{t}\text{w}}\) represents the total volume of water displaced by free and forced imbibitions of oil. The Amott water index is expressed as:  
\[I_{\text{w}}=\frac{V_{\text{o}\text{i}}}{V_{\text{o}\text{t}}} \tag{2}\]  
where \(V_{\text{o}\text{i}\text{i}}\) is the volume of oil displaced by spontaneous imbibition of water and \(V_{\text{o}\text{t}}\) denotes the total volume of oil displaced by spontaneous and/or forced imbibition of water. The Amott indices, \(I_{o}\) and \(I_{\text{t}\text{w}}\), range from 0 to 1. \(I_{o}\) and \(I_{\text{t}\text{t}\text{v}}\) values near 1 represent strongly oil- and strongly water-wet systems, respectively. The difference between \(I_{\text{w}}\) and \(I_{o}\) is known as the Amott-Harvey wettability index [3; 32; 33; 34; 35]:  
\[I_{AH}=I_{\text{w}}-I_{o} \tag{3}\]  
The \(I_{AH}\) index varies from \(-1\) for strongly oil-wet to 1 for strongly water-wet cores. Systems with \(I_{AH}\) values between \(-0.3\) and \(+0.3\) are commonly considered intermediate-wet. [PERSON] et al. [36] proposed the USBM method to characterize the wettability of rocks based on the areas under forced displacement capillary pressure curves. The USBM index is given by  
\[I_{\text{U}\text{SBM}}=\log\biggl{(}\frac{A_{1}}{A_{2}}\biggr{)} \tag{4}\]  
where \(A_{1}\) and \(A_{2}\) are the areas under the oil and water drive capillary pressure curves, respectively. The USBM index theoretically varies from \(-\infty\) to \(+\infty\). Usually, the USBM is mistakenly assumed to vary over the range of \(-1\) to 1 and compared with other indices. [PERSON] [66] showed that in practice the lower and upper bounds of this index are not fully known. As a result, comparing USBM with other indices may cause erroneous interpretations due to dissimilar ranges of variation (other indices vary in the range of \(-1\) to 1). [PERSON] [66] highlighted the bounded form of the USBM index denoted as USBM\({}^{*}\), which varies between \(-1\) (strongly oil-wet systems) and 1 (strongly water-wet systems), and suggested that it should replace the traditional form of the USBM index. \[I_{\text{U}\text{SBM}*}=\frac{A_{1}-A_{2}}{A_{1}+A_{2}} \tag{5}\]  
[PERSON] [38] introduced three rules of thumb based on relative permeability curves for the qualitative evaluation of wettability. In his approach, relative permeability is defined as the effective permeability of a fluid divided by oil permeability measured at interstitial water saturation. According to [PERSON]'s first rule, water relative permeability at residual oil saturation is generally less than 0.3 in water-wet systems, whereas its value is greater than 0.5 in oil-wet porous media. The second rule views a rock as water-wet, if water saturation at the intersection point of relative permeability curves is greater than 50%, otherwise oil-wet. According to the third rule in a water-wet system the value of interstitial water saturation is usually greater than 20 to 25% pore volume, whereas this is generally less than 15% pore volume (frequently less than 10%) for an oil-wet rock. [PERSON] et al. [39] presented another qualitative method to determine wettability from relative permeability curves, based on the concept of fractional flow Equation (6), called the normalized water fractional flow curve. \[f_{w}=\frac{q_{w}}{q_{t}}=\frac{q_{w}}{q_{w}+q_{o}}=\frac{1}{1+\frac{\mu_{w}E_{w }}{\mu_{w}E_{w}}} \tag{6}\]  
where \(q_{w}\) is the water flow rate, \(q_{o}\) is the oil flow rate, and \(q_{t}\) is the total flow rate, \(\mu_{w}\) is the water viscosity, \(\mu_{o}\) is the oil viscosity, \(k_{ro}\) is the oil relative permeability, and \(k_{rw}\) is the water relative permeability. [PERSON] et al.