Gas-Lift Troubleshooting

Fluid Saturation of Reservoir Rocks

The concept of fluid saturation can be explained through a glass filled with different fluids (Figure 5.1). Figure 5.1a shows a glass filled entirely with water, meaning that the entire pore volume (glass volume) is occupied by water and thus the water saturation is 100%. Fluid saturation is the volume of a particular fluid in a rock sample divided by the pore volume. In Figure 5.1b, an identical glass is occupied by both water and oil. Here, the water saturation cannot be 100% as the oil is sharing some space with the water. Finally, Figure 5.1c has water, oil, and gas in the same glass, and thus the saturation of each fluid will be less than 100%.

Figure 5.1: Schematic showing identical glasses filled with different fluids: (a) the glass is filled with 100% water, representing S_w = 1, (b) the glass is filled with 50% water and 50% oil, representing S_w = 0.5 and S_o = 0.5, and (c) the glass is filled with 50% water, 30% oil, and 20% air (gas), representing S_w = 0.5, S_o = 0.3, and S_g = 0.2.

Similarly, rocks are filled with one or more fluids. Fluid saturation helps us quantify the amount of hydrocarbons or water in the rock.

Definition

Saturation is defined as the fraction or percent of the pore volume occupied by a particular fluid (oil, gas, or water).

 We can classify the saturation into three categories: water, oil, or gas. Water saturation, Sw, is the volume of water in a rock divided by the pore volume:

where Sw is the water saturation [dimensionless], Vw is the volume of water in the pore spaces [cm3], and Vp is the pore volume [cm3].

Similarly, oil saturation, So, is the oil volume divided by the pore volume:

where So is the oil saturation [dimensionless], Vo is the volume of oil in the pore spaces [cm3], and Vp is the pore volume [cm3].

Finally, gas saturation, Sg, is the gas volume in a rock divided by the pore volume:

where Sg is the gas saturation [dimensionless], Vg is the volume of gas in the pore spaces [cm3], and Vp is the pore volume [cm3].
The summation of saturations of all the fluids in a reservoir has to be 1 as the pores have to be filled with at least one fluid. If a reservoir contains water, oil, and gas, then the equation becomes:

However, if a reservoir only contains oil and water, then Equation will reduce to Sw + So = 1. Although Equation is very simple, it is helpful in finding an unknown fluid saturation mathematically.

Similar to porosity, fluid saturation is either presented as a fraction or a percentage; however, bear in mind that it should always be used as a fraction in calculations.
Figure 5.2 shows an example of a microscopic rock slice illustrating water, oil, and gas saturations in the pore spaces. Similar to porosity, fluid saturation is important to estimate the amount of hydrocarbons in a reservoir. However, it is important to distinguish between porosity and fluid saturation. Porosity tells us the maximum storage capacity of a medium, while fluid saturation depicts the exact amount of fluid occupying the pore spaces of the same medium.

Figure 5.2: Schematic showing a cross section of a rock at the microscopic scale: (a) all the pore spaces are filled with water (S_w = 1), (b) the pore spaces are filled with water and oil (S_w + S_o = 1), and (c) the pore spaces are filled with water, oil, and gas (S_w+S_o+S_g= 1).

Critical oil saturation, S_oc

The saturation of the oil must be greater than a specific threshold, known as "critical oil saturation," in order for the oil phase to flow. At this specific saturation, the oil stays in the pores and will essentially not flow.

 

Residual oil saturation, S_or

During the displacing process of the crude oil system from the porous media by water or gas injection (or encroachment), there will be some remaining oil that is quantitatively characterized by a saturation value that is greater than the critical oil saturation. This saturation value is SOR stands for residual oil saturation. The term "residual saturation" is usually associated with the nonwetting phase when it is being displaced by a wetting phase.

Movable oil saturation, S_om

Movable oil saturation S_om is another saturation of interest and is defined as the fraction of pore volume occupied by movable oil as expressed by the following equation:

where Swc is connate water saturation and Soc is critical oil saturation

Critical gas saturation, Sgc

Gas evolves from the oil phase as the reservoir pressure drops below the bubble-point pressure, and as a result, the saturation of the gas rises as the reservoir pressure drops. Up until a specific saturation level, known as the critical gas saturation, above which gas starts to move, the gas phase is immobile.
Critical water saturation, Swc
The greatest water saturation at which the water phase will remain immobile is frequently referred to by the terms critical water saturation, connate water saturation, and irreducible water saturation interchangeably.

 

Measuring Fluid Saturation

Fluid saturation measurements can be classified into two types: direct and indirect. Direct measurements include conventional core analysis techniques such as extraction methods (retort distillation and Dean-Stark method), while indirect measurements include electrical properties and capillary pressure, respectively.

Extraction Method: Retort Distillation

For the retort distillation method (Figure 5.3), a core sample is placed in a chamber and heated to around 1100 °F (≈593 °C). This is to evaporate all the fluids in the system (oil and water). The vapors will rise and reach a condensing tube where cold water is being circulated. The vaporized liquids will condense back to liquid form and will be collected in the graduated cylinder after passing through the condensing tube. Once we have the volumes of oil and water from this method and by knowing the pore volume of the core sample, we can calculate the water and oil saturations using Equations respectively. The advantages of the retort distillation method are that it can directly measure oil and water saturations, and is a relatively fast method (usually takes less than one hour). The main disadvantage of this method is that subjecting the core to very high temperatures can damage it, thereby preventing the core from being used for additional experimentation and analysis.

Figure 5.3: Schematic showing the experimental set-up for the retort distillation extraction method.

Extraction Method: Dean-Stark

This method is also known as Soxhlet extraction or solvent extraction. Chemists Dean and Stark first designed this experimental set-up in 1920. For this experiment, a core sample is placed at the top of a solvent flask, as shown in Figure 5.4. The solvents used are usually toluene (hydrocarbon solvent) or a mixture of toluene and methanol. Methanol can be used in the presence of salty water. The solvent is heated to around 230 °F (110 °C, the boiling point of toluene), so that the water present in both the core and the solvent evaporates when the temperature in the system exceeds the boiling point of these fluids. The toluene vapor will strip the oil from the core and travel upward as toluene is miscible with oil. Once the vapor goes upward, it will reach the condensing tube with circulating cooling water. Both fluids (water and solvent) will drop down in the graduated cylinder. Since water is denser than the solvent, it will settle at the bottom of the graduated tube, while the condensed solvent (being less dense) will accumulate on top of the water until it drops down to the solvent flask. This method can measure the volume of water directly, and the water saturation can be calculated using Equation if the pore volume of the core sample is known. Oil volume needs further calculations using material balance. We cannot measure the oil volume/saturation from the Dean-Stark method directly, as the solvent mixes with oil to form a new fluid that has different fluid properties than the original oil. Therefore, collecting both fluids will be impractical. However, we can calculate the oil saturation mathematically since the summation of all saturations is equal to 1 and compare the value with the one obtained from the material balance method. The advantage of the Dean-Stark method is that it does not damage the core, and the core sample can be used for future analysis. The disadvantages are that the experiment is time-consuming as it usually takes about 48 hours, and that time required for the experiment is also a function of the permeability; the lower the permeability, the more time is required. Furthermore, in this experiment, we can only measure saturation of one fluid directly, which is water, unlike the retort distillation method which measures both water and oil saturations.

Figure 5.4: Schematic showing the experimental set-up for the Dean-Stark extraction method.

Material Balance

As mentioned earlier, the Dean-Stark method can only measure the water volume. In order to find the oil volume and saturation, we need to use material/mass balance.
However, now we need to assume that there are two fluids in the system (assuming no gas occupying the pores). It is important to note that we need to record the weight of the core sample prior to the extraction process. First, we know that the weight of the saturated core (assuming it contains oil and water) prior to extraction is equal to:

Ws = Wd +Ww +Wo

where Ws is the saturated weight [g], Wd is the dry weight of the sample that can be obtained after the extraction process [g], Ww is the weight of the water in the core sample [g], and Wo is the weight of the oil in the core sample [g].

We can say that the weights of water and oil in the core sample are equivalent to their densities multiplied by their volumes, as shown below:

Ws = Wd +ρwVw +ρoVo

where ρw is the density of water [g/cm3], Vw is the volume of water in the core [cm3], ρo is the density of oil [g/cm3], and Vo is the volume of oil in the core [cm3]. We know that:

Vw + Vo + Vg = Vp

where Vg is the volume of gas in the core [cm3], and Vp is the pore volume of the core [cm3].

Since we only have oil and water, Equation can be reduced to:

Vw + Vo = Vp

For simplicity, let us assume:

Vo = x

Then, we can rewrite Equation to obtain:

Vw = Vp − x

Then, we can substitute Equations obtain:

Ws = Wd + ρw(Vp − x) + ρox 

After that, we can rearrange the equation to obtain:

Ws − Wd − ρwVp = x(ρo − ρw)

Now, we can solve for x and replace it with Vo:

Finally, we can divide both sides by the pore volume to find the oil saturation: 

We can cross-check the water saturation value obtained from the Dean-Stark method using the following simple term:

where Sw is the water saturation [dimensionless] and So is the oil saturation [dimensionless].

It is important to mention that the use of material balance to find the fluid saturations can go beyond the Dean-Stark method to measure fluid saturations obtained from different experiments.

Average Saturation

The saturation values must be weighted by both the interval thickness hi and interval porosity I in order to average saturation data properly. The following formulae can be used to compute the average saturation of each reservoir fluid:

Where the subscript i refers to any individual measurement and hi represents the depth interval. 

factors affecting fluid saturation determination

There are many factors that can affect the determination of fluid saturation, including:

• The method used to determine fluid saturation. 

    Different methods have different limitations and uncertainties. For example, core analysis can be very accurate but is also destructive and time-consuming, while wireline logging is non-destructive but can be less accurate. The most common methods for determining fluid saturation are core analysis and wireline logging. Core analysis involves taking a sample of the reservoir rock and measuring the fluid saturation in the laboratory. Wireline logging is a non-destructive method that uses electrical or nuclear techniques to measure the fluid saturation in the rock from the wellbore.

• The properties of the reservoir rock. 

    The porosity and permeability of the rock can affect the distribution of fluids in the rock, which can make it difficult to determine the fluid saturation. The porosity and permeability of the rock are important factors that affect the distribution of fluids in the rock. Rocks with high porosity and permeability will have more uniform fluid saturation than rocks with low porosity and permeability.

• The properties of the fluids in the reservoir.  

    The viscosity, density, and interfacial tension of the fluids can also affect the distribution of fluids in the rock, and therefore the fluid saturation. Viscosity is a measure of how thick or thin a fluid is, density is a measure of how heavy a fluid is, and interfacial tension is the force that exists between two different fluids. Fluids with high viscosity or density will be less likely to move through the rock, and fluids with high interfacial tension will be more likely to form droplets or films at the interface between two different fluids.

• The presence of contaminants. 

    The presence of contaminants, such as drilling fluids or other chemicals, can also affect the determination of fluid saturation. The viscosity, density, and interfacial tension of the fluids in the reservoir can also affect the distribution of fluids in the rock. The presence of contaminants, such as drilling fluids or other chemicals, can also affect the determination of fluid saturation. These contaminants can interfere with the methods used to measure fluid saturation, and they can also change the properties of the fluids in the reservoir.

• The accuracy of the equipment used. 

The accuracy of the equipment used to determine fluid saturation can also affect the results. The accuracy of the equipment used to determine fluid saturation can also affect the results. It is important to use equipment that has been calibrated and that is known to be accurate for the specific application.

Summary

Fluid saturation is a percentage that indicates how much fluid the pore space inside a rock contains, which is defined as the volume of fluid in a rock divided by its pore volume. In reservoir rocks, the fluids are usually hydrocarbons or water. Some extraction methods used to measure fluid saturation include retort distillation and the Dean-Stark method. In both of these methods, the fluid is extracted from the rock sample and then measured. The Dean-Stark method can only measure water saturation, unlike retort distillation that can measure both oil and water saturations. Therefore, material balance analysis is used to supplement the Dean-Stark method to calculate the oil saturation as well. Drilling muds make it difficult to evaluate the reservoir’s saturation using extraction methods because they interfere with the saturation of the extracted samples. Similarly, extreme temperatures and pressures while extracting the core samples also cause changes within them, due to which the extraction methods cannot accurately determine the saturation within the reservoir. 

Video lecture on the saturation of reservoir rocks: 

You can watch the lecture on the saturation of petroleum reservoir rocks on YouTube. It is converted from the lecture on the saturation of rocks in PDF and PowerPoint, and the link is here

keywords:

Critical oil saturation, Material Balance, Extraction Method, Dean-Stark, 

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