Saturation:

Let us consider a representative elementary volume of the reservoir, with the pores filled with oil, gas and water. In volumetric terms, this can be written as follows:

which leads to the definition of saturation, S, as a fraction of the pore volume occupied by a particular fluid:

where n denotes the total number of fluid phases present in the porous medium.Consequently,

If two fluids coexist (say, oil and water), they are distributed unevenly in the pore space due to the wettability preferences. See Fig. 3.2. Simply, the adhesive forces of one fluid against the pore walls (rock-grain surface) are always stronger than those of the other fluid. In the vast majority of petroleum reservoirs, both siliclastic and carbonate, the pore water is the wetting phase and oil is a non-wetting phase.

Importantly, the fluid saturation (So, Sg and Sw) in a reservoir varies in space, most notably from the water-oil contact to the reservoir top (see figures in previous chapter), and also in time during the production. In short, different parts of the reservoir may have quite different fluid saturations, and also the saturation in any elementary volume of the reservoir changes progressively during the production.

3.1 Residual SaturationNot all the oil can be removed from the reservoir during production. Depending on the production method, or the actual "drive mechanism" of the petroleum displacement, the oil- recovery factor may be as low as 5-10% and is rarely higher than 70%. Part of the oil will remain as residue, this is called the residual oil. One has to distinguish between the residual oil and possibly gas saturation reached in a reservoir after the production stage, and the residual saturation of fluid phases in a reservoir-rock sample after a well coring operation. A fresh, "peel-sealed" core sample is taken to the laboratory, where the reservoir saturation and the oil-recovery factor are estimated. The laboratory process is illustrated in Fig. 3.3, where water is displacing the initial oil in the core sample.

If the pore volume Vp of the core sample in known, then

where Voi is the initial volume of trapped oil in the core sample, andVo is the displaced orproduced oil.

Laboratory Determination of Residual Oil and Water SaturationThe cores recovered from wells contain residual fluids (depleted due to the drilling-fluid invasion, the changes in pressure and temperature, etc.) that are assumed to reflect:• The fluid saturation at the reservoir conditions.• The possible alterations due to the drilling-fluid invasion into the core.• The efficiency of possible oil displacement from the reservoir rock represented by the core.The modern techniques of core-samples collection prevent dramatic alterations of the rock fluid characteristics, (foam-based drilling fluid, rubber sleeves containing the core samples and maintaining their reservoir pressure, deep freezing of retrieved cores, etc.)

Two laboratory techniques are commonly used for determining the residual oil and watersaturation,• a high temperature retort distillation method and• the Dean-Stark method.

The Retort Distillation MethodThe core sample is weighed and its bulk volume measured or calculated. The sample is then placed in a cylindrical metal holder with a screw cup at the top and a hollow stem projecting from the bottom. The top is sealed and the sample holder is placed in a retort oven. A thermostat controller raises the temperature of the core to a selected level, at which point the water within the core is vaporised and recovered. The temperature is then increased to_ 650oC (1200oF) to vaporise and then distil oil from the sample. The vaporised fluids are first collected in the sample holder and then released vertically downwards through the hollow stem (downdraft retort). They are subsequently condensed and measured in a calibrated receiving tube.See Fig. 3.4.

N.B.! Samples are usually destroyed in this test due to the high temperature and for this reason small-diameter samples or "plugs" (small cores from the well core), are normally used.

The calculation of the oil and water saturation is straightforward. The following parameter values are derived from the laboratory test:

• Vb,r – the sample bulk volume and rock density, determined prior to the experiment.• Vo;Vw – the recovered oil and water volumes, registered during the test..• Vp – the pore volume, which is calculated.

The water and residual oil saturation are calculated as follows:

where the saturation are fractional parts of the pore volume. Frequently, saturation are also given in %.

The Dean-Stark Apparatus for Measuring Initial FluidsWhen the core to be analysed is weighed, the measurement includes the weight of rock grains, and the pore fluid. The sample is then placed in the tare apparatus (to be sure that no sand grains are lost from the core sample during its analysis, which might otherwise lead to an erroneously high oil saturation!) and this unit is suspended above a flask containing a solvent, such as toluene, as shown in Fig. 3.5.

There are several requirements for choosing a proper solvent,• it must have a boiling temperature higher than that of water,• it must be immiscible with water and• it must also be lighter than water.

Toluene satisfies all of those requirements.

When heat is applied to the solvent, it vaporises. The hot solvent vapour rises, surrounds the sample and moves up to the condensing tube, where it is cooled and condensed. The condensate collects into the calibrated tube until the fluid there reaches the spill point, here upon the solvent condensate drips back onto the sample containing the reservoir fluids. The solvent mixes with the oil in the sample and both are returned to the solvent flask below. See Fig. 3.5. The process continues until the sample’s temperature has risen above the boiling point of water. At that point, the water vaporises, rises in the condensing tube, condenses therein and falls back into the calibrated tube. Because it is heavier than the solvent, it collects at the bottom of the tube, where its volume can be directly measured. When successive readings indicate no additional water recovery, the water volume is recorded for further calculations. After all the oil and water have been recovered from the sample, it is dried and weighed again. The difference between the original and final weights equals to the weight of the

oil and water originally present in the sample. Because the water collected in the calibrated tube is distilled, with a density of 1.0 g/cm3 and a known volume, the weight of oil in the sample can be calculated. This information is subsequently combined with the estimated porosity of the clean, dry sample, the volumes of the oil and water can be converted into percent pore-space fraction (saturation).

N.B. The samples in the process are not destroyed and can be further used in other measurements,i.e., pore volume pycnometry or perhaps capillary measurements, etc.The calculation of the oil and water saturation is straightforward. The following parameters are derived from the laboratory test:• Wi – the initial weight of the core sample, determined prior to the tests.• Wd – the weight of the dry, clean core sample, determined directly after the tests.

• , Vb – the rock’s porosity and the core sample’s bulk volume, determined after the tests.• Vw – the reservoir volume of water, registered during the test.• Vo – the recovered volume of oil, which is calculated.Water and oil (residual) saturation is calculated according to Eqs. (3.5), where both the retort distillation method and the Dean-Stark method are capable of yielding fluid saturation values within ±5% of the true values.