4.3. Water saturation and watering.

Let’s consider two important physical concepts, which are widely used for the description and modeling of the processes characterizing the oil recovery. The water saturation and the watering, both words have the same roots, the root of "water", but have quite different physical sense.

In Chapter 1, paragraph 1, it is said that the water saturation coefficient determines the amount of water in the pore space of the reservoir and is defined as

(4.1)

The coefficients of relative-phase permeabilities (well then the phase permeabilities) depend on saturation factors. This connection is established by the interpretation of the core laboratory researches. For each lithological composition of the sample, the composition and properties of the fluids this dependence will be "peculiar", individual dependence. Usually the dependence is built between the coefficients of relative-phase permeability and water saturation factor, shown in figure 4.6.

Fig. 4.6. Experimentally built dependence of the relative-phase oil k_н^*() and water k_в^*() permeability by water saturation . _{св –} bound water coefficient, ^{* -} maximum notion of water saturation factor when the oil filtration stops.

Figure 4.6 shows that in the interval < <^* there is a zone of dual filtration (oil-water) in the reservoir. When k^*_н(^*) - oil filtration stops and only water moves in the reservoir. The values of the coefficients bound and maximum water saturation vary widely. It is important that ^* is always less than 1.

Similarly to the water cut coefficient Chapter 3 paragraph 3.6.3., let’s consider the share of moving water in the reservoir in the total volume of the filtered fluid, the symbols will stay the same.

(4.2)

Here V_в, V_н – the volumes of water and oil in the random cross-section of the formation, q_в,,q_н - oil-water bulk expenses according to the Darcy law:

, , (4.3)

Where S – filtration area, v_в,, v_н the speed of water and oil filtration, k, k^*_в, k^*_н - absolute and relative phase permeability of water and oil, - oil and water pressure differential.

Let’s put (4.3) in (4.2), will get

(4.4)

- the ratio of dynamic water and oil viscosity in the reservoir conditions.

If we don’t take into consideration the capillary effects on the oil-water boundary interphase, the pressure differential will be equal. Such kind of model is called Backley-Leverett model.

(4.5)

The function f() is called Backley-Leverett function. It describes non-reciprocating oil displacement by water with the known functional dependencies of relative phase permeabilities on water saturation.

The physical meaning of the Backley – Leverett function characterizes the share of water in the filtration flow of liquid in the arbitrary cross-section of dual phase filtration zone. Under surface conditions f() is equal to the water cut factor. When =^* (4.5) and figure 4.4, it follows that the water cut is equal to 1, and water saturation is less than 1.

Thus, the water saturation coefficient characterizes the share of water in the pore space of the formation and it is not necessary that the water is moving. Water cut coefficient is determined on the surface after the separation of the output into water and oil, and corresponds to the share of water in the extracted liquid.