4.1. Porous formation models.

The formation models are divided into deterministic and statistic [7].

4.1.1. Deterministic model

The accumulated data about geological structure, pool-reservoir properties of the deposit, net pay thicknesses and others information are used to reflect more accurate the actual structure and properties of the reservoir.

The formation is split into sections with the same or similar values of the fundamental physical parameters (Fig.4.1). Differential equations describing the processes of filtration and oil displacement agents, are replaced by finite-difference, algebraic equations. The solution of algebraic equations allows you to determine the current development parameters.

Fig. 4.1.The scheme of deterministic formation model.

The practical application of the deterministic model has become possible thanks to the development of mathematical methods of processing of large volumes of information using the modern computer facilities.

4.1.2. Stochastic-statistical model.

In this case the real formation is compared with some hypothetical formation that has the same characteristics as the real one.

These models include:

a) The model of homogeneous formation – the basic characteristics of the formation - porosity and permeability are averaged out;

b) The model of homogeneous-anisotropic formation – permeability is various in vertical and along directions of the stratification.

The use of stochastic - statistical models has become possible thanks to the development of methods of underground hydromechanics, which enabled to understand and explain the processes of fluid movement in different formation conditions [7].

4.2. The models of fractured-porous reservoir.

4.2.1. The model with dual porosity and permeability.

This model, developed by G.I. Barenblatt and Y.P. Zheltov [7,8], is a fractured - porous reservoir in the form of two continuous media, nested into each other and with different pool reservoir properties (porosity and permeability). The media are interconnected by the flow function. The first medium considers filtration in a porous medium, the second - in the fissures.

4.2.2. Warren-Ruth model [9].

Fractured-porous media are presented in the form of blocks - rectangular parallelepipeds and system of fissures. The fluid flow moves to the bottom of the well through the fissures, from blocks due to the differential pressure oil spills in the fissures.

Fig.4.2. Warren-Ruth model. 1,3 – fissures, 2 - blocks

4.2.3. Kazemi model [10].

Fractured-porous reservoir is represented in the form of two interlayers: the 1st - high-permeable formation (interlayer) (HPF) corresponds to the fissures, 2nd-low-permeable formation (LPF). The fluid flow to the borehole is happened due to the HPF. Fluid flows from the HPF to the LPF. Fluid filtration from the HPF to the LPF is described by a function of the flow.

Fig.4.3. Kazemi model. V- the flow function from low-permeable to high-permeable interlayer, h₁ , h₂ high-permeable and low-permeable interlayers’ thickness.

There are multi-layered model of the formations where there are pointed out several distinct layers with different pool-reservoir properties that can be hydrodinamically connected or divided by the clay interlayers.

Fig. 4.4. The model of stratified formation, consisting interlayers of different permeability and porosity thickness.

Serra K., Reynolds A.K., Raghavan R. model [11] interprets fractured - porous formation of several horizontal blocks, separated by horizontal fissures or low-permeable layers, separated by high-permeable interlayers.