Conclusion.

This tutorial describes the main methods and technologies used nowadays for the development of oil fields. The choice of the development system, placement and choice of the well operation drive depends substantially on the geological structure of a formation. Of great importance is the development of a geological model of a production facility. The basis of the used hydrodynamic models of the development is physical laws that are not always known by the users and the authors of the models do not always speak about it. Each model has its own area of application, and something that works for one object may not match the other. There is no one universal method of oil deposits development. But it is absolutely necessary to choose the optimal one.

In the description of the methods of enhanced oil recovery also a special attention is given to the physical processes occurring in the technology. The changes that happen in the real formation under the influence of the injected reagents, change of the operational drive, a violation of the original pool-reservoir properties and their change over the time can be predicted. The basic methods, technologies of enhanced oil recovery were developed in the mid-20th century. Their use at that time was limited by the imperfection of the necessary technical means and materials. But the physical processes, happening in porous and fractured environment, have not changed. Their description, the boundaries of the implementation scope and possibilities of achieving of the final goal: namely, enhanced oil recovery, have being defined.

It seems appropriate to quote by many authors a wise statement of academician A.P. Krylov "....without the understanding of the processes, happening in the formation and without attempt to apply appropriate measures, we can lose millions of tons of oil, and not even notice it."

The Annexes provide brief information about possible scientific directions for the future holders of master’s degree and postgraduate students.

Annex 1.

Ex.1.1 Stationary oil filtration. Dupuy formula.

When stationary, steady filtration, the pressure and flow rate do not depend on the time t, but depend only on the spatial coordinate r. On the external boundary R the constant pressure P₀ is supported. The pressure at the well bottom is constant and equals P_c . The pressure distribution in the zone between the well radius r_c and external boundary radius R changes according to the logarithmic law:

(ex.1.1)

Well inflow rate is determined by Dupuy formula

= (ex.1.2)

Here k – phase permeability coefficient, h – the thickness, drilled up oil saturated formation part, Δp=P₀ -P_c- pressure drawdown at the bottom-hole, µ - dynamic viscosity, – hydraulic conductivity factor.

The “beauty” of the Dupuy formula is in the following: at the given pressure drawdown the well production rate is determined by the parameters of the formation and properties of filtering fluid. At high permeability there is received a higher production rate. The more oil-saturated thickness, the greater the production rate is. The higher the oil viscosity, the lower the rate is. That is, it is possible to predict exactly the output for the homogeneous reservoir (formation, interlayer).

It is possible to estimate qualitatively the contribution of every interlayer to the total production rate for the complex in structure reservoir with the average number of permeable intervals more than 1, consisting of several layers (strata) of different permeability and thickness, (ex.1.2.). Oil is displaced by water first of all from the high-permeability interlayers that are watered quickly when water is injected to the formation. The main part of the recoverable reserves, is usually located in low-permeability layers and is not covered by the development, reservoir sweep flooding coefficient is less than the planned. To involve low-permeability interlayers in the process of development it is necessary to carry out the actions to change the injectability profile of the injection wells and isolation of the watered out interlayer of the producing wells.

If we divide the flow rate in depression (drawdown pressure) in (ex.1.2), you will get the productivity factor of the well which is the most important characteristic of the well efficiency that determines the drive of operation of the wells, the equipment for mechanized operation.

(ex.1.3)

The coefficient of well productivity depends on the reservoir properties of the reservoir and the dynamic viscosity of the fluid.

Ex.1.2. The radius of pressure disturbed zone in the deposits of low-viscosity oils.

During well operation there are possible two drives: operation with constant flow rate or constant depression. In any case, with the beginning of the well operation the depression cone begins to spread from the well bottom-hole and the radius of pressure disturbed zone p(t) depends on time and does not exceed the radius of the external boundary R, figure ex.1.

Fig. ex.1. Radius of pressure disturbed zone.

To define ρ(t) there are several formulae, got by different approximate methods by the soviet scientists [32]. In general, it looks like that:

(ex.1.4)

Where - piezoconductivity coefficient, t – time, a – numerical coefficient, depending on the determination method that equals 2, 4, 6, 12, π. When the external boundary is reached R there is occurred stationary filtration. The time of the external boundary achievement depends on piezoconductivity coefficient.

, (ex.1.5)

Where k – phase permeability coefficient, µ - dynamic viscosity, β^* - elastic capacity coefficient, determining elastic properties of the formation and fluid, i.e. characterizes deformation energy of the compressed saturated formation.

Time T the external boundary achievement R is determined by the formula:

(ex.1.6)

For low-permeability interlayers of the complex reservoir the time to reach the external boundary is more than for high-permeability interlayers. Formula (ex. 1.6) is valid only for crude oils with a low viscosity. For high-viscosity oil T is much more, and is calculated differently.

Ex. 1.3.The radius of pressure disturbed zone in the high-viscosity oil deposits.

The composition and physical properties of high-viscosity oil impose special conditions on filtration. Physical models of high-viscosity fluids flow are considered in the works of Soviet scientists [33,34]. Classic Darcy law for high-viscosity oil with filtration rate and pressure differential does not work.

One of the first physical models, describing filtration of high-viscosity oil as a viscoplastic fluid in a porous medium is the model with the initial pressure differential.

To illustrate the notion of "initial pressure differential" let’s consider the following example. Let two bodies be on a rough horizontal surface: the first body weight is100 grams, the second one is 100 kilograms. You need to move the bodies. It requires the strength that will be applied to each of body. According to the Coulomb’s law the friction forces, preventing the movement, will be proportional to the weight of each body, multiplied by the coefficient of friction. Therefore, each body must be applied different forces. The first body can be moved easier than the second, and, the less the weight of the first body, the less efforts should be applied to start a movement. A similar situation arises in oil filtration process: for low-viscosity oil the current pressure differential, even at small values, causes fluid movement in the reservoir; for viscous-plastic oils to provide filtration the current pressure differential must exceed some value - the initial pressure differential or, by analogy, the coefficient of static friction.

For the radial filtration of viscoplastic fluid the Darcy law has the following view:

(ex.1.7)

Well production rate is determined as:

(ex.1.8)

Here v – filtration velocity, k – phase permeability coefficient, µ - dynamic oil viscosity, - current pressure differential, g – initial pressure differential. S – filtration area.

Filtration stats at . For low-viscosity, light oils in (ex.1.7) g=0, classic Darcy law is implemented. The initial pressure differential reflects not only the structural - mechanical properties of oil, but also filtration properties of the reservoir that is typical for low-permeability differences [35].

From equations (ex.1.7, ex. 1.8) it evident that the higher the viscosity of oil in situ, the less filtration rate, and hence the flow rate. The decrease of oil viscosity at heating of the heat-transfer agent increases the speed of filtration and flow rate.

The equation of piezoconductivity for viscoplastic oils has the following view [33]:

(ex.1.9)

where p(r,t) – current pressure at , r_c – well radius, p₀ –initial reservoir pressure, χ and ε- piezoconductivity and hydraulic conductivity coefficients, g – initial pressure differential, ρ(t) – the radius of pressure disturbed zone (depression funnel). Solving the equation (ex.1.9) by the method of integral transformations of G.I. Barenblatt [8], at stable production rate Q, we will have the pressure distribution in the disturbed zone and the equation to determine ρ(t) [36]

. (ex.1.10)

Here , n=1,2,3.. numerical parameter.

Approximate solution (ex.1.10) will give

(ex.1.11)

From (ex.1.11) it is evident that the radius of the zone of disturbance is proportional to the cubic root of time and depends on well production rate, hydroconductivity and piezoconductivity coefficients, from the initial pressure differential g.

Thus, for viscous-plastic oils the funnel depression is spread much slower than for low-viscosity oil. Pressure in the zone of disturbance pressure depends on the radius of the zone of disturbance, and thus on time [37].

Annex 2

Ex.2.1. FHF (Formation hydraulic fracturing) in stratified reservoirs.

Chapter 12 examines the operation of the wells after hydraulic fracturing in homogeneous layers. In practice homogeneous layers practically do not occur, according to the results of the GIS, compartmentalization coefficient is always greater than 1. If the filtration parameters of the interlayers differ not much from each other, the reservoir can be considered homogeneous according to permeability. Otherwise, when the operation drive of the well is being chosen after hydraulic fracturing it is necessary to consider the filtration parameters of each interlayer with different permeability. For two-layer model of the reservoir - model Kazemi model works – the formula (12.2) takes the form:

(ex.2.1)

Here S₁, S₂ – the filtration areas of the first and second interlayers; k₁, k₂ - phase permeability coefficients of the first and second interlayers; - pressure differentials in the interlayers.

Let the index 1 refers to the high-permeability interlayer (HP), the index 2 is to the low-permeability (LP). There are two options: the first - the interlayers are hydrodinamically not associated, separated by clay bed; the second – the interlayers are hydrodinamically associated.

Let’s consider the first option. Let the thickness of the layers is equal, so the filtration areas will be equal too. If the permeability of the HP interlayer is much more than of LP (k₁ =150mD, k₂ =10mD), the interlayer 1will be watered out quickly. Liquid, including oil, from the second interlayer will flow into the fracture, but the oil reserves of the second formation will remain unrecovered. Hydraulic fracturing efficiency will be found to be unsatisfactory due to the rapid watering. If the permeability of the HP equals 80mD, the LP is 10mD, in this case watering over time will increase, but the FHF will be profitable for a much longer time.

If the interlayers are hydrodinamically connected, then at large differences of permeability the pressure in the HP will be less than in the NP, the liquid from the LP will flow to the HP, that is, as with cyclic flooding the hydraulic fracturing efficiency will be influenced by the filtration parameters of interlayers, their capacitive properties.

Thus, even for the simple Kazemi model there is a great choice of calculation of the hydraulic fracturing efficiency. If the layer is stratified (Serra model), the situation is complicated, you need reliable data about the geological structure of the reservoir and its properties.

Ex. 2.2. What does depend the duration time of FHF efficiency on?

In this paragraph we will consider the stress - deformed state on the borders of lateral surfaces of the vertical fracture.

In the middle of the 20th century by academician S.I. Tekhnitskiy [38] by means of the Lame task there are obtained the expressions for the principal components of the stress tensor in homogeneous reservoir in the cylindrical coordinates (Fig. ex. 2.1)

, , . (ex.2.1)

Here p_г – mountain pressure, _z, _0, _r - vertical, tangent и radial tension,  - Poisson coefficient, p_с – bottom-hole pressure, r_c - well radius, r – coordinate.

Fig.ex.2.1. The main tensions on the element of the formation bottom-hole zone. Top view.

For the porous reservoir (elastic medium) Poisson coefficient changes in the range . At =0,5 the medium transfers to the plastic condition.

Let’s consider the elastic formation. In this case, the Poisson coefficient and the module of longitudinal strain (deformation) (Jung) E values are constant. In the bottom-hole formation zone at the main tensions will be equal

(ex.2.2)

Tangent tension in the bottom-hole zone is more than radial. With the reduction of the bottom-hole pressure ₀ is increased. Therefore, the deformation ε₀ in the plane that is perpendicular to the z axis and the fracture length defines and makes the main influence on the fracture opening. Tangent deformation is equal to:

(ex.2.3)

With the pressure drop at the bottom the tangent deformation increases. Fracture opening at the bottom decreases, so, the volume of the fracture also should reduce. Volume deformation ε is associated with the average tension  and is equal to the sum of the principal tensions, by the ratio:

(ex.2.4)

If the bottom-hole and rock (mountain) pressures remain constant, then the deformation and ε do not change, it is contradictory to the field data, the flow rate falls over time. It follows that the reservoir is viscoelastic medium where the deformations grow at constant load. This phenomenon is called creep. For viscoelastic media the modules of deformation are the functions of time, the increase in deformation happens slowly and depends on the physical properties and structure of the medium. In the case of hydraulic fracturing the fracture opening openness decreases; the filtration characteristics of the reservoir, fracture volume, filtration area also decrease that leads to the reduction of the flow rate, and determines the time efficiency of hydraulic fracturing.

It should be noted that at large values of, but less than 0.5, volumetric deformation increases faster. "Closeness" of  to 0.5, to the plastic properties of the medium depends on the content and composition of the cementing substancesof the solid phase of the rock. For clay cement the creep is more evident. For carbonate cement the rock becomes more brittle, elastic, the impact of the creep is minimal.

Annex 3.

Ex.3.1. Oil composition classification

Oil composition and the content of asphaltenes, resins, paraffins, sulfur in it significantly affect the physical properties of oil , the processes of displacement and, therefore, the choice of method and oil recovery technology.

According to the adopted document GOST R 51858-2002 the oils are classified as the following:

According to the sulphur content

Sulphur content percentage	Oils types
Up to 0,6%	Low-sulphur
From 0.6 to 1,8%	Sulphur
From 1,8 to 3,5 %	High-sulphur
More than 3,5 %	Extra high-sulphur

According to the paraffin content

Paraffin content percentage	Oils types
Up to 1,5%	Low-paraffin
From1,5 to 6%	Paraffin
More than 6 %	High-paraffin

According to the asphaltenes and resins content

Content	Oils types
Up to 5%	Low-resinous
From 5 to 15%	resinous
More than 15 %	High-resinous

According to the density

Oil density at 15˚, kg/m3	Oil density at 20˚, kg/m3	Oils types
Up to 834,5	Up to 830	Extra light
From 834,5 to 854,4	From 830 to 850	light
From 854,4 to 874,4	From 850 to 870	middle
From 874,4 to 899,3	From 870 to 895	heavy
More than 899,3	More than 895	bituminous

According to the viscosity

Oil viscosity, mPа×sec.	Oils types
≤5	With small viscosity
>5 ≤10	Low-viscosity
>10 ≤30	With heighten viscosity
>30	High-viscosity

Ex. 3.2. Effective temperature

The effective temperature is determined by the results of laboratory tests, depends on the composition and properties of oils, thermophysical characteristics of the reservoir rock, oil, injected water. In the figure ex. 3.1. there is represented the dependence of the dynamic viscosity changing on temperature. The shaded area is the interval of changes of the effective temperature Т_эф,, which is determined by the results of the laboratory tests [23,24]. Further heating of oil does not give any significant reduction in viscosity, therefore, allows to reduce the cost on heat energy.

Fig.ex.3.1. the dependence of dynamic viscosity on temperature of А-4 formation of Gremikhinskoye field.

Ex.3.3. Initial pressure differential.

Annex1 shows the equation of piezoconductivity of viscoplastic oils (ex.1.9.), in the right part of which there is the initial pressure differential g. In the woks[39,40] there is developed a method for the initial pressure differential determination by means of the interpretation results of hydrodynamic researches of the wells at the steady filtration drives. The adjusted formula to define the initial pressure differntial is:

(ex.3.1)

where g - initial pressure differential, ∆p^* - pressure drawdown, necessary to overcome the initial pressure differential. R - external boundary radius, r_c - adjusted well radius. In fig. ex.3.2. there is represented an indicator diagram of the well 12 of the field Russkoye.

Fig.ex. 3.2. Indicator diagram well 12 Russkoye field.

From the equation of the straight (indicator diagram) built up in the range of the coordinates ∆p – Q, there is determined ∆p^* at Q=0.

The correlation coefficient is equal to 0,987. Δp*=2,17 MPa. Changing the value of the external boundary radius R from 10 m up to 100 m, we will find the average value of the initial pressure differential by formula (ex. 3.1), equal to 0,087 MPa/m. It should be noticed that with the increasing of r_с=0,2m the value of initial pressure differential increases and is equal to g =0, 0903MPa/m.

The productivity factor of the well, in our opinion, should be defined as the ratio of the output to the actual measured drawdown pressure, although the indicator straight line does not pass through the origin.

Δp – measured drawdown pressure.

Since the radius of the external boundary R is not known in advance, then [39] there is developed the method of iterations to determine the initial pressure differential with the replacement of R (ex. 3.1) the value of p(t) from the formula (ex. 1.11).

The rates of wells’ productivity operating the accumulation of heavy oil will be lower than the rates of productivity of the wells in the deposits of low-viscosity oil, even with the same filtration parameters of the reservoir.

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