Phase rule, construction of state diagrams. Phase transitions
A one-component heterogeneous system is one substance that is in different states of aggregation or polymorphic modifications. In accordance with the Gibbs phase rule, at K = 1 C = 3 F. the number of simultaneously existing phases in a one-component heterogeneous system can be no more than three. In the absence of polymorphism, these are liquid, solid, and vapor phases. The two-phase equilibria possible in such a system are “liquid-steam”, “solid-steam”, and “solid-liquid”. Each of these equilibria is characterized by a certain relationship between the parameters P and T, established by the Clausius-Clapeyron equations for the corresponding processes: evaporation, sublimation and melting.
These relationships can also be established empirically, by methods of physicochemical analysis. They are depicted graphically in the "pressure-temperature" coordinate axes, in the form of curves Р = f(T).
A graphical representation of phase equilibrium states for different P and T is called state diagram, or phase diagram. Consider, as an example, the phase diagrams of water and sulfur.
4.5.1. Phase diagram of water
The state of water was studied in a wide range of temperatures and pressures. It is known that at high pressures, ice can be in various crystalline modifications, depending on the physical conditions (P and T). This phenomenon, called polymorphism, is inherent in many other substances. We will consider the state diagram of water at low pressures (up to 2000 atm).
The diagram has three phase fields ( rice. 4.1):
AOB - fluid field,
BOS (under the curve) - field of unsaturated vapor,
AOS is the field of the solid phase.
Rice. 4.1. Phase diagram of water
At any point in the field, the system is single-phase and bivariant (K = 1; F = 1; C = 2), i.e. within certain limits, it is possible to change the temperature and pressure without changing the number of phases and their nature. For example, point 1 corresponds to liquid water, which has parameters t 1 and P 1 .
If two phases are in equilibrium in the system, then K = 1; F = 2; C = 1, i.e. the system is monovariant. This means that one parameter can be changed arbitrarily within certain limits, while the other must change depending on the first. This dependence is expressed by the curve Р = f(Т): RH - evaporation (or condensation) curve; OS - sublimation (or sublimation) curve; AO - melting (or solidification) curve. For example, point 2 characterizes an equilibrium system in which at temperature t 2 and pressure Р 2 water and saturated water vapor are in equilibrium. If P 2 \u003d 1 atm, then t 2 is called the normal boiling point.
The OM water evaporation curve breaks at the critical point (B) at t= 374С and P = 218 atm. Above this point, liquid and vaporous water are indistinguishable in properties. This was established by D.I. Mendeleev in 1860
The AO ice melting curve at pressures up to 2047 atm has a left-hand slope, which corresponds to the condition V f.p.< 0 (мольный объем льда >molar volume of water). Such ice is lighter than water, it floats on water, therefore living organisms are preserved in natural reservoirs that do not freeze to the bottom. At higher pressures, ice passes into denser modifications, then the AO melting curve is tilted to the right. Seven crystalline modifications of ice are known, of which six have a density higher than that of liquid water. The last of them appears at a pressure of 21680 atm. The transformation of one form of ice into another is an enantiotropic transition (see below for polymorphism).
The dotted curve OD (continuation of OB) characterizes the metastable equilibrium: supercooled water ↔ saturated steam.
Metastable are called equilibria in which there are all external signs of phase equilibrium, but the isobaric potential of the system has not reached the minimum absolute value and may decrease further. Water, crystallizing on impurities, will turn into ice. Point O is a triple point. Its coordinates for water in the absence of air: P = 4.579 mm Hg. Art., t= 0.01C. In the presence of air at 1 atm, the three phases are in equilibrium at 0°C. In this case, the total pressure is 1 atm, but the partial pressure of water vapor is 4.579 mmHg. Art. In this case, the freezing point decrease by 0.01º is caused by two reasons: the solubility of air in water (see the section “Decrease in the freezing point of solutions”) and the influence of the total pressure on the freezing point of liquids (an increase in the total pressure in the system lowers it). This is the only point where all three phases are in equilibrium: water, ice and steam. At this point, the system is invariant: C = 0.
7.2.1 Phase p–t diagram. When considering the individual phases of a pure substance, one usually means its state of aggregation: solid, liquid and gaseous. However, in the general case, the concept of "phase" is somewhat broader than the concept of "aggregate state", since some substances in the solid state, for example, ice, carbon, can have several phases.
Phase transition, i.e. the transition of a substance from one phase to another, is accompanied by a change in the properties of the substance, the release or absorption of heat (the heat of the phase transition). Equilibrium coexistence of several phases is possible only under certain combinations of state parameters (for example, temperature and pressure). Knowledge of the conditions for the equilibrium coexistence of various phases is important for solving many technical problems, for example. to determine the conditions for boiling liquids in hydraulic systems, to assess the conditions for the occurrence of cavitation in pumps, etc.
Analysis of the conditions of thermodynamic equilibrium of phases is based on the Gibbs phase rule. It establishes a relationship between the number of independent state parameters (degrees of freedom of the system) ψ, number of phases k and the number of system components n. Mathematically, the Gibbs phase rule is formulated as follows:
ψ = n – k + 2 .
For a pure substance (one-component system n= 1) the Gibbs phase rule has the form:
ψ = 3 – k .
In this case, a single-phase system (solid, liquid or gas) has two degrees of freedom, i.e. two independent state parameters. This means that if you arbitrarily set two state parameters (for example, p and t), then all others will be uniquely determined. At the same time, this means that in a single-phase state, a substance can exist with arbitrary combinations p and t.
Two-phase system ( k= 2) has only one degree of freedom ( ψ = 1); here, only one state parameter can be set arbitrarily. Consequently, the equilibrium coexistence of two phases (solid and liquid, liquid and gaseous, solid and gaseous) is possible only with a certain combination of values p and t; those. each value p corresponds to a well-defined temperature at which the coexistence of phases is possible.
On the rice. 7.2 shows a typical phase p– t diagram with lines of phase equilibrium. Here AK is the line of phase equilibrium of liquid and gas (steam), AC is the line of solid and liquid; AB is the line of the solid state and gas. In other words: AK is the line of vaporization (condensation), AC is the line of melting (solidification), AB is the line of sublimation (desublimation). The AK line is also called the saturation line, which ends critical point K. Three lines intersect at one point A, which is called triple point. At this point, three phases exist simultaneously, since according to the Gibbs phase rule at k= 3 the number of degrees of freedom of a one-component system is zero ( ψ = 0). For example, for water at the triple point p BUT = 616 Pa, t A \u003d 0.01 ° C, and for carbon dioxide p A = 0.518 MPa, t A \u003d - 56.7 ° С.
Using the phase diagram, it is possible to establish in what state (solid, liquid, gaseous, two- or three-phase) a particular substance will be at given values p and t. In addition, the phase diagram can be used to determine the phase transition temperature at a given pressure and vice versa.
The phase diagram also establishes the nature of the transition of matter from one state to another. For example, when p 1 > p A the transition from a solid to a gaseous state occurs through a liquid state. Under pressure p2< p А the existence of a substance in a liquid state is impossible; here the solid phase passes into the gaseous phase, bypassing the liquid stage. At the same time, at pressures exceeding the pressure at the critical point, the coexistence of the gaseous and liquid phases is impossible, and at temperatures exceeding the temperature at the critical point (see below), the substance exists only in the gaseous (vapor) phase.
7.2.2 Phase p-v diagram. Processes of changing the parameters of a real gas during a phase transition liquid-steam can be best represented with p–v charts ( rice. 7.3).
In this diagram, the area of equilibrium of two phases ("liquid - vapor") is not depicted as a line, but occupies a certain area. Three areas can be distinguished here: I - liquid state, II - two-phase state (phase equilibrium "liquid-vapor") and III - gaseous (vapor) state. Curve MK - is a locus of points that determine the state of a liquid heated to the boiling point (saturation) at the appropriate pressure. It separates the liquid region from the saturated vapor region and is called the liquid boundary curve (here X = 0).
The points of the NK curve determine the state dry saturated steam. This curve separates the saturated vapor region from the superheated vapor region and is called steam boundary curve; here X= 1.0. On the p- vdiagram in the area of the two-phase state plotted lines of constant vapor dryness ( X 1 ; X 2 etc.). With increasing pressure and, accordingly, the temperature at which the phase transition occurs, the specific volume of the boiling liquid increases, and the specific volume of saturated vapor decreases. At some pressure, which is quite specific for each substance, the boundary curves converge to the point To, which is called critical point.
On the rice. 7.3 several isotherms are plotted ( T = const). It can be seen that in the region of the superheated state, the isotherm has a form close to that of an ideal gas. In the area of the two-phase state of matter (“liquid–vapor”), the isotherm is also an isobar. This follows directly from the Gibbs phase rule, according to which a two-phase one-component system has only one degree of freedom. In the region of the liquid state, an increase in pressure leads to an insignificant change in the volume of the liquid due to low compressibility. At the critical temperature, the horizontal section turns into a point (critical point), which is the inflection point on this isotherm. The state of matter at this point is characterized by critical parameters: pressure R k, temperature T to and specific volume v j. Critical parameters of some substances are given in Table 7.1.
Table 7.1 Critical parameters of some substances
Critical point K belongs simultaneously to both boundary curves and corresponds to a state of matter in which there is no difference between liquid and vapor. This is illustrated by the temperature dependence of the heat of vaporization for water ( rice. 7.4), from which it can be seen that at the critical point the heat of vaporization becomes equal to zero ( r= 0). At temperatures above the critical value, the isotherms do not have horizontal sections. At these temperatures, for any pressure, the substance is in a vaporous (gaseous) state, and the type of isotherms as the temperature increases approaches the isotherms of an ideal gas.
From p– v diagrams follows an important conclusion about the different nature of the transition of liquid to vapor at different pressures. At subcritical pressures, when heat is applied to the liquid, the liquid is sequentially heated to the boiling point, vaporization, during which the substance is in a two-phase state, and vapor overheating. At supercritical pressures (line x-y) the transition from liquid to gaseous state occurs continuously, bypassing the two-phase state. The boundary between the liquid and gaseous phases in this case is conditional.
When a liquid passes into vapor at subcritical pressures, an abrupt change in the properties of a substance occurs. As follows from rice. 7.5, which shows the dependence of hydrogen density on temperature at two pressures, at supercritical pressure this process proceeds with a continuous accumulation of differences between liquid and vapor. This should be kept in mind when designing and analyzing the operation of technical devices in which phase transitions are possible (heat exchangers, cooling systems, refrigeration units, steam generators of power and power plants).
Using the critical parameters of a substance, one can determine the constants a and b in the van der Waals equation: a = 27 R 2 T 2 k /64 P k , b = R T k /8 P k , R = 8 P k v k /3 T k . The parameters of a substance related to the corresponding parameters in the critical state are called given parameters:
Here p k, T k are the critical values of pressure and temperature of the given substance. Using the given parameters, the van der Waals equation can be written in the following form, which is called reduced van der Waals equation of state. For all substances at the critical point, the given parameters have the same value equal to unity.
For practical calculations with an error of 15%, you can use the equation of state of a real gas in the following form:
p υ = z∙R∙T ,(7.2)
which was obtained on the basis the law of the corresponding states. Here z- compressibility factor depending on pressure p and temperature T and determined experimentally. Based on the analysis of experimental data, it was found that, with a certain accuracy, the function z = z (π, τ) is universal, i.e. quite common for various substances. For a particular substance, it can be determined from z -π diagram shown in rice. 7.6.
Attitude z k = R T k / p k v k at the critical point is called critical coefficient and taking into account the above relations for critical parameters ( a, b, R) is constant and equal to 8/3 = 2.67.
Thus, expression (16.14) should determine the true equilibrium vapor pressure at a given temperature. Since and are functions of the pressure and temperature of the corresponding phases, (16.14) is the equation of the transition line between two phases. Thus the equation of a transition line, such as a vapor pressure curve or a melting curve, is the relationship between and Therefore, the best way to represent the various phases is a .beta. diagram. FIG. 29 shows a conventional .beta.-diagram. The vapor pressure curve separates the gas and liquid phases, while the melting curve separates the liquid and solid phases.
The vapor pressure curve ends at the critical point K. At temperatures above the critical point, gas and liquid continuously pass into each other without absorbing or releasing heat and without a sudden change in density, which occurs, for example, in the case of evaporation. Repeated attempts have been made to find a similar "critical" point at the end of the melting curve, but even at very high pressures no such point has been found.
As the temperature decreases, the vapor pressure decreases. But at the same time, the pressure at which the liquid crystallizes (melting pressure) also decreases. At a certain temperature, the vapor pressure becomes equal to the crystal melting pressure (point in Fig. 29). At these temperatures and pressures, the gas, liquid, and solid (crystalline) phases can exist in equilibrium with each other; called the triple point. Below these temperatures and pressures, the gas can directly pass into the solid phase, and the solid phase can sublime (sublimate); the corresponding transition line is sometimes called the sublimation curve (or sublimation curve).
Fig. 29. -diagram.
Typically, the melting point rises with increasing pressure, so the melting curve in the diagram is tilted to the right. However, in some cases the melting point decreases with increasing pressure, for example for water between 0 and 2000 atm (Fig. 30). The melting point of water, that is, the melting point at a pressure of 1 atm, is, by definition, 0 ° C. The triple point lies slightly higher; its coordinates are 0.007 C and 4.6 mm Hg. Art.
The example of water shows that the phase diagram is not always as simple as shown in Fig. 29. Water can exist in the form of several solid phases, which differ in their crystalline structure. The helium phase diagram (Fig. 31) stands apart and differs from other diagrams in the absence of a sublimation curve: the liquid zone extends to absolute zero. Instead of a triple point, we have in this case the so-called -curve, which separates two different zones, usually denoted by Roman numerals.
Fig. 30. -diagram of water.
The transition between two liquid phases I and II manifests itself not in an abrupt change in density and not in the presence of the heat of transition, as is the case with conventional transitions (melting, condensation and sublimation), but in a sharp change in the coefficient of thermal expansion, compressibility and specific heat capacity, t i.e. derivatives of basic thermodynamic quantities. These transitions are often called transitions of the second kind.
From equation (16.14) of the line of transition of two phases, we can derive the relationship between different
characteristic thermodynamic values of the transition line. Consider a point on the transition line (Fig. 32); at this point If we now increase the temperature by and the pressure by so as to remain on the transition line, we will arrive at a point where both phases are again in equilibrium.
Fig. helium chart.
Thus, if there is an increase in the thermodynamic potential for phase 1 and - its increase for phase 2, then we have
Comparing with (16.14), we see that
where there is a small increase in the thermodynamic potential of phase 1 or 2 along the transition line.
According to § 13, the thermodynamic potential is equal to the free enthalpy of one kilomol, whence, taking into account (13.3), we obtain
where are small increments along the transition line and are the entropies and volumes of one kilomol of each phase along the transition line. Expression (16.17) can be rewritten as
Fig. 32. To the derivation of the Clausius-Claiperon equation.
Since the temperature remains constant during the transition, the entropy difference between the two phases is equal to the heat of transition divided by the temperature, from which we finally obtain the so-called Clausius-Claiperon equation
A number of important consequences follow from this equation. If, for example, we raise the temperature and approach the critical point along the vapor pressure curve, then the difference in the densities of the vapor and liquid, and therefore the difference in specific volumes in the denominator of equation (16.19), decreases continuously. But the slope of the vapor pressure curve on the p-T diagram, as experience shows, does not become infinite at the critical point. Therefore, on the basis of (16.19), we can conclude that as we approach the critical point, the heat of evaporation continuously decreases and, finally, becomes equal to zero. This is consistent with experimental data.
It also follows from equation (16.19) that the value is positive if the molar volume of the second phase is greater than the volume of the first phase and if heat must be supplied to the system to effect the transition from the first phase to the second. This is also consistent with the shape of the various transition lines obtained experimentally. It should be noted that the slope of the curve
melting water is negative, despite the fact that the value is positive. Equation (16.19) shows that in this case the volume of the second phase (water) must be less than the volume of the first phase (ice), while usually the solid phase has a smaller molar volume. These special properties of water have long been known from experience.
Real chemical substances, which practically have to be dealt with, and even ultrapure crystals of elementary semiconductors Ge and Si, always contain residual impurities, that is, they always represent substances consisting of several chemical elements. The interaction of the chemical elements that form this material can be very complex. The specific result of this interaction depends on the crystal-chemical nature of the interacting elements, their concentration, as well as on external factors - temperature and pressure.
The main means of depicting the results of the interaction of chemical elements or compounds that form a given substance are diagrams of the state of the system. The state diagram shows stable states, that is, states that, under given conditions, have a minimum of free energy. Therefore, a state diagram can also be called a phase equilibrium diagram, since it shows which equilibrium phases exist under given conditions. In accordance with this, the changes in the state of the system, which are reflected in the diagram, refer to equilibrium conditions, that is, in the absence of overcooling or supersaturation in the system. However, phase transformations cannot occur under equilibrium conditions (see below), so the state diagram is a theoretical case. However, the role of state diagrams in understanding the nature and results of the interaction of various chemicals and predicting these results is extremely important, because it is the nature of the interaction that determines the properties of the resulting material. In practice, state diagrams are used to consider transformations at low cooling or heating rates.
state diagram systems is called a geometric representation of the equilibrium phase states of a single or multicomponent thermodynamic system as a function of the parameters that determine these states (concentration, temperature, pressure).
Let us define some concepts used in the description of state diagrams.
thermodynamic system called a body of macroscopic dimensions (a set of bodies), between the individual parts of which (between
between which) heat transfer and diffusion of at least one of the components of the system is possible and for which (which) the laws of thermodynamics are valid.
Thermodynamic systems are divided into homogeneous and heterogeneous. homogeneous called a thermodynamic system, within which there are no interfaces between phases separating from each other parts of the system that would differ either in crystal structure or in their physical and chemical properties. heterogeneous the system consists of parts having either a different structure or different physico-chemical properties and separated from each other by phase interfaces. An example of a heterogeneous system is water,
in equilibrium with steam.
Phase- this is a homogeneous system or a system that is a collection of homogeneous systems identical in crystal structure and physico-chemical properties, separated from each other by interfaces. In the example above, the phases are water and steam, which differ, for example, in density.
Phase interfaces are layers of finite thickness, in which at least one of the system parameters changes in the direction from one phase to another. The interfaces of phases in relation to the adjacent phases have excess energy (surface tension energy).
For solids, the most important feature of a phase is its crystal lattice.1 Each solid phase has its own, unique crystal lattice, which differs from the lattices of other phases either in type or parameters. The solid crystalline phase can be obtained in the form of a single crystal or a polycrystal, which is a collection of grains or crystallites. The crystallites of a polycrystal, differently oriented in space, are separated from each other by interfaces into several atomic layers (see Chap. 3). Obviously, grain boundaries are not interphase boundaries.
Thermodynamic systems can be single or multicomponent.
System component called a part of the system, the number of which can vary regardless of the number of other parts. In our case, the components of the system can be chemical elements or compounds. The number of system components, generally speaking, may not be
1In principle, the solid phase can also be amorphous or glassy. Both of these phases are characterized by the absence of long-range order in the arrangement of atoms, rather resembling a liquid. Here we will consider only crystalline materials.
Rice. 4.1. State diagram of the Ge–Si system.
is equal to the number of different chemical elements in the system. For example, water (H2O) is made up of hydrogen and oxygen, but it is a one-component system. On fig. 4.1 and fig. 4.2 shows the phase equilibrium diagrams of two characteristic two-component (binary) semiconductor systems - Ge-Si and InSb-AlSb. The components of the system in the first case are Ge and Si, and in the second case, InSb and AlSb, and not Sb, Al, In, since the amount of In and Al in the system depends on the amount of Sb, and the amount of InSb does not depend on the amount of AlSb. That's why number of system components is the minimum number of chemicals required to form any phase of a given system.
A thermodynamically equilibrium state of a system is a state in which the parameters of this state do not change over time and there are no flows of any type in the system.
The equilibrium state of the system can be single-phase, two-phase and multi-phase. When two or more solid phases are mixed, solid solutions, compounds and mechanical mixtures. The latter is realized if these phases do not interact with each other. The phases that form a mixture can be elements, compounds or solid solutions based on them, as well as allotropic modifications of the same chemical element (α and β-tin, etc.). The maximum possible number of phases in equilibrium is determined by the Gibbs phase rule. The phase rule establishes the relationship between
Rice. 4.2. State diagram of the InSb–AlSb system.
by the number of phases, components and degrees of freedom of the system:
c= k− f+ 2, (4.1)
where c- number of degrees of freedom of the system, k- number of system components, f- number of phases in the system.
Under number of degrees of freedom systems understand the number of external and internal parameters (temperature, pressure and concentration), which can be changed without changing the number of phases in the system. If the number of degrees of freedom is equal to zero, then it is impossible to change the external and internal parameters of the system without causing a change in the number of phases. If the number of degrees of freedom is equal to one, then it is possible to change one of the parameters within certain limits and this will not cause a decrease or increase in the number of phases.
For example, consider the case of crystallization of a pure substance (an elementary semiconductor) at constant pressure. In this case, the Gibbs rule takes the form c= k− f+ 1.2 When a semiconductor
is in a liquid state f= 1, the number of degrees of freedom is 1 ( c= k− f+1 = 1 − 1 + 1 = 1). The temperature in this case can be
change without changing the state of aggregation. At the time of crystallization
f= 2 (two phases - solid and liquid), c= k− f+1 = 1 − 2+1 = 0. This is
means that the two phases are in equilibrium at a strictly defined
2 The independent variables in the Gibbs equation are concentration, temperature and pressure. If the pressure is constant, then the number of variables in the equation will decrease by one.
temperature (melting point), and it cannot be changed until one of the phases disappears (an area appears on the temperature-time graph T= const, the length of which will be equal to the time from the beginning to the end of crystallization). The source of maintaining a constant temperature in this case is the released latent heat of crystallization equal to the difference between the heat content of the old and new phases. Upon completion of crystallization, only one solid phase remains in the system, that is, the temperature can again change (decrease) without changing the number of phases.
State diagrams depict the phase composition of the system at different concentrations of components X, temperatures T and pressure P. State diagrams are generally spatial. The dimension of space depends on the number of independent variables whose function is the phase composition. These variables are the coordinates in which the chart is built. The simplest type of phase diagram characterizes the state of a pure one-component material as a function of pressure and temperature, for example, the well-known state diagram of water. However, we will not consider such single-component systems, but will immediately proceed to the consideration of multicomponent systems, since it is precisely multicomponent diagrams that are used in the production of semiconductors. Most often, such diagrams are built in temperature-concentration coordinates ( T− X). AT
In this case, for binary (two-component) systems, diagrams are displayed on a plane. For ternary (three-component) systems, diagrams are constructed in three-dimensional space, etc. If, in addition to temperature, pressure is also variable, then even for binary systems, diagrams become three-dimensional ( P− T− X diagrams). In what follows, we will mainly consider only binary systems constructed in coordinates T− X. However, this chapter will also discuss P− T− X diagrams of some semiconductor binary systems of great practical importance.
Typically, the concentration on the diagrams is expressed in weight or mole fractions of one of the components or in atomic percent. Therefore, the area of concentration change plotted on the axis X, is limited and extends from zero to one or up to 100%. For semiconductor systems, along with diagrams built on a linear scale, diagrams are sometimes built in which the concentration of a component is plotted in atoms per cubic centimeter or in atomic percent, but a logarithmic scale is used. This is due to the fact that, as a rule, the limiting solubility (see Chap. 7) is most
Rice. 4.3. State diagram of the Si–Au system with different scales along the concentration axis (in the region adjacent to the semiconductor, the atomic percent of the dopant is plotted on a logarithmic scale, and then the concentration in atomic percent is plotted on a linear scale).
The content of elements (impurities) in semiconductors in the solid state is small (less than 0.1 at.%) and the actually used doping in concentration is 1015–1019 atoms/cm3, that is, 10−5–10−2 at.% (see Fig. 4.3 ).
Phase diagrams of the state provide information about the nature of the phases and the phase composition of the system with a change in the concentration of one or more components, temperature and pressure. With the help of equilibrium state diagrams for given conditions, it is possible to determine: 1) the number of phases in the system; 2) the composition of each phase, its nature (elementary substance, compound, solid solution) and the conditions under which it is formed; 3) the relative amount of each of the phases.
Phase diagrams are built on the basis of physical and chemical analysis data. This analysis is based on the experimental study of the dependences of physical properties on such parameters as concentration, temperature, and pressure. Knowledge of these dependencies allows one to establish the nature of the phases and the boundaries of their existence. The most common methods used to construct phase diagrams are thermographic and dilatometric methods. Their essence lies in the fact that for an alloy of a given composition, the temperatures of phase transformations are determined by a jump-like change in the enthalpy H(heat content) or volume V system, fixed on the temperature-time curves (the temperature is noted at certain time intervals) or temperature-volume in the process of cooling or heating the alloy. Having thus determined the points of phase transformations for alloys of different compositions of a given system, it is possible to construct the entire state diagram. These methods determine only phase transformations of the first kind. These transitions should be distinguished from phase transformations of the second kind (ferromagnetic–paramagnetic states, superconducting–nonsuperconducting, ordered–disordered), accompanied by a jump-like change in the compressibility coefficient and heat capacity. In this case, composition-property diagrams are built or, for a given composition, temperature-property diagrams, etc.
SCHEMES OF PHASE TRANSFORMATIONS
BASIC CONCEPTS OF THE PHASE STATE
During the development of deposits in the reservoirs, the pressure, the quantitative ratio of gas and oil is constantly changing. This is accompanied by continuous changes in the composition of the gas and liquid phases with their mutual transition.
Particularly intense processes of such transformations occur when oil moves along the wellbore. Due to the rapid drop in pressure, a significant amount of gas is released from the oil, and near the mouth the flow sometimes turns into a finely dispersed suspension of oil droplets in a gaseous medium.
The further movement of oil to the consumer is also accompanied by continuous phase transformations, for example, from oil that no longer contains gas, they try to extract and capture the most volatile liquid fractions to reduce the loss of oil products from evaporation during storage in tanks.
Natural hydrocarbon systems consist of a large number of components, and these are not only hydrocarbons of the paraffin series, but also hydrocarbons belonging to other groups. The phase state of a mixture of hydrocarbons depends on its composition, as well as on the properties of individual components.
A typical phase diagram of a multicomponent mixture (Fig. 21) in the pressure - temperature coordinates has a loop-like form, i.e. differs from the corresponding phase diagram of a pure substance, which is depicted as a single monotonically increasing curve concave to the temperature axis with one end (critical) point. Before proceeding to a discussion of the features of this diagram, let's define some important physical concepts associated with this diagram.
"Critical point" (point To in fig. 21) corresponds to pressure and temperature values at which the properties of each phase become identical.
"Critical temperature" - temperature corresponding to the critical point.
"Critical Pressure" - pressure corresponding to the critical point.
"Intensive properties" are those properties that do not depend on the amount of the substance in question.
"Extensive properties" are properties that are directly proportional to the amount of the substance in question.
"Curve BUT boiling points” - a curve passing through points corresponding to pressures and temperatures at which the first gas bubble is formed during the transition of a substance from a liquid state to a two-phase state.
"Dew Point Curve b» - a curve passing through points corresponding to pressure and temperature at which the first drop of liquid is formed during the transition of a substance from a vapor state to a two-phase state.
"Two-Phase Region" - the region bounded by the curves of the initial boiling points and dew points, within which the gas and liquid are in equilibrium.
"Krikondenterm" ( M) - the highest temperature at which liquid and vapor can coexist in equilibrium.
"Krikondenbar" (N) - the highest pressure at which liquid and vapor can coexist in equilibrium.
"Retrograde region" (shaded area in Fig. 21) - any region within which condensation or vaporization occurs in the opposite direction to normal phase changes.
"Retrograde condensation" (limited by the KDM curve) means that the liquid condenses or when the pressure is reduced at a constant temperature (line ABD), or with increasing temperature at constant pressure (line F GA
"Retrograde evaporation" (limited by the NHK curve) means that the formation of vapor occurs when the temperature decreases at constant pressure (line AGF) or with increasing pressure at constant temperature (line DBA).
"Line of constant volume" (qualitative lines) - lines passing through points of the same volumetric liquid content inside a two-phase region.
From the consideration of Fig. 21 some important observations can be made. The boiling point curve and the dew point curve converge at a critical point. The boiling point curve corresponds to 100% liquid content in the system, and the dew point curve corresponds to 100% gas content. The shaded areas correspond to the area of retrograde phenomena. Area bounded by curves passing through points K bmd, corresponds to the region of isothermal retrograde condensation.
The phase diagram (Fig. 21.) with all its features is inherent in any multicomponent mixtures, but the width of its loop and the location of the critical point, and hence the retrograde regions, depend on the composition of the mixture.
From an oilfield point of view, multicomponent systems are roughly divided into oils and gases. In addition, multicomponent systems are subdivided depending on the state in which the hydrocarbon mixture is in the reservoir and after it is extracted to the surface.
The phase state of the reservoir hydrocarbon mixture and the features of their phase behavior during field development are determined by reservoir pressures and temperatures, as well as the composition of the mixture.
If the reservoir value of the temperature of the mixture T pl is greater than the cricondentherm M(dot F) and during the development of the field, the pressure drops (line FT 4), then this mixture will always be in a single-phase gaseous state. Such mixtures form gas fields.
If the reservoir temperature is between critical and cricondentherm, then such mixtures are classified as gas condensate. In this case, depending on the ratio between the initial formation pressure and the pressure of the beginning of condensation (point AT) the existence of three types of gas condensate deposits is possible: reservoir pressure can be higher (single-phase unsaturated), equal (single-phase saturated) or lower (two-phase) to the pressure of the beginning of condensation.
If the reservoir temperature is below the critical temperature of the mixture, i.e. is to the left of the critical point, then such mixtures are typical for oil fields. Depending on the initial values of reservoir temperature and pressure (the location of the point corresponding to these values relative to the boiling point curve), oil fields are distinguished with undersaturated, saturated oils and fields with a gas cap.
When the reservoir temperature is above the cricondentherm, the oil contains a large amount of gaseous and low-boiling hydrocarbons and has a greater shrinkage. Such oils are called light. They are distinguished by a high gas-to-oil ratio and a density approaching that of gas condensate.
Oil. Mixtures of hydrocarbons that are in the reservoir conditions in a liquid state are called oils. In terms of shrinkage on the surface, oils can be low and high..shrinkage.
The phase diagram for oil with low shrinkage is shown in fig. 22. Two salient features follow from this diagram. The critical point is located to the right of the crikondenbar, and the lines of equal volumetric liquid content in the mixture are closely located near the dew point curve. In addition, at atmospheric pressure and reservoir temperature, the mixture is in the region of a two-phase state. Under separation conditions, a significant amount of liquid is obtained from the mixture, even if its volume content in the mixture is very low. This phenomenon is due to a significant expansion of the gas phase at low pressures. A characteristic feature of this phase diagram is the presence of a relatively large amount of heavy components in the mixture.
"Depending on the initial reservoir conditions, oils are divided into saturated and undersaturated. If the initial reservoir conditions correspond to the point BUT on the boiling point curve (Fig. 22), then, therefore, the oil is completely saturated with gas.
As can be seen from the diagram, when the pressure is reduced by an infinitesimal amount, gas is released from saturated oil. If the initial conditions correspond to the point A / located above the boiling point curve, then the oil is undersaturated with gas. In order for this undersaturated oil to begin to release gas, the pressure must be reduced by a significant amount (to point A).
Oil with high shrinkage contains more light hydrocarbons than oil with low shrinkage. The critical temperature for such oils is closer to the reservoir temperature, and the lines of the same liquid volume content in the mixture are less closely grouped near the dew point curve.
A typical phase diagram for high shrinkage oil is shown in fig. 23. In this case, both in the reservoir and at the surface, much smaller amounts of fluid are obtained as a result of pressure reduction. This oil can be either saturated (point A) or undersaturated (point AND") gas.
"Different classes of hydrocarbons, in addition to phase diagrams, can be characterized by composition, specific gravity of the produced liquid and gas factor.
Oils with little shrinkage have GORs of ~180 m 3 / m 3, and the specific gravity is 0.80 g/cm 3 and more. Oils with high shrinkage have a GOR of 180 to 1400 m 3 / m 3, specific gravity 0.74-0.80 g/cm3.. The classification of most reservoir systems can only be carried out after a detailed study of samples of reservoir mixtures.
