Q913 rfp w3 lec 11

Reservoir Fluid Properties Course (1st Ed.)

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http://www.about.me/AlamiNia

mailto:[email protected]

http://www.about.me/AlamiNia

1. Cubic EoS:A. SRK EoS

B. PR EoS

C. Other Cubic EoS

2. Non Cubic EoS

3. EoS for Mixtures

4. Hydrocarbons A. Components

B. Mixtures

C. Heavy Oil

2013 H. AlamiNia Reservoir Fluid Properties Course: Flash and Equilibrium Ratios 2

1. PT-Flash Process

2. Equilibrium Ratios

3. PT-Flash Calculations

4. Mixture Saturation Points


Flash Calculations

Flash calculations are an integral part of all reservoir and process engineering calculations.

They are required whenever it is desirable to know the amounts (in moles) of hydrocarbon liquid and gas coexisting in a reservoir or a vessel at a given pressure and temperature.

These calculations are also performed to determine the composition of the existing hydrocarbon phases.


PT-Flash Process Procedure

A feed stream consisting of a mixture of N components is led to a flash separator kept at a constant temperature and pressure.

Two phases are present in the separator.

In a gas–oil separator, the gas is let out at the top and the oil at the bottom.


PT-Flash Process Results

If P, T, and component mole fractions in the feed (z 1, z 2, …, z N) are known, a flash calculation will provide the following results:1. Number of phases.

2. Molar amounts of each phase (moles of Liquid and gas phase).

3. Molar compositions of each phase.



Principle of PT-Flash Process for a Hydrocarbon Reservoir Fluid Mixture

Figure illustrates a two-phase PT-flash process

The term β for the vapor mole fraction, (y 1, y 2, …, y N) for the

component mole fractions in the gas phase, and the (x 1, x 2, …, x N) for

the component mole fractions in the liquid phase

Phases Occurring in Petroleum ProductionA phase is defined as that part of a system which is

uniform in physical and chemical properties, homogeneous in composition, and separated from other coexisting phases by definite boundary surfaces.

The most important phases occurring in petroleum production are the hydrocarbon liquid phase and the gas phase. Water is also commonly present as an additional liquid phase.


Phases Coexistence

These can coexist in equilibrium when the variables describing change in the entire system remain constant with time and position.

The chief variables that determine the state of equilibrium are system temperature, system pressure, and composition.

These types of calculations are based on the concept of equilibrium ratios.


K-Factors Expression

The following relations apply for two phases in equilibrium:

The vapor and liquid phase fugacity coefficients of component i, ϕ iV and ϕ iL

Ki is the equilibrium ratios or K-factors (for low pressures and ideal gas and ideal solutions is equal to vapor pressure of component i divided by total system pressure Ki=Pvi/p)


𝑲𝒊 =𝒚𝒊𝒙𝒊=𝝓𝒊𝑳

𝝓𝒊𝑽 , 𝒊 = 1,2, … ,𝑵

Equilibrium Ratios Assumption

The equilibrium ratios, which indicate the partitioning of each component between the liquid phase and gas phase, as calculated by (ki=pvi/p) in terms of vapor pressure and system pressure, proved to be inadequate.

The basic assumptions behind Equation (ki=pvi/p) are that:The vapor phase is an ideal gas as described by Daltons

Law

The above combination of assumptions is unrealistic and results in inaccurate predictions of equilibrium ratios' at high pressures.


Equilibrium Ratios For Real Solutions

For a real solution, the equilibrium ratios are no longer a function of the pressure and temperature alone, but also a function of the composition of the hydrocarbon mixture. This observation can be stated mathematically as

Ki = K (p, T, Zi)

Numerous methods have been proposed for predicting the equilibrium ratios of hydrocarbon mixtures. These correlations range from a simple mathematical

expression to a complicated expression containing several compositional dependent variables.


K-Factor Determination: Correlations

Wilson's Correlation: A simplified thermodynamic expression for estimating K-values. Ki=Pci/p*EXP [5.37(1+ω i) (1-Tci/T)]

Where Pci & Tci= critical pressure & temperature of component i

The above relationship generates reasonable value for the equilibrium ratio when applied at low pressures.


K-Factor Determination: Convergence Pressure MethodEarly high pressure phase-equilibria studies

revealed that when a hydrocarbon mixture of a fixed overall composition is held at a constant temperature as the pressure increases, the equilibrium values of all components converge toward a common value of unity at certain pressure.

This pressure is termed the convergence pressure Pk of the hydrocarbon mixture



Equilibrium Ratios vs. P Relationship

A Schematic Diagram of Equilibrium Ratios vs. P Relationship

K-Factor Determination: Convergence Pressure Method (Cont.)The convergence pressure is essentially used to

correlate the effect of the composition on equilibrium ratios.

The illustration shows a tendency of the equilibrium ratios to converge isothermally to a value of Ki = 1 for all components at a specific pressure, i.e., convergence pressure.

A different hydrocarbon mixture may exhibit a different convergence pressure.


Component Material Balance

A material balance for each component yields

In addition, the component mole fractions must for each phase sum to unity, yielding one additional relation in the form suggested by Rachford and Rice


𝒛𝒊 = 𝜷𝒚𝒊 + 1 − 𝜷 𝒙𝒊 , 𝒊 = 1,2, … ,𝑵

𝒊=1

𝑵

𝒚𝒊 − 𝒙𝒊 = 0

Component Mole Fractions in the Liquid and Gas Phase

The liquid phase is an ideal solution as described by Raoult's Law

Using the equations we have:


𝒚𝒊 =𝒛𝒊𝑲𝒊

1 + 𝜷 𝑲𝒊 − 1, 𝒊 = 1,2, … ,𝑵

𝒙𝒊 =𝒛𝒊

1 + 𝜷 𝑲𝒊 − 1, 𝒊 = 1,2, … ,𝑵

𝒂𝒏𝒅

𝒊=1

𝑵

𝒚𝒊 − 𝒙𝒊 =

𝒊=1

𝑵𝒛𝒊 𝑲𝒊 − 1

1 + 𝜷 𝑲𝒊 − 1= 0

Fugacity

In chemical thermodynamics, the fugacity (f) of a real gas is an effective pressure which replaces the true mechanical pressure in accurate chemical equilibrium calculations. It is equal to the pressure of an ideal gas which has the same chemical potential as the real gas.

The fugacity f is a measure of the molar Gibbs energy of a real gas.

The fugacity has the units of pressure, in fact, the fugacity may be looked upon as a vapor pressure modified to represent correctly the escaping tendency of the molecules from one phase into the other.


Fugacity Determination

Fugacities are determined experimentally or estimated from various models such as a Van der Waals gas that are closer to reality than an ideal gas.

In a mathematical form, the fugacity of a component is defined by the following expression:

Where f = fugacity, psia, p = ideal gas pressure, psia, Z = compressibility factor

The ratio of the fugacity to the pressure, (f/p), is called the fugacity coefficient ϕ.


𝒇 = 𝒑𝒆 0𝒑𝒁−1𝒑𝒅𝒑

Solving Equations

With T and P fixed, the number of variables is also (N + 1), these being (K 1, K 2, …, K N) and β. Before solving Equations, it is necessary to make sure

that there are really two phases present and not just a single gas or a single liquid (oil) phase. Solution of the two equations is further complicated by

the fact that the fugacity coefficients entering into k-factor Equation are functions of the phase compositions resulting from the flash calculation, meaning that the fugacity coefficients have to be determined in an iterative manner. Before dealing with the flash problem in general, it

may be useful to first consider some simplified cases.


Flash Calculations Procedure

Step 1. Calculation of the total number of moles in the vapor (gas) phase (β)

Equation can be solved for β by using the Newton-Raphson iteration techniques.

Step 2. Calculation of total number of moles in the liquid phase (1-β)

Step 3&4 Calculation of xi and yi


𝒇(𝜷) =

𝒊=1

𝑵𝒛𝒊 𝑲𝒊 − 1

1 + 𝜷 𝑲𝒊 − 1= 0

𝒙𝒊 =𝒛𝒊

1 + 𝜷 𝑲𝒊 − 1, 𝒚𝒊 =

𝒛𝒊𝑲𝒊1 + 𝜷 𝑲𝒊 − 1

, 𝒊

= 1,2, … ,𝑵

Pure Component Vapor Pressures from Cubic Equations of StateNeglecting solid states, a pure component will

either form a single-phase gas, a single-phase liquid, or a gas and a liquid phase in equilibrium.

For a given temperature, two phases in equilibrium can only exist at the pure component vapor pressure.

Pure component vapor pressures may be determined from a cubic equation of state, but in an iterative manner.


Mixture Saturation Points from Cubic Equations of StateIf a single component is not at its vapor pressure,

only one phase exists at equilibrium.

With two or more components present, the determination of the number of phases is less trivial because the equilibrium phase compositions are unknown.

Before considering the general PT-flash problem, it may be useful to first consider the problem of locating mixture saturation pressures.


Mixture Bubble and Dew Point PressureBubble point

For a mixture initially in liquid form, the saturation point pressure is detected as the pressure at which the first gas bubble is seen to form in the liquid.

A saturation point of a liquid is therefore also called a bubble point.

Dew point For a mixture initially in gaseous form, the saturation

point is the pressure at which the first liquid drop is formed.

The saturation point of a gas is therefore also known as a dew point.


Mixture Bubble Point Pressure from Cubic EoSAs compared to the general PT-flash calculation,

bubble and dew point calculations are simpler, in the sense that one of the equilibrium phases equals the feed composition.

At the bubble point pressure, the vapor mole fraction β equals zero, and Equation Σ (zi (Ki-1))/ (1+β (Ki-1)) =0 can be simplified to


𝑭 =

𝒊=1

𝑵

𝒛𝒊 𝑲𝒊 − 1 = 0

Wilson K-Factor Approximation

For a given estimate of the bubble point pressure, a K-factor estimate may be obtained from the K-factor approximation (Wilson, 1969)

The liquid phase equals the feed composition and an initial estimate of the vapor phase composition at the bubble point may be obtained from yi= (ziKi)/ (1+β (Ki-1)) with K-factors from above.


𝒍𝒏𝑲𝒊 = 𝒍𝒏𝑷𝒄𝒊𝑷+ 5.373 1 + 𝝎𝒊 1 −

𝑻𝒄𝒊𝑻

K-factor Methods

Explain different k-factor methods


Applications of the Equilibrium Ratio

Some of the practical applications are:Determination of the Dew Point Pressure

Determination of the Bubble-Point Pressure

Separator Calculations


1. Mixture Saturation Points Calculation

2. Surface Separation

3. Phase Envelope

4. Phase Identification


1. Pedersen, K.S., Christensen, P.L., and Azeem, S.J. (2006). Phase behavior of petroleum reservoir fluids (CRC Press). Ch6.


Q913 rfp w3 lec 11

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