PAB3053

Reservoir Modeling and Simulation

Semester: MAY2015

Compositional SimulationPetroleum Engineering Department

Berihun M. Negash

UNIVERSITI TEKNOLOGI PETRONAS

CHAPTER OUTCOMES

At the end of this session students should be able to

Understand the concept of compositional simulation

Discover Application areas of Compositional simulation.

Apply the Governing Equations for Compositional Simulation.

Exercise

Depict the five reservoir fluid types on a multicomponent phase

diagram.

Describe black oil and compositional models by making use of

a simple schematic diagram.

Briefly explain the application areas of a compositional model.

Why compositional model is not used for all types of problems.

Why simulate?

PVT data

Black Oil

Volatile oil

Retrograde gas

Wet gas

Dry gas

Why analyze PVT data?

Why we need PVT

properties of fluids?

Where in the

production stage do

we need PVT

properties of the

hydrocarbon fluids?

Answer!!!

we need to know how the fluids behave

within the reservoir,

within the wells,

at surface conditions,

in the network and at the refinery.

The fluid properties need to be known over a wide

range of temperatures and pressures.

When gas is injected into the reservoir, we also need to

know how the properties of the original reservoir fluid

will change as the composition changes.

We also need to predict PVT fluid

properties

The composition of well stream as a function of time

Completion design, which depends on the properties of the wellbore liquids

Whether to inject or re-inject gas, and if so

The detailed specification of the injected gas - how much C3, 4, 5s to leave in

separator configuration and stage for injection gas

Miscibility effects that may result from the injected gas

The amounts and composition of liquids left behind and their physical properties: density, surface tension, viscosity.

Separator/NGL Plant Specifications

H2S and N2 concentration in produced gas

Product values vs. time

Black Oil and Compositional

Fluid Models

Black Oil Model

Oil and Gas phases are represented by two components:

one component called oil and another component

called gas.

Compositional Model

Compositional Model

Oil and Gas phases are represented by multicomponent

mixtures.

Uses of Compositional Simulation

Volatile oil (oAPI changes, oil vaporizes)

Miscible EOR (CO2, LPG)

Condensate (cycling, oil flows)

Gas cycling (injection of dry gas)

Injecting new fluid (N2)

Cases where gas injection/re-injection into an oil produces a

large compositional changes

Surface facilities department needs detailed compositions

of the production stream.

Phase Diagram

Contd

If the reservoir temperature and pressure are close to

the critical point of the reservoir fluid, or if they get

close to each other during the simulation

Even if we are not injecting gas into a reservoir, we

may still need to consider compositional simulation if

there are:

Large compositional variations with depth

Large temperature variation with depth

Large compositional variation in the x-y direction

When to use Black Oil Simulation!

If the reservoir stays as a single-phase oil or a single-phase gas

during its entire history, away from the critical point, then it

can in general be can be modeled with a black-oil model.

If the reservoir is two-phase at any time during the

simulation then there will be some compositional effects. In

many cases however these can be approximated by varying

gas/oil and oil/gas ratios to mimic small compositional

changes.

Condensate dropout or gas liberation should be a small part

of the hydrocarbon in place.

Remaining hydrocarbon composition should not change

significantly when gas is liberated or condensate drops out

Advantages of Compositional Simulation

Compositional simulators can account for the effects of

composition on:

Changes in phase behavior

Multi-contact miscibility

Immiscible or near-miscible displacement behavior in

compositionally dependent mechanisms such as

vaporization, condensation, and oil swelling

Composition-dependent phase properties such as

viscosity and density on miscible sweep-out

Interfacial Tension (IFT) especially the effect of IFT

on residual oil saturation.

Difficulties with Compositional

Simulation

There are a number of issues that may need to be

considered when running any compositional

simulator.

Calculating phase composition around the critical point can

be difficult.

Modeling viscous fingering in large grid blocks is not easy.

Numerical dispersion is an issue in both black-oil and

compositional simulation, but can have a greater effect in

compositional.

Larger computational time

Summary

Black Oil Simulation

Components: Oil and gas Phase: Oil and gas

HC composition remains constant

All fluid properties are assumed to be determined by oil pressure and bubble point pressure only

mass transfer between the two phases is normally described by the solution gas-oil ratio term, Rso

Compositional Simulation

Components: HCs (C1, C2, )Non HCs (CO2, H2S,) Phases: Oil and gas

HC composition varies as the reservoir is produced

All fluid properties are assumed to be determined by oil pressure, bubble point pressure and Composition

Mass transfer is dealt with Flash Calculation (either using K-Values or EOS)

Differences Between black Oil and Compositional Simulations

The General equation

For a two phase Oil/gas System

Black Oil

+ =

+

Compositional

+ =

+

PVT prediction methods

The methods used for PVT prediction are as follows:

1) K-value, pk (convergence pressure) method.(This

method is faster and can be matched with lab data and

EOS , but it needs correction for the density of oil and the

density of gas)

2) Equation of State method (EOS).( It matches more

accurate with the lab data and we can get the density of

oil and gas)

a) Peng-Robinson

b) Redlich-Kwong

K-Value Method

When the vapor and liquid phases are in

equilibrium, the molecules of each component are

condensing and vaporizing at the same rate.

vapor = 1.0 = mole fraction of component in vapor phase

= 1.0 = mole fraction of component in liquid phase

= 1.0 = total mole fraction of component

=

Consider one mole of a fluid of composition z1, z2...

zN that splits at some pressure and temperature (P,

T) into L moles of liquid of composition x1, x2...xNand V moles of vapor composition y1, y2... yN.

Then

+ = 1

+ = Substituting for L and using the definition of

=

1+ 1and =

1+ 1

From which

=1

= =1

1

1 + 1= 0

The equation is called Rachford-Rice equation

K-values tend to get closer to 1 as pressure and temperature increases.

QUIZ: what does a K-value of 1 indicate??????

Example

Consider a fluid made up of only three components,

C1, C3 and C10. The composition of the fluid is

Z1 = 0.8 so we have 80% C1

Z2 = 0.1 so we have 10% C3

Z3 = 0.1 so we have 10% C10

K1 =11, K2 = 1, K3 = 0.1

what is the value of V?

what is the value of L?

What is the composition of the oil and of the gas?

EOS Methods

Van der waals:

+

2

=

The constants a and b have positive values and are characteristic of the individual gas.

The van der Waals equation of state approaches the ideal gas law PV=nRT as the values of these constants approach zero.

The constant a provides a correction for the intermolecular forces.

Constant b is a correction for finite molecular size and its value is the volume of one mole of the atoms or molecules.

.

EOS Methods

Redlich Kwong: P =

+Where

a =0.4272

2

and b =

0.08664

= 1 + 0.48508 + 1.55171 0.156132 1 0.5

2

is the acentric factor and

=

=

= log 1: = 0.7

.

EOS methods contd

Peng Robinson

=

2 + 2 2

Where

a =0.4572352

2

, b =

0.077796

= 1 + 1 0.5

2

= 0.37464 + 1.54226 0.269922

Using the Van der Waals EOS to calculate

molar volume and compressibility

A shallow reservoir in Malaysia is at a temperature of 100F and

a pressure of 300 psia (2.0 MPa). The fluid is pure methane.

1. Calculate the molar volume of methane at reservoir

conditions using the Van der Waals EOS. What is the

compressibility factor? You will need to iterate a few times

until convergence to find the solution.

2. Calculate the specific volume of methane at reservoir

conditions using the ideal gas equation. What is the

compressibility factor?

Using the PengRobinson EOS to model the phase behavior

Propane has the following properties: a critical

temperature of 370 K; a critical pressure of 42.5 bars;

and an acentric factor of 0.152. The gas constant is 83.1

cm3bar/mol/K. Calculate the attraction and co-volumeparameters, a and b and the temperature

dependence parameter at a temperature of 40C.

Tc=370k

Pc=42.5*10^5Pa

=0.152

Black Oil

Primary depletion

Water flooding

Immiscible gas injection

Imbibition

Compositional

Miscible Gas injection CO2 flooding).

Gas condensate reservoir depletion (Gas cycling, oil flows).

The modeling of gas injection into near critical reservoirs

Miscible flooding by CO2or enriched gas injection

Injecting new fluid (N2)

SummaryUses of Black Oil and Compositional Simulation

The Governing Equations

We define

Ckg = mass fraction of component k present in the gas

phase and

Cko = mass fraction of component k present in the oil

phase.

Thus, we have the conditions that for a system of Nccomponents:

=1

= 1 =1

= 1

Contd

Then, a mass balance of component k may be written (in

one dimension, for simplicity):

+ =

+

Darcy's equations for each flowing phase are identical to

the Black Oil equations:

=

=

where = , = and + =1

Thus, we may write flow equations for Nc components as:

+

=

+

= 1, 2, 3,

The properties of oil and gas phases depend on pressures

and composition, so that the functional dependencies may

be written:

The equilibrium K-values may be used to determine

component ratios:

The Black Oil model may be considered to be a

pseudo-compositional model with two components.

Again neglecting water

component 1 is gas

component 2 is oil

Assignment

Use the definitions in the previous slide and show

that the flow equations for the black oil simulation

model are the same as a pseudo compositional

model.