q913 re1 w5 lec 18

Reservoir Engineering 1 Course (1st Ed.)

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http://www.about.me/AlamiNia

1. Oil Recovery

2. Waterflooding Considerations

3. Primary Reservoir Driving Mechanisms

4. Secondary Recovery Project

5. Flooding Patterns

1. Recovery Efficiency

2. Displacement Efficiency

3. Frontal Displacement

4. Fractional Flow Equation

Overall Recovery Efficiency

The overall recovery factor (efficiency) RF of any secondary or tertiary oil recovery method is the product of a combination of three individual efficiency factors as given by the following generalized expression:

In terms of cumulative oil production, it can be written as:

Where RF = overall recovery factor

NS = initial oil in place at the start of the flood, STB

NP = cumulative oil produced, STB

ED = displacement efficiency

EA = areal sweep efficiency

EV = vertical sweep efficiency

2013 H. AlamiNia Reservoir Engineering 1 Course: W5L18 Recovery / Frontal Displacement 5

Displacement Efficiency

Displacement efficiency The displacement efficiency ED is the fraction of

movable oil that has been displaced from the swept zone at any given time or pore volume injected. Because an immiscible gas injection or waterflood will always

leave behind some residual oil, ED will always be less than 1.0.


Areal Sweep Efficiency

Areal sweep efficiency The areal sweep efficiency EA is the fractional area of

the pattern that is swept by the displacing fluid.

The major factors determining areal sweep are:Fluid mobilities

Pattern type

Areal heterogeneity

Total volume of fluid injected


Vertical Sweep Efficiency

The vertical sweep efficiency EV is the fraction of the vertical section of the pay zone that is contacted by injected fluids. The vertical sweep efficiency is primarily a function of:

Vertical heterogeneity

Degree of gravity segregation

Fluid mobilities

Total volume injection


Volumetric Sweep Efficiency

Note that the product of EA EV is called the volumetric sweep efficiency and Represents the overall fraction of the flood pattern that

is contacted by the injected fluid.


Reservoir Heterogeneity

In general, reservoir heterogeneity probably has more influence than any other factor on the performance of a secondary or tertiary injection project.

The most important two types of heterogeneity affecting sweep efficiencies, EA and EV, are the reservoir vertical heterogeneity and areal heterogeneity.


Vertical Heterogeneity

Vertical heterogeneity is by far the most significant parameter influencing the vertical sweep and in particular its degree of variation in the vertical direction.

A reservoir may exhibit many different layers in the vertical section that have highly contrasting properties. This stratification can result from many factors, including

change in depositional environment, change in depositional source, or particle segregation.


Vertical Heterogeneity (Cont.)

Water injected into a stratified system will preferentially enter the layers of highest permeability and will move at a higher velocity. Consequently, at the time of water breakthrough in

higher-permeability zones, a significant fraction of the less-permeable zones will remain unflooded.

Although a flood will generally continue beyond breakthrough, the economic limit is often reached at an earlier time.


Areal Heterogeneity

Areal heterogeneity includes Areal variation in formation properties (e.g., h, k, ϕ,

Swc),

Geometrical factors such as the position, any sealing nature of faults, and

Boundary conditions due to the presence of an aquifer or gas cap.


Vertical vs. Areal Heterogeneity

Operators spend millions of dollars coring, logging, and listing appraisal wells, all of which permits direct observation of vertical heterogeneity. Therefore, if the data are interpreted correctly, it should

be possible to quantify the vertical sweep, EV, quite accurately.

Areally, of course, matters are much more uncertain since methods of defining heterogeneity are indirect, such as attempting to locate faults from well testing analysis. Consequently, the areal sweep efficiency is to be

regarded as the unknown in reservoir-development studies.


Displacement Efficiency Definition

All three efficiency factors (i.e., ED, EA, and EV) are variables that increase during the flood and reach maximum values at the economic limit of the injection project.

As defined previously, displacement efficiency is the fraction of movable oil that has been recovered from the swept zone at any given time.


Displacement Efficiency Expression

Mathematically, the displacement efficiency is expressed as:

Or

Where Soi = initial oil saturation at start of flood

Boi = oil FVF at start of flood, bbl/STB

S-o = average oil saturation in the flood pattern at a particular point during the flood


Displacement Efficiency Calculation

Assuming a constant oil formation volume factor during the flood life, the Equation is reduced to:

Where the initial oil saturation Soi is given by:

However, in the swept area, the gas saturation is considered zero, thus:


Displacement Efficiency Calculation (Cont.)The displacement efficiency ED can be expressed

more conveniently in terms of water saturation by substituting the above relationships into the Equation, to give:

Where w = average water saturation in the swept area

Sgi = initial gas saturation at the start of the flood

Swi = initial water saturation at the start of the flood


Displacement Efficiency Calculation (Cont.)If no initial gas is present at the start of the flood:

The displacement efficiency ED will continually increase at different stages of the flood, i.e., with increasing w. ED reaches its maximum when the average oil saturation

in the area of the flood pattern is reduced to the residual oil saturation Sor or, equivalently, when w = 1 – Sor.


Average Water Saturation in the Swept Area ED will continually increase with increasing water

saturation in the reservoir. The problem, of course, lies with developing an

approach for determining the increase in the average water saturation in the swept area as a function of cumulative water injected (or injection time).


Frontal Displacement Theory

Buckley and Leverett (1942) developed a well-established theory, called the frontal displacement theory, which provides the basis for establishing such a relationship. This classic theory consists of two equations:Fractional flow equation

Frontal advance equation


Fractional Flow Equation

The development of the fractional flow equation is attributed to Leverett (1941). For two immiscible fluids, oil and water, the fractional

flow of water, fw (or any immiscible displacing fluid), is defined as the water flow rate divided by the total flow rate, or:

Where fw = fraction of water in the flowing stream, i.e., water cut,

bbl/bblqt = total flow rate, bbl/dayqw = water flow rate, bbl/dayqo = oil flow rate, bbl/day


Flash Back: Fluid Potential in Tilted Reservoir

Where Φi = fluid potential at point i, psi

pi = pressure at point i, psi

Δzi = vertical distance from point i to the selected datum level, ft

ρ = fluid density under reservoir condition, lb/ft3

γ = fluid density under reservoir condition, g/cm3; this is not the fluid specific gravity (SG)


Fluid Density Under Reservoir Condition vs. Specific Gravity (SG)


𝑺𝑮 = 𝜸𝒐 =𝝆𝒐𝝆𝒘

=𝝆𝒐

𝒍𝒃𝒇𝒕3

𝝆𝒘 = 62.4𝒍𝒃𝒇𝒕3

=>𝝆

𝒍𝒃𝒇𝒕3

1441

𝒇𝒕2

𝒊𝒏2

=62.4 𝜸

144= 0.4333 𝜸

𝝆𝒍𝒃

𝒇𝒕2 ∗ 𝒇𝒕

1441

𝒇𝒕2

𝒊𝒏2

𝒍𝒃

𝒊𝒏2𝒇𝒕

=𝝆

𝒈𝒄𝒎2 ∗ 𝒄𝒎

∗1

453.59𝒍𝒃𝒈

12.54 2 = 6.4516

𝒄𝒎2

𝒊𝒏2∗

130.48

𝒄𝒎𝒇𝒕

𝒍𝒃

𝒊𝒏2𝒇𝒕

= 0.4335𝒍𝒃 ∗ 𝒄𝒎3

𝒈 ∗ 𝒊𝒏2𝒇𝒕∗ 𝝆

𝒈

𝒄𝒎3

𝒍𝒃

𝒊𝒏2𝒇𝒕

Linear Displacement in a Tilted System

Consider the steady-state flow of two immiscible fluids (oil and water) through a tilted-linear porous media as shown in Figure. Assuming a

homogeneous system, Darcy’s equation can be applied for each of the fluids (sin (α) = positive for

updip flow and negative for downdip flow):


Fractional Flow Expression

Subtracting the above two equations yields:

From the definition of the capillary pressure pc:

Combining Equations gives:


Fractional Flow Expression (Cont.)

From the water cut equation:

Replacing qo and qw in previous slide with above Equations gives:

Where fw = fraction of water (water

cut), bbl/bblko = effective permeability of

oil, mdkw = effective permeability

of water, mdΔρ= water–oil density

differences, g/cm3kw = effective permeability

of water, mdqt = total flow rate, bbl/dayμo = oil viscosity, cpμw = water viscosity, cpA = cross-sectional area, ft2


Fractional Flow Expression (for Water)

Noting that the relative permeability ratios kro/krw = ko/kw and, for two-phase flow, the total flow rate qt are essentially equal to the water injection rate, i.e., iw = qt, previous Equation can be expressed more conveniently in terms of kro/krw and iw as:

Where iw = water injection rate, bbl/day fw = water cut, bbl/bblkro = relative permeability to oilkrw = relative permeability to waterk = absolute permeability, md


Fractional Flow Parameters

The fractional flow equation as expressed by the above relationship suggests that for a given rock–fluid system, all the terms in the equation are defined by the characteristics of the reservoir, except:Water injection rate, iw

Water viscosity, μw

Direction of the flow, i.e., updip or downdip injection


Fractional Flow Expression (General)

It can be expressed in a more generalized form to describe the fractional flow of any displacement fluid as:

Where the subscript D refers to the displacement fluid and Δρ is defined as:


Gas Fractional Flow

For example, when the displacing fluid is immiscible gas, then:


Fractional Flow: Neglecting Pc

The effect of capillary pressure is usually neglected because the capillary pressure gradient is generally small and, thus, Equations are reduced to:

Where ig = gas injection rate, bbl/dayμg = gas viscosity, cpρg = gas density, g/cm3


Fractional Flow Range

From the definition of water cut, i.e., fw = qw/ (qw + qo), we can see that the limits of the water cut are 0 and 100%. At the irreducible (connate) water saturation, the water

flow rate qw is zero and, therefore, the water cut is 0%.

At the residual oil saturation point, Sor, the oil flow rate is zero and the water cut reaches its upper limit of 100%.

The implications of the above discussion are also applied to defining the relationship that exists between fg and gas saturation.


Fractional Flow Curves a Function of SaturationsThe shape of the

water cut versus water saturation curve is characteristically S-shaped, as shown in Figure.

The limits of the fw curve (0 and 1) are defined by the end points of the relative permeability curves.


Effects of Displacement Efficiency

Note that, in general, any influences that cause the fractional flow curve to shift upward (i.e., increase in fw or fg) will result in a less efficient displacement process. It is essential, therefore, to determine the effect of

various component parts of the fractional flow equation on the displacement efficiency.


Relation between fo & fw

Note that for any two immiscible fluids, e.g., water and oil, the fraction of the oil (oil cut) fo flowing at any point in the reservoir is given by:fo + fw = 1 or fo = 1− fw

The above expression indicates that during the displacement of oil by waterflood, an increase in fw at any point in the reservoir will cause a proportional decrease in fo and oil mobility.


1. Ahmed, T. (2006). Reservoir engineering handbook (Gulf Professional Publishing). Ch14

1. Water Fractional Flow Curve

2. Effect of Dip Angle and Injection Rate on Fw

3. Reservoir Water Cut and the Water–Oil Ratio

4. Frontal Advance Equation

5. Capillary Effect

6. Water Saturation Profile

q913 re1 w5 lec 18

Education

vertical sweep efficiency

overall recovery efficiency

areal sweep efficiency

areal sweep efficiency

volumetric sweep efficiency

displacement efficiency

displacement efficiency

reservoir heterogeneity