Chapter 2 reservoir rock properties and core anlysis

Special types of fluid saturations Connate interstitial water saturation, Swc Critical oil saturation, Soc Residual oil saturation, Sor Movable oil saturation, Som Critical gas satur

Vietnam National University - Ho Chi Minh City

University of Technology

Faculty of Geology & Petroleum Engineering

Department of Drilling - Production Engineering

Course

Reservoir Engineering

Trần Nguyễn Thiện Tâm

Email: trantam2512@hcmut.edu.vn

References

Holditch Resevoir Engineering (Schlumberger)

Chapter 2

Reservoir rock

properties

Reservoir

A subsurface body of rock having sufficient porosity and

permeability to store and transmit fluids

p

V

V V

V V Porosity     

Porosity

Comparison of Total and Effective Porosities

 Very clean sandstones: ϕ t = ϕ e

 Poorly to moderately well -cemented intergranular materials:

ϕ t ≈ ϕ e

 Highly cemented materials and most carbonates: ϕ e < ϕ t

Permeability

Permeability is a property of the porous medium and is a measure of the capacity of the medium to transmit fluids

Absolute Permeability

When the medium is completely saturated with one fluid, then the permeability measurement is often referred to as specific or

absolute permeability

Relative Permeability

Relative permeability is defined as the ratio of the effective permeability to a fluid at a given saturation to the effective permeability to that fluid at 100% saturation

Oil:

Water:

Gas:

eo ro

k k

k



ew rw

k k

In-Situ Saturation

Fluid Saturation

The saturation of each individual phase ranges between zero to 100% By definition, the sum of the saturations is 100%, therefore

Sg + So + Sw = 1.0

Example

A core, 2.75 cm long and 2.75 cm in diameter has a porosity of 25% It is saturated with oil and water, where the oil content is 1.8 cm3

a) What is the pore volume of the core?

b) What are the oil and water saturations of the core?

Average porosity

Arithmetic average ϕ = Σϕ i /n

Thickness-weighted average ϕ = Σϕ i h i /Σh i

Areal-weighted average ϕ = Σϕ i A i /ΣA i

Volumetric-weighted average ϕ = Σϕ i A i h i /ΣA i h i

where n = total number of core samples

hi = thickness of core sample i or reservoir area i

ϕi = porosity of core sample i or reservoir area i

Ai = reservoir area i

Average permeability

Average Permeability (Parallel Flow):

Average Permeability (Series Flow):

avg n

i i

k h k

i

L k

L k





 



Flow direction

Original hydrocarbon volume in place

One important application of the effective porosity is its use in

determining the original hydrocarbon volume in place

Consider a reservoir with an areal extent of A acres and an average thickness of h feet

The total bulk volume of the reservoir can be determined from the following expressions:

Bulk volume = 43,560Ah, ft3

or

Bulk volume = 7,758Ah, bbl

where A = areal extent, acres

h = average thickness

Original hydrocarbon volume in place

The reservoir pore volume in cubic feet gives:

Darcy’s Equation

kA dp q

dL



 

Darcy’s Equation

TABLE 2.1 – UNIT SYSTEMS USED FOR DARCY’S LAW

SI British cgs Darcy Oilfield

Example

Calculation of Permeability of Porous Media

A fluid of viscosity of 1.2 cp flows through a cylindrical core at a rate of 0.25 cm3/s with a pressure drop of 2.5 atm Core dimensions are a length of 12 cm and a 5 cm2 flow area (i.e., the area perpendicular to the direction of flow) Determine the core permeability

Example

A sand body is 2000 feet long, 200 feet wide and 12 feet thick It has a uniform permeability of 345 md to oil at 17 per cent connate water saturation The porosity is 32 percent The oil has

a reservoir viscosity of 3.2 cp Answer the following:

i If flow takes place parallel to 2000 ft length above saturation

pressure, what pressure drop will cause 100 barrels per day (BPD) to flow through the sand body, assuming the fluid behaves essentially as an incompressible fluid?

ii What is the apparent velocity of the oil in feet per day at the

100 BPD flow rate?

iii What is the interstitial average velocity in feet per day?

iv Calculate initial oil in place in barrel

Example

Note: Darcy equation in field units is Qo = 0.001127 A.Ko.ΔP/μ.L, here flow rate is in BPD, ΔP is in psi, viscosity is in cp, permeability is in mD, length is in ft, and area is in sq ft, 1 Barrel

= 5.61 cubic feet

Example Relative Permeability Calculations

From Steady-State Tests

Table 2.2 shows a set of steady-state

experiments measured at several

water saturations Assuming the core

size and conditions are the same as

Example

Special types of fluid saturations

Connate (interstitial) water saturation, Swc

Critical oil saturation, Soc

Residual oil saturation, Sor

Movable oil saturation, Som

Critical gas saturation, Sgc

Critical water saturation, Swc

Connate (interstitial) water saturation, Swc

The terms irreducible water saturation, connate water saturation, and critical water saturation, generally denoted by Swi(or Siw), are extensively used interchangeably to define the water

saturation at which the water phase remains immobile

Critical oil saturation, Soc

For the oil phase to flow, the saturation of the oil must exceed a certain value, which is termed critical oil saturation At this

particular saturation, the oil remains in the pores and, for all practical purposes, will not flow

Residual oil saturation, Sor

During the displacing process of the crude oil system from the

porous media by water or gas injection, there will be some remaining oil left that is quantitatively characterized by a

saturation value that is larger than the critical oil saturation This

saturation value is called the residual oil saturation, Sor The term residual saturation is usually associated with the nonwetting phase when it is being displaced by a wetting phase

Movable oil saturation, Som

Movable oil saturation Som is another saturation of interest and is

defined as the fraction of pore volume occupied by movable oil as

expressed by the following equation:

S om = 1 − S wc − S oc

Critical gas saturation, Sgc

As the reservoir pressure declines below the bubble-point pressure, gas evolves from the oil phase and consequently the saturation of the gas increases as the reservoir pressure declines

The gas phase remains immobile until its saturation exceeds a certain saturation, called critical gas saturation, above which gas begins to move

Critical water saturation, Swc

The critical water saturation, connate water saturation, and irreducible water saturation are extensively used

interchangeably to define the maximum water saturation at which the water phase will remain immobile

Rock Wettability

Rock wettability is the tendency of

either the water phase or the oil

phase to preferentially maintain

contact with the rock surface in a

multiphase fluid system

The most common method of

determining rock wettability is by

measurement of the contact angle,

θ between the rock surface and the

fluid system

The rock surface is considered to be

water-wet when θ < 90o and oil-wet

when θ > 90o

Surface and interfacial tension

In dealing with multiphase systems, it is necessary to consider the effect of the forces at the interface when two immiscible

fluids are in contact When these two fluids are liquid and gas, the term surface tension is used to describe the forces acting on the interface When the interface is between two liquids, the acting forces are called interfacial tension

Surface and interfacial tension

Surface tension

Interfacial tension

2 cos

w gw

Capillary Pressure

Capillary pressure, p c is commonly defined as the difference in the pressure of the non-wetting phase and the pressure of the wetting phase This is represented as:

p c = p nw – p w

p nw = pressure in the non-wetting phase;

p w = pressure in the wetting phase

Capillary Pressure

For a water-wet rock in an oil/water system, the capillary

pressure derived from Eq is:

Capillary Pressure

Gas-liquid system

where σ gw = gas-water surface tension, dynes/cm

Oil-water system

where σ ow is the water-oil interfacial tension, dynes/cm

g = acceleration due to gravity, cm/sec2 (980.7)

Capillary Pressure

The phenomenon of capillarity in reservoirs can be discussed in terms of capillary pressure as measured in capillary tubes For a capillary tube, capillary pressure is determined as:

p c = capillary pressure, dynes/cm2;

σ = the interfacial tension between the two immiscible phases,

dynes/cm;

θ = contact angle, degrees; and

r = radius of the capillary tube, cm

Capillary Pressure

One such experiment is called

the restored capillary

pressure technique, which

was developed primarily to

determine the magnitude of

the connate water saturation

A diagrammatic sketch of this

equipment is shown in Figure

4-4

Capillary Pressure

One such experiment is called

the restored capillary

pressure technique, which

was developed primarily to

determine the magnitude of

the connate water saturation

A diagrammatic sketch of this

equipment is shown in Figure

4-4

Capillary Pressure

Procedure: this procedure

consists of saturating a core

100% with the reservoir

water

 Placing the core on a

porous membrane, which

is saturated 100% with

water and is permeable to

the water only, under the

pressure drops imposed

during the experiment

Capillary Pressure

Procedure:

 Air is then admitted into

the core chamber and the

pressure is increased until

a small amount of water is

displaced through the

porous, semi-permeable

membrane into the

graduated cylinder

Capillary Pressure

Procedure:

 Pressure is held constant

until no more water is

displaced, which may

require several days or even

several weeks, after which

the core is removed from

the apparatus and the

water saturation is

determined by weighing

Capillary Pressure

Procedure:

 The core is then replaced in

the apparatus, the pressure

is increased, and the

procedure is repeated until

the water saturation is

reduced to a minimum

Capillary Pressure

The data from such an

experiment are shown in

Figure 4-5

Two important phenomena

can be observed in Figure

4-5

Capillary Pressure

First, there is a finite

capillary pressure at 100%

water saturation that is

necessary to force the

nonwetting phase into a

capillary filled with the

wetting phase This

minimum capillary pressure

is known as the

displacement pressure, p d

Capillary Pressure

If the largest capillary opening is considered as circular with a

radius of r, the pressure needed for forcing the nonwetting fluid out of the core is:

This is the minimum pressure that is required to displace the wetting phase from the largest capillary pore because any capillary of smaller radius will require a higher pressure

Capillary Pressure

As the wetting phase is displaced, the second phenomenon of any

immiscible displacement process is encountered, that is, the

reaching of some finite minimum irreducible saturation This irreducible water saturation is referred to as connate water

Capillary Pressure

Figure 4-6 is an example

of typical oil-water

capillary pressure curves

In this case, capillary

pressure is plotted versus

water saturation for four

rock samples with

permeabilities increasing

from k 1 to k 4

Capillary Hysteresis

Pore spaces of reservoir rocks were originally filled with water, after which oil moved into the reservoir, displacing some of the

water and reducing the water to some residual saturation

When discovered, the reservoir pore spaces are filled with a connate water saturation and an oil saturation

All laboratory experiments are designed to duplicate the saturation history of the reservoir

Capillary Hysteresis

The process of generating the capillary pressure curve by

displacing the wetting phase, i.e., water, with the nonwetting phase

(such as with gas or oil), is called the drainage process

The process of generating the capillary pressure curve by

displacing the nonwetting phase (such as with oil) with the

wetting phase (e.g., water), is called the imbibition process

Capillary Hysteresis

The process of saturating and

desaturating a core with the

nonwetting phase is called

capillary hysteresis

Figure 4-7 shows typical

drainage and imbibition

capillary pressure curves The

two capillary

pressure-saturation curves are not the

same

Initial Saturation Distribution in a Reservoir

The height h above the freewater level

h = height above the free-water level

p c = capillary pressure

Δρ = density difference

144 pch







Example

The capillary pressure

curves for a sandstone

reservoir are shown in the

Fig Estimate the height, in

feet above the free water

table, where Sw drops below

100% and where it is equal

to 45% Oil and water

densities are 50 and 65

lb/ft3, respectively

p c = capillary pressure, psi;

σ = interfacial tension, dynes/cm;

θ = contact angle, degrees;

k = rock permeability, md; and

J S



Example

Calculation of the Leverett J Function

The set of four oil/water capillary pressure curves shown in Table 2.5 was measured for four cores from the same reservoir

The oil/water interfacial tension and angle of wettability are σ =

72 dynes/cm and ϕ = 45°, respectively Calculate and plot the

J-function curve

Example