Geophysics

Data
analysis
Depth
conversion
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correlation

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design Facies
modelling
Property modelling
And Upscaling

Building the Dynamic Reservoir

Model – SCAL Data
TM4112 Karakterisasi & Pemodelan Reservoir
Reservoir Rock-Fluid Property
Data
 This section contains rock properties
usually derived from special core analysis
 Small number of samples, so not enough
data to generate maps, or distributions, of
these properties
 Usually assume these properties are
constant throughout a particular zone, or
stratum
Reservoir Rock-Fluid Property
Data
 Relative permeability
 Capillary pressure
 Hysteresis in capillary pressure and
relative permeability
 Pressure-dependent porosity and
permeability functions
Effective and Relative
Permeability
Instructional Objectives
(Effective and Relative Permeability)

 List 2 uses of relative permeability data

 Define absolute permeability, effective permeability,
and relative permeability
 List 3 parameters that affect relative permeability
 Explain hysteresis in two phase relative permeability
data
 Explain how the use of relative permeability curves is
tied with the reservoir mechanism and/or the depletion
process
 Explain the concept of three-phase relative
permeability
 Average relative permeability data
Uses of Effective and Relative
Permeability
 Reservoir simulation
 Flow calculations that involve multi-phase
flow in reservoirs
 Estimation of residual oil (and/or gas)
saturation
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
Calculating Absolute
Permeability
 Absolute permeability is often calculated
from the steady-state flow equation
Effective Permeability
 When the rock pore spaces contain more
than one fluid, then the permeability to a
particular fluid is called the effective
permeability
 Effective permeability is a measure of the
fluid conductance capacity of a porous
medium to a particular fluid when the
medium is saturated with more than one
fluid
Calculating Effective
Permeability
Relative Permeability
 Relative permeability is defined as the ratio
of the effective permeability to a fluid at a
given saturation to a base permeability
 The base permeability is commonly taken
as the effective permeability to the fluid at
100% saturation (absolute permeability) or
the effective non-wetting phase
permeability at irreducible wetting phase
saturation
Calculating Relative
Permeabilities
Oil-Water Relative Permeability
Fundamental Concepts
 Water phase
 Water is located in smaller pore spaces and
along sand grains
 Therefore, relative permeability to water is a
function of water saturation only (i.e., it does
not matter what the relative amounts of oil and
gas are)
 Thus, we can plot relative permeability to
water against water saturation on Cartesian
coordinate paper
Fundamental Concepts
 Oil phase
 Oil is located between water and gas in the
pore spaces, and to a certain extent, in the
smaller pores
 Thus, relative permeability to oil is a function
of oil, water, and gas saturations
 If the water saturation can be considered
constant (i.e., the minimum interstitial water
saturation), then kro can be plotted against So
on Cartesian coordinate paper
Fundamental Concepts
 Gas phase
 Gas is located in the center of the larger pores
 Therefore, the relative permeability to gas is a
function of gas saturation only (i.e., it does
not matter what the relative amounts of oil and
water are)
 Thus, we can plot krg against Sg (or Sw + So)
on Cartesian coordinate paper
Common Multi-Phase Flow
Systems
 Water-oil systems
 Oil-gas systems
 Water-gas systems
 Three phase systems (water, oil, and gas)
Exercise 1
 What are the relative permeability data sets
we need to use for the following
situations?
 Water flooding an oil reservoir above the
bubble point
 Production from an oil reservoir with a gas-
cap and water aquifer
Exercise 1 Solution
 For water flooding an oil reservoir above
the bubble point :
 Water-oil relative permeability
 For three phase flow :
 Water-oil relative permeability
 Gas-oil (or gas-liquid) relative permeability

 3 phase relative permeability

Oil-Water Relative Permeability
Oil-Gas Relative Permeability
Exercise 2
Exercise 2 Solution
 Curve (1) is oil relative permeability
 Curve (2) is water relative permeability
 Values are:
 Swi = 15%
 Sor = 20%

 kro @ Swi = 1.0

 krw @ Sor = 0.35

Importance of Relative
Permeability Data
 Relative permeability data affect the flow
characteristics of reservoir fluids.
 Relative permeability data affect the
recovery of oil and/or gas.
Example 1
Effect of Relative Permeability
Example 1
Effect of Relative Permeability
Factors Affecting Effective and
Relative Permeabilities
 Fluid saturations
 Geometry of the rock pore spaces and
grain size distribution
 Rock wettability
 Fluid saturation history (i.e., imbibition or
drainage)
Effect of Wettability
Effect of Saturation History

 Types of relative permeability curves

 Drainage curve
 Wetting phase is displaced by the nonwetting
phase, i.e., the wetting phase saturation is
decreasing
 Imbibition Curve
 Non-wetting phase is displaced by wetting phase,
i.e., the wetting phase saturation is increasing
Effect of Saturation History
Choosing the Right Curve

 When simulating the waterflood of a water-

wet reservoir rock, imbibition oilwater
relative permeability curves should be
used.
 When modeling gas injection into an oil
reservoir, drainage gas-oil relative
permeability curves should be used.
Three-Phase Relative
Permeabilities
Relative Permeability to Water in
a Three-Phase System
Relative Permeability to Oil in a
Three-Phase System
Averaging Relative
Permeability Data Technique
 Averaging Oil-Water relative permeability
data
 Averaging Oil-Gas relative permeability
data
I- Averaging Oil-Water
Relative Permeability Data
 Plot krw and kro versus Sw
 Normalize the relative permeabilit curves
 Average the normalized oil-water relative
permeability curves
 De-normalize the data to obtain average
relative permeability curves for the
reservoir
Exercise-3

 Average the following 4 oil-water relative

permeability data sets to obtain one
average oil-water relative permeability
curve for the reservoir.
1- Plot krw and kro Versus Sw
2- Normalize the Relative
Permeability Data
2- Normalize the Relative
Permeability Data
3- Average the Normalized
Oil- Water Relative Permeability Curves
Average the Normalized
Oil- Water Relative Permeability Curves
4-De-normalize the Data to Obtain Average
Relative Permeability Curves for the Reservoir
Average Relative Permeability Curves for
the Reservoir
 Exercise-4
 Average the
following 2 sets
of Oil-Gas relative
permeability data
to obtain one
average Oil-Gas
relative
permeability
curve for the
reservoir.
II-Averaging Oil-Gas Relative
Permeability Data
1. Plot krg and kro versus Sg
2. Normalize the relative permeability curves
3. Average the normalized oil-Gas relative
permeability curves
4. De-normalize the data to obtain average
relative permeability curves for the
reservoir
1 - Plot krg and kro Versus Sg
2 - Normalize the Relative Permeability
Curves
Normalize the Relative Permeability
Curves
3-Average the Normalized Oil-Gas
Relative Permeability Curves
4-De-normalize the Data to Obtain Average
Relative Permeability Curves for the Reservoir
Average Relative Permeability Curves for
the Reservoir
Capillary Pressure
Instructional Objectives
(Capillary Pressure)
 List four uses of capillary pressure data
 Define hysteresis
 Sketch capillary pressure curves for typical
drainage and imbibition processes
 Explain the relation between capillary
pressure data and reservoir fluid saturation
 Define oil-water and gas-oil transition zones
 Convert capillary pressure lab data to
reservoir conditions
 Define the J-function
Uses of Capillary Pressure
Data
 Determine initial water saturation in the
reservoir
 Determine fluid distribution in reservoir
 Determine residual oil saturation for water
flooding applications
 Determine pore size distribution index
 May help in identifying zones or rock types
 Input for reservoir simulation calculations.
Capillary Pressure Concept
Capillary Pressure Definition
 The pressure difference existing across the
interface separating two immiscible fluids.
 It is usually calculated as:

 Pc = pnwt - pwt

Example 1
 Define capillary pressure in the following
systems:
 Water-gas system
 Water-wet water-oil system

 Oil-gas system
Solution of Example 1
 Define capillary pressure in the following
systems: Pc = pnwt – pwt
 Water-gas system
Pc =pg - pw

 Water-wet water-oil system

Pc =po - pw

 Oil-gas system
Pc =pg - po
Relation Between Capillary
Pressure and Fluid Saturation
For uniform sands, reservoir fluid saturation is
related to the height above the free-water level
by the following relation:
Fluid Distribution in
Petroleum Reservoirs
Fluid Distribution
Class Exercise 1
 Calculate water-oil transition zone height
for two cases:
 heavy oil
 light oil
Class Exercise 1
 Capillary pressure was measured to be 5 psia
at connate water saturation. Water density is
66.5 lbm/ft3. Calculate the length of the
transition zone in the following two situations:
 oil density = 59.3 lbm/ft3
 oil density = 43.7 lbm/ft3

This example assumes the rock quality is the

same in both situations.
Solution of Class Exercise 1
 Rearranging the relation between capillary
pressure and height:
Converting Laboratory Capillary Pressure Data
to Reservoir Conditions

 Basic equations
Converting Laboratory Capillary Pressure Data
to Reservoir Conditions

 Setting rL = rR and combining equations

yields

 Capillary pressure at reservoir conditions

 Example 2
 Convert the laboratory capillary pressure data for sample 28
in the attached capillary pressure curve (obtained using
mercury injection method) to reservoir conditions for a
formation containing oil and water.
 Calculate reservoir capillary pressure data for mercury
saturations of 70, 60, 50, 40, 30, 20, and 10 percent.
 Laboratory Data: σHg = 480 dynes/cm, θHg = 140°
 Reservoir Data: σow = 24 dynes/cm, θow = 20°
 Note: The reservoir data are very difficult to obtain. The
reservoir data above are representative values based upon
industry literature.
Example 2 Capillary Pressure Curve
 Example 2 Solution
 Steps:
 Solve the equation that relates lab capillary pressure data to
reservoir capillary pressure data for the conditions we have.
 Obtain laboratory capillary pressure data from the curve for Sample
28.
 Convert the lab numbers to reservoir capillary pressure.
Example 2 Solution

Converting lab capillary pressure data to reservoir conditions:

Typical Drainage and Imbibition
Capillary Pressure Curves
 Drainage Process
 Fluid flow process in which the saturation of the
nonwetting phase increases
 Mobility of nonwetting fluid phase increases as
nonwetting phase saturation increases

 Example:
 Hydrocarbon (oil or gas) filling the pore space and displacing the
original water of deposition in water-wet rock
 Waterflooding an oil reservoir in which the reservoir rock is
preferentially oil-wet
 Gas injection in an oil- or water-wet oil reservoir
 Pressure maintenance or gas cycling by gas injection in a
retrograde condensate reservoir
 Imbibition Process
 Fluid flow process in which the saturation of the wetting
phase increases and the nonwetting phase saturation
decreases
 Mobility of wetting phase increases as wetting phase
saturation increases

 Example:
 Waterflooding an oil reservoir in which the reservoir
rock is preferentially water-wet
 Class Exercise 2

 The above figure is the result of

core flood experiments on a water-
wet rock. Answer the following
questions:
 What process does curve 1
represent?
 What process does curve 2
represent?
 What is the irreducible water
saturation?
 What is the critical oil saturation?
 What is the displacement pressure?
 Solution of Class Exercise 2

 (1) Drainage process

 (2) Imbibition process
 (3) Sw = 0.25

 (4) Sor = 0.13

 (5) Pd = 15 psi
 Averaging Capillary Pressure Data
Using the Leverett J-Function
 A universal capillary pressure curve is impossible to generate
because of the variation of properties affecting capillary
pressures in reservoir
 The Leverett J-function was developed in an attempt to convert
all capillary pressure data to a universal curve
Definition of Leverett J-Function
Example J-Function for West Texas
Carbonate
 Use of Leverett J-Function

 J-function is useful for averaging capillary pressure data from a

given rock type from a given reservoir.
 J-function can sometimes be extended to different reservoirs
having same lithologies.
 J-function usually does not predict an accurate correlation for
different lithologies.
 If J-functions are not successful in reducing the scatter in a given
set of data, then this suggests that we are dealing with different
rock types.
Example 3 Calculation of J-function

Using the average capillary pressure data from the table, calculate
and plot the Leverett J-function. Use the following rock and fluid
properties:

σ = 72dyne/cm, θ= 0o, k = 47md, φ = 0.194

 Example 3 Solution
 Example calculation – Leverett
J-function for: Sw = 59.0% and
Pc = 8 psia

 In the table above, we have

not multiplied through by the
conversion factor 0.22.
 Example 4 Estimating Pc from
J-function
 Estimate capillary pressures from Leverett
J- function calculated in Example 3 for a
different core sample.
 Properties of core sample: k = 100 md Φ =
10 %
Example 4 Solution
 Example calculation –
Capillary pressure from
Leverett J-function for: Sw =
59.0%