Calculating porosity and water saturation

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College of Engineering
Petroleum department
Forth stage
by:
Haider Shabaan

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Abstract
In this report , the work depend on interactive petrophysics program(IP) .
we calculated RW in different methods :- SP, formation temp ,picket plot
and RWa and choose which one is accurate to use in calculation . And then
calculate water saturation depend on different types of porosity and
different methods of measurement .
Introduction:-
First we rely on final geological report of Dujaila-2 because we must
know the formation that we have and where are the region of oil and
area of cavitation before starting work on( IP) and compare the results
that we get it from( IP) with the fgr report to make sure the precision
inaction
The most common technique for calculating Sw is the use of resistivity
logs with a model (empirical or theoretical) that relates Sw to Rt, Rw,
and porosity. As mentioned previously, a large number of Rt/Sw
models have been published. The models are applied at every data
point in the reservoir where deep resistivity, porosity, and shale-
volume estimates, if required, are available. The evaluation of all other
necessary parameters (constant or variable Rw values, a, m, n, QV, Vsh,
R0 = F • Rw, etc.) has been discussed previously. Several commercial
software packages are available that perform these S w calculations for
a variety of log models..

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Well information

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Theoretical part
A- SW
Water saturation
Water saturation can be defined as the amount of pore volume that
occupied by the formation water.
Techniques for calculating water saturation
Sw in wellbores can be determined by the following primary methods:
 Sw calculations from resistivity well logs by application of a model
relating Sw to porosity, connate-water resistivity, and various rock
electrical properties.
 Sw determination from well log data
 Sw calculations from laboratory capillary pressure/saturation
(Pc/Sw) measurements by application of a model relating Swto
various rock and fluid properties and height above the free-water
level.
 Sw calculations using oil-based mud (OBM)-core-plug Dean-Stark
water-volume determinations.
 Combinations of these methods.

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1.archie's equation
Archie developed his famous equation to calculate Sw , from well log
parameters, the water saturation (Sw) of the uninvaded zone in a
formation next to a borehole. The Archie equation for clean formation
can be expressed as follows:
where:
 Sw = water saturation of the uninvaded zone
 n = saturation exponent, which varies from 1.8 to 4.0 but normally
is 2.0
 Rw = formation water resistivity at formation temperature
 Φ = porosity
 m = cementation exponent, which varies from 1.7 to 3.0 but
normally is 2.0
 Rt = true resistivity of the formation, corrected for invasion,
borehole, thin bed, and other effects.
 a = 1 ( for carbonate formation)
a =0.62 ( for sandstone )

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2. Sw =√ 𝐑𝐨/𝐑𝐭𝟐
In water bearing zone
Where:
Ro = the resistivity of the fully saturated rock
3. Quick look method
A . Rwa method
Rwa or Rw apparent is used to estimate the value of Rw, the resistivity
of the waters filling the pores of a reservoir rock. Rwa is derived from
the most basic concepts of well log analysis, the formation resistivity
factor, F and water saturation Sw.
Sw=√ 𝑅𝑤𝑎/𝑅𝑤
Where :
Rwa = Rt/F
B . Rxo/Rt method
The Rxo/Rt quicklook method can be used to identify hydrocarbon-
bearing formations and to indicate hydrocarbon movability
(producibility). When Sw/Sxo is 1 in a permeable zone, the zone will
produce water or be nonproductive regardless of water saturation. A
value Sw/Sxo significantly less than 1 indicates that the zone is

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permeable and contains some hydrocarbons, and that the
hydrocarbons have been flushed (moved) by invasion. Thus, the zone
contains producible hydrocarbon.
Sw=10∆𝑆𝑃/−1.6𝐾
4. Cross Plot method
A . pickett plot
Procedure:
1. Plot points of matching porosity and true resistivity (Rt ) on log-
log paper.
2. Plot Rw point on the Rt scale.
3. Determine m using the table of values.
4. Plot the 100% Sw line.
5. Plot the lines representing lower values of Sw

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B . Hingle plot
„ One can determine water saturation directly from the plot,
without … knowing Rw, or … having to calculate porosity. „ In
addition, the plot will predict matrix values of sonic or density, so
porosity can be more confidently calculated. „ But, one has to
assume values for a, m, n, „ And special paper must be used, which
depends on the assumed value of m.
6.Ratio method
When no porosity data is available, saturation can be obtained
by comparing the shallow and deep resistivity logs. This
formula is not shale corrected..
Sw =[(𝑅𝑥𝑜/𝑅𝑡)/(𝑅𝑚𝑓/𝑅𝑤)]^5/8

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B- RW
There are six ways to calculate formation water resistivity
1. Archie’s Equation
If water zone is present.
Where:
Rw: formation water resistivity
Ro: formation resistivity when (100%) saturation of water
F: formation resistivity factor
*Formation resistivity factor is depend on type of rock and porosity.
2. Rwa Approach (apparent formation water resistivity).
We choose the lowest value of the curve of (Rwa) and we consider it the
value of (Rw).
Requirements:
1.Rw is constant.
2.lithology is constant.
3.A water zone exists and is identifiable.

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Procedure:
3. Resistivity – Porosity Crossplots
a.Picket Plot

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b. Hingle Plot
4. SP log method:
5. Direct measurement of representative (water sample.(laboratory))
6. Chemical analysis of water sample. (laboratory)

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Another models of water saturation
1-Poupon-Leveaux (Indonesia) model
The Indonesia model was developed by field observation in
Indonesia rather than by laboratory experimental measurement
support. [9] It remains useful because it is based on readily available
standard log-analysis parameters and gives reasonably reliable
results. The formula was empirically modeled with field data in water-
bearing shaly sands, but the detailed functionality for hydrocarbon-
bearing sands is unsupported, except by common sense and long-
standing use. Sw results from the formula are comparatively easy to
calculate and, because it is not a quadratic equation, it gives results
that are always greater than zero. Several of the other quadratic and
iterative-solution models can calculate unreasonable
negative Sw results.
....................(5)
....................(6)
The Indonesia model, and other similar models, are often used
when field-specific SCAL rock electrical-properties data are
unavailable but are also sometimes used where the SCAL exponents
do not measure the full range of shale volumes. Although it was

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initially modeled on the basis of Indonesian data, the Indonesia
model can be applied everywhere. The inputs are the effective
porosity, ϕe, shale volume and resistivity (Vsh and Rsh), and water and
deep resistivities (Rw and Rt). The Sw output is usually taken to be
the water saturation of the effective porosity, but it has been recently
suggested that the output is likely to estimate Swt.[7]
Many other log-
based shaly-sand models have been proposed[23]
but, for brevity, are
not discussed here.
2- Waxman-Smits-Thomas and dual-water models
Swt, the water saturation of the total porosity, is calculated at each
reservoir data point by iterative solution of the complex
multiparameter Waxman-Smits-Thomas (WST) and dual-water (DW)
equations (Eqs. 7 and 8). For brevity, the details of the solution
methods are not presented here. The WST and DW models are total-
porosity/Sw system models.
The WST model is based on laboratory measurements of resistivity,
porosity, and saturation of real rocks. Qv is the cation-exchange
capacity (CEC) per unit PV.
....................(7)
where Swt = water saturation of the total porosity as shown
schematically in Fig. 1,

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B = specific cation conductance in (1/ohm•m)/(meq/mL), and QV =
CEC in meq/mL of total PV. The exponents m* and n* apply to the
total PV

Fig. 1 – Total, effective, and core porosities and their associated water saturations in
shaly sands (after Woodhouse and Warner).
3-The DW model
is also based on the WST data. It uses clay-bound-water
conductivity instead of WST’s BQv factor (see Eqs. 7 and 8) and an
alternative shale-volume descriptor, Swb, the saturation of physically
bound water in the total PV (see Fig. 1). [1][14]
When Vsh is zero, Swb is
zero; and when Vsh is 100% BV, Swb and Swt are also 100% PV.

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....................(8)
where Rwb = resistivity of clay-bound water in the shales,
and Rwf = resistivity of free formation water in the shale-free
water zones. Because of the different model assumptions, DW
exponents mo and no must always be smaller than the WST
exponents[24]
and may be values similar to "clean" sand exponents.
Where the WST and DW models have been properly applied, the
hydrocarbon pore volume (VHCP) results should be equal.
All Swt calculations from the WST and DW methods must be checked
to ensure that they are greater than Swb. After this check, they are
used with ϕt to obtain the VHCP. For the DW model, when the outputs
require conversion to effective porosity, ϕe, and effective water
saturation, Swe, the properties are converted with Eqs. 9 and 10,
respectively.
....................(9)
And ....................(10)

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Porosity and Water Saturation Parameters :

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Result
1-SW by use Density and Neutron devices:
2-SW by use Density-Neutron and sonic devices:

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3-SW by use ND, Sonic, Neutron and Density devices:

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4-SW depend on ND porosity by Archie, Dual Water,
Indonesian methods
5-SW depend on ND porosity by Juhasz, , simandoux
,Mod Indonesian methods

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6-RW from formation temp. , SP
7-RW from formation Picket Plot at fully water zone
only

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8- The zone that taken RW picket plot in water bearing
zone

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Discussion:
1-the reading of Vsh from sp, Gr and cross plot are not converge.
2- the value of m and rw we should corrected because the values of sw
become greater than 100 ./. if we not corrected ,the value of m and rw we
can corrected from peck plot,Tf,sp if the value converge that will be right.
3- we shuold calculate the sw from several methods and then compare its.
4- we must use the shlumberger chart to corect the porosity because its
effect in the value of sw in calculation.
5-The effective porosity is always less than the total porosity because it
equal the total porosity minus the (porosity of shale*volume of shale).
6-must be compute PHIE and SW for each way (NeuDen ,Neutron
,Density,Sonic) and then compare between them .
7-Different (m) values affect the water saturation dramatically and lead to
completely unreliable petrophysical interpretation ,while differebt in (a) or
(n) values does not affect the water saturation as much as (m) .
8-The evaluation of all other necessary parameters (constant or variable
Rw values, a, m, n, QV, Vsh, R0 = F • Rw, etc.)