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Water saturation is the fraction (or percentage) of the pore volume of the reservoir rock that is filled with water.
It is generally assumed, unless otherwise known, that the pore volume not filled with water is filled with hydrocarbons.
Determining water and hydrocarbon saturation is one of the basic objectives of well logging.
DETERMINATION OF SATURATION IN CLEAN FORMATIONS
In the determination of saturation, resistivity logs are those that are most depended on
For a formations with homogeneous intergranular porosity saturation determination are based on Archies water saturation equation;
Archies equation is stated as
Equation 1 (with n = 2) is solved, in nomograph form, in Chart Sw-1.
For Sxo, the water saturation in the flushed zone, a similar expression exists
The saturation exponent n is usually taken as 2;has shown to be good estimates
The accuracy of the Archie equations depend on the accuracy of the input parameters (Rw(or Rmf), F, and Rt(or Rxo) )
The formation water resistivity (Rw) should be verified in as many ways as possible:
calculation from the SP curve, water catalogue, calculation from nearby water-bearing formation, and/or water sample measurement.
Formation factor F is usually obtained from the measured porosity of the formation through the relationship
a is the tortuosity factor
m is the cementation exponent
The formation factor is also defined by another relationship as the ratio of the resistivity of the rock completely saturated with brine to the resistivity of the brine and is given below.
The values of a and m in Equation 3 are subject to more variation
F = 1/ 2 is usually used;
F = 0.62/ 2.5 (Humble formula), or
F = 0.81/ 2 (a simpler form practically equivalent to the Humble formula).
While the Humble formula is satisfactory for sucrosic rocks, better results are obtained
using F = 1/ 2.2 to 1/ 2.5 in compact or oolicastic rocks
In some severely oolicastic rocks, m may even be as high as 3
True Formation Resistivity Rt
This is measured by either a deep laterlog or a deep induction logging tool in the borehole
The following factors must be taken into consideration whilst using Rt value in the Archie's equation
it is important to evaluate the invasion profile and, if
necessary, perform the necessary corrections The determination of Rt can be a problem in case of thin
beds; resolution of tool should be taken in consideration
If there are clays present in the formation, the bound water in clays can act as a conductor and this can decrease the Rt value
Also the overburden pressure at in-situ downhole can cause a significant increase in Rt.
Using the Humble Equation
Step 1: Determine from acoustic, density or Neutron log.
Step 2: Determine F from Humble Formula
Step 3: Determine Rt from deep reading resistivity (induction or laterolog) log
corrected for borehole, bed thickness and invasion.
Step 4: Determine Rw
Step 5: Determine Sw from the Archie Equation (Equation 1) or from Chart SW-1
Flushed Zone in Humble Formula Procedure
Step 1: Determine porosity from acoustic, density or Neutron log.
Step 2: Determine F from Humble Formula
Step 3: Determine and use Rxo from shallow resistivity log in place of Rt from deep reading resistivity log
Step 4: Determine and use Rmf in place of Rw
Step 5: Determine Sw from the Archie Equation (Equation 1)
Saturation Determination SW-1
This nomograph solves the Archie water saturation equation
If Ro (resistivity when 100% water saturated) is known, a straight line from the known Ro value through the
measured Rt value gives water saturation, Sw. If Ro is unknown, It may be determined by connecting the formation
water resistivity, Rw, with the formation resistivity factor, FR, or porosity, .
NB: Chart Sw-1 is constructed using the F = 1/ 2 porosity-to formation factor relationship. For any
other porosity-to-formation factor relationship the nomograph should be entered with the formation factor
Chart Sw-1 may also be used to solve Equation 2 for the flushed zone water saturation.
To do this, the Rxo reading is inserted on the Rt leg of
the nomograph and the Rmf value is inserted in the Rw leg
RESISTIVITY VS POROSITY CROSSPLOTS
Combining Equation 1 and 3, the Archie saturation equation may be written
If n and m are equal to 2, and a = 1, then Which can be written as
A plot of vs the inverse square root of Rt can be used to determine a number of parameters including Sw
Rt value, is usually the log reading of the deep resistivity device provided the readings are not much influenced by invasion or other environmental factors
Resistivity vs porosity crossplot Example
Figure shows several points plotted over an interval in which formation-water resistivity is constant
Assuming that at least some of the points are from 100% water bearing formations, a line drawn from the pivot point (f = 0, Rt = ) through the most north-westerly plotted points corresponds to Sw=1
The slope of this line defines the value of Rw.
Rt values on this line corresponds to Ro values at the reference porosities. Thus for = 10%, Ro = 6.5 ohm-m.
Rw can also be determined using any with its corresponding Ro. Thus, for f = 10%, F = 100. Since Rw = Ro/F, Rw = 6.5/100 = 0.065 ohm-m as shown.
For other Sw values, Rt and Ro are related by the equation Rt = Ro/SW
2. For Sw = 50%, 1/SW2 = 4, and Rt =
4 Ro. This relation establishes the line for Sw = 50%.
Plots of the values of Ro for Sw = 10%, 20%, 30% and 50%, using the above relationship, for a set of porosities can be determined
Sw in the zones of interest can be determined from the position of the plotted points in relation plot saturation lines
The term Rwa is apparent formation water resistivity
It is only equal to Rw in 100% water-bearing formations
In hydrocarbon-bearing formations, Rwa computed from will be greater than Rw
The relationship between Sw, Rwa, and Rw Is given as
At 100% water saturation, the Archie equation can be written as
The Rwa technique can, therefore, be useful for identifying potential hydrocarbon bearing zones and for obtaining Rw values
Since the Rwa technique, as normally applied, requires that deep resistivity (Rdeep) Rt, invasion must be shallow enough that the deep resistivity reads essentially the same as the true resistivity.
Calculated Rwa values will approximate Rw values in clean water-bearing sands
Usually, an Rwa value at least three times that of Rw is needed to indicate possible hydrocarbon potential
A continuous log of Rwa can be recorded at the wellsite using resistivity and porosity logs.
Figure 4 is an example computed from the BHC sonic log and induction-SFL log combination
The Rwa combination indicates the lower sand to be predominately water bearing with a good show of hydrocarbons at its top
RESISTIVITY RATIO METHODS
In resistivity ratio methods, it is assumed that a formation is divided into two distinct a flushed or invaded zone and a non-invaded zone
The resistivities of the two zones must be measurable or derivable from logs, and methods for determining the resistivity of the water in each zone must be available.
Flushed Zone Method
If n = 2 is assumed, Archies equations for Sw and Sxo can be compared to give
This equation gives the ratio of Sw to Sxo, and no knowledge of formation factor or porosity is needed
Rxo may be found from a MicroSFL log, Rt from an induction or laterolog, and Rmf /Rw from a measured values or from the SP curve
The ratio Sw/Sxo,is valuable in itself as an index of oil movability.
If Sw/Sxo = 1, then no hydrocarbons have been moved by invasion, whether or not the formation contains hydrocarbons.
If Sw/Sxo is about 0.7 or less, movable hydrocarbons are indicated.
The value of Sw/Sxo along with and Sw, is useful in evaluating reservoirs
To determine Sw from Equation , Sxo must be known
For moderate invasion and average residual oil saturation, an empirical relation between Sxo and Sw has been found useful: Sxo = Sw1/5. giving
DETERMINATION OF RW
In addition to formation factor or porosity, values of formation water resistivity, Rw, and mud filtrate resistivity, Rmf, are needed for the water saturation calculations
Mud resistivity, Rm, mudcake resistivity, Rmc, and Rmf are generally measured at the time of the survey on a mud sample from the flowline or mud pit
These values are recorded on the log heading
Rw can be determined in a number of ways
From the SP Log
From water saturation equation in a 100% water-bearing formation
From produced water samples
From water catalogues
Rw from water saturation equation in a 100% water-bearing formation
When the water saturation is assumed to be 100%, the Archie water saturation equation
reduces to: Where Rt is from a deep-investigation resistivity log,
and F is computed from a porosity log reading
The values of Rwa can be calculated for a number of water bearing zones and if the same then the value of Rwa can be assumed to be equal to Rw
Step 1: Identify a permeable, water bearing zone near to the hydrocarbon bearing zone of interest.
Step 2: Read the resistivity of the zone of interest from a deep investigation resistivity log.
Step 3: Determine the Formation Resistivity Calculate F from the Humble formula.
Step 4: Determine Rwa from Equation above Step 5: Compare values of Rwa:
The values in the water bearing zone should be similar.
The lowest value of Rwa is generally the value of Rw.
If the calculated value of Rwa at a particular depth is over
three times that of Rw determined in a definite water bearing zone then the zone is potentially hydrocarbon bearing