Formation Evaluation Lectures (Prepared by Dr. Fadhil S.

Kadhim)

Reservoir Fluid Saturation

Introduction

The pore spaces in reservoir rocks are occupied by fluids. In petroleum reservoirs, the fluids are
usually water and hydrocarbons. The relative volumes of water and hydrocarbons in the pore volume
of the reservoir rock are designated as saturations. Water saturation in the reservoir rock
is the fraction of the pore volume occupied by water. By the same definition, hydrocarbon saturation
in the reservoir rock is the fraction of the pore volume occupied by hydrocarbons. The sum of the
water and hydrocarbon saturations in the reservoir rock is equal to unity. This relationship
can be expressed simply as:

Sh + Sw = 1 (1)

Where: Sh= hydrocarbon saturation, fraction; and Sw=water saturation, fraction.

If the hydrocarbon in the reservoir exists in oil and gas phases, the above equation can be written as:

Sg+So+Sw=1 (2)

Where: So=oil saturation, fraction; and Sg= gas saturation, fraction.

 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
The presence of low water saturations in the reservoir indicates the presence of high hydrocarbon
saturations. Conversely, high water saturations are interpreted as representing the presence of low
hydrocarbon saturations. For calculation of the volume of hydrocarbons in a reservoir, a general
equation that applies is expressed as:

(3)

Where : HCPV= hydrocarbon pore volume; Area=hydrocarbon-bearing area of the reservoir;

Thickness= net productive thickness or pay of the reservoir; Ф=porosity, fraction;
and Sw= water saturation, fraction.

If the water saturation data are incorrect, it could result in the over- or under-estimation of the
volume of hydrocarbon present in the reservoir. The economic impact of erroneous calculation of in-
place-hydrocarbon volume can not be overstated. It could lead to execution of uneconomic projects
with erroneously high estimated in-place-hydrocarbon volumes or lead to the abandonment of
projects with erroneously low estimates of in-place-hydrocarbon volumes.
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)

There are various models and equations used for the calculation of water saturations in clean sands,
shaly sands, and carbonate reservoirs are presented. The widely used Archie equation for clean sands
is presented. This is followed with the presentation of models for shaly sands, such as the Waxman-
Smits model, Simandoux equation, Poupon-Leveaux equation, and the Dual-Water model. The
application of the Archie equation to carbonate reservoirs is discussed. This section ends with a
presentation on the use of nuclear magnetic resonance (NMR) logs for the determination of in-situ
fluid saturations for most types of reservoirs.

Water Saturation in Clean Sands

Clean sands are classified as sands that satisfy the assumptions used in the development of the Archie
equations. These are sands that do not contain clays or clay minerals. In such sands, conduction of
electricity occurs only through free ions within the formation water. There is an absence of the “shale
effect.” Archie equations are assumed to apply at these “perfect” rock conditions. In practice, Archie
equations are generally applied under rock conditions that do not meet these ideal conditions.

Archie Equations

The derivation of Archie equations follows from the definition of resistivity index (IR) as the ratio of
the true resistivity (Rt) of a reservoir rock partially saturated with water to the resistivity of the rock
(Ro) if fully saturated with water . Thus, the resistivity index is defined as:
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)

(4)

(5)

(6)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Determination of Archie Parameters n, m, and a

The Archie parameters can be determined by applying the expression derived by rearranging Eq. (12)
as:

Pickett Formula
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
A least-squares straight line drawn through a log-log plot of versus data based on core samples has a
negative slope equal to the parameter m and an intercept equal to the parameter a. Note that the
entire core data used in this plot must be obtained at as required by the definition of formation factor
in Eq. (7). The Following Figure shows the Pickett method to determine Archie’s parameters
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Shaly Sands

Shaly sands can be described as reservoir rocks that contain shales. These sands are sometimes
described as “non-Archie” rocks, and exhibit the effects of the presence of shales on the electrical
conductivity of rocks. The presence of shales causes reservoir rocks to become conductive, which
adds to the conductivity of the formation water. Archie equation assumes that the formation water
is the only conductive phase in the formation and the reservoir rock is non-conductive. To
account for the effects of shales on the extra conductivity of reservoir rocks, many shaly sand
models have been proposed in the literature. Most of the shaly sand saturation models have the
following forms:
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
1. Waxman-Smits Model

The Waxman-Smits model is based on the results of an extensive experimental study on the effects of
shales on the conductivity of shaly sands. The model takes the form of Eq. (21) and is represented as:

2. Simandoux Equation

The Simandoux equation takes the form of Eq. (20), and is represented as:
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
3. Poupon-Leveaux Equation

The Poupon-Leveaux equation is also of the form of Eq. (20). It is expressed as:

4, The Dual-Water Model

The Dual-Water model proposed by Clavier et al.11 assumes that the clay-bound water and the
free non-clay water act as two parallel conductive layers that contribute to the total conductivity,
Ct, measured in the formation. The Dual-Water model is expressed as:
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Carbonate Rocks

Carbonate rocks, unlike sandstones, have complex pore systems. These pore systems may have bi- or
tri-modal pore size distributions. Pore sizes may range from less than an inch to feet. The pore
geometry of carbonate rocks is very heterogeneous and variable. The texture and structure of
carbonate rocks are further rendered more complex by the diagenesis caused by chemical dissolution,
precipitation, dolomitization, leaching, and fracturing. Due to these reasons, petrophysical models
comparable in terms of simplicity to the Archie equation have not been developed for carbonate
rocks. In some petrophysical analyses, the Archie equation is used to calculate water saturation in
carbonate rocks. This approach could lead to significant errors. An alternative approach is to base
the calculation of water saturation of carbonate rocks on data from NMR logs.
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Hydrocarbon Reserve Estimation

The basic equation for hydrocarbon reserve estimation is:

 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)

Example (1):

Calculate the volume of HIP for an oil reservoir with the following parameters:
Drainage area = 80 a, So= 0.50 Ф = 0.10, h = 10 ft

Solution:
By setting recovery factor equal to 1.00 in the Eq.
HIP = (7758 bbl/acre-ft) x (80 a) x (1) x (0.5) x (0.10) x (10)
= 310,320 bbl

Example (2):

RH= (7758 bbl/acre-ft) x (0.20) x (80 a)x (0.6 x 0.2 x 20ft+ 0.7 x 0.1 x 5 ft)
= 341,352 bbl
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Example (3):

RF= 0.5 and 0.7

Solution :
At reservoir conditions of temperature and pressure, you have a recovery factor of 0.5

For a recovery factor of 0.70

 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Thus, at formation temperature and pressure (reservoir conditions)

Now, you convert a volume at reservoir conditions to a volume at surface temperature and pressure by
multiplying the volume at reservoir conditions by the factor. The gas volume at surface conditions is
found by multiplying the volume at reservoir conditions by:
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)

Q1/ Is the assumption that hydrocarbon saturation is equal to 1 minus the water saturation always
valid? Explain your answer.
No. The assumption that hydrocarbon saturation is equal to 1 less the water Saturation is not always
valid. However, it is necessary to assume this is true to calculate hydrocarbon saturation. This
necessity arises because you can only calculate water saturation from most common well log tool
responses.
Q2/ Calculate the average porosity and the average water saturation for the two pieces of core.
Core 1: [1 ft. thick, porosity = 0.50, water Saturation = 1.00]
Core 2: [9ft. thick, porosity = 0.10, water saturation = 0.56]
What is the average hydrocarbon saturation? Is 0.50 a realistic value for porosity of a typical
sedimentary rock?
 Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)

Average hydrocarbon saturation is found as 1 less average water saturation (1 - 0.717 = 0.283), but
substituting hydrocarbon saturations for the two zones (1 - 1 = 0 for Core 1 and 1 - 0.56 = 0.44 for
Core 2).
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)
Formation Evaluation Lectures (Prepared by Dr. Fadhil S. Kadhim)