THERMAL PROPERTIES OF OIL AND GAS RESERVOIRES ROCKS MODELINGCristina Jugastreanu 1, Seyed Mehdi Tabatabai 1, Timur Chis 2 1 PH.D. School, Oil-Gas University Ploiesti, Romania2 Chemical and Chemical Engineering Department, Ovidiu’s University, Constanta, Romania |
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Received 25 January 2022 Accepted 26 February 2022 Published 09 March 2022 Corresponding Author Timur Chis, timur.chis@gmail.com DOI 10.29121/granthaalayah.v10.i2.2022.4512 Funding: This research
received no specific grant from any funding agency in the public, commercial,
or not-for-profit sectors. Copyright: © 2022 The
Author(s). This is an open access article distributed under the terms of the
Creative Commons Attribution License, which permits unrestricted use, distribution,
and reproduction in any medium, provided the original author and source are
credited. |
ABSTRACT |
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When, for a hydrocarbon deposit, the porosity,
density and saturation of the rock, saturating fluid, the permeability, and
the electrical formation factor are known, formulas for calculating the
equivalent thermal conductivity can be used, by which this property is
expressed, depending on the properties of deposit, more easily measurable. These computational expressions are the result of
correlations between experimental determinations performed for the physical
properties of a very large number of samples in the field. But these equations introduce measurement errors or
interpretations by the authors of the research, which often lead to quite
large differences from reality. That is why we introduced an experimental model to
determine the thermal conductivity and we determined this property on rocks
taken from the productive layers of crude oil and gas from some geological
research wells conducted in the Moesica Platform,
Romania. We also managed to introduce computational
relationships between thermal conductivity and density and porosity of
extracted rocks. The role of these experiments is to find a new
method for determining the thermal conductivity, a property necessary to
simulate the flow of oil fluids and the design of oil recovery techniques. |
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Keywords: Oil and Gas Reservoir, Regression Modeling, Thermal Conductivity,
Rocks Porosity, Rocks Density 1. INTRODUCTION
Thermal conductivity is another characteristic property of oil and gas
deposits, analogous to electrical permittivity, magnetic permeability,
electrical conductivity, filtration coefficient and molecular diffusion
coefficient Cristescu (1998). Estimation of thermal conductivity by
calculation is possible in two ways Cristescu (2009) ·
considering an
idealized model, consisting of a solid and a fluid: the solid medium is
supposed to have a certain geometry, and the fluid environment is immobile;
the thermal conductivity of the fluid and solid and the porosity are known. ·
expression
according to other properties of the porous medium saturated with fluids,
more easily measurable (density, porosity, permeability).
It is useful to know the values of the thermal conductivity of the oil
field when designing the exploitation by thermal methods or during the
development of these processes. |
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The experimental law of thermal conduction or Fourier law is given by the expression:
Equation 1
The possibility of heat passing through a body is highlighted by the
thermal conductivity λ which is the heat that normally passes
through the unit of surface, in the unit of time, at a temperature gradient of
1 k/m.
Equation 2
Thermal conductivity is a characteristic property of everybody, which can
be determined experimentally or can be calculated empirically based on other
physical properties.
Conductive heat transport can take place through:
·
Electronic transport-electrons move through high
temperature areas to low temperature areas, transferring energy with them,
·
Transport photon-ions of the body perform oscillating
movements during which there are collisions with heat transfer, the transfer is
performed from close to close, diffusive.
The contribution of ions to heat transfer is shaped by the introduction of
an imaginary, weightless gas called photonic gas, which travels through bodies
from high temperatures to low temperatures, transferring energy without
changing the properties of the body.
·
Radiant transport occurs when the emission and mutual
absorption of radiation between neighboring elementary particles occurs.
In non-ionized gases, gases at t≤1800 ºC, the conductive transport of
heat takes place mainly under the effect of molecular oscillations (photonic
gas) which have a small amplitude and as a result they are bad bodies
conducting heat.
In the case of Newtonian liquids and non-metallic solids, heat transfer
through conductivity takes place both through the oscillations of molecules,
because the distance between them is relatively small, and through radiation Sonney (2010).
The coefficient of thermal conductivity varies with the nature of the body,
with its state of aggregation, with the temperature and pressure, with the
humidity of the body, with the porosity, with the nature and concentration of
the impurities contained in the body, etc.
It is a scalar parameter, in the case of the isotropic medium (gases,
liquids, metals, amorphous dielectric bodies) and vector, in the case of the
anisotropic medium (crystals, materials with stratified arrangement).
One of the specific properties of crystalline bodies is the vectorial or
tensor character that most physical-chemical properties of crystals represent,
including thermal conductivity.
The vector properties can be continuous or discontinuous, which gives the
crystals the fundamental property called anisotropy, which has its origin in
the fact that the interatomic distances are different, depending on the
crystallographic direction.
The most general hypothesis regarding thermal conductivity is given by
Stokes' matrix Jugastreanu et
al. (2022)
Onsanger's postulate Tabatabai et
al. (2022) shows that the matrix of thermal conductivity is
symmetrical and therefore:
Equation 4
Since the experiments did not confirm the existence of the rotary
conduction (, for j ≠
k), the matrix Equation 3 is reduced to the equation:
Equation 5
So, in conclusion, thermal conductivity is a characteristic property of the
environment, analogous to electrical conductivity, magnetic permeability, and
electrical permittivity.
2.
METHODS FOR DETERMINING THERMAL CONDUCTIVITY
Any systematic geothermal research presupposes the knowledge of the heat
transfer mode in the researched environment Jugastreanu et
al. (2022), Tabatabai et
al. (2022)
Heat transfer takes place through three main processes, namely: conduction,
convection, and radiation.
Heat transfer by conduction occurs only in solid media by molecular
interaction Trochim
(2001).
It is the main mechanism of heat transfer in the Earth's crust and the most
important in geothermal probe research.
Convective heat transfer is associated with the free movement of fluids
between two environments at different temperatures.
It becomes important in geothermal areas, in particular,
in areas with volcanic activity and in areas with active groundwater
circulation Tissot
and Welte (1984).
The mechanism of heat transfer by convection must be taken
into account in geothermal research conducted in boreholes, because it
plays a significant role in changing the natural thermal regime of the
geological formations crossed.
Radiative heat transfer occurs, on the one hand, on the Earth's surface,
where temperatures are conditioned by the exchange of heat between the Earth
and the Sun, and on the other hand, in rocks at very high temperatures.
For temperatures encountered at usual probe depths, including deep probes,
the radiative transfer is negligible.
The ability of media to transmit and absorb thermal energy depends on the thermal
conductivity
Thermal conductivity is the property of media to transmit thermal energy to
a greater or lesser degree.
Quantitatively, the thermal conductivity expresses the amount of heat Q
that flows in a time τ through a body with cross section and given
length whose opposite faces are at temperatures t1 and t2:
Equation
6
Where:
·
λ is the thermal conductivity,
·
ΔQ is the amount of heat,
·
Δτ represents the
heat transfer time,
·
∆T is the thermal gradient,
·
A represents the contact area.
Thermal conductivity is the transfer mechanism that occurs at the molecular
level as a result of elastic collisions between
molecules or ions of the substance as a result of their oscillations or
displacement Tissot
et al. (1974), Waples (1985)
Molecules with higher energy by collision with molecules or ions with lower
energy give them some of their kinetic energy, so that heat is transmitted from
close to close throughout the body Tabatabai et
al. (2022), Trochim
(2001)
In liquids and gases, conductivity is the result of elastic collisions
between molecules Cristescu (2009), Sonney (2010)
It is more intense in liquids than in gases because the distance between
molecules is smaller in liquids than in gases.
Because this mechanism is realized at the molecular level, thermal
conductivity is also known as heat transfer through the molecular mechanism.
Thermal conductivity is a characteristic property of the environment,
analogous to electrical permittivity, magnetic permeability, electrical
conductivity, filtration coefficient and molecular diffusion coefficient.
In permanent thermal conduction regime, a fluid-saturated porous medium can
be assimilated with an equivalent continuous medium, for which a thermal
conductivity tensor λ is defined Trochim
(2001), Tissot
and Welte (1984)
2.1. CALCULATION METHODS FOR ESTIMATING THE EQUIVALENT
THERMAL CONDUCTIVITY OF A FLUID - SATURATED POROUS MEDIUM
Thermal conductivity is a characteristic property of the environment,
analogous to electrical permittivity, magnetic permeability, electrical
conductivity, filtration coefficient and molecular diffusion coefficient Cristescu
(2009), Sonney (2010)
In the permanent thermal conduction regime, a porous medium saturated with
fluids can be assimilated with an equivalent continuous medium, for which a
thermal conductivity tensor λ is defined.
The values of the components of this tensor depend on the thermal
conductivity and the distribution of each phase, the saturation in fluids, the
porosity, the direction of the thermal flow, the thermodynamic parameters of
state (pressure and temperature).
If it is assumed that the
fluid-saturated porous medium is thermally isotropic, the thermal conductivity
tensor is spherical and defined with the scalar λ - equivalent
thermal conductivity.
Estimation by calculation of equivalent thermal conductivity is possible in
two ways:
·
considering an idealized model, consisting of a solid
and a fluid: the solid medium is supposed to have a certain geometry, and the
fluid environment is immobile; the thermal conductivity of the fluid and the
solid and the porosity are known Tissot
and Welte (1984).
·
expression according to other properties of the porous
medium saturated with fluids, more easily measurable (density, porosity,
permeability) Tissot
et al. (1974).
The solids and fluids that make up a hydrocarbon deposit are a
fluid-saturated porous medium.
When designing the exploitation by thermal methods or during the
development of these processes, it is useful to know the values
of the thermal conductivity of the oil field Tabatabai et
al. (2022).
2.1.1. CALCULATION METHODS BASED ON IDEALIZED MODELS
1)
The series model Cristescu
(1998), Cristescu
(2009)
The solid medium and the fluid medium consist of a succession of parallel
layers, and the heat flux is perpendicular to the layers (Figure 1).
Equation 7
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
2)
The parallel models Cristescu
(1998), Cristescu
(2009)
The solid medium and the fluid medium have the same arrangement as in the
case of the series model, but the heat flux is parallel to the layers (Figure 1).
Equation 8
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
3) Weighted geometric
mean Cristescu
(1998), Cristescu
(2009)
It does not have a physical basis, but it is easy to apply, and an
intermediate value is obtained compared to the two variants set out above.
Equation 9
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
4) Maxwell's equation
Cristescu
(1998), Cristescu
(2009)
It has been proposed for the calculation of electrical conductivity in the
case of some distribution of solid spheres in a continuous fluid environment.
|
Figure 1 Thermal conductivity calculation models (series and
parallel) |
Applied by Eucken for the calculation of equivalent thermal conductivity,
the equation has the form:
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
Equation Equation 10 is only applicable if the porosity has a high
value, which implies that the solid spheres are sufficiently far apart and do
not interact with each other.
5) The Beck Model Cristescu
(1998), Cristescu
(2009)
It is a modified Maxwell model which, in the opinion of the one who
proposed it, leads to good results, if the porous medium has the following
characteristics și .
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
Equation Equation 11 is based on the real physical situation, in which
fluid spheres, of thermal conductivity are dispersed in a solid environment, of thermal
conductivity .
6)
Model de Vries Cristescu
(1998), Cristescu
(2009)
The model is a generalization of Maxwell's equation for a medium consisting
of a continuous fluid phase and a dispersed solid phase consisting of
ellipsoidal particles.
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
and:
şi Equation 13
xj, refers to the
shape of the particles.
When (spherical particles), the relationship Equation 11 se reduce la forma Equation 12.
D.A. de Vries considered si , which corresponds to particles in the shape of an ellipsoid of revolution, with the major axis 6 times the minor axis.
7)
Model Woodside and Messmer Cristescu
(1998), Cristescu
(2009)
Theoretical and experimental research has led to the adoption of an
equivalent resistor model, in a modified form.
The three-element resistor model belongs to Wyllie and Southwick and has
been proposed to calculate the equivalent electrical conductivity of a
fluid-saturated porous medium.
The model comprises a conductive particle aggregate, saturated with a
conductive electrolyte. They are arranged as three components in parallel.
Element 1 is a series group of particles and the electrolyte, element 2 is
formed by the particles, and the 3rd is the electrolyte (Figure 2).
The equivalent conductivity of this aggregate is calculated by the
relation:
Factors have certain forms for the calculation of
equivalent electrical conductivity.
It is considered that the use of equation Equation 14, for the calculation of the equivalent thermal
conductivity of an unconsolidated environment, leads to results close to those
obtained experimentally, if the following relations are adopted:
Equation 15
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
|
Figure 2 Three-element resistor model for porous environment
Cristescu (1998), Cristescu (2009) |
8)
Model Krupiczka Cristescu
(1998), Cristescu
(2009)
The calculation formula proposed by this model is:
where:
şi Equation 17
The porosity is between 0,215 şi 0,476.
Where:
· is the coefficient of thermal conductivity of the analyzed deposit, W/ (m K)?
·
is the coefficient of thermal conductivity
of the fluids to oil deposit, W/
(m K)?
·
is the coefficient of thermal conductivity
of the rocks to oil deposit, W/
(m K)?
· porosity.
Testing 165 data from specialized publications Tabatabai et
al. (2022),Trochim (2001) it was found that, in 76% of them, the difference
between the values obtained experimentally and those calculated
with the relation Equation 16 is ± 30% Tabatabai et
al. (2022).
3. MATERIALS AND METHODS
The oil field is a porous medium saturated with fluids.
The extremely complicated and varied composition of a hydrocarbon deposit,
as well as the conditions in which it is located, are the reasons why the
physical properties have specific values for each case.
The existence on Earth of large accumulations of heavy and / or viscous
crude oil, shale and bituminous sands, as well as the fact that, after the
application of the classic methods of exploitation, 60-70% of the geological
reserve remain in the field, on the one hand, and on the other hand,
maintaining the predominant place of hydrocarbons as a resource in world energy
are the factors that have captivated the interest in the application of thermal
methods of oil exploitation.
These are hot fluid injection, underground combustion, and combinations
thereof.
It is useful to know the values of the thermal conductivity
of the oil field when designing the exploitation by thermal methods.
The equivalent thermal conductivity of an oil field can be estimated by
calculation, either by applying idealized models or by expressing this heat
transfer property as a function of other properties of the field (density, porosity,
permeability).
Using data appropriate to the oil fields, equivalent thermal conductivity
values can be obtained Tabatabai et
al. (2022), Trochim
(2001)
Experimental research has been undertaken to measure the equivalent thermal
conductivity for rock and reservoir fluids.
Thus, the effect of factors such as the mass composition of the rock and
the nature of the fluid that saturates the rock pores can be highlighted. and
calculation models can be proposed that lead to results consistent with the
measurements.
The measurement of the thermal conductivity of non-metallic solid bodies,
in stationary regime, is determined from the expression of Fourier's law,
aiming that, after reaching the stationary regime, to ensure the constancy of
the thermal flux transmitted through the test material and the temperatures at
its surfaces. (Through which the heat exchange takes place).
Electric heaters are generally used as heat sources, and the temperatures
on the outer surfaces of the samples are measured with small thermocouples
evenly distributed on them.
Various methods and devices for determining the thermal conductivity of
solid materials are described in specialized publications Cristescu
(1998), Cristescu
(2009), Sonney (2010), Jugastreanu et
al. (2022), Tabatabai et
al. (2022)
Of these, the method of the plate, the cylindrical tube and the spherical one
is distinguished by the shape of the test specimens.
The plate method determines the thermal conductivity of a material in the
form of perfectly flat and parallel plates, of surface A and thickness h,
crossed by a heat flux ,
and a temperature
difference .
Figure 3 shows a device for determining the thermal
conductivity by the plate method, with a single specimen.
The heat flux, represented by the electrical power consumed by the
resistors 4, is read at a wattmeter inserted in their supply circuit.
The thermal flow, transmitted through the test tube 1, is taken over by the
water circuit 7 whose thermostat ensures the uniformity of the temperatures on
the lateral surfaces of the sample, temperatures measured by the thermocouples
2.
In addition to the thermal insulation 6 of the entire device, the side
faces of the test plates are protected by guard rings 3, made of the test
material, in the form of annular bodies; by heating with electrical resistances
5, the guard rings are kept inwards at a temperature approximately equal to the
average temperature of the side faces of the protected parts Jugastreanu et
al. (2022), Tabatabai et
al. (2022)
|
Figure 3 Device for determining the
thermal conductivity by the plate method, with a single test tube Jugastreanu et al. (2022), Tabatabai et al. (2022) |
1 - test plate; 2 - thermocouples; 3 - guard ring; 4 - electrical
resistance; 5 - electrical resistance of the guard ring; 6 - thermal
insulation; 7 - water cooler; 8 - compensation plate; 9 - electrical resistance
of the compensation plate
To measure the thermal conductivity of these preparations, capsules were
made in which the mixtures of solids and liquids were introduced.
The capsules were text Olite cylinders, 32.4 / 42 mm in diameter and 24.5
mm high, with metal caps, screwed.
The lids are 42/44 mm in diameter and 1.5 mm thick.
The thermal conductivity of the cover materials is 40 W / make and as a
result, their thermal resistance to heat transfer through conduction is very
low.
Also, the side walls of the text Olite were further thermally insulated to
reduce the heat flux dissipated through the side walls to the outside
environment.
In order to make such determinations,
the possibilities existing in a series of laboratories were analyzed, but the
work with crude oil, which when the temperature increases flows or even starts
to burn, as well as a certain geometry of the specimens, imposed by the
respective equipment, have limited approaches.
The text Olite capsules, described above, have been designed and made so
that their shape and dimensions correspond to those required by the
conductivity measuring apparatus.
Also, the materials were in the form of pastes, for which the thermal
conductivity could not be measured, if they were not placed in the supports
described.
In fact, during the measurement of the thermal conductivity, as the
temperature increased, the oil and water began to flow from the capsules, which
created difficulties.
Another set of samples was the carrots.
The cores come from various areas of the oil fields I studied.
The thermal conductivity of some samples containing crude oil could not be
measured because, under the thermal effect, they started to smoke.
In the case of other samples, the thermal conductivity was determined for
the solid matrix, after the oil traces had vaporized.
When measuring the thermal conductivity, following the study and
calculations regarding the thermal resistances that appear in the process of
heat transfer through conduction and the comparison of the data obtained with
the specific ones from the works it is estimated that the error is 10%.
In the case of samples prepared in the laboratory, the error is mainly
caused by the thermal contact resistances between the test tube and the plates
of the apparatus, by the heat dissipated to the external environment and the
thermal resistances of the metal caps of the capsules.
4. RESULTS AND DISCUSSIONS
Knowing the thermal conductivity of rocks is important due to the
implications of this property in the exploitation of oil fluid deposits.
Thermal conductivity conditions the distribution of heat in the earth's
crust through the phenomenon of conductive transmission.
Also, the study of the crust-mantle discontinuities and the explanation of
the distribution of temperatures inside the earth and of the geothermal flow,
is another property of conductivity.
Fluid saturation and thermal conductivity influence the equivalent thermal
conductivity of the oil field.
It is observed that samples with identical solid composition have different
values of thermal conductivity, depending on the nature of the
fluid they contain.
Also, calculations were performed to determine the equivalent thermal
conductivity, applying the relation:
Equation 19
This ratio is recommended for unconsolidated rocks, with porosity 28-37%. It follows
that, for unconsolidated rocks, the relation Equation 18
can be used to estimate the equivalent thermal conductivity.
Transitional measurement methods (non-stationary)
Transitional
measurement methods, (, can be performed in practice in multiple variants.
In some variants, a cylindrical sample with a uniform initial temperature,
is constantly heated by a source-line and the temperature increases over time.
The temperature rise at a point of a heated sample (via a line source) can
be written as follows:
Where:
·
, is the amount of heat per unit length of the source,
·
is the radial distance of the measuring
point from the source-line,
·
it is the time that has passed since the
beginning of the warm-up,
Equation 21
Where:
·
is Euler
number = 0,5772.
If is small, that is, when is large and r
smal, the terms in x2, and higher powers can be neglected so that
equation Equation 20 can be written:
Equation 22
For two measurement times și , the temperature rise will be:
Equation 23
So, the thermal conductivity K can be evaluated from the slope of the line .
Equation 24
Transient working methods are characterized by rapid measurements, good
accuracy, good accuracy and in the conditions of rocks saturated with
hydrocarbons and water, there is no fluid displacement in the porous space,
respectively uneven distributions of saturation fluid.
These methods are used to determine the thermal conductivity of
unconsolidated rocks (ocean floor sediments).
Methods of measurement in stationary thermal regime
In this case and the principle of the method is to measure the temperature of a split bar consisting of two polycarbonate disks as the reference material with known thermal conductivity and the analyzed sample (Figure 4).
After a sufficient time to reach thermal equilibrium, assuming that the
heat flux is axial and there are no significant radial losses between the
disks:
Equation 25
Equation 26
Gathering the above relationships:
Equation 27
|
Figure 4 The main scheme for
determining the thermal conductivity |
So, the heat flux through the rock sample can be taken as the sum of the
fluxes and .
Equation 28
Equation 29
Where:
· is the thermal conductivity of the rock sample with cross section and thickness , (mcal/ ºC cms)?
·
is the thermal conductivity of textolite with
cross section and thickness , (mcal/ºC
cms)?
So, the thermal conductivity
is:
Equation 30
Measurement data
In the first part of the practical work, we determined the thermal
conductivity of polycarbonate.
The equation of variation of the thermal conductivity of polycarbonate with
respect to temperature is (Figure 5):
y = 0,001x + 0,1295 Equation 31
where:
·
y represents the value of thermal
conductivity, mcal/ºC cms,
·
x is the temperature of determination, ºC.
The analysis of the thermal conductivity of the cores taken from the
geological structures analyzed in the chapter starts from the determination of
the conductivity of the productive layers.
|
Figure 5 Thermal conductivity of polycarbonate |
Table 1 Analysis of the productive states of the studied deposits (oil and gas) |
||||
Drilling position |
Drilling depth |
Geologic layer |
rocks |
mcal/ºC cms |
Belciugatele |
3350 |
Malm |
Chalk |
18,126 |
Slobozia |
1603 |
Cretacic lower |
Chalk |
27,273 |
Slobozia |
1603 |
Cretacic lower |
Fisure chalk |
19,808 |
Smeeni A |
4343 |
Sarmațian |
Marl |
0,6794 |
Smeeni A |
4343 |
Badenian |
Compact
clay |
0,6363 |
Smeeni A |
4343 |
Badenian |
Chalk |
11,353 |
Suraia A |
4956 |
Sarmațian |
Compact
clay |
12,735 |
Suraia B |
4330 |
Sarmațian |
Compact
floor tiles |
15,299 |
Smirna |
4050 |
Carbonifer |
Floor
tiles |
20,923 |
Smirna |
4050 |
Devonian
higher |
Compact
clay |
17,226 |
Smirna |
4050 |
Devonian
lower |
Compact
clay |
19,403 |
Smirna |
4050 |
Devonian
lower |
Conglomerate |
10,831 |
Ianca Berlescu |
3550 |
Sarmațian |
Compact
Chalk |
19,686 |
Ianca Berlescu |
3550 |
Devonian |
Chalk
/Fissure dolomite |
16,704 |
Ianca Berlescu |
3550 |
Devonian |
Chalk
/dolomite compact |
20,696 |
Cireșu A |
3146 |
Sarmațian |
Fissure
marl |
0,2890 |
Zăvoia |
3500 |
Sarmațian |
Marne
whith inclusion |
0,9095 |
Zăvoia |
3500 |
Albian |
Chalk |
15,827 |
Zăvoia |
3500 |
Malm |
Limestone
tiles |
15,127 |
It is found that the values of this thermal transport
property depend on the composition of the porous medium, respectively the
deposit area where they come from.
The cores were consolidated rocks, and the results obtained refer to the
solid matrix, because either this is how they were initially presented, or
during the measurements the oil was expelled from the rock pores
Statistical relationships between rock properties
The cores harvested from the wells were subjected to other determinations,
namely:
·
Density, g/cm3,
·
Porosity, %,
·
Permeability, mD.
For some analyzed geological layers we performed statistical analyzes to
see what the correlation equations between thermal conductivity are and the above-mentioned
properties.
The equations are of the type:
Equation 32
Where:
·
is the property determined above (density,
porosity, permeability) and y is the thermal conductivity?
·
a and b are numerical coefficients.
Table 2 Statistical equations for determining the density (g/cm3) as a function of thermal conductivity (mcal/ºC cms) |
|||||
Drilling |
Roks |
kr |
Density,
g/cmc |
Ecuation |
R2 |
Slobozia |
Chalk |
19,808 |
2,76 |
y
= 0,2858x + 2,1612 |
1 |
Slobozia |
Fisure chalk |
27,273 |
2,95 |
||
Smeeni A |
Chalk |
0,6363 |
2,69 |
y
= 0,1367x + 2,605 |
1,00 |
Smeeni A |
Compact
clay |
0,6794 |
2,7 |
||
Smeeni A |
Compact
floor tiles |
11,353 |
2,76 |
||
Smirna |
Floor
tiles |
10,831 |
2,56 |
y
= 0,2045x + 2,3353 |
0,9952 |
Smirna |
Compact
clay |
17,226 |
2,68 |
||
Smirna |
Compact
clay |
19,403 |
2,73 |
||
Smirna |
Conglomerate |
20,923 |
2,77 |
||
Ianca Berlescu |
Compact
Chalk |
16,704 |
2,3 |
y
= 1,4071x - 0,0341 |
0,9623 |
Ianca Berlescu |
Chalk
/Fissure dolomite |
19,686 |
2,8 |
||
Ianca Berlescu |
Chalk
/dolomite compact |
20,696 |
2,83 |
||
Zăvoia |
Marne
whith inclusion |
0,9095 |
2,5 |
y
= 0,3778x + 2,1556 |
0,9976 |
Zăvoia |
Chalk |
15,127 |
2,72 |
||
Zăvoia |
Limestone
tiles |
15,827 |
2,76 |
Table 3 Statistical equations for determining the porosity as a function of thermal conductivity (mcal/ºC cms) |
|||||
Drilling |
Roks |
kr |
porozivity, % |
ecuations |
R2 |
Slobozia |
Chalk |
19,808 |
0,5 |
y
= 0,3561x + 2,022 |
1 |
Slobozia |
Fisure chalk |
27,273 |
2,2 |
||
Smeeni A |
Chalk |
0,6363 |
0,8 |
y
= 0,9509x + 0,2231 |
0,9875 |
Smeeni A |
Compact
clay |
0,6794 |
0,9 |
||
Smeeni A |
Compact
floor tiles |
11,353 |
1,3 |
||
Smirna |
Floor
tiles |
10,831 |
1,2 |
y
= 0,7897x + 0,2975 |
0,9164 |
Smirna |
Compact
clay |
17,226 |
1,50 |
||
Smirna |
Compact
clay |
19,403 |
1,9 |
||
Smirna |
Conglomerate |
20,923 |
1,99 |
||
Ianca Berlescu |
Compact
Chalk |
16,704 |
1 |
y
= 11,588x - 18,651 |
0,8409 |
Ianca Berlescu |
Chalk
/Fissure dolomite |
19,686 |
3 |
||
Ianca Berlescu |
Chalk
/dolomite compact |
20,696 |
6,2 |
||
Zăvoia |
Marne
whith inclusion |
0,9095 |
5,2 |
y
= 9,4431x - 3,4729 |
0,9534 |
Zăvoia |
Chalk |
15,127 |
10 |
||
Zăvoia |
Limestone
tiles |
15,827 |
12,2 |
Table 4 Statistical equations for determining the permeability (mD) function of thermal conductivity (mcal/ºC cms) |
|||||
Drilling |
Roks |
kr |
permeability
mD |
Equations |
R2 |
Slobozia |
Chalk |
19,808 |
0,01 |
y
= 0,775x + 1,1923 |
1 |
Slobozia |
Fisure chalk |
27,273 |
1,2 |
||
Smeeni A |
Chalk |
0,6363 |
0,005 |
y
= 3,6512x - 2,3481 |
0,999 |
Smeeni A |
Compact
clay |
0,6794 |
0,1 |
||
Smeeni A |
Compact
floor tiles |
11,353 |
1,8 |
||
Smirna |
Floor
tiles |
10,831 |
0,016 |
y
= 0,0048x + 0,0103 |
0,806 |
Smirna |
Compact
clay |
17,226 |
0,017 |
||
Smirna |
Compact
clay |
19,403 |
0,02 |
||
Smirna |
Conglomerate |
20,923 |
0,021 |
||
Ianca Berlescu |
Compact
Chalk |
16,704 |
0,03 |
y
= 0,0048x + 0,0103 |
0,91 |
Ianca Berlescu |
Chalk
/Fissure dolomite |
19,686 |
0,397 |
||
Ianca Berlescu |
Chalk
/dolomite compact |
20,696 |
0,8 |
||
Zăvoia |
Marne
whith inclusion |
0,9095 |
0,01 |
y
= 1,3172x - 1,1884 |
1 |
Zăvoia |
Chalk |
15,127 |
0,8 |
||
Zăvoia |
Limestone
tiles |
15,827 |
0,9 |
Qualitative analysis of the thermal conductivity of
the geological layers analyzed according to the data from the literature
The literature has given values for the thermal conductivity
of geological strata and for density. The accuracy of our determinations can be
expressed by the absolute deviation ratio (AAD%) calculated with the equation:
Equation 33
where:
·
, experimental
values.
·
, calculated values.
Table 5 Differences between the thermal conductivity of geological layers and density (determined values and values in the literature) |
||||||
Geologic layer |
Thermal conductivty
(calculated) , (mcal/ºC cms) |
Thermal conductivity (analysis), , (mcal/ºC cms) |
Absolute deviation, thermal conductivity (%) |
Density calculated , (kg/m3) |
Density determinations , (kg/m3) |
Absolute deviation, thermal conductivity2 Density (%) |
Cretacic |
1,85 |
19,809 |
6,56 |
2620 |
2950 |
11,18 |
Carbonifer |
1,73 |
20,923 |
17,22 |
2780 |
2770 |
6,85 |
The error is
a maximum of 17% for carboniferous.
Table 6 Differences between the thermal conductivity of geological layers and density (determined values and values in the literature) |
||||||
Rocks |
Thermal conductivity, (calculated) , (W/mºC) |
Density, value of literatures , (kg/m3) |
Thermal conductivity, Measurenment, kr (W/mºC) |
Absolute deviation, thermal conductivity (%) |
Density
determinations, , (kg/m3) |
Absolute deviation, density (%) |
Marne
whith inclusion |
0,65 |
2,77 |
0,64 |
1,56 |
2,77 |
24,47 |
Shale clay |
0,48 |
2,57 |
0,53 |
9,43
|
2,68 |
35,72 |
Chalk |
0,6 |
11,455 |
0,66 |
9,09
|
2,80 |
29,69
|
Chalk with inclusion |
0,9 |
2,62 |
0,82 |
9,76 |
2,83 |
26,87
|
The error is a maximum of 10% in conductivity, in the case of shale clay, due to the fact that it was not pure.
The density errors are large because the chosen cores were not pure, being
impure with other materials.
5. CONCLUSIONS AND RECOMMENDATIONS
The purpose of this analysis was to compare the experimental results with
those obtained by calculation, so as to recommend the
most suitable theoretical models for estimating the equivalent thermal
conductivity of an oil field.
In the initial state, before applying a process of thermal recovery or in
areas of deposit downstream of the thermal front, far from it, of the idealized
models, the Krupiczka model is recommended, for rock
saturated with crude oil or crude oil and water.
The series model is suitable for water-saturated rock.
It should be noted that it is necessary to know the composition and thermal
conductivity of the phases.
The calculation ratio, based on the correlation with more easily measurable
properties (porosity, saturation), is also appropriate in the case of solid
environment composed of unconsolidated rocks.
Experimental research has shown changes in thermal conductivity depending
on the composition of the fluid-saturated porous medium.
The equivalent thermal conductivity of the fluid-saturated porous medium
increases as the thermal conductivity of the solid medium and that of the fluid
medium increase.
The solid environment of the oil field is the bedrock, and the fluid one is
made up of crude oil, water, gas.
Their thermal conductivity depends on the composition and thermal
conductivity of the components, where they come from.
The analyzed cores were consolidated rocks, and the results obtained refer to the solid matrix, because either this is how they were initially presented, or during the measurements the oil was expelled from the rock pores.
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