Modelling of temperature distribution around salt diapirs: Application to hydrocarbons

assessment

Author

Camilo Arenas Pardo

Advisors

José María Jaramillo and Jillian Pearse

Submitted to Geoscience Department

of Universidad de Los Andes in partial fulfillment

of the requirements for the degree of Bachelor

of Geoscience

Bogotá D.C.

2016

Table of contents

Abstract………………………………………………………………………………………………………………………… 3

Introduction….................................................................................................................. 4

Conceptual Framework…................................................................................................. 5

Petroleum System Elements….............................................................................. 6

Pre-salt and Sub-salt plays……………………………………………………………………………….. 10

Geologic Framework...................................................................................................... 12

Campos Basin…................................................................................................... 12

Santos Basin…..................................................................................................... 12

Theoretical Framework…............................................................................................... 14

Finite difference theory….................................................................................... 14

Methodology….............................................................................................................. 15

Methodology…................................................................................................... 1 5

Mesh Convergence…........................................................................................... 17

Results….......................................................................................... .............................. 19

Discussion….......................................................................... ......................................... 27

Conclusions…................................................................................................................. 28

Appendix…..................................................................................................................... 29

Acknowledgements…..................................................................................................... 3 1

References….................................................................................................................. 32

Abstract

Finite difference methods have been used to calculate the temperature distribution in the

surrounding sediments of a salt diapir. In this model, results are in agreement with the work

of Jensen, P.K. (1983). The temperature distribution around the salt diapir depends on the

scale and its geometry; therefore, salt domes show a temperature gap above and beneath

of them. The model presented here shows that the major positive anomaly of temperature

above the salt dome is around 22-25°C, while the lowest anomaly varies from -20 to -25°C

some meters beneath the bottom of the dome. Hence, in the presence of salt domes the

maturity of the sequence changes, so hydrocarbons will be generated at a different time in

the thermal history of the basin if salt domes are present. The case of Santos basin at Brazil

shows the change in the rate of maturity; therefore, the potential reserves of oil increased

in this country. Finally, it is important to study temperature anomalies because this

phenomenon could explain the discoveries in ultra-deep water of Gulf of Mexico and some

exploratory wells in Africa, allowing an increase of oil potential around the world.

Introduction

The temperature distribution at a sedimentary basin is a very important factor to investigate.

The local temperature has great importance in the generation of hydrocarbons, organic

matter transforms to oil or gas only in appropriate temperature conditions. These optimal

temperatures are called the generation window (60°-120°). Therefore, it is important to

understand the thermal conditions of a basin through the analysis of the isotherms and their

variations. One of the factors that varies the isotherm distribution is the presence of salt in

the basin. Due to its high heat conductivity, the salt acts like a fridge, and this contributes to

the hydrocarbon maturation.

The accumulation of hydrocarbons in a sedimentary basin is high, so there is a huge interest

by the industry in those places. This economic interest lies in the potential hydrocarbons

reserves of the basin; thus, it is necessary understand which are the processes that govern

the accumulations. As a first step, it should be a minimal amount of organic matter present

in the layer. The organic matter is the base of hydrocarbons, so its presence is essential.

Secondly, it is important that at the deposition location the presence of oxygen must be poor

because under anoxic conditions the organic matter preserves more auspiciously. After the

deposition takes place, layers which are rich in organic matter must be buried to reach the

suitable temperature to enter into the generation window. Finally, there must be migration

from the source rock to the reservoir, and the reservoir must be able to store oil and gas.

With the purpose of understanding the temperature distribution in a basin, a theoretical

model of a sedimentary basin was developed. The goal of the model is to show the effect of

the salt diapirs on the temperature. However, it is also important to show models of the

basin without the presence of diapirs because it can be compared with those which have

these structures. The model was developed using the finite deference centered method

applied to the heat conduction equation in two dimensions.

Conceptual framework

The importance of sedimentary basins in the regional geology is crucial. It is in these places

where the sediments coming to the continent are concentrated. Moreover, sedimentary

basins are controlled by tectonics, weathering and sediment’s input. The two last mentioned

factors are of vital importance in the development of a sedimentary basin because it is

necessary to have knowledge about the quantity of continental sediment’s input and how

much has been eroded when they arrive to the basin. In addition, tectonics makes it more

complicated. Because tectonics are present, the sedimentary basin may have more or less

accommodation space available, due to subsidence in the deposition zone. Subsidence is

generated by the sediment’s input that due to gravity will cause the depocentre to reach a

greater depth (which varies according to the basin). Furthermore, sediments suffer some

deformation through tectonics, so this deformation can indicate the type of the sedimentary

basin. (Einsele, G., 2013, pp. 3)

As well, sedimentary basins are classified depending on the tectonic setting (Einsele, G., 2013,

pp. 3-9) In general, there are two main types. Sedimentary basins associated with passive

margins and others associated with active margins. It is common that basins associated with

passive margins have greater extent than those associated with active margins. Basins

associated with active margins can be divided into three types: those associated with

transform, divergence and convergence boundaries. Thus, the basins with more economical

interest are the ones associated with passive margins because their large scale.

As mentioned above, the economic interest in sedimentary basins is elevated because these

are the places in which the sediments with organic matter are deposited. After the

deposition of the organic matter takes place, these sediments have to be buried and at the

right temperature and pressure conditions, they will become hydrocarbons (oil and gas). The

pressure and temperature conditions are functions of different variables, such as the

thermal conductivity of the rock, heat generation for decay of radioactive elements, heat

flux coming from the mantle, density of the rock, depth and time of burial. All these factors

affect the local geotherm. Geotherm is what determinates the depth that rock has to reach

in order to be in the hydrocarbons generation window.

Resuming the topic of sedimentary basins, recently it was discovered that the presence of salt layers has a fundamental role in the thermal history of a basin (Mello et al., 1995 y McBride et al., 1998). The salt can act as a refrigerant due to its high thermal conductivity and physical properties. This phenomenon takes place when the salt layers are overpressured by the sediments on top and as a result, salt diapirs are formed. The diapirs are similar to conduits that evacuate the heat from the mantle; therefore, one sedimentary basin with presence of salt layers, buried to the needed depth, will generate hydrocarbons at a different point of the burial history because the isotherms change. Because of that it is

important to know where salt deposits are, and if they have proper scale to produce the fridge phenomenon; for instance, in the Atlantic Ocean near the Brazilian shores, a series of boreholes were drilled with the previous knowledge that the prospect was a gas field. However, what they found there was oil. The reason for this was that the basin was refrigerated due to salt diapirs giving rise to a supergiant field in the Brazilian offshore.

Moreover, it is worth highlighting that not only sedimentary basin associated with passive

margins can contain hydrocarbon reservoirs. Also in convergent sedimentary basins, there

is hydrocarbon accumulation; for example, recently in Colombia the hydrocarbons that come

from the basins of Valle Medio del Magdalena and Valle superior del Magdalena are

associated with active margins. Although in Colombia salt deposits do not have a large

enough scale to produce the fridge phenomenon, it is important to know and analyze this

process because it is present in some important basins on the world, for instance, the Gulf

of Mexico and Santos basins.

Finally, this work is focussed on sedimentary basins and their thermal evolution, in order to

understand the isotherm variations depending on the quantity of sediment and the presence

of salt diapirs and layers. The importance of this phenomenon for the industry is high, so the

interpretations of the results are focused on the hydrocarbons evaluation. The factors that

are taken into account in this analysis are the temperature distribution, the variations in the

isotherms, depth of burial of sediments and entrapment of oil in the sedimentary basin.

It is also important to define a petroleum system because the temperature is not the only

factor that influences the generation of hydrocarbons. There are some other necessary

elements to have oil and gas generation, which include the source rock, seal rock, reservoir

rock and overburden of the source rock. In addition, there are also processes that allow the

formation of hydrocarbons. These processes are the trap formation (stratigraphic or

structural), the migration, the accumulation and the generation that is directly related to the

temperature reached by the rocks, maturation and the organic matter. Therefore, the

prospect evaluation of a petroleum play takes into account each of these elements and

factors. The real problem for the prospect is that it has to have all of these: if even just one

is not present, the play is useless.

To Understand the importance of these elements and processes is important define each

one separately.

Source rock

The source rock is the rock with the highest content of organic matter. At the right

temperature it will produce petroleum. Generally, high organic matter sediments are

deposited in areas of high organic productivity and stagnant water (Gluyas and Swarbrick. 2013).

Examples of high productivity areas are swamps, shallow seas, jungles and lakes. However,

the vast majority of the organic matter is not preserved because of oxidation and superficial

processes. Hence, in order to preserve organic matter the concentrations of oxygen in the

environment need to be very low. Moreover, different sorts of organic matter produce

different sorts of petroleum (Gluyas and Swarbrick. 2013); for instance, organic matter from

algae tends to yield oil and gas (more maturation), yet organic matter from woody tissues

produces gas reservoirs.

Seal rock

Because the density of oil and gas is less than water, hydrocarbons will rise through the

sedimentary column until they reach a seal. Usually, seals tend to have low grain size or

vitreous textures. Some common seals are mudstone or shale, cemented limestones, chert,

salt and in general low-permeability rocks (Gluyas and Swarbrick. 2013). Thus, seals block the

passage of the hydrocarbons to the surface, and trap them preventing them to migrate from

reservoir.

Reservoir rock

A reservoir rock is a rock with the presence of voids. In geological terms it is a rock with high

permeability and porosity. Oil, gas and water fill these voids located between the grains of

the rock. Reservoir rocks mostly are coarse-grained rocks such as coarse-grained sandstones

or carbonates. Accordingly, good reservoirs have high permeability as well as porosity, but

these properties vary hugely (Gluyas and Swarbrick. 2013).

Trap

Trap is the term that refers to the geometry of the seal or petroleum container (Gluyas and

Swarbrick. 2013). Mainly, traps are a mixture of tectonics and stratigraphy because they are

formed from sediments in forms shaped by tectonic forces. The simplest trapping

configurations are four dip closures, which are geological structures that close in the three

dimensions. In addition, examples of traps are faults, folds and unconformities. Basically,

there are two types of traps, the first one is the stratigraphic one and the second one is the

structural trap.

Stratigraphic

Stratigraphic traps are mostly formed simultaneously with the deposition of

sediments. There are three types of stratigraphic traps. First, pinchouts are when one

lithology ends in contact with another but with a smaller thickness than in its central

part. Second, unconformities are surfaces between two rock layers that establish a

break (hiatus) in the geologic record. Generally, unconformities are indicators of

erosion, deformation, subsidence or sea level changes (unconformities, n.d). Finally,

fossilized coral reefs which are beneath and/or above of permeable and

impermeable rocks. They act like a trap because their high porosity and permeability,

and they are sealed by other formations with low values of these properties

(Caldwell, Engelmark, Norman, 1997).

Pinchout

Fig. 1. Modified from Gawthorpe, R. L., Sharp, I., Underhill, J. R., & Gupta, S. (1997).

Structural

Structural traps are formed due to the effect of tectonics after the sediments are

deposited. There are two big groups of structural traps, anticlines and faults. The first

one, anticline, is a geologic structure with the form of an arch where the ancient

sediments are in its core. Consequently, this shape is favorable for hydrocarbon

accumulation because of the density difference between oil, gas and water. On the

other hand, fault associated traps require that the plane of the fault be impermeable

to prevent flow outside the structure.

Fig. 2. Taken from http://www.tulane.edu/~sanelson/eens1110/energy.htm

Migration

Migration is the process by which hydrocarbons move from their place of formation (source

rock), to the surface of the earth. At superficial conditions some components of petroleum

will be broken down by bacteria and environmental conditions; however, the path from the

source rock to the surface can be truncated. Hydrocarbons accumulate in a trap, and rest

there if the structural and stratigraphic conditions are appropriate.

The migration process occurs in three main steps. In first place, primary migration is the

expulsion of petroleum from the source rock by pressure. Secondary migration is concerned

with the journey from source rock to the trap. Ultimately, tertiary migration is the leakage

of the hydrocarbons at Earth’s surface.

Thermal history

It is important to measure the temperature of the borehole at different depths because that

allows reconstruction of the thermal history of the stratigraphic sequence. In order to

measure the temperature a thermometer is attached to wireline logging tools, but some

corrections have to be done before estimating the important data. It is worth saying that the

lithologies with high conductivities such as salt, should be avoided in the thermal analysis

because they do not represent much thickness of the full rock section. After whole

corrections are done, and values of temperature are available for two or more depth points

of known stratigraphic age, a geothermal gradient, and thus the thermal history can be

estimated (Gluyas and Swarbrick. 2013, p. 76).

Although the thermal history is mainly controlled by temperature, time also is fundamental.

The effects of temperature in rocks occur during any interval of time; as a result, some

chemical reactions take place in this stage. The effects of the change in temperature over

the sediments are estimated by some parameters; for example, vitrinite reflectance (%Ro),

illite crystallinity, clay dehydration states, biological markers, max temperature, and apatite

fission track analysis (Gluyas and Swarbrick. 2013, p. 76).

Reserves

Reserve is the term used to quantify the amount of hydrocarbons (could be oil or gas) that

was discovered within the earth. Also reserves vary based on the crude oil prices, so reserves

are mostly an economic term because it takes into account not only the size of the

accumulation but also the current prices of oil and gas. Reserves can augment or diminish

depending on the economic fluctuations.

Non conventionals

The theory given before is for conventional oil deposits, but there are some deposits that do

not fall into this category. Unconventional oil and gas do not flow naturally from the source,

so the reservoir rock generally is the same as the source. Unconventional often refers to low-

permeability rocks; thus, the movement within the formation is difficult for hydrocarbons.

Nevertheless, this type of deposit is called to be the future of the oil and gas industry.

Although unconventional fields differ in some aspects to conventional ones, temperature is

also important in the development of hydrocarbons.

Temperature and time, as said before determine the thermal history of the sequence; hence,

geotherms have to be calculated in order to assess the availability of petroleum. The effects

of temperature in the sediments are crucial, regardless of lithology and other processes.

Temperature always has to be evaluated and determined in the play or prospect evaluation.

Pre-salt and Sub-salt plays

Oil accumulations beneath salt layers are commonly called pre-salt plays. However, there is

a difference in the concept of pre-salt and sub-salt. Pre-salt refers to sediments that are

older than salt and underlie autochthonous salt; in contrast, sub-salt is referred to

sediments that are younger than salt and underlie allochthonous salt.

Fig. 3. Taken from (Craig, Carl, Bize, Boyd, Frydman, Zerilli, Dribus, Moreira and Capeleiro., 2010).

The problems with pre-salt and sub-salt plays are various. One of them is the poor quality

of seismic images beneath salt deposits, so the uncertainty about the presence of

reservoir rock is high. Another problem is that the plays are at a great depth; hence, the

costs of exploration are also very high. Nonetheless, the accumulations of oil estimated in

Brazilian pre-salt plays overcome the risk and costs, so recently there is an interest of the

industry to explore in pre-salt oil accumulations. The drilling and exploitation costs for

some gas fields in Brazil were not economical, but with the temperature anomaly beneath

of salt diapirs the maturation was slowed. Thus, what was thought to be a gas deposit

actually is an oil deposit, and it is economical to explore. The estimates for a Tupi field in

Santos Basin are approximately of 5 to 8 billion bbl, so it is important to analyze and study

pre salt accumulations due to the large amount of potential reserves that they have.

Geologic Framework

Campos Basin

Campos Basin is located in the Atlantic coast of Brazil. It ranges from the offshore coast of Vitoria (State of Espírito Santo) to the south until Arraial do Cabo, some kilometers to the east of the city of Rio de Janeiro (Fig. 4). Campos basin has an approximate area of 1x10⁶ square kilometers. The basin is really prolific because recently more than 70 plays were discovered including seven giant oil fields in deep water [Campos Basin, main operations Petrobras (s.f.)].

Campos basin was formed on the western flank of the south Atlantic passive margin as a result of the break-up of Gondwana, and contains sediments of ages from Lower Cretaceous to Holocene. The structure of the basin is a series of grabens, NE and NW trending horsts, fault associated structure due to Campos fault and salt dome provinces in ultra-deep water. These sequences observed in the basin comprises lacustrine to hypersaline alluvial fans, carbonate banks and lacustrine sediments overlaying a basement. The Upper Cretaceous-Paleocene bathyal sequence contain turbidites, in which ideposition was affected by salt tectonics (Allen, P.A., & Allen, J. R. (2013)).

The petroleum system of the basin includes the source and reservoir rocks, traps and migration. The source rock is the Barremian Lagoa Feia organic-rich shale. It has a thickness of 100-300m which contains oil-prone Type 1 kerogen. Also it is known that more than one event of generation and migration took place. The depositional environment was small alkali lakes bordered by a gulf or lagoon with episodic marine incursions. Reservoir rocks

include Barremian carbonates and vesicular Necomian basalts, Albian shallow-water shelf carbonates, Upper Cretaceous turbidites and Oligocene-Miocene turbidites. Generation began in the Coniacian-Santonian, reaching a peak during the Late Miocene, and continues to the present day. Traps are comprised by pinch-outs of turbidite or carbonate reservoirs, and salt-tectonic seals. Generation and entrapment was synchronous. Finally, migration was short-distance into reservoirs, and was enhanced by good carriers beds, window through the salt, and pathways along listric faults (Allen, P.A., & Allen, J. R. (2013)).

Santos Basin

Santos Basin is the largest offshore sedimentary Basin in Brazil; it has a total area of approximately 350x10³ square kilometers comprising from Cabo frio (State of Rio de Janeiro) to Florianopolis (State of Santa Catarina) (Fig. 4). The majority of oil fields on Santos Basin are underway in the Santos Basin pre-salt area. The discovery of the sub-salt play in Santos Basin is one of the greatest exploration discoveries, and is comparable to the ultra-deep-water Gulf of Mexico, unconventional gas discoveries in the U.S., and the super- giant oil and gas fields at the Caspian area. Although discoveries have been made, the pre- salt play is in the early stages of maturity, so the petroleum potential is not well understood.

The sub-salt play extends beyond the Santos Basin into the Campos and Espírito Santo basins. Nevertheless, there is problem to understand the migration of the petroleum from the Barremian organic-rich rocks to the post-salt reservoirs because in the pathway are the Aptian evaporites (seals). In addition, another problem in locating the sub-salt reservoirs in Santos Basin is that the seismic data beneath the sequence of salt layer and evaporites does not have the same detail. The Basin is comprised by two major tectonic settings. First, the southern part is a compressional salt regime with presence of grabens and NE-SW trending horsts. In the north, the extensional salt regime is compounded by salt domes, salt walls and mini basins.

The regional structural framework and sedimentary processes have been crucial to the development of sub-salt petroleum system in the basin. The petroleum system is comprised of: the rich lacustrine source rocks analogous to the Campos basin's ones, a seal of Aptian evaporites, structural traps associated with rifting, shallow marine carbonate reservoirs (coquinas and limestone) and finally a suitable thermal history for hydrocarbon generation influenced by the presence of salt thermal properties (Allen, P.A., & Allen, J. R. (2013)). It is worth saying that the base of salt is of Aptian age in the compressional salt regime of the basin.

Fig. 4. Taken from Craig et al. (2010). Location of Santos, Campos and Espírito Santo Basins

Theoretical Framework

Finite difference theory

The goal of the finite difference method is to find a numerical solution to a physical problem. In general, the problem is described by differential equations, which with this method are approximated by a linear equation system. This algebraic system is easy to solve by matrix methods.

Basically, there are three types of finite difference methods. They are: forward finite differences, backwards finite differences and centered finite differences; moreover, all of them may include variation in time or space. Depending on the problem, one can choose the best finite difference method. The choice among each method should be based on the stability of the solution; hence, it is important have prior knowledge of the problem in order to implement the best method to solve the problem. In this project, it was determined that the best method was the centered difference method because, unlike the other two methods, the centered one presents a small error (of the order of h3, where h is

the size of the step) because the Taylor series approximation is used.

The derivatives through this method are approximated by differences in each property between two or more nodes. For the centered finite difference method in two dimensions, each node is related with four surrounding nodes, i.e. up, down, right and left. For the special case that the node is located next to one or two boundaries the relation continues being with four nodes, but the difference is that one or two of the related nodes are the specified boundary conditions. Thus, the equation for an arbitrary node located in the i position written by the approximation of centered difference method (Eq. 1):

(a)

(b)

Fig. 5. (a) Explanation about the location of the points of the finite difference method. (b) Geometrical interpretation of finite difference method. Taken from http://www.mathematik.uni-dortmund.de/~kuzmin/cfdintro/lecture4.pdf

∂2u

∂2xi

ui−1,j − 2ui,j + ui+1,j = h2

(1)

∂2T

∂2yi

ui,j+1 − 2Ti,j + ui,j−1 = h2

Where h is the size of the step between two nodes, x and z are the planes of the space, and u is the temperature. Therefore; because the heat conduction equation for two dimensions is (Eq. 2):

∂ 2 T ∂ 2 T A

(2)

∂2x + ∂2y

= − k

Where A is the radiactive heat production and k is the conductivity of the each layer.

The complete approximation of this equation to finite differences is (Eq. 3):

ui−1,j + ui+1,j + ui,j−1 + ui,j+1 − 4ui,j A (3)

h2 = −

k

Methodology

The next step was to define the size of the mesh in order to change the indices i and j for only one index. If the mesh has a size of n x n then the equation converts to (Eq. 4):

uk−1 + uk+1 + uk−n + uk+n − 4uk A

h2 = −

k (4)

That was done just for the purpose of making the computational part of the problem easier, because the computational time diminishes with that simplification.

So the problem coverts to a linear algebraic one, and the solution for each node gives the general solution of the problem. Basically the problem is:

Au = c

Where A is the matrix of coefficients for each node, u is the vector of temperatures and c is the constant of the problem which in this case is A/k. taking into account the formulae for finite differences, the matrix A for nine nodes as an example is defined as:

− 4 1 0 1 0 0 0 0 0 1 − 4 1 0 1 0 0 0 0 0 1 − 4 0 0 1 0 0 0 1 0 0 − 4 1 0 1 0 0 0 1 0 1 − 4 1 0 1 0 0 0 1 0 1 − 4 0 0 1 0 0 0 1 0 0 − 4 1 0

0 0 0 0 1 0 1 − 4 1

[ 0 0 0 0 0 1 0 1 − 4 ]

One can see that there is a pattern in the distribution of the constants for the matrix, and this pattern is always the same for a matrix of size n x n. Also the vector u is defined as:

( u1 u2 u3 ⋯ un ⋯ unxn )

Finally, the constant is also a vector of size n x n defined as:

( c1 c2 c3 ⋯ cn ⋯ cnxn )

It is important that the constant c is related to the boundary conditions if it is applicable to the node.

After defining the matrix and the constant it is necessary to find the vector u, so the

solution is:

u = A−1c

This is the solution for the temperature corresponding to each node.

When the solution for each node is known, one can plot the final result for vector u.

Figure 5 shows an example solution for five layers with a distance in x and z of 60 and a step size of one.

°C

Fig. 6 Temperature distribution for five-layer model

It is important to mention that the sequences modeled in this work were always sedimentary sequences including sandstone, shale, limestone and salt. Overall, the lithologies in contact were sandstone-shale, shale-limestone, limestone-salt, shale-salt and sandstone- salt. The conductivities for each lithology were obtained from the work done by Robertson (1988) and Middleton (1993).

Lithology Thermal conductivity W/m °C Sandstone 2.5-4.0 Shale 1.8-2.0 Limestone 2.3-3.0 Salt 5.0-6.2

Table 1. Thermal conductivities used in the model for different types rocks

Mesh convergence

The models that use nodes to calculate and approximate the solution to some physical phenomenon should discretize the problem. Generally, a group of nodes that comprise the discretized space for any problem is called mesh. In this model, the mesh is the only free parameter, so it does not depend on the physical properties of the problem. Therefore, this parameter can be manipulated to give the problem a better stability of the solution. The Mesh convergence means changing the step size in order to see how the solution changes and how it looks. Figures 6, 7 and 8 show the mesh convergence for a step size of five, two and one units of length respectively.

Fig. 7 Model with step size of five length units, fineness of the grid is one node each five length units

Fig. 8. Model with step size of two length units, fineness of the grid is one node each two length units

Fig. 8.1. Model with step size of one length unit, fineness of the grid is one node each one length unit

The consequence of changing the size of the step in the mesh is that the smaller the step is, the better the solution fits with the real physical problem. In other words, the solution adjusts more closely to the analytical solution. Furthermore, the detail of the solution in the whole space is better with a small step size.

Results

Temperature distribution change with the presence of the salt dome. Generally, there is a zone above the dome that is hotter respect to the model with no diapir, and also beneath the diapir is cooler. The Parameters used in the simulation were the conductivity of each lithology, the heat generation rate, and the mesh. Six models were run varying between presence of salt diapir, position of the salt layer and salt diapir.

The model developed in this project was compared with one model of the Finite-Element Abaqus software in order to see if the model compares well to other software that were tested better. Results were also compared with experimental data and the analytical solution for the two dimension steady state heat conduction problem .

°C

Fig.9. Temperature distribution in the model developed

Fig.10. Temperature distribution modeled in Abaqus

The boundary conditions for the model are fixed on the four boundaries, so for the lateral

boundaries the model is not valid because the temperature at surface in lateral boundaries

is the same as at depth. Therefore, the model is valid displacing some nodes in the opposite

direction of the boundary because the temperature in the surface cannot be the same as

the temperature at depth. In the center of the model the temperature distribution is valid;

therefore that part of the model is the one that should be analyzed.

In the model, the position of the salt layer does not affect much the temperature

distribution of the sedimentary basin. The reason for that is that the model was developed

in the equilibrium condition (i.e. using the time-independent heat equation), so the

temperature will distribute equally if the time is big enough. To show this result an image is

shown (Figure. 11).

Fig. 11. Image above is with the salt layer, two layers above the bottom layer. Image bellow is with the salt layer above the layer of the bottom.

However, it is important to know that taking into account the time in the model the isotherms certainly will vary depending on the lithology. For example, because the salt layer has a high conductivity it will appear cooler than a layer of shale or sandstone, which has a low conductivity, which happens because less energy is lost in the form of heat in the salt layer than in the shale or sandstone. Otherwise, if there is a salt diapir, even in the equilibrium condition the temperature distribution is different, depending on the lithology.

The density of salt is considerably less compared to other geologic layers, so if salt layers are present and sediments are deposited above there is an interesting phenomenon. The contrast of density is noticeable between salt and sediments; hence, the salt will behave as a fluid when pressure is applied over the salt body. The result is the genesis of salt diapirs, and these diapirs have an important effect on temperature distribution. As said before, the conductivity of salt is higher and therefore the diapirs act as a heat conduit from the bottom to the top. Moreover, the effect of the diapir is also to cool the sediments bellow the salt. This model shows that the biggest temperature anomaly is about -20 to -25°C some distance below the diapir, and of 20 to 25°C at some distance above the diapir.

Different dimensions of the diapir were observed in order to evaluate the affected area for the temperature anomaly. As the height of the diapir increases the area for the positive thermal anomaly also increases; as well as, the negative thermal anomaly also increases in area.

Fig. 12. Effect of salt diapir of eight nodes of length and eighteen of height in temperature distribution

Fig. 13. Effect of salt diapir of two nodes of length and eighteen of height in temperature distribution

Fig. 14. Effect of salt diapir of eight nodes of length and twelve of height in temperature distribution

Fig. 15. Effect of salt diapir in a temperature distribution (Abaqus model)

Fig. 16. Heat flow distribution with salt diapir modeled in Abaqus

Comparing the model developed in python with the model in Abaqus, it is clear that the effect of the diapir is noticeable on temperature distribution as well as in the heat flow. The scale of the diapir (height and width) are very important in the area distribution of the temperature anomaly. In the model, it is not possible to know what distance in international units affects the anomaly; however, a proportion of nodes to kilometers can be done. Assuming a scale of 5 km in the horizontal and 10 km for the vertical axis of the

section of the sedimentary basin; the effect of a diapir with height 1.2 km and width of 600 m is a heating above the diapir of approximately 20°C over a distance of 750 m. In addition, there is a cooling of 15°C in a distance of 250 m below the diapir. Varying the size of the dome to 2.5 km of height and 125 m of width; the distance above that is heated is 250 m, and the distance below the diapir that is cooled is 700 m. The temperature anomaly is approximately 12°C and -20°C respectively. Finally, for a diapir with a height of 2.2 km and a width of 625 m the affected distances above and below of the dome are 500 m and 800 m respectively. The anomalies for this dome are a heating above the dome of 15 °C and a cooling below it of approximately 27°C. Meanwhile the heat flow (show in Abaqus) is greater in the salt than in the surrounding sediments: approximately 22.5 mW/m2 for salt compared to 7 mW/m2 for the other sediments.

Geothermal profiles were taken from the model with sedimentary layers including salt (model 1) and the diapir-model (model 2). The profiles are from these thermal distributions:

(a) (b)

Fig. 17. (a) Temperature distribution with a diapir in the middle (model 2) (b) Temperature distribution for sedimentary layers (model 1)

It is clear that the difference between the model 1 and the model 2 is that at the same depth (beneath the diapir) the temperature is lower in the model 2 than in the model 1; as well as, above the diapir, at the same depth, the temperature is higher in the model 2 than in the model 1

Fig. 18. Geothermal profiles for model 1 and model 2

Discussion

The simplified model developed in this work is not applicable for any real situation, but it allows understanding of the heat transfer phenomenon in a section of a sedimentary basin. Besides, the distribution of temperature across salt domes is also shown with acceptable accuracy in the model (comparing with Abaqus). Salt domes tend to cool the layers beneath of them producing a fridge effect, so the maturation of the rocks is delayed by a reduction of temperature. Hence, rocks will be more time in an oil preservation window, retarding its change to wet gas. There are some cases in the world that show evidence of this phenomenon. Santos Basin in Brazil is one of them. The estimated reserves for the Santos Basin after the discovery of pre-salt plays range from 50 to 80 billion barrels of oil (Chakhmakhchev, A., & Rushworth, P. (2010)). Therefore, scales of salt deposits in Santos basin are great enough to potentiate the reserves of oil in Brazil. In addition, in the Gulf of Mexico the ultra-deep exploration beneath salt deposits can be a potential of the pre-salt and sub- salt play deposits.

The Geothermal profile shows that depending on the presence of salt diapirs, the temperature of a rock volume is different. For the same depth, the temperature is less for a model 2 comparing to model 1. A maximum anomaly of 25 °C was estimated for the models; as a result, the maturation changes. Organic indicators such as vitrinite reflectance and biomarkers (progressive maturation of organic matter ranging from anthracite to bituminous coal), fission track analysis and mineralogical and geochemical indices can help to calculate the delay in the rate of maturation of the source rocks. Beside the diapirs acting like a fridge at the bottom, at sides and top the diapir acts like a heater, so organic matter tends to be more mature close to salt domes due to high values of heat flow. In conclusion, a delay or advancement in the maturation rate can cause a preservation window for petroleum in terms of temperature, preventing oil to over-maturate as gas.

Conclusions

Chemical reactions are fundamental in order to transform the organic matter in sediments into petroleum and gas; thus the law of Arrhenius is worth taking into account. The law says that for an increment of 10 °C in a temperature of the environment twice as many chemical reactions will be produced, so in the model the increment of approximately 20 °C below the diapir would cause an increase of four times more chemical reactions. Consequently an increase in chemical reactions implies a greater chance of maturation. Thermal anomalies exist in sedimentary basins, and can be interpreted as salt diapirs in some cases. Salt domes are evidence of tectonic influences in these places, so thermal anomalies could be explained by salt tectonics. Besides the temperature anomaly near salt diapirs, tectonics in salt deposits may produce good traps for hydrocarbons due to the low permeability of salt. Hence, it is important to investigate more salt deposits in petroleum assessment.

Finally, models give a good approximation to the thermal conduction phenomenon allowing a detailed analysis of thermal distribution and heat flow around salt diapirs. Still there is a lot of work to improve the models. A precise model could include fluid flow, heat transfer and phase changes, dependence function temperatures for the sides of the profiles, heat conduction in boundary layers and rate of erosion and sedimentation.

Appendix The code for the model was written in python. The code is relatively easy to understand, so here is a copy for the diapir-model.

Acknowledgments

The culmination of this document would not be possible without the help of Ph.D. Jillian Pearse, who helps me in the developing of the model. In addition, Ph.D. Jose Maria Jaramillo was an important tutor along the work helping me with analysis and the hydrocarbons application. Thanks also to Camilo Alfonso who helped me a lot with the code in python, correcting me and giving good ideas developing the model. Finally but not less in importance, I am very grateful to all my professors in the university because they teach me that science is always applicable to real life.

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