Bachelor Thesis Galijasevic

7/22/2019 Bachelor Thesis Galijasevic

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Characterisation and Imbibition Simulation

of a Moroccan Hydrocarbon Reservoir

Jan Galijasevic

School of Petroleum Engineering

Montan University Leoben

A thesis submitted for the degree of

Bachelor of Science

Leoben 2013



2

Executive Summary

The main objective of this thesis is to give an insight into the characterisation

and imbibition simulation of a potential sandstone and carbonate oil reservoir

in Morocco.

A cross sectional map, which resulted from a fieldtrip in the region of the High Atlas Mountain, was used as a reference for the 2D flow model. Various petro

physical and fluid parameters had to be identified to enable water sweep

simulations with a simulator created with the CSMP++ library.

The evaluation of the reservoir characterisation yields a net-to-gross ratio of

37% and a pore volume of 18,233 m!. The outcome of a Monte Carlo

simulation for standard oil initially in place achieved a result of 12,412 sm!

proven, 14,948 sm! probable and 18,217 sm! possible oil reserves.

Six different sweep scenarios with varying injection pressures and

displacement directions were conducted to evaluate the recovery potential.

Imbibition simulations with maximum injection pressure resulted in a recovery

factor of about 67% (10,982 m! cumulative produced oil) after 20 years of

production with a water sweep from the right to the left borderline of the model.

A recovery factor of 63% (10,307 m! cumulative produced oil) was achieved

with a sweep from the left to the right boundary.

In addition two simulations with different well placement were run to evaluate

possible production scenarios. Well scenario 1 achieved a recovery factor of

33% (5,457 m! cumulative produced oil) and well scenario 2 one of 35%

(5,810 m! cumulative produced oil) after 10 years of simulated production time.



3

Contents

1. Introduction ................................................................................................ 7

2. Geological Background ............................................................................. 8

3. Methodology ............................................................................................. 11

3.1 Flow model creation ...................................................................................... 11

3.2 Flow model characterisation ........................................................................ 14

3.2.1 Fluid properties ......................................................................................... 14

3.2.1.1 Oil properties .................................................................................................. 15

3.2.1.2 Water properties ............................................................................................. 16

3.2.2 Rock properties ......................................................................................... 18

3.2.2.1 Porosity .......................................................................................................... 18

3.2.2.2 Permeability .................................................................................................... 19

3.2.2.3 Fluid saturation properties .............................................................................. 19

3.2.2.4 Capillary entry pressure ................................................................................. 20 3.2.2.5 Brooks-Corey parameter ................................................................................ 21

3.2.3 Fault properties ......................................................................................... 22

3.2.4 Boundary conditions.................................................................................. 23

3.2.4.1 Type of boundary condition ............................................................................ 23

3.2.4.2 Boundary fluid pressure ................................................................................. 23

3.2.4.3 Boundary oil saturation ................................................................................... 24

3.3 Monte Carlo Simulation: Oil in place ........................................................... 25

3.4 Sweep scenarios ............................................................................................ 28 3.4.1 Sweep scenario 1...................................................................................... 31

3.4.2 Sweep scenario 2...................................................................................... 32

3.4.3 Sweep scenario 3...................................................................................... 33

3.4.4 Sweep scenario 4...................................................................................... 34

3.4.5 Sweep scenario 5...................................................................................... 35

3.4.6 Sweep scenario 6...................................................................................... 35

3.5 Well placement ............................................................................................... 36

3.5.1 Well scenario 1.......................................................................................... 37 3.5.2 Well scenario 2.......................................................................................... 37



4

4. Results ...................................................................................................... 39

4.1 Sweep scenarios simulation results ............................................................ 39

4.2 Well scenarios simulation results ................................................................ 42

5. Conclusion................................................................................................ 44

6. Acknowledgements ................................................................................. 45

7. References ................................................................................................ 46

8. Appendix ................................................................................................... 48

8.1 Calculation of the saturated oil viscosity .................................................... 48

8.2 Calculation of the bubble point pressure .................................................... 49

8.3 Calculation of the under-saturated oil viscosity ......................................... 50

8.4 Calculation of the oil formation volume factor ........................................... 51

8.5 Porosity-permeability cross-plots ................................................................ 52



5

List of Figures

1 - Google Earth satellite image of field 11 and an in-field image.................... 8 2 - Position of the taken geological profiles ..................................................... 9 3 - Rock distribution of the geological model. ................................................ 10 4 - In-field sketch of the observed area.......................................................... 11 5 - Rhinoceros flow model. ............................................................................ 13 6 - Google Earth satellite shot with a geothermal map overlaid..................... 14 7 - Example of a normal distribution. ............................................................. 25 8 - Probability density function and expectation curve ................................... 27 9 - Flow model with the initial conditions of fluid pressure ............................. 29 10 - Flow model with the initial conditions of oil saturation. ........................... 29 11 - Distribution of oil in place in the reservoir rocks ..................................... 30 12 - Scenario 1: Sweep simulation progress ................................................. 31 13 - Scenario 4: Sweep simulation progress ................................................. 34 14 - Well scenario 1: Simulation progress ..................................................... 37 15 - Well scenario 2: Simulation progress ..................................................... 38 16 - Recovery factor curves of different sweep scenarios ............................. 39 17 - Ultimate recovery curves of different sweep scenarios .......................... 40 18 - Zoomed in section of the stable displacement front ............................... 41 19 - Recovery factor curves of well scenario 1 and 2 .................................... 42 20 - Ultimate recovery curves of well scenario 1 and 2 ................................. 43 21 - Porosity-permeability cross-plot (fine grained sandstone) ...................... 52 22 - Porosity-permeability cross-plot (grainstone) ......................................... 52 23 - Porosity-permeability cross-plot (dolostone) ........................................... 53



6

List of Tables

1 - Summary of the oil properties calculations ............................................... 15 2 - Summary of the water properties calculations .......................................... 17 3 - Porosity ranges, arithmetic means and source of information .................. 18 4 - Permeability results and their source of information ................................. 19 5 - Summary of the estimated fluid saturation properties .............................. 20 6 - Partial and final results for the capillary entry pressure calculation .......... 21 7 - Assumed Brooks-Corey parameter .......................................................... 21 8 - Petro physical properties of the three different faults ............................... 22 9 - Simulation setup resulting from the model characterisation ..................... 28 10 - Boundary conditions for scenario 1 ........................................................ 31 11 - Boundary conditions for scenario 2 ........................................................ 32 12 - Boundary conditions for scenario 3 ........................................................ 33 13 - Boundary conditions for scenario 4 ........................................................ 34 14 - Boundary conditions for scenario 5 ........................................................ 35 15 - Boundary conditions for scenario 6 ........................................................ 35 16 - Setup for well scenario 1 and 2 .............................................................. 36 17 - Ultimate recoveries and recovery factors of each sweep scenario ......... 41 18 - Ultimate recoveries and recovery factors of the well scenarios. ............. 43 19 - Required data for the calculation of the oil viscosity ............................... 48



7

Chapter 1

Introduction

The purpose of this bachelor thesis is to describe the workflow of the

characterisation and preparation of a reservoir simulation model as well as

the evaluation of various imbibition simulation results concerning field

development strategies.

As part of the Petroleum Geological and Engineering Field Study of the

Montan University of Leoben, about 50 students travelled to the near Atlas

region, Ait Ourir, in Morocco to observe specific areas with significant

outcrops. Observations resulted in a 2D cross-sectional map, which was

converted into a simulation model by using computer-aided design (CAD) and

meshing software. Fluid and rock properties were determined and assigned to

the corresponding regions of the model. The determination of these

parameters was carried out taking in account, various publications concerning

oil and gas exploration and production. A Monte Carlo Simulation was used to

estimate the possible oil reserves within the observed area and delivered

insight into the recovery potential of the reservoir.

To define flow behaviour, several water sweeps with varying injection

pressures and also production scenarios with wells were run with a simulator

created with the Complex Systems Modelling Platform CSMP++ (Matthäi et

al., 2007) library and later on analysed in terms of saturation and fluid

pressure changes. The simulator’s assumptions include immiscible two phase

flow and incompressibility of reservoir rock and fluid. The model setup and

simulations result in a value for the pore volume and the estimation of various

recovery factors after several years of production and were taken as a basisfor further field development tasks.



8

Chapter 2

Geological Background

Field 11, as shown in Figure 1, is located about 50 km east of Marrakesh and

nearby the Foret Ait Ourir. The observed area is approximately 825 m in width

and 750 m in length which results in total size of 0.62 km ". An altitude above

mean sea level from 780 m to 900 m and a standard CLAR-Value of about

320/20 were also registered.

Figure 1 - Google Earth satellite image of field 11 and an in-field image of the observed area

The environment of deposition received fluvial and marine sediments.

Sandstones, which are located mainly in the lower area of the field, are known

to have been deposited in a clastic fluvial environment. They show significant

cross bedding, characteristics of high energy water flow. In the northern part

of the area the carbonates that derived from marine deposits appear as large

lithostratigraphic units.



9

This analysis leads to the two main reservoir types: sandstones of different

grain size and sphericity (fine, medium and coarse grained sandstone) and

carbonate rocks (mostly ooid grainstone and occasionally mudstone). The

latter also shows quite a high degree of secondary and fracture porosity.

Three normal faults offset the carbonate reservoir by several meters and were

considered to be permeable in contrast to the non-reservoir layers. These are

mainly represented by silty mudrock, which are considered no-flow

boundaries due to their very low permeability.

To sketch a 2D geological cross section identifying the various rock layers, a

total of three geological profiles were mapped (see Figure 2). This cross

section was used as a reference for the creation of the flow model.

Figure 2 - Position of the taken geological profiles (Google Earth Satellite Image)



10

A pie chart is shown in Figure 3 to illustrate the distribution of the different

rock types which were observed in the field. By using hand lenses it was

possible to distinguish between siliciclastic units of different grain size and so

to identify the various sandstone reservoir layers. Calcium carbonate rocks

(limestones) and magnesium carbonate rocks (dolostones) were determined

due to the effervescence of the specimen during the reaction with hydrochloric

acid. Therefore a calculation of the net-to-gross ratio was realized and

resulted in 37%.

Figure 3 - Rock distribution of the geological model.

60%8%

6%

3%

1%

2%20%

Silty Mudrock

Fine Grained Sandstone

Medium Grained Sandstone

Coarse Grained Sandstone

Conglomerate

Marlstone

Carbonate Rock



11

Chapter 3

Methodology

3.1 Flow model creation

A rough draft of the 2D cross-section was drawn on-site and is shown in

Figure 4.

Figure 4 – In-field sketch of the observed area

Using this draft, the geological profiles and observations in the field, a couple

of assumptions had to be made to allow the creation of the desired flow model.



12

One assumption is that those areas where no outcrop could be recognized

were assumed to be occupied by silty mudrock, since a lot of grain growth

could be detected there. Of high importance is that the extremely fractured

grainstone and the relatively insignificant dolomite layers were showing very

similar petrophysical properties. They were therefore merged to ensure a

lower computational cost for the simulation.

After measuring and adjusting the dip direction and angle of the faults, a lower

dimensional representation (i.e. line elements) was used with constant

properties throughout to characterise the faults. A transition zone from water

to oil bearing layers was neglected, due to a very good sorting, so that no

capillary fringe is present and the water-oil contact is assumed to be located

at the bottom of the reservoir model.

Besides the mentioned assumptions also the following data, which was given

by the Institute of Reservoir Engineering, had to be considered:

• Reservoir reference depth (top of the model) is at 2200 m

• Fluid pressure at reservoir reference depth is 218 bar

Due to the 2D simulation assumptions, a reservoir lateral thickness of 1 m

was assumed for the following various kinds of calculations and imbibition

simulations. Figure 5 shows the final version of the flow model, which was

modelled using Rhinoceros Software and afterwards meshed with ANSYS

Software by teaching assistants.



13

Figure 5 - Rhinoceros flow model with size of 880 m x 294 m and therefore resulting in a bottom

depth (OWC) of 2494 m.

0 15 m



14

3.2 Flow model characterisation

The purpose of this section is to estimate the properties of the reservoir fluids,rocks, faults and also the boundary conditions of the model required for the

simulation processes.

3.2.1 Fluid properties

An overlay of a geothermal gradient map over Field 11 resulted in a gradient

of 3.25°C/100 m, as shown in Figure 6. By assuming an average surface

temperature of 20°C a reservoir temperature of approximately 96°C was

determined. This temperature was used for all relevant correlations and

calculations to achieve representative (and constant) fluid property results.

Figure 6 - Google Earth satellite shot with a geothermal map (Rimi, 1990) overlaid.

An arithmetic average of 32°C/km was determined in this particular area.

Geothermal Gradient [°C/km]



15

3.2.1.1 Oil properties

Since no oil production with significant information about reservoir fluids could

be detected in Morocco, Algerian oil marketed as Saharan Blend, was used

as a reference, due to the similar geological conditions in this world area.

Saharan Blend is a very light crude oil with an API gravity of 45.3° (sample

taken by Maersk Oil, 1998) and a very low GOR. Conversion from API gravity

to absolute density resulted in a value of 800.3 kg/m3 and therefore in a value

of 0.8 concerning specific gravity.

Several calculations were needed to estimate the viscosity of the

undersaturated oil (see Appendix). By assuming a rather low gas-oil ratio of

70 scf/bbl and using, since it is best suited to the ruling pressure and

temperature conditions, the correlation from Beggs and Robinson (1975), the

viscosity of the saturated oil was estimated. Afterwards the correlation by

Vasquez and Beggs (1980) defined the undersaturated oil viscosity. To use

the correlation by Vasquez and Beggs, it was necessary to estimate the

bubble point pressure with the correlation published by Marhoun (1988),

which is based on Middle East reservoirs. All assumptions and results are

summarized with the following table.

Property ValueMethod of

calculation

Temperature 96°C calculated

API gravity 45° assumed

Oil specific gravity 0.8 calculated

Gas specific gravity 0.6 assumed

GOR 70 scf/bbl assumed

Bubble point pressure 807 psia correlated

Oil viscosity 2.01 cP correlated

Table 1 - Summary of the oil properties calculations needed for the simulations



16

3.2.1.2 Water properties

Since the oil-water contact is located at the bottom of the reservoir model and

a capillary fringe was neglected, it was assumed that also the free water level

(FWL) is based approximately at the same depth. It was thus possible to

determine the water density, due to the given reference depth, reference

pressure and the intersection point of the oil and water gradient at the OWC.

First it was necessary to calculate the pressure at the bottom of the model

(at 2494 m depth):

!!"# ! !!"# !" !"#$% ! !!"#$% !!"# !

!!"# !!"# ! !"

!! !"# ! !""!!" ! !!!"

!"! ! !"#!!" !"#

followed by the density of the water in the reservoir:

!!"#$% !!!"#

! !!"#$%&'

! !"#$!!"#

!!"#$% !!"#!!" ! !"

!! !!!"#$% ! !"

!

!!!" ! !"#" ! !"#

!"

!!

To estimate the water viscosity at average reservoir temperature, the paper

“Viscosity of liquid water in the range -8°C to 150°C” (J. Kestin et al, 1978)

and was used and resulted in value of 0.3 cP.



17

Property Value Method of

calculation

Temperature 96°C calculated

Pressure at top of model 218 bar given

Oil density 800.34 kg/m3 assumed

Water density 981 kg/m3 calculated

Water viscosity 0.3 cP correlated

Table 2 - Summary of the water properties calculations needed for the simulations



18

3.2.2 Rock properties

In order to determine the petro physical rock properties, information from

several subject related publications was taken, but also correlations and

specific calculations with reasonable assumptions were used.

3.2.2.1 Porosity

A detailed research resulted in a variety of porosity ranges for each type of

rock layer, as presented in Table 3. The arithmetic average of each range was

used for the parameter definition of the imbibition and likewise for the Monte

Carlo Simulations.

Rock Type ! ! Source of Information

from to Arithmetic Mean

Silty Mudrock 0.06 0.27 0.17

Permeability and petro physical

properties of 30 natural mudstones

(Yang & Aplin, 2007)

Fine Sandstone 0.02 0.40 0.21

Groundwater hydrology and

hydraulics (McWorter & Sunada,

1977)

Medium Sandstone 0.12 0.41 0.27



1977)

Coarse Sandstone 0.18 0.43 0.31



1977)

Fine Conglomerate 0.01 0.10 0.06Estimation, due to a high degree of

cementation

Marlstone 0.01 0.25 0.13Estimation, due to a high degree of

compaction

Limestone 0.05 0.25 0.15

Microfacies of carbonate rocks:

analysis, interpretation and

application (Fluegel, 2009)

Dolomite 0.05 0.30 0.18

Geometry and petrogenesis of

dolomite hydrocarbon reservoirs

(Braithwaite et al., 2006)

Table 3 - Porosity ranges, arithmetic means and source of information for each rock type



19

3.2.2.2 Permeability

Using field observations (e.g. permeability measurements) and correlations

with porosity data (see cross-plots in Appendix), values for permeabilities

were estimated, as summarized in Table 4.

Rock Type k [mD] Source of Information

Silty Mudrock 0.0005Permeability and petro physical properties of 30 natural mudstones

(Yang & Aplin, 2007)

Fine Sandstone 1,100

Origin of Sedimentary Rocks

(Blatt, Middleton and Murray, 1980)

Medium Sandstone 1,215 In-field permeability measurement

Coarse Sandstone 5,650 In-field permeability measurement

Fine Conglomerate 0.0003 Estimation, due to a high degree of cementation

Marlstone 0.0004 Estimation, due to a high degree of compaction

Limestone 200 Carbonate reservoir characterization (Lucia, 2007)

Dolomite 150 Carbonate reservoir characterization (Lucia, 2007)

Table 4 - Permeability results and their source of information for each rock type

3.2.2.3 Fluid saturation properties

Concerning the fluid saturation properties, it was necessary to estimate the

connate water saturation, the residual oil saturation and also the initial

saturation of both phases at the beginning of the imbibition. Due to theimpossibility to take laboratory measurements, each value had to be

correlated or assumed by using petro-physical literature, e.g. Carbonate

Reservoir Characterization (Lucia, 2007) for limestones or dolomites, the

Morris-Biggs Equation (1967) for sandstones, but also various measurements

or examples.

Since the reservoir is assumed to be undersaturated and fully oil saturated,

the actual or present water saturation equals the connate water saturation.



20

Rock Type Sor Swc So Sw

Silty Mudrock 0.18 0.20 0.80 0.20Fine Sandstone 0.17 0.07 0.93 0.07

Medium Sandstone 0.16 0.13 0.87 0.13

Coarse Sandstone 0.14 0.09 0.91 0.09

Fine Conglomerate 0.11 0.14 0.86 0.14

Marlstone 0.20 0.15 0.85 0.15

Limestone 0.17 0.07 0.93 0.07

Dolomite 0.16 0.16 0.84 0.16

Table 5 - Summary of the estimated fluid saturation properties

3.2.2.4 Capillary entry pressure

The capillary entry pressures were calculated by assuming a grain size

distribution after the Udden-Wentworth scale (Wentworth, 1922) for

siliciclastic and after Dunham (1962) and Lucia (2007) for carbonate rocks.

A typical interfacial tension of 25 dyn/cm was used and all present rock types

were considered to be water wet with an average contact angle of 30

degrees.

Another main assumption was that the grains were expected to be perfectly

shaped spheres and adjusted in a square meshed way, so that a easy

calculation of the biggest pore radii was possible. Afterwards the various

capillary entry pressures could be determined with the Young-Laplace

equation.



21

Rock Type Grain Size [mm] Grain Size [mm] Pore Radius [!m] pD [Pa]

Smallest Largest Largest Available

Silty Mudrock 0.004 0.0625 0.063 !" ""#$

FineSandstone

0.0625 0.25 0.156 "% !""&

MediumSandstone

0.25 0.5 0.375 '& $$&

CoarseSandstone

0.5 2 1.250 %$( !)'

FineConglomerate

2 4 2.500 $!& &#

Marlstone 0.004 0.0625 0.033 ' )%&&

Limestone 0.25 2 0.250 $% &")

Dolomite 0.004 0.2 0.102 %! %*$* Table 6 - Partial and final results for the capillary entry pressure calculation

3.2.2.5 Brooks-Corey parameter

The degree of grain sorting is determined by the Brooks-Corey parameter,

which is also a major influencing parameter on the relative permeability

curves. It typically ranges from 0.8 to 3.0 and was assumed by hand

specimen observations with hand lenses in the field.

Rock Type "

Silty Mudrock 2.5

Fine Sandstone 3.0

Medium Sandstone 2.5

Coarse Sandstone 2.0

Fine Conglomerate 0.8

Marlstone 2.5

Limestone 3.0

Dolomite 2.5

Table 7 - Assumed Brooks-Corey parameter depending on the grain sorting of the rock layers



22

3.2.3 Fault properties

It was also necessary to define likewise the petro-physical properties of each

fault, since the faults offset the reservoir layers by several meters and have

therefore also a major influence on flow behaviour of the model.

Since the frequency of thin and alternating layers of silty mudrock and

sandstone layers is rather high, a lower dimensional representation with

constant properties was used for reasons of simplicity. Otherwise a detailed

fault seal analysis would be required.

Therefore the following parameters were assumed for the modeled faults.

Parameter LeftFault

CentreFault

RightFault

Porosity # [-] 1.0 1.0 1.0

Permeability k [mD] 50 50 50

Residual oil saturation Sor [-] 0 0 0

Connate water saturation Swc [-] 0 0 0

Initial oil saturation So [-] 1.0 1.0 1.0

Initial water saturation Sw [-] 0 0 0

Capillary entry pressure pD [Pa] 0 0 0

Brooks-Corey parameter $ [-] 1.0 1.0 1.0

Width of fault (from field observations) [m] 0.5 0.5 0.8

Table 8 - Petro physical properties of the three different faults



23

3.2.4 Boundary conditions

To ensure a proper reservoir simulation the type of boundary condition, the

fluid pressure and the oil saturation had to be set at the borders of the model.

These components differ depending on the direction of motion of flow and

therefore on the chosen scenario.

3.2.4.1 Type of boundary condition

To run water sweep simulations from one border to another, Dirichlet

boundary conditions were applied at the left and right end of the reservoir

model. This kind of condition prescribes a constant value of a variable at the

boundary. In this case fixed pressure and oil saturation conditions were used

to represent either a water injection well with higher constant injection

pressure at the inlet boundary or a production well with lower constant bottom

hole pressure at the outlet boundary.

Since the layers below (mostly basalt as basement rock) and above (sealing

layers) the reservoir are considered to be impermeable, the top and bottom

borderlines were defined as no flow boundaries.

3.2.4.2 Boundary fluid pressure

It is essential to determine the maximum allowable injection pressure to avoid

the generation of stresses that will exceed the rock’s strength and therefore

fracture it. At first the minimum principal stress, in this case the horizontal

stress, had to be determined by correlation of the vertical stress, which arises

from the weight of the overburden rock material.



24

An average and also typical sedimentary rock density of 2.2 g/cm3 was

assumed and a ratio of average horizontal to vertical stress of 0.575 was

determined by using “Trends in relationships between measured in-situ

stresses and depth” (Brown & Hoek, 1978).

Also the depth of the bottom of the model was applied to calculate the

average horizontal stress and afterwards the maximum constant injection

pressure of 309 bar.

!! ! ! ! ! ! ! !!!"! ! !!"" ! !!!" ! !"#"

!"! ! !"# !"#

On the opposite boundary the bottom fluid pressure of 241 bar (fluid pressure

at a depth of 2494 m) was set to guarantee a sufficient pressure gradient to

allow fluid flow. The hydrostatic gradient at the boundaries from bottom to the

top of the flow model is automatically calculated and considered by the

simulation software.

3.2.4.3 Boundary oil saturation

A Dirichlet condition for saturation with zero oil saturation (100% water) was

necessary at the inflow boundary to simulate a well injecting pure water into

the reservoir or to represent an aquifer support at this region. At the outflow

no fixed boundary condition for saturation is required since both phases are

supposed to exit the model and are accordingly produced. Another, more

technical, reason is that numerical discretization is used, which involves a

degree of "upwinding", meaning that only saturation information immediately

upstream of an outflow cell is needed.



25

3.3 Monte Carlo Simulation: Oil in place

For the estimation of the oil initially in place, a Monte Carlo simulation was runto account for uncertainties in porosity and connate water saturation (equals

initial water saturation).

Due to the fact that not all layers are producible, only the relevant parameters

and uncertainties of the reservoir rocks and the storage volume of the faults

were taken into account. For porosity a log normal distribution, due to the

observed trend of higher values than the mean one and for connate water

saturation a normal distribution were assumed.

Proper values for the standard deviation had to be assumed, since it was not

possible to take any samples to measure the porosity or water saturation.

Given the ranges for latter from publications, the arithmetic mean was

calculated and the standard deviation was chosen in such a way that the

ranges of the values lie within 2 standard deviations (equals 96%) of the

mean, illustrated in Figure 7. The remaining 4% are intended for potential

outliers.

Figure 7 - Example of a normal distribution. The ranges for the values for porosity and connate

water saturation lie within the grey area of the distribution.



26

Using Rhinoceros Software the surface area of each rock type was

determined and equals the bulk volume, since a lateral thickness of the

reservoir of 1 m was used for all dimensionally dependent calculations.

In Table 9 the setup for the Monte Carlo Simulation is summarized.

Rock Type V ! ! ! Swc Swc Swc

m3 from to Mean Deviation from to Mean Deviation

Fine Sandstone 19768.16 0.02 0.40 0.21 0.080 0.03 0.11 0.07 0.020

Medium Sandstone 14119.54 0.12 0.41 0.27 0.060 0.10 0.16 0.13 0.015

Coarse Sandstone 6772.33 0.18 0.43 0.31 0.055 0.05 0.13 0.09 0.020

Limestone 45795.64 0.05 0.25 0.15 0.042 0.05 0.09 0.07 0.010

Dolomite 2094.05 0.05 0.30 0.18 0.070 0.14 0.18 0.16 0.011

Table 9 - Input parameters for the Monte Carlo Simulation for the estimation of the OIP

The following common equation for the OIP calculation was applied within the

simulation.

!"# ! !! !! !!! !!"!!

!

!!!

!

Since the oil in place determination with CSMP++ is carried out at reservoir

conditions and a comparison with the results of the Monte Carlo Simulation is

of interest, the formation volume factor was not considered in the equation

above. It was just used afterwards to determine the STOIP for an economic

point of view.



27

A total number of 5 runs and 5000 randomly picked values were used. A

probability density function as well as an expectation curve (see Figure 8)

were computed using @RiskSoftware and Microsoft Excel.

Figure 8 - Probability density function and expectation curve for the OIP estimation

In the petroleum industry it is quite common to use the expressions p90, p50

and p10, defined by the Society of Petroleum Engineers and the World

Petroleum Council in 1997, for proven, probable and possible oil reserves.

Since the expectation curve or cumulative distribution function shows a rather

steep slope, a low range of uncertainty between the p90 and p10 has been

noticed. For the calculation of the oil in place at standard conditions (STOIP) a

formation factor of 1.07 bbl/STB was applied by using the correlation by Glaso

(1980), since it shows the best accuracy compared with the other ones (see

Appendix).

Probability Term OIP STOIP

[m#] [sm#]

90% Proven Oil Reserves 13,281 12,412

50% Probable Oil Reserves 15,994 14,948

10% Possible Oil Reserves 19,492 18,217Table 10 - Summary of the results for OIP and STOIP of the Monte Carlo Simulation



28

3.4 Sweep scenarios

This section provides an overview of the setup of the six different sweepscenarios with varying injection pressures at the boundaries and direction of

motion of flow.

Three water sweep simulations were run from the right to the left border

(Scenario 1 – 3) and three from the left to the right border of the model

(Scenario 4 – 6) by using the Complex Systems Modelling Platform CSMP++.

Afterwards the transient changes of the oil saturation and fluid pressure were

visualized in ParaView Software to predict flow behaviour and reservoir

performance.

The output files were also used to estimate initial, in this case deterministic, oil

in place and pore volume, but also changes in oil saturation, recovery factor

and ultimate recovery over production time.

Table 9 shows again the simulation setup, after conversion of the values to

the required SI-Units for the CSMP++ software.

Type k ! pD $ Sor Swc So Sw

[m2] [-] [Pa] [-] [-] [-] [-] [-]

Silty Mudrock 4.77E-19 0.17 3345.23 2.5 0.18 0.20 0.80 0.20

Fine Sandstone 1.10E-12 0.21 1338.09 3.0 0.17 0.07 0.93 0.07Medium Sandstone 1.22E-12 0.27 557.54 2.5 0.16 0.13 0.87 0.13

Coarse Sandstone 5.65E-12 0.31 167.26 2.0 0.14 0.09 0.91 0.09

Fine Conglomerate 3.00E-19 0.06 83.63 0.8 0.11 0.14 0.86 0.14

Marlstone 4.00E-19 0.13 6288.03 2.5 0.20 0.15 0.85 0.15

Limestone 2.00E-13 0.15 836.31 3.0 0.17 0.07 0.93 0.07

Dolomite 1.50E-13 0.18 2049.77 2.5 0.16 0.16 0.84 0.16

Faults 5.00E-14 1.00 0.00 1.0 0.00 0.00 1.00 0.00Table 9 - Simulation setup resulting from the model characterisation



29

The initial conditions resulting from the simulation setup can be visualized in

terms of fluid pressure contour lines (see Figure 9) and oil saturation (see

Figure 10).

Figure 9 - Flow model with the initial conditions of fluid pressure displayed with contour lines for

a sweep from the right to the left boundary. Due to the high pressure drop in the impermeable

silty mudrock layers, a very small spacing between the contour lines can be observed in the

lower right part of the model, resulting in a slower penetration into the lower reservoir layers.

The figure also includes the permeability distribution indicated by the colouring of the rocktypes.

Figure 10 - Flow model with the initial conditions of oil saturation. The fine sandstone, carbonate

layers and the faults show the highest values.



30

The pore volume of the reservoir rocks resulted in a value of 18,233 m3 and

the estimation of the oil in place in approximately 16,320 m3 at reservoir

conditions (distribution shown in Figure 11). This value is similar to the p50

result of roughly 16,000 m3 of the Monte Carlo Simulation indicating reliable

results.

Figure 11 - Distribution of oil in place in the reservoir rocks

Fine Grained

Sandstone(3856.94 m3)

Medium

Grained

Sandstone

(3315.33 m3)Coarse Grained

Sandstone

(1909.99 m3)

Carbonates

(6680.44 m3)

All Faults

(560.374 m3)



31

3.4.1 Sweep scenario 1

For the first scenario, the maximum allowable overpressure was applied

through water injection at the right boundary to ensure a water sweep from

the right to the left border of the model. Table 10 shows the setup of the

boundary conditions for the first simulation.

Boundary Location Condition Type Value

Right Dirichlet oil saturation 0

Right Dirichlet fluid pressure 3.09E+07 Pa

Left Dirichlet fluid pressure 2.41E+07 Pa

Top No Flow - -

Bottom No Flow - -

Table 10 - Boundary conditions for scenario 1

Figure 12 shows snapshots of the flow simulation representing the change of

the oil saturation after various periods of time during the production.

Figure 12 - Scenario 1: Sweep simulation progress after 1 year, 22 months (at water

breakthrough) and also after 10 and 20 years of production time



32


For the second scenario, a lower pressure than the maximum allowable

injection pressure was set at the right boundary to estimate the variation in the

oil recovery. A value of 292 bar was chosen since it represents an

overpressure of 75% of the differential pressure:

!!"# ! !!"#$% ! !!"#

! !!"#$% ! !!!"

!!"# ! !"#! !"#! !"# ! !!!"

!!"# ! !"! !"#

Table 11 summarizes the specification of the boundary conditions for scenario

2.





Top No Flow - -

Bottom No Flow - -

Table 11 - Boundary conditions for Scenario 2



33


In this scenario an overpressure of 50% of the differential pressure was

applied at the right borderline of the flow model which results in a rather small

pressure gradient.

!!"# ! !!"#$% ! !!"#

! !!"#$% ! !!!"

!!"# ! !"#! !"#! !"# ! !!!"

!!"# ! !"# !"#

Table 12 shows the setup of the boundary conditions for the third scenario.





Top No Flow - -

Bottom No Flow - -

Table 12 - Boundary conditions for Scenario 3

Since the visualizations of the simulation processes differ only minimal from

scenario 1, a capture of the time steps of scenario 2 and 3 has been waived.



34


The water sweep from the left to the right boundary was configured similar to

the first scenario, but with a reversed pressure setup. The maximum allowable

injection pressure is now located at the left side of the model whereas the fluid

pressure is on the right side. Table 13 summarizes the boundary conditions

for scenario 4.


Left Dirichlet oil saturation 0



Top No Flow - -

Bottom No Flow - -

Table 13 – Boundary conditions for scenario 4

Figure 13 shows the progress of the sweep simulation of scenario 4 after

several time steps and is again very similar to the visualization of the following

scenarios.

Figure 13 - Scenario 4: Sweep simulation progress after 1 year, 2 years (at water breakthrough)

and also after 10 and 20 years of production time



35


Likewise to scenario 2, an injection pressure of 292 bar was used, but in this

case set at the left boundary of the model.

Table 14 shows the setup of the boundary conditions for the fifth scenario.





Top No Flow - -

Bottom No Flow - -



An overpressure of 50% of the differential pressure was applied at the left

borderline of the flow model.

Table 15 shows the setup of the boundary conditions for the sixth scenario.





Top No Flow - -

Bottom No Flow - -




36

3.5 Well placement

A further development plan would propose a producer well placement nearthe left border of the model, to reach the deeper sandstone layers, and an

injector installation on the right side of the model to make sure to sweep the

units in their whole length.

Therefore two additional simulations with different well placements were run

to estimate the recovery potential in which only the interconnected sandstone

and carbonate layers were perforated, since the it was not intended to

produce oil from non reservoir rocks due to their low permeability.

A constant bottom hole pressure of 150 bar was set for both producer of the

two well placement scenarios and to determine the water injection rates it was

important not to exceed the fracture strength of the rocks by checking the

present injection pressures in ParaView.

The setup for the well scenarios is summarized in Table 16.

Well

Scenario

Injector

perforation

length

Production

perforation

length

Producer

BHP

Injection

Rate

[m] [m] [bar] [m3 /m*s]

1 98 136 150 8.0E-6

2 78 148 150 8.0E-6

Table 16 – Setup for well scenario 1 and 2



37

3.5.1 Well scenario 1

In the first scenario a vertical production well was placed near the left border

and a vertical injector well right of the center of the reservoir model to sweep

the carbonate as well as the lower fine sandstone layers, as shown in Figure

14.

Figure 14 - Well scenario 1: Simulation progress after 57 days, 1 year (at water breakthrough)

and also after 2 and 10 years of production time. The upper carbonate and bottom sandstone

layer could not be swept entirely due to the no-flow boundaries at these locations.

3.5.2 Well scenario 2

In the second scenario a slanted production well with an inclination of 25° and

a total length of 322 m was installed left of the centre to reach the carbonate

and also the sandstone layers at the left side of the reservoir. A vertical

injection well was placed at the right border of the model to ensure a sufficient

distance. Figure 15 shows snapshots of the simulation of well scenario 2.



38

Figure 15 - Well scenario 2: Simulation progress after 50 days, 1 year (at water breakthrough)

and also after 2 and 10 years of production time. Since a direct injection into the fine sandstone

layers below the carbonate layers was not realizable with this well placement, a entire swept of

these layers like in scenario 1 could not be achieved.



39

Chapter 4

Results

4.1 Sweep scenario simulation results

By comparing the recovery factor curves of the different sweep scenarios for a

wide range of years, as shown in Figure 16, a sweep from the right to the left

border is more efficient than one in the opposite direction.

Figure 16 - Recovery factor curves of different sweep scenarios for 75 years of production time

0

10

20

30

40

50

60

70

80

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

R e c o v e r y F a c t o r [ % ]

Time [years]

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

Scenario 6

water breakthrough (sweep scenario 1)



40

Especially from an economic point of view, it is of high interest to know the

progress of cumulative oil production or ultimate recovery under reservoir

conditions during the time of production, displayed in Figure 17.

Figure 17 - Ultimate recovery curves of different sweep scenarios for 75 years of production time

A recovery factor of 67% (10,982 m! of cumulative produced oil) with sweep

scenario 1 and a recovery factor of 63% (circa 10,307 m! of ultimate oil

production) with sweep scenario 4 was estimated after 20 years of simulated

production. Multiple reasons, like the dip direction of the faults and/or the

location of the more permeable layers on the left side of the model, could be

deciding.

The ultimate recoveries and the recovery factors of all sweep scenarios and

several time steps is summarized in Table 17.

0

2000

4000

6000

8000

10000

12000

0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75

U l t i m a t e R e c o v e r y [ m # ]

Time [years]

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

Scenario 6

water breakthrough (sweep scenario 1)



41

Scenario Production Time

2 years 5 years 10 years 20 years 50 years

m3 % m3 % m3 % m3 % m3 %

1 7,240 44.35 9,328 57.14 10,307 63.14 10,982 67.28 11,449 70.14

2 6,273 38.43 8,923 54.67 10,093 61.83 10,838 66.40 11,383 69.73

3 4,739 29.03 8,156 49.97 9,684 59.33 10,609 65.00 11,285 69.14

4 6,691 40.99 8,415 51.56 9,541 58.45 10,307 63.15 11,117 68.11

5 5,891 36.09 8,041 49.26 9,204 56.39 10,102 61.89 10,930 66.96

6 4,375 26.81 7,471 45.77 8,638 52.92 9,714 59.51 10,630 65.13

Table 17 - Summary of the ultimate recoveries in m3

and recovery factors in % of each sweep

scenario.

A fast propagation and an early water breakthrough could be estimated

especially in the sandstone layers, since the flow occurs between two no-flow

boundaries. Due to a lower permeability and higher capillary entry pressure,

the carbonate reservoir units are swept with a lower velocity. And since

several layers are unconnected and also not connected to any of thepermeable faults, no oil could be produced from these during the process.

Their oil saturation did not change and stayed equal to the one at initial

conditions.

For all the production scenarios, the simulation process shows only a non-

significant gravity under-ride which results in a stable displacement front of

the water flood, as illustrated in Figure 18.

Figure 18 - Zoomed in section of the stable displacement front



42

4.2 Well scenarios simulation results

The comparison of the results of the well scenarios simulations showed ahigher recovery factor (and higher ultimate recovery) for the second well

scenario after 2 years of production time.

Figure 19 displays the recovery factor of the well scenarios for a range of 10

years.

Figure 19 - Recovery factor curves of well scenario 1 and 2 for 10 years of production time

Also the change of cumulative oil production has been evaluated for both well

placement scenarios and is shown in Figure 20.

0

5

10

15

20

25

30

35

40

0 1 2 3 4 5 6 7 8 9 10

R e c o v e r y F a c t o r [ % ]

Time [years]

Well Scenario 1

Well Scenario 2

water breakthrough



43

Figure 20 - Ultimate recovery curves of well scenario 1 and 2 for 10 years of production time

The ultimate recoveries and the recovery factors of all well scenarios and

several time steps is summarized in Table 18.

Scenario Production Time

2 moths 1 year 2 years 5 years 10 years

m3 % m3 % m3 % m3 % m3 %

1 963 5.89 2,798 17.13 3,629 22.22 4,741 29.03 5,457 33.41

2 955 5.85 2,686 16.45 3,635 22.26 4,832 29.59 5,810 35.58

Table 18 - Summary of the ultimate recoveries in m3 and recovery factors in % of the well

scenarios.

0

1000

2000

3000

4000

5000

6000

0 1 2 3 4 5 6 7 8 9 10

U l t i m a t e R e c o v e r y [ m # ]

Time [years]

Well Scenario 1

Well Scenario 2

water breakthrough



44

Chapter 5

Conclusion

The purpose of this thesis was to give an overview on the steps involved in

the characterisation and simulation of a potential oil reservoir in Morocco.

The model characterisation resulted in a pore volume of 18,233 m!, which is

occupied by an oil volume of approximately 16,000 m! (probable oil reserves).

Therefore the 2D model, especially because of its rather small size and a

thickness of 1 m, represents a reservoir of remarkable oil volume and good

quality, in particular due to the high permeable sand layers in greater depth.

But also the lower permeable, but thick carbonate layers in the upper part of

the reservoir show a notable percentage of pore volume (about 41%) and

represent a large contribution to the oil initially in place. Also the layer units

which do not percolate the entire model, but are connected to the faults, are

drained though at a lower rate. However, to guarantee a highly efficient and

fast sweep the major interconnected reservoir layers should be drilled and

perforated. By comparing different sweep scenarios with various injection

pressures, the best simulation results was achieved with a right-to-left sweep,

resulting in an ultimate recovery of about 11,000 m3 (recovery factor of 67%)

after 20 years. Therefore a well placement with a producer near the left and a

injector near the right border of the model was chosen. Especially due to the

no-flow boundaries at the top and the bottom of the model, a high recovery

factor above the industry standard of 30% could be achieved with both

scenarios. Since the recovery factor of well scenario 2 starts to increase at a

higher rate after 2 years of production than the one of well scenario 1 and the

injection rate is of both scenarios is equal, the second well scenario is beingrecommended for further development.



45

Chapter 6

Acknowledgements

I would like to show my greatest appreciation to the faculty and staff of the

Departments of Reservoir Engineering and Petroleum Geology that have

always been supportive during the whole fieldtrip and preparation of the

poster presentation and this thesis.

First, I would like to thank especially Dr. Matthäi, Chair of Reservoir

Engineering at the Montan University of Leoben, for the whole marvellous

organisation and help during the work in the field and also on the thesis.

I also want to express my gratitude to Professor Sachsenhofer, Assistant

Professor Reischenbacher and Caroline Milliote who provided us with

professional advice and geological experience during the trip.

Last, but by no means least, I thank Philipp Lang, Ph.D. student at Imperial

College London and Assistant Professor Julian Mindel, who guided us

students through the whole workflow of characterisation, modeling and

simulation, advised us on writing the thesis and were always open to

questions of any kind.



46

Chapter 7

References

Beggs, H. D., and Robinson, J. R. 1975. Estimating the Viscosity of

Crude Oil Systems, JPT, 9, pp. 1140–1141.

Blatt, H. , Middleton, G., and Murray, R. 1980. Orig in of

Sedimentary Rocks, 2nd ed., PrenticeHall, Englewood Clif fs, NJ.

Braithwaite, C. J. R., Rizzi, C., Darke, G. 2006. Geometry and

petrogenesis of dolomite hydrocarbon reservoirs, Geological Society of

London, pp. 352.

Brown, E.T. and Hoek, E. 1978. Trends in relationships between

measured rock in situ stresses and depth. Int. J. Rock Mech. Min. Sci.

& Geomech. Abstr . 15, pp. 214.

Dunham, R.J. 1962. Classification of Carbonate Rocks According to

Depositional Texture. In, W.E. Hamm (Ed.), Classification of Carbonate

Rocks, A Symposium. American Association of Petroleum Geologists,

pp. 108-121.

Flügel, E. 2004. Microfacies of Carbonate Rocks: Analysis,

Interpretation and Application, Springer Verlag, pp. 898.

Glaso, O. 1980. Generalized Pressure-Volume-TemperatureCorrelations, JPT, 5, pp. 785–795.



47

Kestin, J., Sokolow, M., and Wakeham, W.A. 1978. Viscosity of liquid

water in the range -8 – 150 °C, J. Phys. Chem. Ref. Data, 7, pp. 941-

948.

Lucia, F. J., 2007. Carbonate reservoir characterization, 2nd edition:

New York, Springer-Verlag, pp. 42-52.

Marhoun, M. A. 1988. PVT Correlation for Middle East Crude Oils, JPT,

5, pp. 650–665.

McWorter, D.B., and D.K. Sunada 1977. Groundwater Hydrology and

hydraulics, Water Resources Publications.

Morris, R. L., and W. P. Biggs, 1967. Using log-derived values of water

saturation and porosity , Transactions of the SPWLA 8th Annual

Logging Symposium, Paper X.

Rimi, A. 1990. Geothermal gradient and heat flow trends in Morocco,

Geothermics, 19, 5, pp. 443-454.

Vasquez, M., and Beggs, D. 1980. Correlations for Fluid Physical

Properties Pre-diction, JPT, 6, pp. 968–970.

Wentworth, C.K., 1922. A scale of grade and class terms for clastic

sediments, Journal of Geology , 30, pp. 377-392.

Yang, Y., and Aplin, A.C. 2007. Permeability and petro physical

properties of 30 natural mudstones, Journal of Geophysical Research,

112.



48

Chapter 8

Appendix

API gravity (°API) 45.30 °

Reservoir temperature (T) 664.97 °R

GOR (Rs) 70.00 scf/bbl

Oil specific gravity ( !o) 0.8

Gas specific gravity ( !g) 0.6

Table 19 - Required data for the calculation of the oil viscosity

8.1 Calculation of the saturated oil viscosity

Beggs-Robinson Correlation (1975):

!!" ! !"!! !

where:

! ! ! ! ! !"# !!!!"#

! ! !"!

! ! !!!"#$ ! !!!"!"#$ !"#



49

resulting in:

! ! !!!"#" ! ! !"#!!""# ! ! !!!!"#

and for the saturated oil viscosity:

!!" ! !!!"#! !"

8.2 Calculation of the bubble point pressure

Marhoun’s Correlation (1988):

!! ! !!!

!!!!!!

!!!

where:

! ! !!!"#"" ! !"!!

! ! !!!"#$%& ! ! !!!!""!# ! ! !!!"#$ ! ! !!!"#$%

Result for the bubble point pressure:

!! ! !"#!!"#$ !"#$



50

8.3 Calculation of the under-saturated oil viscosity

Vasquez-Beggs Correlation (1980):

!! ! !!"

!!"#$!%#

!!

!

where:

! ! !!! !!!!"# !"!

with:

! ! !!!! !"!!

! ! !

!!"#$!%# ! !!"#!!"#! !"#$

resulting in:

! ! !!!!"#$

! ! !!!"!#

Finally the under-saturated oil viscosity results in a value of:

!! ! !!!"#" !"



51

8.4 Calculation of the oil formation volume factor

Glaso’s Correlation (1980):

!! ! !!!! !"

!

where:

! ! !!!!"!## ! !!!"#$! !"#!!"! ! !!!"#$% !"#!!"! !

!!"!! !!

!!

!!

!!!"#

! !!

!"# !!!"#

resulting in:

!!"!! !"#!!"#!

! ! !!!!"#$

and for the oil formation volume factor:

!! ! !!!"



52

8.5 Porosity-permeability cross-plots

Figure 21 - Porosity-permeability cross-plot for the estimation of the permeability of a fine

grained sandstone with an average porosity of 21% (from Blatt, Middleton & Murray, 1980)

Figure 22 - Porosity-permeability cross-plot for the estimation of the permeability of Class 1

grainstone with an average porosity of 15% (from Lucia, 2007)



Figure 23 - Porosity-permeability cross-plot for the estimation of the permeability of Class 2

dolostone with medium crystal grain size and an average porosity of 18% (from Lucia, 2007)

Bachelor Thesis Galijasevic

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