D
RAINAGE IN
N
ATURALLY
F
RACTURED
R
ESERVOIRS
D
RAINAGE IN
N
ATURALLY
F
RACTURED
R
ESERVOIRS
Proefschrift
ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus prof. ir. K. C. A. M. Luyben, voorzitter van het College voor Promoties,
in het openbaar te verdedigen op maandag 15 december 2014 om 15:00 uur
door
A. AMERI
Master of Science in Chemical (Process) Engineering geboren te Shiraz, Iran.
Samenstelling promotiecommissie:
Rector Magnificus, Technische Universiteit Delft, voorzitter Prof. dr. H. Bruining, Technische Universiteit Delft, promotor Dr. R. Farajzadeh, Technische Universiteit Delft, copromotor Prof. dr. W. R. Rossen, Technische Universiteit Delft
Prof. dr. C. van Kruijsdijk, Technische Universiteit Delft Prof. dr. P. Zitha, Technische Universiteit Delft Dr. K-H. Wolf, Technische Universiteit Delft
Dr. S. Suicmez, Maersk Oil / Imperial College London Prof. dr. G. Bertotti, Technische Universiteit Delft, reservelid
This research was carried out within the context of the Recovery Factory programme, a joint project of Shell Global Solutions International and Delft University of Technology. The research was conducted in the Laboratory of Geoscience and Engineering at Delft University of Technology.
Published and distributed by: A. Ameri E-mail: aminameri@gmail.com
Cover design: Maryam Shojai Kaveh Printed by: Proefschriftmaken.nl
Copyright © 2014 by A. Ameri ISBN 978-94-6295-040-5
All rights reserved. No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system, without written permission of the author.
wife or mother, if it is both, he is twice blessed indeed.
Dedicated to
My true love-
Maryam
and
Increased world energy demand and increased difficulty in exploring new energy sources have formed the main driving force of many researches around enhanced oil recovery techniques in the past two decades. If energy demand will continue to increase, the logical question is: how will the energy industry respond to this demand? Will production from unconventional and complex geological formations become a must?
This thesis has its origin in the concept that gas injection into naturally fractured reservoirs can improve the oil recovery through the gravity drainage mechanism. Naturally fractured reservoirs are traditionally considered as poor candidates for enhanced oil recovery by gas injection. Throughout this thesis, the limitations and possibilities of improving oil recovery from naturally fractured reservoirs by miscible and immiscible gas injection are investigated.
The idea of conducting this research was triggered by my supervisors, Prof. J. Bruining and Dr. Farajzadeh. I am very grateful to them for having given me the opportunity to carry out this research and indeed for their excellent guidance from the beginning to the completion of this thesis.
Furthermore, I would like to thank Dr. S. Suicmez and Dr. M. Verlaan for all the technical discussions that we had during this research study.
I learned to work hard as soon as I came to know Dr. K-H Wolf, who forced me to collect the zero-permeability rock samples from the sidewalk in cold winter 2010. You kept me motivated by teaching me this priceless lesson! Thank you Dr. Wolf.
During my years at TU Delft, I had the great opportunity to work with the skillful and distinguished technical staff of the laboratory of the Department of Geoscience and Engineering. You are amazing. Thank you all for being always friendly and helpful.
The support staff of the department are highly appreciated for taking care of and facilitating the most difficult work, among others, in the department viz. the paper work. A special thank to all of you.
I wish to express my gratitude to my friends and colleagues who made my time in TU Delft a joyful period of my life. Thank you for sharing your wonderful moments with me! I sincerely thank my dear mum and dad, my brothers, Omid and Hamid, and my mother- and father-in-law, who nurtured my curiosity and provided all options to me. Mum and Dad: you have invested your life in your children. There are no words that can explain how much I appreciate all the things you have done for me. Thank you!
Last, but definitely not least, I wish to sincerely acknowledge the precious love and support that I receive every day and moment from my lovely wife Maryam. You have been always at my side. Without you I would have not been able to achieve as much as I have today. Thank you very much!
A. Ameri Delft, December 2014
List of Figures xi
List of Tables xv
1 Introduction 1
1.1 Enhanced oil recovery . . . 1
1.2 Naturally fractured reservoirs . . . 2
1.3 Classical Gravity Drainage in NFRs . . . 2
1.4 Extensions to Classical GOGD. . . 5
1.5 Outline of the thesis. . . 7
References . . . 9
2 Non-Equilibrium Gas Injection in NFRs 13 2.1 Introduction . . . 14 2.2 Experiments . . . 15 2.2.1 Materials . . . 16 2.2.2 Experimental set–up . . . 16 2.2.3 Experimental procedure . . . 17 2.3 Simulation model . . . 18
2.4 Results and discussions . . . 19
2.4.1 Experiment 1: Immiscible CO2, effect of miscibility . . . 19
2.4.2 Experiment 2: Miscible co2, improved gogd . . . 24
2.4.3 Experiment 3: Immiscible co2, effect of capillary barrier . . . 26
2.4.4 Experiment 4:Immiscible n2, effect of gas solubility . . . 30
2.4.5 Experiment 5: Immiscible flue gas, effect of gas composition . . . . 33
2.5 Conclusions. . . 35
References . . . 37
3 Interfacial Interactions among Oil-Brine-Rock-CO2 41 3.1 Introduction . . . 42
3.2 Materials and Method. . . 43
3.2.1 Materials . . . 43
3.2.2 Experimental setup . . . 44
3.2.3 Methodology. . . 44
3.3 Results and discussions . . . 46
3.3.1 Multiphase Contact Angle . . . 46
3.3.2 Effect of salinity and pressure . . . 47
3.4 Evaluation of the contact angles . . . 50
3.5 Conclusions. . . 56
References . . . 57 ix
4 Effect of Matrix Wettability on CO2Injection in NFRs 61
4.1 Introduction . . . 62
4.2 Experimental work . . . 63
4.3 Simulation model . . . 65
4.4 Results and discussions . . . 66
4.4.1 Two-phase system . . . 66
4.4.2 Three-phase system . . . 67
4.5 Conclusions. . . 72
References . . . 74
5 Matrix-Fracture Interactions During Solvent Injection 77 5.1 Introduction . . . 78
5.2 Experimental work . . . 79
5.2.1 Experimental procedure . . . 81
5.3 Numerical model and governing equations . . . 82
5.4 Results and discussion . . . 84
5.4.1 Effect of solvent injection rate . . . 84
5.4.2 Effect of fracture aperture . . . 90
5.4.3 Effect of oil viscosity . . . 93
5.4.4 Effect of water saturation . . . 95
5.4.5 Effect of matrix wettability . . . 100
5.5 Dimensional Analysis . . . 101
5.6 conclusion . . . 103
References . . . 104
6 Conclusions 109 6.1 Non-Equilibrium Gas Injection in NFRs. . . 109
6.2 Interfacial Interactions among Oil, Brine, Rock, and CO2 . . . 110
6.3 Effect of Matrix Wettability on CO2Injection in NFRs . . . 111
6.4 Interactions between Matrix and Fracture During Solvent Injection . . . . 112
Summary 115
Samenvatting 117
1.1 Single block with the fluid pressure gradients . . . 2 1.2 Capillary pressure and corresponding capillary height . . . 3 1.3 Typical oil and gas production rates during an immiscible gravity drainage
process. . . 3 1.4 Effect of capillary contacts on the oil production rate and ultimate oil
recovery by immiscible gas-oil gravity drainage. . . 4 1.5 Schematic representation of a three component phase diagram to mark the
directly miscible, the developed miscible, and the immiscible regions. . . 5 2.1 The two core samples used in the experiments . . . 16 2.2 Schematic of the experimental gravity drainage unit . . . 17 2.3 Capillary pressure curves optimized to simulate immiscible CO2, immiscible
N2, and immiscible flue gas experiments. . . 19
2.4 Geometry of the model . . . 19 2.5 Comparison between the recovery factor and drainage rate data obtained
from Experiment 1 (i.e., immiscible CO2followed by miscible CO2) and the
simulations. . . 20 2.6 Calculated oil and gas viscosities versus CO2composition in oil and gas
under miscible conditions (i.e., 85 bar and 30°C) . . . 21 2.7 The recovery factor as in Fig. 2.5 versus PV CO2injected for immiscible and
miscible CO2injection experiment (i.e., Experiment 1) . . . 22
2.8 Model results of the composition of produced fluid with time for Exp. 1 . . 23 2.9 Simulation results of the overall mol% of CO2in the matrix for immiscible
CO2injection . . . 23
2.10 Comparison between recovery factor and drainage rate data obtained from Experiment 2 (i.e., miscible CO2) and the numerical simulations . . . 24
2.11 Development of an unstable gas-oil front in the simulations of fully miscible CO2experiment. . . 25
2.12 Calculated oil and gas densities versus CO2composition in oil and gas under
miscible conditions (i.e., 85 bar and 30°C). . . 26 2.13 Simulation results of CO2mol fraction for miscible CO2experiment (i.e.,
Experiment 2) at four consecutive times . . . 27 2.14 Coarse grid representation of the volume flux of each phase in the matrix
and fracture system . . . 27 2.15 Comparison between recovery factor and drainage rate data obtained from
Experiment 3 (i.e., stacked core) and the simulations. . . 28 xi
2.16 Simulated oil saturation during the stage of immiscible CO2injection and
in the stage of miscible CO2injection for the stacked core experiment (i.e.,
Experiment 3) . . . 28 2.17 The arrow plot of volume flux of oil phase for the stacked core simulation
under immiscible conditions . . . 29 2.18 Comparison between recovery factor and drainage rate data obtained from
Experiment 4 and the simulations . . . 31 2.19 Model results for composition of produced fluid with time for Exp. 4 . . . 31 2.20 Molar composition of nitrogen and carbon dioxide in the matrix at the end
of immiscible gas injection . . . 32 2.21 The recovery factor as in Fig. 2.18 but now versus PV gas injected . . . 32 2.22 Comparison between recovery factor and drainage rate obtained from
Experiment 5 and the simulations . . . 33 2.23 Model results of composition of produced fluid with time for Experiment 5
(i.e., immiscible flue gas) . . . 34 2.24 Normalized oil density, viscosity, and IFT as a function of CO2concentration
in the injected gas under immiscible conditions viz., 50 bar and 30°C . . . 35 2.25 The ratio between density difference and oil viscosity (proportional to the
gravity driving force) versus the CO2concentration in the injected gas. . . 35
3.1 Schematic representation of the pendant drop cell setup . . . 45 3.2 Digital photograph of the inside of the modified pendant drop cell . . . 45 3.3 Schematic of a captive bubble contact angle system. . . 47 3.4 Stable contact angles for partially water-wet substrates as a function of
pressure and brine salinity . . . 48 3.5 Stable contact angles for the effectively oil-wet and partially water-wet
substrates . . . 49 3.6 Bentheimer sandstone samples used in contact angle determinations . . . 49 3.7 Digital images of CO2bubble on the oil saturated-Bentheimer surface . . 50
3.8 Contact angle as function of pressure for the system oil-wet, CO2, distilled
water (SB-5, saturated with crude B) . . . 52 3.9 Calculatedγsvvalues versus pressure . . . 52
3.10 Contact angle as function of pressure for the system oil-wet substrate, CO2,
and brine with 35000 salinity . . . 54 3.11 Calculated IFT-values versus pressure . . . 55 4.1 Contact-angle determinations for untreated and treated Bentheimer . . . 64 4.2 Schematic of the experimental gravity drainage unit. . . 65 4.3 Geometry of the model. . . 65 4.4 Experimental and simulated recovery factors obtained from Experiments 1
and 2 in the absence of any water . . . 67 4.5 Simulation results and experimental data for recovery history and drainage
rate for Experiment 3 . . . 68 4.6 Simulation results and experimental data for recovery history and drainage
rate for Experiment 4, where an oil-wet core was used. CO2was injected as
4.7 Simulation results and experimental data for recovery history and drainage rate for Experiment 5, where a water-wet core was used as matrix block and
N2 was injected as the injection gas. . . 70
4.8 Simulation results and experimental data for recovery history and drainage rate for Experiment 6, where an oil-wet core was used as matrix block and N2was injected as the injection gas. . . 71
4.9 Simulation results and experimental data for recovery history and drainage rate for Experiment 7, where a water-wet limestone core was used as matrix block and CO2was injected as the injection gas. . . 72
4.10 Simulation results and experimental data for recovery history and drainage rate for Experiment 8, where an oil-wet limestone core was used as matrix block and CO2was injected as the injection gas. . . 72
5.1 Schematic of the experimental set-up . . . 79
5.2 Contact-angle determinations for untreated and treated Bentheimer . . . 82
5.3 Geometry of the model . . . 82
5.4 Comparison between measured and calculated viscosities and densities at different solvent concentrations for hexadecane-hexane system . . . 83
5.5 Grid number sensitivity analysis for the simulations . . . 84
5.6 Recovery factor from matrix versus time at different injection rates obtained from Experiments 1-4. . . 86
5.7 Simulation results of the oil drainage rate for Experiments 1 and 2. The analytical drainage rate calculated from Eq.( 5.9) is also shown. . . 87
5.8 Process visualization of Experiment 1 and the simulation results of the oil saturation in the matrix and fracture at corresponding times . . . 87
5.9 Process visualization (saturation distribution) of Experiment 2 and the simulation results for the oil saturation in the matrix and fracture . . . 88
5.10 Process visualization of Experiment 3 . . . 88
5.11 Process visualization of Experiment 4 (hexadecane-hexane system under no injection flow (static) conditions) . . . 89
5.12 Simulation results of Exp. 4 for the velocity map within each grid cell . . . 89
5.13 Initial maximal dimensionless oil rate (drainage enhancement factor) versus dimensionless timeτ (residence time divided by diffusion time) . . . . 90
5.14 Experimental recovery from the matrix versus pore volume solvent injected at different flow rates . . . 91
5.15 Recovery data obtained from simulation and Experiments 1 and 5 . . . 92
5.16 CT images of Exp. 5 (small fracture aperture) at for consecutive times . . . 92
5.17 Effect of fracture aperture . . . 93
5.18 Recovery from matrix versus time for different oil viscosities . . . 94
5.19 Process visualization of Experiment 7 (ondina933-PE system) . . . 95
5.20 Simulation results of Exp. 7 for the oil saturation inside the matrix . . . 95
5.21 Process visualization of Experiment 8 (silicone oil-hexane system) . . . 96
5.22 Process visualization of Experiment 9 (hexadecane/hexane/water system) during water injection. . . 97
5.24 Capillary pressure data used in the simulations for Exp. 9 . . . 98 5.25 water-oil relative permeability curves used in simulations of Experiment 9 99 5.26 Micro-CT images of oil trapping (water shielding) for a water-wet rock after
water imbibition . . . 100 5.27 Recovery history of Exp. 10 and average oil saturation along the core . . . 100 5.28 Process visualization of Experiment 10 during solvent injection . . . 101 5.29 Comparison between recovery histories obtained from Exp. 2 and Exp. 10. 102 5.30 Oil recovery at 1 PV solvent injection versus the NM −F D . . . 102
2.1 Summary of the gas injection experiments . . . 15
2.2 Properties and dimensions of the two core samples . . . 16
2.3 Fitting parameters used in the simulations for each experiment . . . 18
3.1 Physical Properties of the Oil Samples Used in the Experiments . . . 44
3.2 Summary of the Experiments . . . 46
3.3 Results of the contact Angle Prediction Using the Equation of State Approach for the Oil-Wet Substrate SB-5 (Saturated with Crude B), CO2, and Distilled Water System . . . 51
3.4 Results of the contact Angle Prediction Using the Equation of State Approach for the Oil-Wet Substrate SB-6 (Saturated with Crude B), CO2, and Brine System . . . 53
3.5 Summary of the Calculatedγslandβ Parameters for Oil-Wet and Water-Wet Systems . . . 56
4.1 Experimental conditions considered in this chapter . . . 64
4.2 Corey exponents used in the simulations of each experiment . . . 66
5.1 Properties of the fluids used in the experiments. . . 80
5.2 Experimental conditions considered in this study. . . 80 5.3 Parameters used in Eq.( 5.11) and Eq.( 5.12) for simulation of Experiment 9. 98
1
I
NTRODUCTION
Nature and nature’s laws lay hid in the night; God said ‘Let Newton be!’ and all was light. -Alexander Pope
1.1. ENHANCED OIL RECOVERY
With increasing world population, which is coupled with higher standards of living, the demand for energy is predicted to increase during next few years [1–3]. Moreover, it is anticipated that fossil fuels (oil and gas) will remain as the main source to energy supply even if the contribution of other energy sources (such as renewables) is increasing [4, 5]. Therefore, new oil and gas resources need to be explored and discovered to meet the increased global energy demand. Moreover, enhanced oil recovery methods should be implemented to boost oil production from the conventional reservoirs.
Because most of the easy-to-produce oil reservoirs are already depleted, the other nontrivial options, such as naturally fractured reservoirs, have recently received much attention in the context of improved oil recovery [6]. Naturally fractured reservoirs form about 20%-30% of the world’s oil reserve and production [7]. However, this class of reservoirs poses technical challenges in oil industry in terms of efficient oil production by enhanced oil recovery methods. For example, gas-based enhanced oil recovery processes have been already practiced for a long time to enhance the oil recovery from conventional reservoirs and are considered as mature technologies. Whereas, naturally fractured reservoirs are considered as poor candidates for gas-injection enhanced oil recovery processes [8]. Consequently, it is of practical importance to investigate how efficient oil can be produced from naturally fractured reservoirs by the help of enhanced oil recovery methods.
1
1.2. N
ATURALLY FRACTURED RESERVOIRS
All petroleum reservoirs incorporate some natural or artificially induced fractures. If the effect of existence of these fractures on fluid flow within the formation is negligible, the reservoir is considered as “conventional” reservoir. In contrast, naturally fractured reservoirs are characterized by the presence of highly conductive and interconnected fracture networks, which significantly influence (positively or negatively) fluid flow in the formation [9, 10]. Accordingly, production mechanisms in naturally fractured reservoirs differ considerably from the non-fractured or conventional reservoirs. In fractured reservoirs the presence of a high permeability fractured network will lead to a relatively low pressure drop [11, 12]. Therefore, the oil production from the matrix is controlled by gravity, capillary forces and diffusion processes, which may be enhanced by natural convection effects [13, 14].
In naturally fractured reservoirs, the rock matrix with low permeability contains most of the oil. However, the oil production occurs mainly through the high permeability fracture system. Thus, matrix-fracture interactions play a key role in fluid flow in naturally fractured reservoirs [15, 16]. The interactions between matrix and fracture are governed by different physical mechanisms viz., oil expansion due to pressure decline in the reservoir, diffusion, water (spontaneous) imbibition, and gravity drainage by gas injection, which is the main topic of this research.
1.3. C
L ASSICAL
GRAVITY
DRAINAGE IN
NFRS
Gas-oil gravity drainage (GOGD) has been proven to be an efficient method to recover substantial volume of oil from NFRs. In some cases,for example for water drive reservoirs with oil-wet matrix, it is the only drive mechanism that allows recovery and production of oil from the matrix blocks. In a gravity drainage process,the gas phase enters the matrix from the top and displaces the oil phase at the bottom of the block [17]. In an immiscible gravity drainage process, the oil production is determined by the competition between gravity and capillary forces. This situation is schematically shown in Fig. 1.1, where a single matrix block is surrounded by a fracture. The gas pressure gradient is close to zero as the gas density and viscosity are very small. As a result the gas-phase pressure remains almost constant with depth. However, the oil-phase pressure shows a finite slope. The deviation from capillary gravity equilibrium is the driving force for oil drainage. It is possible to convert the capillary pressure data to a curve, which shows the capillary height (capillarity/gravity = Pc/∆ρg H) versus the oil saturation, as shown in Fig. 1.2.
1
Figure 1.2: Capillary pressure and corresponding capillary height [19].
The oil production occurs when∂zpc+ ∆ρg > 0 as shown in Fig. 1.1 and Fig. 1.2. The
oil production stops, when the gravity forces are in equilibrium with the capillary forces. The drainage rate from a 1-D matrix block is given by [7]:
q =kkr o µo · ∆ρg −d pc d So d So d z ¸ (1.1) where∆ρ is the density difference between the oil and gas phases, Pc is the gas oil
capillary pressure, Sois the oil saturation, z is the positive upward direction,µois the oil
viscosity, and k and kr oare the absolute and relative permeabilities, respectively. For a
fully-saturated matrix block and at z=0 (i.e., bottom face of the matrix)d So
d z = 0. Therefore,
the initial maximum drainage rate when the matrix is fully saturated with the oil and when there is zero pressure gradient, is given by
qo,max=
kkr o
µo ∆ρg
(1.2) Eq. (1.2) can be used to determine the maximum drainage rate of an immiscible gravity drainage process, where the oil and gas phase properties remain nearly unchanged during the process. An immiscible gas-oil gravity drainage is characterized by an initial period of a constant maximum production rate (qo,max), with a tail production after gas
breakthrough. An example is shown in Fig. 1.3.
1
with capillary discontinuities is block-block interactions [20, 21]. In this situation, oilA major issue in immiscible gas-oil gravity drainage in layered or stacked matrix blocksdraining from one matrix block into the fracture system will be re-imbibed (by gravity and capillary forces) into the underlying matrix block (see Fig. 1.4), assuming that the gas phase is the most non-wetting phase and the oil is the most wetting phase. The reimbibition phenomenon is considered as a crucial factor in describing the behavior of fractured reservoirs. It affects both the production rates by gravity drainage and the distribution of the oil and gas phases in the reservoir. Without this effect being accounted for, all blocks in the stack would produce independently at a rate given by Eq. (1.2). Also, all blocks would desaturate simultaneously, and produce an “even” gas saturation distribution with depth. In reality, oil produced from the top block into the fracture system is re-imbibed in the second block etc, and effectively will have to travel through the entire stack before being produced from the fracture system. Hence, the total stack produces at a total rate given by Eq. (1.1). Fig. 1.4b shows the simulation results for a stack of matrix blocks for two different cases, viz., with block-block interactions and without block-block interactions. Fig. 1.4b shows that the existence of capillary barriers reduces the production rate considerably. Moreover, the ultimate oil recovery is much less than the case with capillary continuity. The results from Fig. 1.4b clearly show that block-block interactions and oil reimbibition have to be considered in reservoir simulations when dealing with the layered and heterogeneous matrix blocks.
(a) (b)
Figure 1.4:Effect of capillary contacts on the oil production rate and ultimate oil recovery by immiscible gas-oil gravity drainage.
One possible method to increase the ultimate oil recovery by gravity drainage is to inject the gas under completely miscible conditions [22, 23]. The miscibility status between oil and the injected gas can be illustrated with a three component mixture of solvent (e.g., CO2), a heavy component (C10), and a light component C4), which
is illustrated in Fig. 1.5. The line from the injection fluid tangent to the two-phase envelop marks a region right of this line of oil compositions that are directly miscible with the injected fluid (green in Fig. 1.5). The two-phase region contains tie-lines, experimental lines that connect compositions in the gas-phase and the liquid phase
1
that are in equilibrium. The critical tie line passes through the critical point at the given pressure and temperature. The domain between the critical tie line and the line tangent to the two-phase region marks compositions where developed miscible processes can occur (yellow in Fig. 1.5). The injected gas is enriched with the original oil to form a gas phase with compositions along the phase envelop until the critical point is reached. The gas with the critical point composition is directly miscible with the oil. Finally the composition can be left of the critical tie-line. In this case the displacement is purely immiscible (red in Fig. 1.5). In all cases the oil is swept from the fractures and replaced with the solvent.
Figure 1.5: Schematic representation of a three component phase diagram to mark the directly miscible
region(green), the developed miscible region (yellow) and the immiscible region (red). In this case the injected gas composition consists of pure CO2, but it can be any gas composition left of the critical tie-line. CO2is usually considered as one of the promising gases for miscible gas injection
processes because it can develop miscibility with oil at lower pressures as it is highly soluble in the oil phase. For a fully miscible fluid system, the capillary effects are by definition absent and thus the oil production is not limited by the capillary forces. However, the possibility of improving oil recovery using carbon dioxide and hydrocarbon gases from fractured reservoirs in which gravity drainage is the dominant production mechanism is controversial. For example, the density difference between CO2in the
fracture and oil in the matrix decreases at higher pressures, which leads to a less efficient gravity drainage potential. In addition, a large volume of pressurized CO2is required to be
injected into fracture system. Moreover, there are considerable matrix-fracture cross-flows due to the diffusion and mixing between the miscible gas/solvent in the fracture and oil in the matrix. These aspects need to be addressed carefully for a successful miscible gas-oil gravity drainage.
1.4. EXTENSIONS TO
CL ASSICAL
GOGD
Understanding the production mechanisms that contribute to hydrocarbon production from naturally fractured reservoirs through the gas-oil gravity drainage process is of great importance. It is generally assumed that oil production from NFRs under immiscible gas injection conditions is mainly governed by equilibrium between gravity and capillary forces [17, 24, 25]. Therefore, there are two major parameters, which affect the effectiveness
1
of the process, viz. the density difference between gas and oil, and the relative differencebetween the position of the gas-oil contact in the matrix and in the fracture. This isperhaps the simplest picture of the actual process and more aspects have to be considered in order to be able to produce oil from naturally fractured reservoirs, efficiently. The research performed by Hagoort [17] was a pioneer work to study oil production by gravity drainage. Hagoort [17] developed an analytical model to estimate the oil recovery by gravity drainage in a homogeneous 1-D model assuming that the gas and oil phase properties remain unchanged during the process. This assumption cannot be justified if the gas phase can exchange mass with the oil phase. For example, CO2can experience
significant mass-exchange with the oil phase even at immiscible conditions. The mass transfer changes the oil properties such viscosity and density. Accordingly, some lighter components might be extracted by CO2and transferred into the gas phase, which indeed
would change the gas phase properties too. This mass exchange effect would directly influence the production characteristics of the reservoir when a non-equilibrium gas is injected into the formation. Consequently, a simple model based on capillary-gravity equilibrium, which does not include mass transfer aspects, is insufficient for practical purposes. Moreover, at fully miscible conditions, the system is usually simply characterized by single phase flow equations. However, for an accurate description, the interactions between miscible fluids (e.g., diffusion or convective mixing) need to be taken into account.
In addition to fluid-fluid, fluid-rock interactions (i.e., wettability) can influence the efficiency of the gravity drainage process. It is generally assumed that the gas phase is the most non-wetting phase. This is perhaps due to the fact that in most of the experimental studies concerning the effect of rock wettability on the gas oil gravity draiange performance, air/nitrogen has been used as displacing gas [26–29]. However, recent studies have shown that CO2can be the wetting phase under specific conditions
[30–32]. Similar to other recovery mechanisms from NFRs, the performance of the gravity drainage process is mainly limited by component exchange between matrix and the fracture system, which is mostly influenced by the wettability conditions of the matrix block. Therefore, the gas oil gravity draiange process will benefit from the wettability conditions if the gas phase can be the wetting or intermediate-wetting phase. This issue and its effect on the effectiveness of a gravity drainage process has not been addressed adequately yet. Therefore, it is crucial to examine the effect of matrix wettability on the performance of a gravity drainage process at different miscibility conditions.
If possible, visualization of the laboratory experiments is always a major step forward to validate the theories behind the processes. In case of gravity drainage processes, visualization of the matrix-fracture interactions at different process conditions is expected to be one of the most important aspects that need be further investigated. Indeed, the visualized results will help to a large extent to improve understanding the physical mechanisms behind the process.
Mathematical modeling and numerical simulations are valuable tools to gain insight into the complicated flow in NFRs. Indeed, it is not feasible to investigate all the aspects experimentally. Therefore, it is necessary to develop numerical models that can elucidate the underlying physics at the required accuracy of the process under investigation. This is crucial for successful oil production.
1
This research aims to study experimentally and theoretically the above-mentioned challenges related to the application of miscible and immiscible gravity drainage in NFRs. To this end, experiments and numerical simulations are performed at relevant conditions to identify the potentials and limitations of application of miscible and immiscible gas-oil gravity drainage in NFRs. One final motivation of this research derives from the fact that a large volume of the proven oil reserves reside in NFRs. This makes it challenging to design and implement efficient oil recovery processes from NFRs to meet the increasing need for energy resources.
1.5. OUTLINE OF THE THESIS
Successful oil production from NFRs poses a great challenge to reservoir engineering practice. This is mainly due to the fact that NFRs exhibit a large degree of heterogeneity in terms of reservoir properties and thus the relation between the production behavior and the controlling parameters become complicated. Understanding the mechanisms responsible for enhanced oil production by gas injection at different miscibility conditions is of practical interest to oil and gas industry. Throughout this thesis, the possibilities and limitations of improved oil recovery from NFRs is investigated. Particularly, the mass exchange between matrix and fracture under different miscibility is the central topic of this thesis.
Chapter 2 is concerned with an experimental and simulation study to investigate the performance of gas-oil gravity drainage process in NFRs. Gas-oil gravity drainage experiments were conducted at different miscibility (i.e., immiscible and fully miscible) conditions using CO2, N2and a synthetic flue gas composed of 20 v/v% CO2and 80
v/v% N2. The impact of switching from an immiscible (i.e., nitrogen or flue gas) gas to a
non-equilibrium and fully miscible CO2injection is investigated. The effect of miscibility
on the block-block interaction is also examined using a stacked core with an impermeable barrier. It is shown that gas solubility has a considerable effect on the gravity drainage performance. Moreover, it is shown that injection of non-equilibrium CO2into the
fracture leads to an enhanced gravity draiange production rate, which is higher than the analytically calculated draiange rate.
Chapter 3 is devoted to the investigation of the interaction between rock, oil, brine, and CO2, which is characterized through contact angle determinations. The results from
Chapter 3 provide valuable information for the wettability behavior in systems with carbon dioxide, brine, and oil-saturated rock at different pressure, temperature, and salinity conditions. The results are described using a surface free energy analysis and the relative importance of each of the interfacial tensions at different rock wettability conditions is discussed. The results from Chapter 3 are used to design the gas injection experiments in Chapter 4, where the effect of matrix wettability on the performance of a gravity drainage process is examined. It is shown that for an oil-wet matrix block, CO2is
the intermediate-wetting phase, which leads to an improved gravity draiange potential by CO2injection.
Chapter 5 is directed towards visualizing the matrix-fracture interaction when a fully miscible solvent is used in a fractured medium to recover oil from the matrix. The success of this method depends to a large extent on the degree of enhancement of the mass-exchange rate between the solvent flowing through the fracture and the oil residing
1
in the matrix. The mass-exchange between the matrix and the fracture is visualized usinga medical CT scanner. The results from the CT scanning can be used to validate theoriesof enhanced transfer in fractured media. The effects of injection rate, fracture aperture, water saturation, matrix wettability, and fluid properties on the recovery behavior have been examined.
Chapter 6 summarizes the main conclusions of the research and as well as the outlook for the future work.
Note from the author: This text is based on the some of the published papers in reviewed journals and scientific conferences. Consequently, the reader may find similar texts and sentences in some parts of the thesis.
1
REFERENCES
[1] C. Wolfram, O. Shelef, and P. J. Gertler, How will energy demand develop in the developing world?, Tech. Rep. (National Bureau of Economic Research, 2012). [2] B. Lin and X. Ouyang, Energy demand in china: Comparison of characteristics between
the US and China in rapid urbanization stage, Energy Conversion and Management
79, 128 (2014).
[3] F. Mulder, Implications of diurnal and seasonal variations in renewable energy generation for large scale energy storage, Journal of Renewable and Sustainable Energy 6, 033105 (2014).
[4] G. S. Alemán-Nava, V. H. Casiano-Flores, D. L. Cárdenas-Chávez, R. Díaz-Chavez, N. Scarlat, J. Mahlknecht, J.-F. Dallemand, and R. Parra, Renewable energy research progress in mexico: A review, Renewable and Sustainable Energy Reviews 32, 140 (2014).
[5] M. Winskel, N. Markusson, H. Jeffrey, C. Candelise, G. Dutton, P. Howarth, S. Jablonski, C. Kalyvas, and D. Ward, Learning pathways for energy supply technologies: Bridging between innovation studies and learning rates, Technological Forecasting and Social Change 81, 96 (2014).
[6] P. Lemonnier and B. Bourbiaux, Simulation of naturally fractured reservoirs. state of the art-part 1–physical mechanisms and simulator formulation, Oil & Gas Science and Technology–Revue de l’Institut Français du Pétrole 65, 239 (2010).
[7] A. Firoozabadi, Recovery mechanisms in fractured reservoirs and field performance, Journal of Canadian Petroleum Technology 39, 13 (2000).
[8] S. Mohammadi, M. Khalili, and M. Mehranfar, The optimal conditions for the immiscible gas injection process: A simulation study, Petroleum Science and Technology 32, 225 (2014).
[9] R. Farajzadeh, B. Wassing, and P. M. Boerrigter, Foam assisted gas–oil gravity drainage in naturally-fractured reservoirs, Journal of Petroleum Science and Engineering 94, 112 (2012).
[10] A. Moinfar, W. Narr, M.-H. Hui, B. T. Mallison, S. H. Lee, et al., Comparison of discrete-fracture and dual-permeability models for multiphase flow in naturally fractured reservoirs, in SPE Reservoir Simulation Symposium, 21-23 February, The Woodlands, Texas, USA (2011).
[11] Q. Tao, A. Ghassemi, and C. A. Ehlig-Economides, A fully coupled method to model fracture permeability change in naturally fractured reservoirs, International Journal of Rock Mechanics and Mining Sciences 48, 259 (2011).
[12] E. Stalgorova, T. Babadagli, et al., Field-scale modeling of tracer injection in naturally fractured reservoirs using the random-walk particle-tracking simulation, SPE Journal
1
[13] J. E. T. Ladron De Guevara and A. Galindo-Nava, Gravity drainage and oilreinfiltration modeling in naturally fractured reservoir simulation, in InternationalOil Conference and Exhibition in Mexico, 27-30 June, Veracruz, Mexico (2007). [14] C. Grattoni, X. Jing, and R. Dawe, Dimensionless groups for three-phase gravity
drainage flow in porous media, Journal of Petroleum Science and Engineering 29, 53 (2001).
[15] E. Ranjbar and H. Hassanzadeh, Matrix–fracture transfer shape factor for modeling flow of a compressible fluid in dual-porosity media, Advances in Water Resources 34, 627 (2011).
[16] M. Saidian, M. Masihi, M. Ghazanfari, R. Kharrat, and S. Mohammadi, An experimental study of the matrix-fracture interaction during miscible displacement in fractured porous media: A micromodel study, Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 36, 259 (2014).
[17] J. Hagoort et al., Oil recovery by gravity drainage, Society of Petroleum Engineers Journal 20, 139 (1980).
[18] R. Askarinezhad, R. Kharrat, and S. Shadizadeh, A new approach to the modeling of a simple re-infiltration gravity drainage process in naturally fractured reservoirs, Petroleum Science and Technology 30, 1004 (2012).
[19] P. M. Boerrigter, M. Verlaan, and D. Yang, Eor methods to enhance gas oil gravity drainage, in SPE/EAGE Reservoir Characterization and Simulation Conference, 28-31 October, Abu Dhabi, UAE (2007).
[20] L. S. Fung et al., Simulation of block-to-block processes in naturally fractured reservoirs, SPE reservoir engineering 6, 477 (1991).
[21] A. Firoozabadi and J. Hauge, Capillary pressure in fractured porous media, Journal of Petroleum Technology 42, 784 (1990).
[22] M. Verlaan, P. M. Boerrigter, et al., Miscible gas-oil gravity drainage, in International Oil Conference and Exhibition in Mexico, 31 August-2 September, Cancun, Mexico (2006).
[23] E. Stalgorova and T. Babadagli, Modeling miscible injection in fractured porous media using random walk simulation, Chemical Engineering Science 74, 93 (2012). [24] J. E. Ladron de Guevara-Torres, F. Rodriguez-de la Garza, A. Galindo-Nava, et al.,
Gravity-drainage and oil-reinfiltration modeling in naturally fractured reservoir simulation, SPE Reservoir Evaluation & Engineering 12, 380 (2009).
[25] G. Di Donato, Z. Tavassoli, and M. J. Blunt, Analytical and numerical analysis of oil recovery by gravity drainage, Journal of Petroleum Science and Engineering 54, 55 (2006).
1
[26] N. Shahidzadeh-Bonn, A. Tournie, S. Bichon, P. Vie, S. Rodts, P. Faure, F. Bertrand, and A. Azouni, Effect of wetting on the dynamics of drainage in porous media, Transport in Porous Media 56, 209 (2004).
[27] N. Shahidzadeh, E. Bertrand, J. P. Dauplait, J. C. Borgotti, P. Vie, and D. Bonn, Effect of wetting on gravity drainage in porous media, Transport in Porous Media 52, 213 (2003).
[28] S. Zendehboudi, N. Rezaei, and I. Chatzis, Effect of wettability in free-fall and controlled gravity drainage in fractionally wet porous media with fractures, Energy & Fuels 25, 4452 (2011).
[29] R. Parsaei and I. Chatzis, Experimental investigation of production characteristics of the gravity-assisted inert gas injection (GAIGI) process for recovery of waterflood residual oil: Effects of wettability heterogeneity, Energy & Fuels 25, 2089 (2011). [30] A. F. Stanley Wu, Effect of salinity on wettability alteration to intermediate gas-wetting,
SPE Reservoir Evaluation & Engineering 13, 228 (2010).
[31] C. Chalbaud, M. Robin, J. M. Lombard, F. Martin, P. Egermann, and H. Bertin, Interfacial tension measurements and wettability evaluation for geological CO2
storage, Advances in Water Resources 32, 98 (2009).
[32] D. Yang, Y. Gu, and P. Tontiwachwuthikul, Wettability determination of the crude oil-reservoir brine-reservoir rock system with dissolution of CO2at high pressures and
2
N
ON
-E
QUILIBRIUM
G
AS
I
NJECTION IN
NFR
S
An investment in knowledge pays the best interest. -Benjamin Franklin
A
BSTRACT:In naturally–fractured reservoirs, improving the matrix–fracture interactions is critical to the success of the applied improved oil recovery method. Therefore, a study of the mechanisms that control the mass exchanges between fracture and matrix can help to optimize recovery. This chapter concerns an experimental and simulation study to investigate the performance of gas–oil gravity drainage process in naturally fractured reservoirs. To this end, five gas injection experiments were conducted at different miscibility (i.e., immiscible and fully miscible) conditions using CO2, N2and asynthetic flue gas composed of 20 v/v% CO2and 80 v/v% N2. The impact of switching
from an immiscible (i.e., nitrogen or flue gas) gas to a non–equilibrium and fully miscible CO2injection is investigated. The effect of miscibility on the block–block interaction is
also examined using a stacked core with an impermeable barrier. The results reveal that injection of non–equilibrium gas with higher solubility in the oil phase results in a zone of decreased oil viscosity, which leads to an improved gravity mediated recovery. The results also show that the ultimate oil recovery increases considerably once miscibility is achieved. A numerical model is implemented to perform compositional simulations of multi–phase multi–component gas injections at different miscibility conditions. Agreement of the developed model with the experimental results indicates that gravity drainage, capillary hold–up and mixing are the main controlling mechanisms.
This chapter was published in Energy & Fuels 27, 6055 (2013) [1].
2
2.1. I
NTRODUCTION
Gas injection has been traditionally considered as an inefficient method for enhancing oil recovery from naturally–fractured reservoirs (NFRs) due to the easier flow path offered to the gas in the fractures, which leaves behind much oil unproduced in the matrix blocks. The success of any enhanced oil recovery method from NFRs highly depends on the degree of mass exchange between matrix and fracture. Viscous forces, gravity forces, capillary forces and mixing (diffusion or dispersion) influence the fluid transfer between matrix and fracture. Because of the existence of highly conductive and interconnected fracture networks, viscous forces are usually negligible compared to gravity forces [2–4]. Capillary forces adversely affect recovery of oil by gas because gas, being the least wetting phase, can only displace the oil phase in the rock matrix from the fracture when it overcomes the capillary barrier. As long as the capillary rise is much shorter than the matrix block height, gas–oil gravity drainage (GOGD) can be effective. In the opposite case most of the oil remains trapped in the matrix blocks [5–9].
Miscible displacement processes have been developed as successful method to overcome the capillary trapping [9–12]. Fully miscible conditions are not easy to obtain as it often requires high pressures or very rich injection gases. High pressure gas injection has two disadvantages: (1) one may need a larger mass of high pressure gas to fill the pore space from where the oil is recovered, and (2) the density of the injected gas increases significantly, which reduces the density difference between the gas and oil. Therefore, it becomes of interest how efficient non–equilibrium immiscible gas and multi–contact miscible gas injection can improve the gas oil gravity drainage [13–15]. Under near–miscible conditions, drainage rates increase due to: (1) lower gas–oil capillary pressure and hence a more effective gravity potential, (2) higher oil relative permeability, [16] (3) less re–imbibition or block–block interactions,[8, 9] (4) mixing due to diffusion and convective dispersion [7, 9] and thereby changing fluid properties such as viscosity, density and IFT, and (5) vaporization of intermediate components leading to multiple contact miscible (MCM) conditions [17].
Several authors have studied immiscible gas and MCM gas injection processes in fractured reservoirs by numerical modeling [8, 9, 18–21]. Uleberg and Høier [17], based on compositional reservoir modeling, showed that the developed miscibility level in a fractured reservoir is significantly higher than for a conventional one–dimensional single–porosity system. In the numerical simulations of Suicmez et al. [13] the best results, regarding ultimate recovery and drainage rate, were obtained for the case where miscibility develops through repeated contacts between the injected gas and the oil in the matrix (i.e., developed miscibility conditions).
Despite promising simulation outcomes, there are still little experimental data to confirm these results. More specifically, there have been few experimental attempts based on the non–equilibrium gas injection. Ringen et al.[15] performed gravity drainage experiments with a rich and a lean non–equilibrium hydrocarbon gas below the expected minimum miscibility pressure. They showed that diffusion improves the oil recovery by non–equilibrium gas injection. Torabi and Asghari [22] conducted a series of gas injection experiments to investigate the influence of water saturation, oil viscosity and matrix permeability on the oil production rate under miscible and immiscible conditions. They found that at pressures above the minimum miscibility pressure, the gravity drainage
2
produced more than 78% of the initial oil. Darvish et al. [23] performed tertiary CO2
injection experiments at reservoir conditions to investigate the mass transfer of CO2and
hydrocarbons between the fracture and the matrix. Their experimental results indicated that the produced oil composition changes in time as CO2is injected into the fracture.
According to Darvish et al. [23], these compositional effects can be explained by the different recovery mechanisms involved in the mass transfer between the matrix and fracture system.
This chapter is concerned with the impact of non–equilibrium gas injection on the gravity drainage rate and oil recovery under different conditions (i.e., immiscible, and miscible). This is of practical importance because when gas is injected into the fracture it is unlikely to be at chemical equilibrium with the oil in the matrix. More importantly, as the compositions change in time and space, the density, viscosity, and interfacial tension (IFT) between the phases will also vary. To address these aspects, non–equilibrium gas injection experiments were conducted using a single vertical core as the matrix block, which is surrounded by a single fracture. In addition, the impact of switching from an immiscible (nitrogen and flue gas) injection gas to non–equilibrium and fully miscible CO2was
examined. The impact of miscibility on the block–block interaction was investigated using a stacked core with an impermeable barrier.
This chapter is organized as follows. First, the procedure of the experiments is described including the physical properties and specifications of the materials, which were used for the experiments. Then, the results of the experiments using CO2, N2or flue
gas are presented, interpreted and compared with the numerical simulation data. Finally, concluding remarks are presented.
2.2. EXPERIMENTS
Table 2.1 summarizes the experimental conditions. All experiments were performed at a constant temperature of 30°C. The first contact miscibility pressure (FCM) between CO2and oil (30 w/w% n–heptane, 30 w/w% n–decane, and 40 w/w% n–hexadecane) was
determined to be 75 bar at 30°C using the PVTsim phase behavior simulator, selecting the Peng–Robinson EoS [24]. The injection pressure in the experiments was taken 10% above the calculated FCM pressure to make sure that a FCM condition was implemented. The nitrogen and flue gas experiments were performed at immiscible conditions (i.e., 50 bar at 30°C).
Table 2.1: Summary of the gas injection experiments
Exp. Displacing gas Injection rate Stage 1 Stage 2 Stage 3
1 CO2 5(mL/min) Immiscible Miscible
2 CO2 5(mL/min) Miscible
3 CO2 5(mL/min) Immiscible Miscible
4 N2/CO2 5(mL/min) Immiscible Immiscible Miscible
2
2.2.1. M
ATERIALSA single Bentheimer sandstone core was used in all experiments except in Experiment 3, where two matrix blocks of Bentheimer were put on top of each other with a Teflon impermeable layer in between. Two impermeable cylindrical Teflon pieces were also used to seal the top and bottom faces of the core (Fig. 2.1). Table 2.2 gives the dimensions, the porosity and the permeability of the cores used in this study. A synthetic three component oil containing 30 w/w% n–heptane, 30 w/w% n–decane, and 40 w/w% n–hexadecane was prepared and used as the hydrocarbon phase. The viscosity and density of the oil phase are 1.22 mPa.s and 733 kg/m3 at room conditions, respectively. CO2and N2with a purity
of 99.8% and a synthetic flue gas composed of 20 v/v% CO2and 80 v/v% of nitrogen from
Linde Gas Benelux were used as injection gases.
Figure 2.1: The two core samples (see Table 2.2) used in the experiments. Left a single core of 40.5 cm; the top
Teflon sealing end piece has a length of 0.43 cm, the bottom solid Teflon sealing end piece has a length of 10 cm to fit the core in the core holder of 51.5 cm. Right a stacked core with a Teflon seal of 0.43 cm between the two equal parts of 25 cm. Not shown are the Teflon end pieces of 0.43 cm each at the top and bottom. This leaves a
small gap at the top. Note stacked core (left) is utilized only in Experiment 3.
Table 2.2: Properties and dimensions of the two core samples
Core k (D) φ (%) H (cm) D (cm) PV (mL)
single core 1.5 21 40.5 11.90 945.9
Stacked core 1.5 21 2×25 11.90 1167.8
core holder 51.5 12.15
2.2.2. E
XPERIMENTAL SET–
UPFig. 2.2.2 shows the process flow diagram of the experimental set–up used in this study. A high pressure stainless steel core holder was used to keep the core vertically centralized. There is 2.5 mm space between the core and inner diameter of the core holder to mimic the fracture surrounding the core. The end cap of the core holder at the bottom was conically machined to provide an easy–flow pathway for the produced fluids. A vacuum unit was used to evacuate and saturate the core prior to each experiment. Several high pressure
2
manual and air–actuated needle valves were included in the set–up to regulate the gas and liquid flow into/out of the system. Two high pressure ISCO syringe pumps with capacities of 500 mL were initially used to pressurize the system and subsequently to inject gas into the fracture at a constant flow rate. A high pressure gas booster accompanied by a transfer cylinder (2000 mL) was used to supply sufficient high–pressure refill gas during each run of the experiments. The pressure in the fracture was kept constant during the experiment using two back pressure regulators installed in series in the production line, because we found that a two–step pressure reduction (from high pressure to a medium pressure and subsequently to atmospheric pressure) is more stable. The produced oil was collected on a digital balance, and data were recorded using a data acquisition system.
Figure 2.2: Schematic of the experimental gravity drainage unit
2.2.3. E
XPERIMENTAL PROCEDUREThe volume of the core holder, before mounting the core sample, was measured using helium. Having mounted the core in the core holder, the system was checked for possible leakage using helium. Thereafter, the whole system was vacuumed for 72 hours. The core was then saturated and pressurized with oil for 24 hours. All the experiments were initiated using the core sample at 100% oil saturation (i.e., without connate water). The matrix oil in place was calculated based on the difference between the volume of the oil used to saturate and pressurize the system and the fracture volume. All the immiscible gas injection runs were followed by a miscible CO2displacement step to investigate the
efficiency of miscible injection in an ongoing gas injection project. Consequently, at the end of each test the core sample was assumed to be at its original state since no connate water was present in the system. The above mentioned procedure was repeated for all the experiments using CO2, N2, and flue gas. When no more oil was produced even
after miscible CO2injection, a mass balance check was applied. The recovery factor was
between 95% and 100%. At this point the experiment was terminated and the pressure was released through the back pressure regulators. The system was vacuumed and prepared again for the next experiment.
2
2.3. SIMUL ATION MODEL
MoReS,Shell’s in–house reservoir simulator, was employed in this study to investigate the isothermal multi–phase, multi–component flow in NFRs when a non–equilibrium gas is injected into the fracture under miscible and immiscible conditions. The simulations were conducted in compositional mode by employing the Peng–Robinson equation of state (EoS) [24]. The dimensions in the physical model are the same as those in the experiments. The flow cell is represented by a cylindrical domain of inner radius of 12.15 cm and a length of 51.5 cm. The outside of the cylindrical domain has no flow boundaries. Inside the cylindrical domain we have concentrically a cylindrical matrix block of uniform permeability k and porosityφ (see Table 2.2). The top and bottom side of the cylindrical matrix has also no flow boundaries. The space between the cylindrical domain and cylindrical matrix represents the fracture. A local porosity ofφ∗f=1 and a very high local permeability of k∗
f=100D were assigned to the fracture grid blocks. The Corey relative
permeability curves were used to characterize the dynamic properties of the two phase flow in the simulations. The Corey correlations are given by
kr g= k◦r g µ S g− Sg c 1 − Swc− Sg c ¶ng (2.1) kr og= kr og◦ µ1 − S g− Sor g− Swc 1 − Swc− Sor g ¶no (2.2) Table 2.3 gives the Corey exponent for each experiment considered in this study. In addition, diffusion coefficients that were used in each simulation run to reproduce the experimental data are also given in Table 2.3.
Table 2.3: Fitting parameters used in the simulations for each experiment
Exp. Step1 Step2 Step3
no ng Dog×109 no ng Dog×109 no ng Dog×109 1 2 2.5 2.5 1 1 2.85 2 1 1 8.6 3 2 2.5 2.5 1 1 2.5 4 2 2 1.3 2.5 2.5 2.5 1 1 2.85 5 2 2 1.3 2.5 2.5 2.5 1 1 2.85
Fig. 2.3 shows the capillary pressure curves used in the model to simulate the immiscible CO2, immiscible N2, and immiscible flue gas experiments. These capillary curves were
used as fitting parameters in the simulations.
The geometry of the model is shown in Fig. 2.4. The solvent is injected at a constant flow rate from the top and oil is produced at constant pressure from the bottom. A radially symmetric grid was applied to solve the equations numerically using the finite difference method. Due to the existence of the highly conductive fracture systems, the viscous pressure drop is negligible. Therefore, the ultimate recovery of the process is mainly controlled by capillarity, gravity and diffusivity. Governing equations can be found in Qin et al.[25] and Chen and Chen [26].
2
Figure 2.3: Capillary pressure curves optimized to simulate immiscible CO2, immiscible N2, and immiscible
flue gas experiments.
Figure 2.4: Geometry of the model. On the top and bottom, the Teflon seals are represented by a layer of zero
permeability. Permeability in the fracture is taken as 1000 Darcy, whereas the matrix permeability is obtained from a single measurement on the block from which the sample is obtained. The yellow open boundary only
indicates that there is no seal on the side.
2.4. RESULTS AND DISCUSSIONS
In this section, each experiment is discussed and analyzed. The analysis of the experiments is based on the following assumptions: (1) the main mechanisms are capillarity, gravity, and diffusivity, (2) the calculated solubility is based on the Peng–Robinson EoS [24] and a Peneloux volume shift correction [27], (3) the phase equilibrium is not influenced by capillary pressure. In other words, it is assumed that at thermodynamic equilibrium all phases have the same pressure, and (4) The impact of interfacial tension change on relative permeability is ignored (see, however, Blom and Hagoort [16]).
2.4.1. E
XPERIMENT1: I
MMISCIBLECO
2,
EFFECT OF MISCIBILITYThe first experiment was conducted at both immiscible and miscible CO2injection
conditions. The core was fully saturated with oil and the system was pressurized up to 50 bars. Thereafter, CO2was injected into the fracture at a constant flow rate of 5 mL/min,
2
from qo= kkr oA∆ρogg µo (2.3) In Eq.( 2.3) it is assumed that flow is incompressible and no mixing occurs between phases and consequently the oil viscosity and density remain constant. With these assumptions, the analytical drainage rate of the immiscible CO2injection step is calculatedto be 4.74 mL/min. Fig. 2.5 compares the experimental results with the model–calculated recovery factor curve for Experiment 1. The fitting parameters in the model are listed in Table 2.3. As can be observed from Fig. 2.5, after about 2000 minutes of CO2injection
under immiscible conditions, the oil recovery increased to 58% of the original oil in the core. When the oil production was ceased, the back pressure valves were readjusted and the system pressure was increased to the first contact miscibility conditions (i.e., 85 bar). Thereafter, high pressure CO2injection was continued at constant flow rate of 5 mL/min.
It can be observed from Fig. 2.5 that miscible CO2injection increased the final recovery
to about 98% of the original oil in the core. From the volumetric point of view, a total of 12.6 matrix pore volumes (PV) of high pressure CO2was used in order to recover the
remaining oil in the matrix block after immiscible CO2injection. Moreover, Fig. 2.5 shows
that the model can reproduce the experimental data reasonably well within an acceptable range of accuracy. The experimental drainage rate data are also shown in Fig. 2.5 and are compared with the numerically calculated drainage rate curve.
Figure 2.5: Comparison between the recovery factor and drainage rate data obtained from Experiment 1 (i.e.,
immiscible CO2followed by miscible CO2) and the simulations. After 2000 minutes the conditions are changed
from immiscible to miscible. Diffusion coefficients of D=2.5×10−9m2/s and D=2.85×10−9m2/s were used for immiscible and miscible stages, respectively, to match the experimental data.
According to Fig. 2.5, the actual oil production rate is less than the analytical drainage rate, which is calculated from Eq.( 2.3). This can be attributed to: (1) mixing between oil and gas in the fracture, which leads to a lower density difference between matrix and fracture and thus a lower drainage rate, (2) compressibility of the gas phase caused by fluid density variations along the core, (3) capillarity, and (4) 2–D flow effects. In case of
2
miscible CO2injection, the density difference between the gas phase flowing through the
fracture and the oil phase in the matrix decreases significantly. Even if the process benefits from the fully miscible conditions (meaning a significant viscosity reduction in the oil; see i.e., Fig. 2.6), the reduced density difference between the injected and produced fluids leads to a lower drainage rate (see Eq.( 2.3). A practical approach to determine the CO2
required for a CO2–based enhanced oil recovery method is based on the CO2utilization
factor, which is defined as the amount of CO2used to recover a unit volume of oil. In this
study, we normalized the injected CO2volume by dividing the cumulative volume of CO2
injected at reservoir conditions by the matrix PV. Thus, the oil recovery can be plotted versus the PV CO2injected, as shown in Fig. 2.7. As can be observed from Fig. 2.7, large
volumes of CO2should be used to recover oil from the matrix. This indicates that the
process requires proper recycling facilities to recover and re–inject the produced CO2.
Therefore, the recycle process and facilities costs should be accounted for to accurately evaluate the economics of this process.
Figure 2.6: Calculated oil and gas viscosities versus CO2composition in oil and gas under miscible conditions
(i.e., 85 bar and 30°C)
The compositional effects during CO2injection can be obtained from the simulation
results by tracing the weight percentage of each component in the produced oil, as shown in Fig. 2.8. Note that the curves for n–C7and n–C10 are on top of each other as the
initial mass fractions in the original oil are the same. When injected in the fracture, some CO2is dissolved in the oil phase. The extent of CO2dissolution is determined by
solubility of the CO2in the oil phase at the system pressure and temperature. Therefore,
the composition of the produced fluid is not the same as the original oil in place and a fraction of the injected CO2is produced with the oil even before the gas breaks through
from the matrix (i.e., when the gas–liquid interface reaches the capillary fringe). As CO2
injection continues, the produced stream is continuously being enriched with CO2and
as a result less hydrocarbon components is produced. However, increasing the system pressure to the first contact miscibility condition leads to an increase in the percentage of hydrocarbon constituents in the produced stream. As can be observed from Fig. 2.8, moving to miscible conditions improves the CO2solubility in the oil phase and results
2
Figure 2.7: The recovery factor as in Fig. 2.5 but now versus PV CO2injected for immiscible and miscible CO2
injection experiment (i.e., Experiment 1). This shows that large volume of CO2should be used to recover oil
from the matrix.
content of the produced stream increases in time until it reaches a maximum, while the CO2content decreases accordingly. This shows that miscible CO2injection recovers
the remaining oil (i.e., residual oil to immiscible gas injection, Sor g) in the matrix after
immiscible CO2injection. Note that, based on the capillary pressure curve employed to
match the immiscible CO2experimental data, the capillary hold–up of the matrix block is
about 15 cm. This implies that immiscible CO2injection can recover oil from the top 25
cm portion of the core. By applying miscible CO2, the unproduced oil from the upper part
of the core (i.e., above the capillary height) is drained downward and is mixed with the oil in the lower part of the core and thus the produced stream is enriched with hydrocarbons. Thereafter, CO2, as a fully miscible solvent, produces the remaining oil from the lower
part of the core and its concentration increases in time until all the oil is produced from the matrix and all the pore spaces are filled with a CO2–rich mixture.
Fig. 2.9 illustrates the simulation results in terms of the CO2molar percentage in the
matrix block at different times of Experiment 1. As can be observed from Fig. 2.9, for the conditions considered in this study, the gravity drainage process develops a relatively stable front, which moves downward and produces the oil in a piston like manner. Initially, CO2penetrates into the matrix from the top of the core. The penetration of CO2is limited
by the equilibrium solubility of CO2in the oil phase, which in this case is 0.59 mol CO2/mol
oil at 50 bar and 30°C. As the process continues, CO2diffuses also into the matrix from
the sides. A diffusion coefficient of D=2.5×10−9m2/s was employed in order to match the experimental data. Nevertheless, the displacement is predominantly vertical and gravity stabilizes the interface between the oil and gas. Behind the front, CO2extracts the
lighter components from the oil and oil saturation is reduced. As a result, the oil viscosity increases, leading to a lower oil relative mobility.
The relative magnitude of the dominant forces (i.e., capillary, and gravity) in an immiscible gravity drainage process can be also quantified using the dimensionless numbers. The inverse Bond number is defined as the ratio of the capillary forces holding
2
Figure 2.8: Model results of the composition of the produced fluid with time for Experiment 1 (i.e., immiscible
and miscible CO2). The mass fractions add up to one. Note that the curves for n–C7and n–C10are on top of
each other as the initial mass fractions are the same. At 2000 minutes the conditions are changed from immiscible to first contact miscible and alkanes from the matrix appear again in the produced stream.
Figure 2.9: Simulation results of the overall mol% (see color bar) of CO2in the matrix for immiscible CO2
injection. We observe a cross–section of the core at six consecutive times. Red indicates the CO2–rich phase and
the blue color indicates the oil–CO2mixture that is in equilibrium with the gas. A diffusion coefficient of
D=2.5×10−9m2/s was used to match the experimental data. Note that we take advantage of the symmetry element and conduct the simulation only in half of the system, i.e. the radius increases from r=0 at the left to
r=R at the right.
the wetting phase in the porous medium to the gravitational forces acting to displace the denser phase. If the gas is in chemical equilibrium with the oil the inverse Bond number for gravity drainage can be written as [28, 29]
NB−1= γog ∆ρogg l2
(2.4) where l is the characteristic length (in this case height of the matrix block) andγogis
