solar thermal enhanced oil recovery

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Universitat Stuttgart - Institut f ur WasserbauLehrstuhl f ur Hydromechanik und Hydrosystemmodellierung

Prof. Dr.-Ing. Rainer Helmig

Diplomarbeit

Cyclic Steam Injection into the Subsurface- solarthermal steam generation for

enhanced oil recovery

Submitted byChristoph KlingingerMatrikelnummer 2195007

Stuttgart, 26th January 2010

Examiners: Prof. Dr.-Ing. Rainer Helmig, Dr.-Ing. Holger ClassSupervisor: Dr.-Ing. Andreas Bielinski


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Contents

1 Introduction 11.1 Global Energy Demand and the Resource Oil . . . . . . . . . . . . . . 1

1.2 Enhanced Oil Recovery through SAGD . . . . . . . . . . . . . . . . . . 21.3 Solarthermal Steam Generation for SAGD . . . . . . . . . . . . . . . . 41.4 Scope of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Fundamentals of the Applied Model 62.1 Essential Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Phases and Components . . . . . . . . . . . . . . . . . . . . . . 62.1.2 Primary Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Secondary Variables . . . . . . . . . . . . . . . . . . . . . . . . 72.1.4 State of Aggregation and Phase Change . . . . . . . . . . . . . 7

2.2 Flow and Transport Processes . . . . . . . . . . . . . . . . . . . . . . . 82.2.1 Advection and Buoyancy . . . . . . . . . . . . . . . . . . . . . . 82.2.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.2.3 Mass Transfer Processes . . . . . . . . . . . . . . . . . . . . . . 102.2.4 Thermal Convection . . . . . . . . . . . . . . . . . . . . . . . . 102.2.5 Thermal Conduction . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Mathematical Formulations . . . . . . . . . . . . . . . . . . . . . . . . 112.3.1 Mass Balance Equation . . . . . . . . . . . . . . . . . . . . . . . 112.3.2 Energy Balance Equation . . . . . . . . . . . . . . . . . . . . . 12

2.4 The 2p1cni Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.5 MUFTE-UG: The Numerical Simulator . . . . . . . . . . . . . . . . . . 13

3 System Properties 153.1 Physical Properties of Water and Steam . . . . . . . . . . . . . . . . . 15

3.1.1 Density and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 153.1.2 Water Saturation Pressure . . . . . . . . . . . . . . . . . . . . . 153.1.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Physical Properties of the Porous Medium . . . . . . . . . . . . . . . . 193.2.1 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.2 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

I


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CONTENTS II

3.2.3 Absolute Permeability . . . . . . . . . . . . . . . . . . . . . . . 203.3 Composite Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 Relative Permeability . . . . . . . . . . . . . . . . . . . . . . . . 203.3.2 Capillary Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 213.3.3 Heat Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Simulations 244.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.1 Denition of the Model Domain . . . . . . . . . . . . . . . . . . 244.1.2 Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . 264.1.3 System Property Values . . . . . . . . . . . . . . . . . . . . . . 264.1.4 Conditions at the Injection Well . . . . . . . . . . . . . . . . . . 27

4.2 Continuous Steam Injection . . . . . . . . . . . . . . . . . . . . . . . . 304.2.1 The Injection Well . . . . . . . . . . . . . . . . . . . . . . . . . 304.2.2 Steam Chamber and Temperature Development . . . . . . . . . 31

4.3 Cyclic Steam Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.1 The Injection Well . . . . . . . . . . . . . . . . . . . . . . . . . 354.3.2 Steam Chamber Growth . . . . . . . . . . . . . . . . . . . . . . 364.3.3 Temperature Development . . . . . . . . . . . . . . . . . . . . . 39

4.4 Comparison of the two Injection Routines . . . . . . . . . . . . . . . . 414.4.1 Steam Chamber Growth . . . . . . . . . . . . . . . . . . . . . . 414.4.2 Temperature Development . . . . . . . . . . . . . . . . . . . . . 44

4.5 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.5.1 Absolute Permeability K . . . . . . . . . . . . . . . . . . . . . . 564.5.2 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574.5.3 Specic Heat Capacity of the Soil Grains csg . . . . . . . . . . . 584.5.4 Heat Conductivity pm . . . . . . . . . . . . . . . . . . . . . . . 594.5.5 Capillary Pressure pc and Van Genuchten Parameter . . . 604.5.6 Results of the Sensitivity Study . . . . . . . . . . . . . . . . . . 60

5 Summary 615.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63


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List of Figures

1.1 Schematic sketch of oil sand reservoir and well arrangement . . . . . . . 31.2 Schematic sketch of steam chamber growth . . . . . . . . . . . . . . . . 3

2.1 Phase diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . 72.2 Phase states and mass transfer processes considered in the 2p1cni model 132.3 The numerical simulator MUFTE-UG . . . . . . . . . . . . . . . . . . . 14

3.1 Water saturation pressure curve . . . . . . . . . . . . . . . . . . . . . . 163.2 Specic enthalpy of liquid water . . . . . . . . . . . . . . . . . . . . . . 173.3 h-T relation of saturated steam . . . . . . . . . . . . . . . . . . . . . . 183.4 h- p relation of saturated steam . . . . . . . . . . . . . . . . . . . . . . 193.5 Relative permeability-saturation relation . . . . . . . . . . . . . . . . . 213.6 Capillary pressure-saturation relation . . . . . . . . . . . . . . . . . . . 223.7 Heat conductivity of a uid lled porous medium . . . . . . . . . . . . 23

4.1 Model domain for the simulations . . . . . . . . . . . . . . . . . . . . . 254.2 Data retrieval nodes within the model grid . . . . . . . . . . . . . . . . 254.3 Seasonal and daily injection cycle . . . . . . . . . . . . . . . . . . . . . 294.4 p, T and S g at the injection node for continuous injection . . . . . . . . 304.5 Steam chamber growth for continuous injection . . . . . . . . . . . . . 324.6 T distribution for continuous injection . . . . . . . . . . . . . . . . . . 334.7 T and S g underneath the overburden for continuous injection . . . . . . 344.8 p, T and S g at the injection node for cyclic injection . . . . . . . . . . . 374.9 Steam chamber growth for cyclic injection . . . . . . . . . . . . . . . . 384.10 T distribution for cyclic injection . . . . . . . . . . . . . . . . . . . . . 404.11 S g for continuous and cyclic injection after 5 years . . . . . . . . . . . . 424.12 S g for continuous and cyclic injection after 4 years and 5 months . . . . 434.13 T for continuous and cyclic injection after 5 years . . . . . . . . . . . . 454.14 Low T areas for continuous and cyclic injection after 5 years . . . . . . 464.15 High T areas for continuous and cyclic injection after 5 years . . . . . . 474.16 Propagation of various T fronts for continuous and cyclic injection . . . 484.17 p at Node2 and Node3 for continuous and cyclic injection . . . . . . . . 504.18 p distribution for continuous and cyclic injection . . . . . . . . . . . . . 51

III


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LIST OF FIGURES IV

4.19 T sat distribution for continuous and cyclic injection . . . . . . . . . . . 524.20 S g at Node2 and Node3 for continuous and cyclic injection . . . . . . . 53

4.21 Model domain for sensitivity analysis . . . . . . . . . . . . . . . . . . . 544.22 Heat conductivity-saturation relation for the sensitivity analysis . . . . 554.23 T front propagation for continuous and cyclic injection with varying K 564.24 T front propagation for continuous and cyclic injection with varying 574.25 T front propagation for continuous and cyclic injection with varying csg 584.26 T front propagation for continuous and cyclic injection with varying pm 594.27 T front propagation for continuous and cyclic injection with varying pc 60


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List of Tables

2.1 Phase states and corresponding primary varibales for the 2p1cni model 8

4.1 Data nodes implemented in the model grid . . . . . . . . . . . . . . . . 264.2 System property values . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.3 System property values and range for the sensitivity analysis . . . . . . 55

V


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Nomenclature

symbol meaning dimension

Q change of heat [J ] U change of internal energy [J ] W v volume changing work [J ]E extensive propertyF res resulting force [N ]Glin linear Gravity number [ ]H enthalpy [ J ]K intrinsic permeability [ m2]K ob intrinsic permeability of overburden [ m2]K f hydraulic conductivity [ m/s ]Re Reynolds number [ ]S saturation of phase [ ]S e effective water saturation [ ]S w water saturation [ ]S w,r residual water saturation [ ]T temperature [ C ]T initial initial temperature [ C ]T sat water saturation temperature [ C ]U internal energy [ J ]V volume [m3]

V pores pore volume [m3

]V total total bulk volume [ m3]

csg specic heat capacity solid phase [ J/kgK ]cp specic heat capacity at constant pressure [ J/kgK ]cv specic heat capacity at constant volume [ J/kgK ]d mean pore diameter [ m]d depth [m]e intensive quantity corresponding to property E

g gravitational constant [ m/s2

]

VI


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Nomenclature VII

g gravitational vectorh piezometric head [m]

h specic enthalpy [J/kg ]h specic enthalpy of phase [J/kg ]hg,sat specic enthalpy of saturated steam [ J/kg ]hwet specic enthalpy of wet steam [J/kg ]hw,sat specic enthalpy of saturated water [ J/kg ]kr relative permeability [ ]kr , relative permeability of phase [ ]kr,n relative permeability of non-wetting phase [ ]kr,s relative permeability of steam [ ]kr,w relative permeability of wetting phase [ ]m mass [kg]m Van Genuchten parameter [ ]mgaseous mass gaseous component [kg]m liquid mass liquid component [kg]n Van Genuchten parameter [ ]n outer normal vector p pressure [P a ] p pressure of phase [P a ] patm atmospheric pressure [ P a ] pc capillary pressure [P a ] pg gas phase (steam) pressure [ P a ] pw water phase pressure [ P a ] pw,sat water saturation pressure [ P a ]q c mass source/sink termq cond conductive heat ux [ W/mK ]q h energy source/sink termq s steam mass ux [kg/sm 2]s entropy [J/K ]t time [s]

u specic internal energy [J/kg ]u specic internal energy of phase [J/kg ]v ow velocity [m/s ]v Darcy velocity [m/s ]v velocity of phase [m/s ]v a , seepage velocity of phase [m/s ]v s steam velocity [m/s ]x steam quality [ ]z height [m]


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Nomenclature VIII

Van Genuchten parameter [1 /P a ] phase

boundary of control volume domain heat conductivity [ W/Km ] f heat conductivity of uid phase [ W/Km ] i heat conductivity of material i [W/Km ]pm equivalent heat conductivity of the porous medium [ W/Km ]s heat conductivity of solid phase [ W/Km ] dynamic viscosity [kg/ms ] dynamic viscosity of phase [kg/ms ]s dynamic viscosity of steam [kg/ms ] kinematic viscosity [m2/s ] domain of control volume porosity [ ]ob porosity of overburden [ ]

mass density [kg/m 3] mass density of phase [kg/m 3]w mass density of water [kg/m 3]b mass density of a body b [kg/m 3]f mass density of a uid f [kg/m 3]sg soil grain density [kg/m 3]

subscript meaning

referring to phase atm referring to atmospheric conditionsb referring to body bf referring to uid f g referring to gas phasei referring to material iinitial initial conditionsn referring to non-wetting phaseob referring to overburdenpm referring to porous medias referring to steamsat referring to saturated conditionssg referring to solid phasew referring to water phasewet referring to wet conditions


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Nomenclature IX

superscript meaning

c componenth enthalpy


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Chapter 1

Introduction

1.1 Global Energy Demand and the Resource Oil

According to the International Energy Agency (IEA), the worldwide economicdownturn since the end of 2008, has lead to a drop in the global energy demand,accompanied by decreasing CO 2 emissions and energy investments. However, thisis assumed to be a short-dated development. On current policies, the global energydemand would quickly resume its longterm upward trend, once economic recovery isunderway ( IEA (2009) [14]). The worldwide primary energy consumption in 2008was estimated to be 11.29 Gt of oil equivalent ( BP (2009) [4]), oil being the biggestprimary energy source with around 34 % or an amount of 3.93 Gt.With no major changes in government policies and measures, fossil fuels are going tobe the dominant source of primary energy in the near future. Oil will thereby remainthe largest single fuel source, although its share is assumed to drop from 34% in2009 to 30 % in 2030. The oil demand is projected to grow 1 % per year from 85mb/ d(million barrels per day) in 2008 to 105 mb/ d in 2030 (IEA (2009) [14]). With theconventional oil production of non OPEC countries assumed to peak around 2010,and the oil reserves to production ratio ( R/ P) being estimated at 42 years, the so-callednon-conventional oil deposits become economically more interesting (the R/ P ratio isan indication for the period the reserve will last assuming a constant consumption rate).

Low viscous oil determined by a relatively good ability to ow, is usually re-ferred to as conventional oil. While highly viscous oil and oil bound to oil sand andoil shale, thus being immobile, is dened as non-conventional oil. For this reason, theoil density can be used to differ between conventional and non-conventional oils. Oilwith a density below 10 API (or above 1 g/ cm 3 ) belongs to the non-conventional oils(BGR (2009) [2]).Such non-conventional oil deposits include bitumen from oil sand and heavy oil, of which vast reserves and resources are found in Alberta, Canada and the Orinocotar belt in Venezuela ( Butler (1991) [5]). According to the German Federal

1


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1.2 Enhanced Oil Recovery through SAGD 2

Institute for Geosciences and Natural Resources (BGR), reserves are dened as thedeposits geologically detected with a high accuracy and economically and technically

producible. Resources, are the deposits geologically proved but currently economicallynot producible, and the deposits which have not been approved but are geologicallyexpected in a certain region.The total oil in place of the worlds oil sands alone, is assumed to be 462 Gt, with188 Gt dened as reserves and resources. The estimated total oil in place in theCanadian oil sands is 272 Gt, of which 110 Gt are claimed to be reserves and resources.The estimated amount of oil in place in the Venezuelan heavy oil elds (which accountsfor more than 97% of the total heavy oil) is 240Gt. Thereof, 54Gt are dened asreserves and resources (BGR (2009) [2]). The total potential, or estimated ultimaterecovery (EUR), of conventional oil is thought to be 400 Gt, with a remaining potentialof 249 Gt (reserves and resources combined).

These numbers indicate the enormous potential of the described non-conventionalreservoirs, even though one is advised not to directly compare between such numbers.This is because different authors and institutions use different denitions of theterms conventional and non-conventional oil deposits or reserves and resources.Furthermore, the quality of the energy data provided by sources, such as governmentsand companies, is not necessarily reliable due to low transparency, economical andpolitical interests, and know-how, as well as technical limitations.

1.2 Enhanced Oil Recovery through SAGD

Highly viscous oil, such as heavy oil or bitumen from oil sand, may be recovered using aspecial method of the enhanced oil recovery technologies, called steam-assisted gravitydrainage (SAGD). It was developed, to remove the oil in a systematic manner, in orderto realise a more complete recovery of the reservoirs than achieved in common steam-ooding processes. The steam-assisted gravity drainage process has since emerged asthe most effective and most promising in-situ technology for the recovery of heavy oiland bitumen from oil sand, buried too deep for surface mining ( Nasr et al. (1998)[19]).Gravity is naturally present in the reservoirs and is used as the main driving force toeffect the oil movement. This way, differential ngering, occuring when viscous oils aremoved by pushing with a less viscous uid, can be avoided ( Butler (1991) [5]). Theprocess of SAGD generally involves drilling paired horizontal wells close to the reser-voir bottom, one well a short distance above the other (5 m to 10 m). The so-calledwell pair is drilled to the desired reservoir depth, where it continues horizontically for500 m to 700m. Several such well pairs, lying parallel to each other, are drilled intothe deposit near the reservoir bottom (see gure 1.1).


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1.2 Enhanced Oil Recovery through SAGD 3

injection

35m

well length appr. 500 700m

production

horizontaldistance appr. 100m

verticaldistance5m

well pair, consisting of a production and injection well

reservoirthickness

400mreservoir depth

overburden

crosssectional area for 2d simulations

low permeable

y

xz

Figure 1.1: Schematic 3D sketch of the typical well arrangement for SAGD in an oilsand reservoir.

The top well of a well pair is used, to continuously inject steam into the oil sand for-mation, creating a steam chamber. Thereby, the steam pressure is usually maintainedat a constant value throughout most of the process. The growing steam chamber issurrounded by colder oil sand. At the interface between the steam front and the porousmedium, steam condenses, transferring heat to the surrounding medium. The heated,less viscous oil near the condensation surface drains, due to gravitational forces, to the

bottom well, where it is produced (see gure 1.2). As the oil and steam condensatesdrain downwards, the steam chamber grows upwards and sideways ( Butler (1991)[5]).

Heated oil flows to production well

Oil and condensate drain

Growing steam chamber

Continuous steam

injectioninto chamber

continuously

Figure 1.2: Vertical 2D slice through an oil sand reservoir including two well pairs.Schematic sketch of the steam chamber growth from the injection well, and the oil andcondensate ow down towards the production well ( Butler (1991) [5]).


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1.3 Solarthermal Steam Generation for SAGD 4

The most dominant features for a successful SAGD operation are the geology and thereservoir properties. The reservoirs average pay zone depth should be above 15 m,

and characterized by a good vertical communication without any thief zones. OftenSAGD operations are compromised by insufficient steam supply. However, as long asthe steam chamber can grow, the ultimate recovery of a SAGD operation can be inthe order of 60% to 70% (Jimenez (2008) [16]).

Reservoir conditions, the production strategy and the depth and quality of theoil deposit dene the steam injection rate, which in turn determines the steaminjection pressure. A steam injection rate of around 180 t/ d (tonnes per day) per wellpair is assumed to be realistic. At a steam pressure of around 40 bar and a steamquality of approximately 90 %, this equals an energy amount of 473 GJ.

Producing one barrel of oil using the SAGD technology, three barrels of waterand the energy equivalent of 1/ 3 of a barrel of oil is needed. According to BGR (2009)[2], 80 % to 90 % of the water can be reused, due to recycling processes.

1.3 Solarthermal Steam Generation for SAGD

As described earlier, the long-term trend of the global oil demand is expected to beincreasing, while no major new discoveries of conventional oil deposits are made. The

so induced rising oil price and the vast potential of non-conventional oil deposits, suchas oil sand, has made the depletion of these less traditional reservoirs more interesting.For instance, bitumen production from the oil sand elds of Alberta, Canada hasalmost doubled from the year 2000 to 2007, according to BGR (2009) [2]. This isfollowed by an increasing demand for gas, to produce steam for enhanced oil recovery,as most of the oil from the Alberta oil sands needs to be produced in-situ. The useof increasingly large amounts of fossil fuel for steam generation presents a number of economic and environmental problems. Common steam generators emit large amountsof greenhouse gases, and the increasing demand for natural gas is feared to inuencethe regional natural gas market.

The motivation for this work is thus, the idea of using the energy of solar radi-ation to generate and inject the steam needed for enhanced oil recovery purposes.Solarthermal power plants use point (solar tower) or line (solar trough) focusingsystems consisting of mirrors, to concentrate direct solar radiation in terms of heat.The captured thermal energy is used to generate steam, which in turn is used toproduce electricity. While line focusing systems are determined by a concentrationfactor of up to 80 and operating temperatures up to 350 C, the concentration achievedwith point focusing systems is higher, and thus is the temperature ( Voss (2005) [22]).Usually, the solar energy is absorbed by a heat storage uid, such as oil or molten


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1.4 Scope of this Work 5

salt. Unlike conventional solarthermal power plants, solarthermal steam generationfor enhanced oil recovery, would require steam at mid-level temperatures, directly

generated with no intermediate heat storage uid, and thus enhancing the overallthermal efficiency of the system (Kraemer et al. (2008) [17]).The result of a solarthermal steam generation process would be an intermittent steaminjection rate, with higher injection rates in comparison to the traditional continuousinjection process (assumption of same total energy input). Assuming the reservoirformation acts as a large thermal accumulator, work on the economical implications of cyclic steam injection in the SAGD process by Birrel et al. [3] suggests, that theeffect of daily and seasonal variations on the average bitumen production is negligible.Based on this assumption, a feasibility assessment of a solarthermal driven SAGDprocess from both, a thermodynamic and economical point of view, is presented inKraemer et al. [17].

1.4 Scope of this Work

It needs to be understood, that the work presented here does not describe the inu-ence of an intermittent steam injection process on the oil production. It is in fact ahydrodynamical study, analysing and explaining the inuence of a cyclic steam injec-tion process on the steam chamber growth and the temperature distribution in thegeological formation. The component oil is thus neglected in this work.

The fundamentals of the applied model, which are specied in chapter 2, determinethe model, which is used to describe the ow and transport processes for the watersteam system. The system properties, which complement the conceptual model, arecharacterized in chapter 3.As specied in chapter 4, the non-isothermal water steam model is used to simulate acontinuous and, based on the assumption of a solarthermal steam generation, a cyclicsteam injection process into water saturated porous media. The steam chamber andtemperature front propagation within the reservoir is analysed for both injection rou-tines. To understand the consequences of a cyclic injection routine, its inuence on theow and transport patterns is compared to a continuous injection process.A summary of the topic, results of this work and an outlook for future work related tothis topic is presented in chapter 5.


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Chapter 2

Fundamentals of the Applied Model

2.1 Essential Terms

2.1.1 Phases and Components

Phases are homogeneous, immiscible matter, separated by a sharp interface(e.g. Helmig (1997) [12]). A phase is characterized by continuous uid properties.Thus, it is possible for several liquid phases to exist in a porous medium, while onlyone gaseous phase can be present. The term phase is furthermore used to describe asubstances state of aggregation (see section 2.1.4), such as gaseous, liquid and solid.

This is, however, not a sufficient enough description within the context of a multi-phasesystem, as several liquid phases such as water and oil may exist within the pores.The term components describes the constituents of a phase. These can be regarded asthe sole chemical substances, which inuence the physical properties of a phase.

2.1.2 Primary Variables

Primary variables are parameters dening physical properties of a system, and are usedto describe the degrees of freedom of a thermodynamical system. They are needed fora denite solution of the system of equations, which describes the applied model. The

choice of primary variables is not explicit. Hence, a different set of primary variablesmay be chosen for the same system.The non-isothermal water steam model discussed in this work, is described by twoequations (one mass and one energy balance). The two unknowns pressure p and tem-perature T or pressure p(T ) and water saturation S w (see equation 2.11 and 2.12) areused as primary variables (see also table 2.1).It is usually dinstinguished between extensive and intensive variables. Extensive vari-ables depend on the size of a system. Examples are the volume V or the mass m. Incontrast, intensive variables are independent of the systems size, such as the temper-ature and the pressure.

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2.1 Essential Terms 7

2.1.3 Secondary Variables

Secondary variables can be calculated from the primary variables, using constitutiverelationships and equations of state (e.g. Ochs (2006) [20]). These secondary pa-rameters depend on the primary variables and help to describe the considered systemin detail. Examples are the density , the viscosity , the capillary pressure pc, therelative permeability kr , the specic enthalpy h, and the heat conductivity .

2.1.4 State of Aggregation and Phase Change

As mentioned before, a substance such as water may occur in different states of aggre-gation. These phase states may be solid, liquid and gaseous. The components transfer

between different phases, due to the change of the thermodynamic state (e.g. by vapor-ization, condensation), is called phase transition (e.g. Helmig (1997) [12]). A phasediagram shows a substances state of aggregation as a function of state variables. Sucha phase diagram is given in gure 2.1, describing the phase state of water, dependingon the primary variables pressure and temperature.

pressure p [bar]

critical point

0.00612

1

221

triple point

0

solid

gaseous

liquid

100 374.25Temperature T [C]

Figure 2.1: Schematic phase diagram of water for temperature and pressure.

The number of existing phases in a multi-phase system is not necessarily constant.Displacement processes or mass transfer processes between the phases may result in aphase state change from a single-phase to a multiphase system or vice versa ( Helmig(1997) [12]). Such a process is called a phase change and may be accompanied by aswitch of the primary variables that are necessary to describe the system.


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2.2 Flow and Transport Processes 8

In the non-isothermal two-phase one-component model (2p1cni) used in this work,water is the only component. Consequently, the total amount of primary variables

sufficient to describe the state of the system is two. Depending on the present phaseswithin the system, the used set of primary variables consists either of gas phase pressure pg and water saturation S w (two-phase system), or gas phase pressure pg and temper-ature T (single-phase system) ( Ochs (2006) [20]). This primary variable switch isshown in table 2.1.

phase state present phases primary variables1 water, gas pg(T), S w2 water pw , T3 gas pg, T

Table 2.1: Phase states and corresponding set of primary variables for the 2p1cnimodel.

2.2 Flow and Transport Processes

A steam injection process into water saturated porous media may be described by

a non-isothermal two-phase one-component system. Therefore, a description of thevarious ow, transport and energetic processes, that have to be considered, is given inthe following section.

2.2.1 Advection and Buoyancy

The process of advection is associated with the movement of a quantity within thevector eld of a uid. An example in porous media would be the transport of a compo-nents concentration according to the uids velocity eld. Darcys Law, emerging froma series of experiments in a permeameter column, describes the slow linear single-phase

ow through porous media on a macroscopic scale ( Darcy (1856) [8]). It states:

v = K f grad (h). (2.1)

Here, v is the Darcy velocity, h is the piezometric head and K f is the hydraulic con-ductivity of water with

K = K f g, (2.2)

where K is the absolute permeability, the dynamic uid viscosity, the uids densityand g the gravitational constant.Darcys Law is valid for seeping ow with a Reynolds number (Re) smaller than 1. The


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dimensionless Reynolds number in a porous medium describes the ratio of inertial toviscous forces and is given by:

Re = dv

. (2.3)

Here, d is the mean pore diameter, v is the typical ow velocity and the kinematicviscosity of the uid.

To determine the advective ux within a multiphase system, Darcys Law hasto be extended for various phases . The consideration of the phase density , thephase pressure p , the relative permeability kr , of the phase, the phases dynamicviscosity , the intrinsic permeability K and the gravitational vector g with theconstant g, yields the velocity of the individual phase v :

v = kr,

K grad ( p ) g . (2.4)

The so-called Darcy velocity v of the phase refers to a ow through the total cross-sectional area of the porous media. To calculate the actual particle speed, the porosity of the medium needs to be considered. This yields the seepage velocity v a , of thephase :

v a , =v

. (2.5)

The extended version of Darcys Law for multiphase systems, describes uid ow pro-cesses due to viscous (advection) and buoyant forces.Buoyancy ow is caused by density differences within one phase (e.g. cold and hotwater) or between different phases (e.g. water and steam). It acts in the opposite di-rection of gravitational forces.Consequently, a balance of forces in vertical direction for a body with density b ,submerged in a uid with density f yields:

F res = buoyant forces gravitational forces = ( b f ) gV. (2.6)

In the case of steam injection into water saturated porous media this results in abuoyant ow, driven by the high density difference between liquid water and steam. Ata pressure of 40 bar and a temperature of 250.35 C, the density of water is 798.37 kg/ m 3 ,whereas the density of fully saturated steam is 20.09 kg/ m 3 .Therefore, buoyancy driven ow is suspected to play an important role in the contextof steam injection into water saturated porous media ( Ochs (2006) [20]). Assuminga hydrostatic pressure distribution in the system ( h = pg + z = const. ), leads to thepressure gradient in z-direction:

grad ( pw) = wg. (2.7)

Combining equation 2.7 with equation 2.4 for the Darcy velocity, results in the steamvelocity:

v s = kr,ss Kg ( w s) . (2.8)


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Equation 2.8 describes the buoyant ow of steam, in the opposite direction of the grav-itational vector, driven by the density difference between steam and liquid water. The

comparison of equation 2.8 with equation 2.4 clearly indicates the difference betweenadvection and buoyancy.

2.2.2 Diffusion

The transport process of diffusion occurs continuously, independent of the uids move-ment. It originates from arbitrary Brownian movement of the molecules and corre-sponds to the second law of thermodynamics which states, that the state of order of any closed system decreases until equilibrium is reached (e.g. Ochs (2006) [20]).As the system described only consists of the one component water, the process of diffusion is neglected. This can be justied, as the inuence of diffusion within one-component systems is very small in comparison to multi-component systems ( Coreyet al (2009) [7]).

2.2.3 Mass Transfer Processes

The multiphase one-component model described in this work, contains the two phaseswater and steam. Both consist of the one present component water. A mass transportbetween the phases, hence only occurs in terms of evaporation and condensation (seegure 2.2).

2.2.4 Thermal Convection

The transport of thermal energy through bulk motion of a uid is called thermal orheat convection. Depending on its origin, it is distinguished between free and forcedconvection. Forced convection is characterized by a uid motion, that is induced byexternal forces, such as during steam injection. Free or natural convection occurswhen temperature gradients, and respectively density differences, cause recirculationprocesses within the uid.For most thermal recovery applications, forced convection is the dominant form of heat transfer ( Hong (1994) [13]). In porous media, the rate of heat transport throughconvection is a function of the uid-ow rate and the thermal properties of the uidand the reservoir. This type of thermal convection is described through an energybalance on the owing uid, as the specic phase enthalpy is considered within theadvection term (see equation 2.12).

2.2.5 Thermal Conduction

Another important energy transfer process is thermal or heat conduction. Thermalconduction is a diffusive process, caused by a temperature gradient. It is the result of


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2.3 Mathematical Formulations 11

an energy transfer from high energetic molecules to less energetic ones. During steaminjection into a reservoir, thermal conduction is responsible for energy losses to the

overburden and the underlying strata ( Hong (1994) [13]). It can also be an importantheat transfer process within the reservoir, when uid ow velocities are small.

According to Fouriers Law, one-dimensional stationary conductive heat transferis described by the following equation:

q cond = i grad (T ). (2.9)

The energy ux related to an area is given by q cond , with the unit J/ s m2 . The thermalconductivity i, is the ability of the material i to transmit heat. It is not only a material

property, but also depends on the geometry and composition of the system described,as discussed in detail later.

2.3 Mathematical Formulations

In order to specify the depicted non-isothermal two-phase one-component system math-ematically, the conservation laws of mass and energy are needed. In uid dynamics,the Reynolds Transport Theorem (RTT) is used to formulate these basic conservationlaws (see equation 2.10). It states that the total rate of change of an extensive systemproperty E equals the rate of change of its corresponding intensive quantity e within axed control volume (CV), plus the net rate change across its boundaries (e.g. Ochs(2006) [20]).

dE dt

= ( e)t d + ( e)(v n )d. (2.10)Using the RTT and considering an innitesimal small CV, a differential formulationfor the conservation of a quantity E (e.g. mass) can be derived. A detailled descriptionof this process is given in Ochs (2006) [20]. The additional consideration of the porespace and the phase saturation of the porous multiphase system, yields the balanceequations for each phase.

For the solution of the multiphase problem, the multiphase extension of DarcysLaw, as given in equation 2.4, is usually used to calculate the phase velocity v (e.g. Helmig (1997) [12]).

2.3.1 Mass Balance Equation

Based on the conservation law of mass, which states t + div( v ) = 0, the balanceof mass is formulated for each component, inserting equation 2.4 for the velocity v .Consequently, any mass transfer from one phase to the other can be accounted for

(e.g. Class (2001) [6]).


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2.3 Mathematical Formulations 12

In case of the depicted two-phase one-component model, the formulation of one massbalance equation, for the one component water is necessary (e.g. Ochs (2006) [20]):

( S )

t

accumulation term

div kr ,

K grad ( p ) g

advection term q c

source/sink term= 0 , {water , steam } (2.11)

with the constant porosity , phase density , phase saturation S , relative perme-ability kr , of phase , dynamic viscosity of phase , the intrinsic permeability Kand the phase pressure p .

2.3.2 Energy Balance Equation

The rst law of thermodynamics states, that in a physical process, energy can not belost but only be transferred from one state to another. In order to describe the energytransfer in a multiphase system, the balance of energy is formulated, as it is done withmass (e.g. Class (2001) [6]).The change of a systems internal energy U equals the change of heat Q acrossthe system boundaries plus the work W v done by change in volume. Assuming localthermodynamic equilibrium, only one single energy balance equation is necessary todescribe the system (e.g. Ochs (2006) [20]).

( S u )

t

accumulation term uid

+ (1 ) ( sgcsgT )

t

accumulation term solid

div pm grad (T )

conduction term

div hkr ,

K grad ( p ) g

convection term q h

source/sink term= 0 {water , steam } (2.12)


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2.4 The 2p1cni Model 13

In equation 2.12, radiation is neglected, u is the specic internal energy of phase, h is the specic enthalpy of phase , sg and csg are the soil grain den-

sity and the specic heat capacity of the solid medium, pm is the equivalent heatconductivity of the system (porous medium including uids), and T is the temperature.

To solve the partial differential balance equations, the following closure relationshipsare necessary:

The sum of the phase saturations adds up to one:

S = 1.

The sum of the pressure of the wetting phase and the capillary pressure equalsthe pressure of the non-wetting phase: pw + pc = pg.

2.4 The 2p1cni Model

For the process of steam injection into the water saturated subsurface, a heterogeneoussystem, containing the two phases liquid water (water phase) and gaseous water (steamphase), is assumed. Hence, a non-isothermal two-phase one-component model (2p1cni),with each phase itself consisting of the one component water, is described in this work.The occuring mass transfer processes for the system are shown in gure 2.2.

waterCondensation

Evaporation

water

water phase (liquid water) steam phase (gaseous water)

Figure 2.2: Mass transfer processes in the two-phase one-component (2p1cni) modelfor the two phases water and steam.

2.5 MUFTE-UG: The Numerical Simulator

In this work, MUFTE-UG is used as the numerical simulator. It stands for MultiphaseFlow Transport and Energy Model on Unstructured Grids. As shown in gure 2.3,it consists of two parts. The MUFTE part of the simulator describes the physicalproblems and the discretisation method of the system ( Helmig et al. (1998) [11]).The UG part with its multigrid data structures, grid renement techniques and thenumerical solvers deals with the partial differential equations ( Bastian et al. (1997)[1]). MUFTE-UG in this work, solves the problem of multi-phase one-component non-

isothermal ow processes in a geological formation.


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2.5 MUFTE-UG: The Numerical Simulator 14

(Helmig et. al 1997, 1998)(Bastian et. al 1997, 1998)

(S. Lang, K. Birken,K. Johannsen et. al 1997)

- multigrid data structures- local grid refinement- solvers (multigrid, etc)

- parallelization- r,h,p-adaptive methods

- graphic representation- user interface

UG (Wittum, Bastian)

Interdisciplinary Center for Scientific Computing (IWR)

- problem description

- discretization methods- physical-mathematical models

- physical interpretation- refinement criteria- numerical schemes

- constitutive relationships

MUFTE (Helmig)

Institute for Hydraulic Engineering (IWS)

Figure 2.3: The numerical simulator MUFTE-UG


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Chapter 3

System Properties

3.1 Physical Properties of Water and Steam

3.1.1 Density and Viscosity

The molar density of water is implemented after Panday et al. (1995) [21] and isa function of temperature and pressure. While the density of the liquid water phaseis assumed to remain constant with changing temperature, the density of the gaseouswater phase (steam) decreases with increasing temperature. Increasing pressure pw,respectively pg, results in an increase of density for both phases, water and steam.

The dynamic viscosity of water is only determined by the temperature. Unlike theviscosity of the liquid water phase, which decreases with increasing temperature, thatof the steam phase increases (e.g. Helmig (1997) [12]).

3.1.2 Water Saturation Pressure

The water saturation pressure, or vapor pressure pw,sat is a function of temperature,and is implemented in the model after the IFC report ( IFC (1967) [15]). In terms of a closed system, it describes the pressure of the gaseoues phase (steam) in equilibriumwith its liquid phase (water) at a certain temperature. It is the pressure, at which the

amount of condensing water molecules equals that of the evaporating ones (e.g. Faer-ber (1997) [10]).Figure 3.1 shows the water saturation pressure as a function of temperature, as imple-mented in the model. The water saturation pressure-temperature relationship is usedto determine the occurence of a second phase within the model, accompanied by aprimary variable switch (for details see section 2.1.4).For gas being the only phase present, and pg pw,sat , the water phase appears. Forwater being the only phase present, and pg pw,sat , the gas phase appears.

15


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3.1 Physical Properties of Water and Steam 16

Figure 3.1: Water saturation pressure depending on temperature. As implemented inthe model.

3.1.3 Enthalpy

The amount of energy within a system capable of doing mechanical work, is calledenthalpy H . It is dened as the sum of the systems internal energy U and the volumechanging work pV (e.g. Helmig (1997) [12]). The division by the systems mass yieldsthe specic enthalpy: h = u + p .The specic enthalpy of water is implemented after IFC (1967) [ 15]. While the spe-cic enthalpy of gaseous water (steam) strongly depends on the volume changing work,the denition of the specic enthalpy of liquid water often neglects this correlation, asa result of the low compressibility of water: h u.Figure 3.2 shows the specic enthalpy of liquid water depending on temperature (con-stant pressure) and pressure (constant temperature). It is observed, that the specicenthalpy of water is more dependent on temperature than on pressure.


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(a) h -T relation of liquid water at constant p

(b) h - p relation of liquid water at constant T

Figure 3.2: Specic enthalpy of liquid water as a function of temperature at constantpressure, and as a function of pressure at constant temperature. As implemented inthe model.


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Dening the specic enthalpy of steam, it is theoretically distinguished between wetsteam, saturated steam and overheated steam. While wet and saturated steam are

determined through the parameters temperature T ( p) and steam quality x, the specicenthalpy of overheated steam is a function of T and p. The steam quality parameterx is a mass ratio, dened as: x = m gaseousm liquid + m gaseous .Steam at boiling temperature, consisting of gaseous and liquid water (0 .0 < x < 1.0)is called wet steam. Steam at boiling temperature, containing 100% gaseous water(x = 1 .0) is called saturated steam. Steam that consists of 100 % gaseous water witha temperature above boiling point is called overheated steam.

For the given process of steam injection into saturated porous media, it is highquality wet steam occupying the pore space besides water. Overheated steamwould require higher temperatures. The specic enthalpy of wet steam hwet iscalculated, using hw,sat of saturated water and hg,sat of saturated steam at boilingtemperature, and combining it with the steam quality x: hwet = (1 x) hw,sat + x hg,sat .

The specic enthalpy of saturated steam as a function of temperature T , as im-plemented in the model, is shown in gure 3.3. For more details see the Mollierh,s-Diagram ( Langeheinecke et al. (2003) [18]).

Figure 3.3: Specic enthalpy of saturated steam ( x = 1.0) as a function of temperature.As implemented in the model.


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3.2 Physical Properties of the Porous Medium 19

Figure 3.3 indicates, that a pressure, respectively temperature increase only results inan increased specic enthalpy for saturated steam up to a certain point. With pres-

sure, respectively temperature exceeding this point, a decrease in enthalpy is observed.This is depicted schematically in gure 3.4. It is pointed out here, that the pressure,respectively temperature to be exceeded for the enthalpy decrease depends on thesteam quality. With lower steam quality, a higher pressure, respectively temperatureis needed to cause the decline of the specic enthalpy. See the Mollier h,s-Diagram(Langeheinecke et al. (2003) [18]) for more details.

pressure p [bar]

221critical point

saturated steamwet steam

saturated water

100C

10

50

1

spec. enthalpy h [kJ/kg]

Figure 3.4: Schematic plot of the specic enthalpy of water as a function of pressure.

3.2 Physical Properties of the Porous Medium

3.2.1 Heat Capacity

The specic heat capacity of a material, is a measure of how much thermal energymust be added to heat up 1 kg of the material by one Kelvin. The unit is kJ/ kg K . Theheat capacity thus describes a substances ability to store heat. A body determined bya high specic heat capacity stores heat well. In thermodynamics, it is distinguishedbetween the specic heat capacity cp at constant pressure, and cv at constant volume.In terms of equation 2.12, the energy content of the uid phase is calculated usingthe specic internal energy u. The energy storage term of the solid phase however, iscalculated using the specic heat capacity of the soil grain material csg. As cp cv forsolid substances, a constant value, independent of pressure and temperature is used forcsg.


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3.3 Composite Properties 20

3.2.2 Porosity

The porosity is dened as the ratio between the pore volume and the total bulkvolume of the porous media: = V poresV total .It is a measure of the volume not lled with soil grains but uids, such as liquid waterand steam. It is furthermore distinguished between porosity and effective porosity,which describes the pore space accessible for a uid entering the porous medium.

3.2.3 Absolute Permeability

The absolute or intrinsic permeability K of a porous medium describes the resistancethat the material opposes to uid ow. The unit is m 2 or D, with 1D 10 12 m2. As

given in equation 2.2, it is only dependent on the properties of the porous medium,because it is correlated to the hydraulic conductivity K f by including the uids vis-cosity and density. For the computation of multiphase ow as shown in equation 2.11,the hydraulic conductivity is extended with the relative permeability kr , of phase (e.g. Helmig (1997) [12]):

K f = K kr , g

. (3.1)

While the intrinsic permeability K is solely a property of the soil grains, the relativepermeability is dependent on the uid and the porous medium properties (for detailssee section 3.3.1).

3.3 Composite Properties

Along the uid and soil properties, additional parameters combining uid and porousmedium properties are needed to describe the multiphase system. As these parameterscan neither be assigned solely to the porous medium, nor to the uid occupying thepore space, they are called composite properties here. They result from the interactionbetween the uid and the porous medium and are no conventional system properties.Composite properties reect the conceptual model, that is used to reproduce the systembehavior ( Ochs (2006) [20]).

3.3.1 Relative Permeability

The relative permeability is a dimensionless number depending on the tortuosity of the porous media, pore space geometry and phase saturation. It is used to scale theintrinsic permeability (see equation 3.1), with the product of K and kr , being calledthe effective permeability of phase (e.g. Helmig (1997) [12]). The introduction of kr , accounts for the fact, that in a multi-phase system, the presence of one phase in aporous medium inuences the ow of the other phase.In the model, the relative permeability-saturation relations of the two phases water and


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steam are implemented after Van Genuchten , as shown in gure 3.5. With waterrepresenting the wetting phase and steam being the non-wetting phase, the relative

permeabilities are calculated as follows:

kr,w = S e[1 (1 S 1

m

e )m ]2

kr,n = (1 S e)13 [1 S

1m

e ]2m . (3.2)

The parameter m results from the denition of the effective water saturation S e as afunction of the capillary pressure pc after Van Genuchten :

S e( pc) =S w S w,r1 S w,r

= [1 + ( pc)n ]m , (3.3)

with the water saturation S w, the residual water saturation S w,r , and m, n and asthe three Van Genuchten parameters (see also section 3.3.2).

Figure 3.5: Relative permeability of the wetting phase (water) and of the non-wettingphase (steam) as a function of the water saturation after Van Genuchten . As im-plemented in the model.

3.3.2 Capillary Pressure

Considering two immiscible uid phases in a state of equilibrium, a pressure differenceat the interface between the wetting and non-wetting phase occurs. It originates from


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molecular cohesion effects, which cause a surface tension at the interface. The resultingpressure difference depends on the pore space geometry and the phase saturation, and

is called capillary pressure pc. In the model, it is calculated using the approach of VanGenuchten (e.g. Class (2001) [6]), as depicted in gure 3.6.

pc =1

(S 1

m

e 1)1n . (3.4)

With m = 1 1n , the two Van Genuchten paramaters and n emerge. The pa-rameter describes the entry behaviour of the non-wetting phase, and the parametern describes the materials uniformity, with a low value for n being associated with anon-uniform material. The effective saturation S e is dened as given in equation 3.3.

Figure 3.6: Capillary pressure as a function of the water saturation after the approachof Van Genuchten , with set to 0.0028 1/ Pa and n set to 4.0 . As implemented inthe model.

3.3.3 Heat Conductivity

The heat conductivity is a parameter combining uid and soil grain properties withrespect to equation 2.12. It describes the averaged ability of the uid lled porousmedia to conduct heat. It is implemented after the approach of Somerton , as shownin equation 3.5 (e.g. Class (2001) [6]).

pm = Sw=0pm + S w(Sw=1pm Sw=0pm ) (3.5)


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In this case, the denition of the effective heat conductivity Sw=1pm for the fully watersaturated and Sw=0pm for the fully steam saturated porous media is necessary. In terms

of steam, saturated steam with a steam quality of x = 1.0 is assumed. To obtain theneeded effective heat conductivities, an average of the heat conductivity sg for thesoil grains and f for the uids (Sw =1pm for water and Sw =0pm for steam) needs to bedetermined. Here, the conservative method of the geometric mean is used:

pm = (1 )

sg f . (3.6)

With sg assumed to be 2.5 W/ m K (Quartz), the value of Sw =1f (liquid water) being0.621 W/ m K and that of Sw =0f (steam) being 0.051 W/ m K . This yields a pm as afunction of the water saturation calculated after equation 3.5, as shown in gure 3.7.

Figure 3.7: Heat conductivity as a function of water saturation. Approach of Somer-ton , using the method of the geometric mean to calculate the effective heat conduc-tivities for the fully water, and fully steam saturated porous media. As implementedin the model.


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Chapter 4

Simulations

Using a non-isothermal two-phase one-component model, described in Ochs (2006)[20], steam injection into a water saturated system is simulated. The inuence of acyclic injection routine on the steam chamber growth and the temperature distributionwithin the porous medium is analysed, and compared to the process of a continuousinjection.

To determine the inuence of the system properties on the simulation results, asensitivity study is carried out. Therefor, a set of porous medium and compositeproperties, assumed to be most relevant for the depicted process, is chosen. Each

parameter is then seperately examined to determine its inuence on the ow processesin the geological formation.

4.1 The Model

4.1.1 Denition of the Model Domain

The development of the steam and temperature front along the horizontal injectionwell, such as described in section 1.2, is assumed to be constant. Therefore, the steamand temperature front development is depicted using a two-dimensional model, thatrepresents a vertical y-z slice through the inner reservoir area, with a thickness in x-direction of 1 m (see gure 1.1).This results in the model domain shown in gure 4.1. The vertical model extension of 40 m represents the full assumed reservoir height of 35 m, plus a 5 m thick, low perme-able overburden on top. The horizontal extension is chosen to include an equal areato the left and right of the well pair, and is set to 120 m. This is, because the distancebetween two well pairs of 100 m leads to the assumption, that at 50 m to the left andright of the injection well, the steam front would link up with that of a neighbouringwell with the same injection routine.Only the steam injection well (upper well of a well pair) is implemented in the model.

24


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4.1 The Model 25

It is located 8 m above the reservoir bottom, in the middle of the reservoir at x = 60 m(see gure 4.1).

The grid discretization of the model domain is set to 0.5 m, resulting in elements of 0.25m2. This allows for a satisfying computation speed, while providing reliable sim-ulation results, and is the conclusion of simulations with different grid discretizations,to analyse the grid sensitivity.To retrieve detailed information on the system properties for certain areas within themodel domain, seven data nodes are implemented at various locations in the grid (seegure 4.2 and table 4.1).

35m

120m

Sw(initial) = 1.0

400m belowsurface

hydrostatic pressure

distribution

hydrostatic pressure

distribution

left boundary:

injection well 8m above bottom boundary

reservoir

low permeable overburden5mp(y=360) = 37bar

p(y=400m) = 41bar

right boundary:

T (initial) and T (initial) and

y

x

top boundary: constant temperature and pressure

bottom boundary: noflow conditions

T(initial) = 10C

Figure 4.1: The model domain and its initial and boundary conditions as used for thesimulation of continuous and cyclic steam injection.

Figure 4.2: The model domain consisting of the permeable reservoir and the low per-meable overburden. Locations of the data nodes implemented to retrieve informationon the system properties, as given in table 4.1.


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4.1 The Model 26

designation x [m] y [m]Node1 60.0 1.0Node2 60.0 8.0Node3 60.0 20.0Node4 60.0 34.5Node5 30.0 34.5Node6 90.0 34.5Node7 60.0 38.0

Table 4.1: Node names and coordinates of the seven nodes implemented in the modelgrid.

4.1.2 Initial and Boundary Conditions

A reservoir depth of 400 m at the reservoir bottom is assumed. This determines the ini-tial reservoir temperature and the pressure distribution (see gure 4.1), and is referringto conditions found in the Canadian oil sand elds.

The domain is assumed to be initially fully water saturated: S w = 1 .0.

The initial reservoir pressure is given by a vertical hydrostatic pressure distribu-tion, using p = patm + d w g. With patm assumed to be 1.013 bar and d as thetotal depth in meter.

The initial temperature T initial is assumed to be 10 C. A vertical temperaturedistribution, according to the geothermal temperature gradient (estimated to be0.03 C/ m), is neglected because of the reservoir being only 35 m in height.

The bottom boundary of the domain is determined by a no-ow condition. Theright, left and upper boundary of the domain is characterized by the temperatureand pressure of the initial situation. The denition of the upper boundary con-dition in combination with the very low permeable overburden, accounts for thefact, that while thermal energy can be lost from the reservoir into the overburdenby conduction, no relevant ux of water or steam into the overburden is possible.

4.1.3 System Property Values

The system properties described in detail in chapter 3 are either dened by a constantvalue, or as a function of the primary variables, often including empirically derivedparameters. Only those properties, respectively parameters, associated with a constantvalue are given in table 4.2. For details on the remaining parameters see chapter 3.


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4.1 The Model 27

The porosity ob and absolute permeability K ob are properties of the overburden andaccount for the difference in permeability between the reservoir and overburden.

The values of the porosity and permeability of the reservoir are chosen to be ratherlow in comparison to observed eld data from Canadian oil sand elds. This is, toaccount for the fact, that the presence of an oil phase in reality leads to a decreaseof the relative permeability of water. This procedure is random, but is considered tobe a rst good approach to the problem. Furthermore, the sensitivity of the absolutepermeability is discussed in detail in section 4.5.1.

parameter value unitspecic heat capacity csg 850 J/ kg K

porosity 0.1 -porosity ob 0.05 -absolute permeability K 40 mDabsolute permeability K ob 0.0001 mDsoil grain density sg 2650 kg/ m 3Van Genuchten parameter 0.0028 1/ PaVan Genuchten parameter n 4 -residual saturation S w,r of water and S g,r of steam 0.0 -

Table 4.2: Values of the system properties.

4.1.4 Conditions at the Injection Well

The injection of steam into the model domain is realised by using a source term. Massand energy is injected at Node2 (see gure 4.2), and characterized by a mole and en-thalpy ux ( mol/ s and J/ s).To analyse the inuence of a solarthermal steam generation, respectively cyclic steaminjection, on the temperature and steam development in the subsurface, a cyclic injec-

tion process is compared to a continuous one. Two injection approaches, determinedby different injection conditions, are thus used.On average, a daily injection of 0.3 t per meter well length (for details see chapter 1),and a steam quality of approximately 90 % ( x = 0 .9) is assumed for both injectionroutines.For the continuous injection approach, this simply results in a mass and enthalpy uxat the injection node of:

12.5 kg/ hr

32875kJ/ hr .


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4.1 The Model 28

For the cyclic injection approach based on solarthermal steam generation, the locallyavailable hours of direct solar radiation, which vary with the seasons, determine the

actual injection rate. For this work, statistical climate data for Edmonton in Alberta,Canada has been used ( Environment Canada (2009) [9]). The data suggests ayearly average of approximately 6.3 hrs/ d of bright sunshine. Based on an average dailyinjection of 0.3 t/ m, respectively 109.5 t/ m per year, the mass and enthalpy ux for thecyclic injection process is calculated to be approximately:

47.6 kg/ hr

125238.1kJ/ hr .

A combination of two injection cycles determines the actual injection period for thecyclic injection process, as a function of time. One describes the different seasons forthe given location of Edmonton (see gure 4.3(a) ). The other represents the actualdaily injection window depending on the season (see gure 4.3(b) ). As the possibledaily injection period varies with the seasons, so does the daily injected amount of energy.To guarantee the same energy input after one full seasonal cycle (12 months) for cyclicinjection as for continuous injection, the actual injection rates have been calculated asdescribed above. It is important to notice, that in case of cyclic injection, it is not theactual injection rate changing with the seasons, but the duration of injection.


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4.1 The Model 29

(a) Seasonal cycle

(b) Daily cycle

Figure 4.3: Seasonal distribution and daily injection window at the location of Edmon-ton in Alberta, Canada, described by a sinusoidal function. Spring is represented bythe areas marked green, summer is marked orange, autumn is brown and winter is light

blue. The actual daily injection time is 3 hrs in winter, 6 hrs in spring and autumn,and 10 hrs in summer.


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4.2 Continuous Steam Injection 30

4.2 Continuous Steam Injection

As described in section 1.2, the application of steam assisted gravity drainage (SAGD)for enhanced oil recovery purposes is based on the injection of high-pressure, high-quality steam. The steam is usually produced by fossil fuel burning steam generators,using gas, oil or LPG (liquied petroleum gas).Such a steam generation process delivers a continuous steam injection rate, in case thefossil fuel and water supply is sufficient.

4.2.1 The Injection Well

A constant mass and enthalpy ux is given at the injection well (see section 4.1.4).

Figure 4.4 shows a plot of the temperature, pressure and steam saturation versus timeat the injection node. It indicates, how a high injection pressure during the start-upphase decreases over time, followed by a similar development of the temperature. Thesteam saturation at the injection node is constant over the whole time.

Figure 4.4: Pressure, temperature and steam saturation at Node2 (injection node atx = 60m and y = 8 m) for a continuous injection process.


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4.2.2 Steam Chamber and Temperature Development

The steam chamber growth and the temperature front development from the injec-tion well are analysed within the model domain. Therefore, steam saturation andtemperature are depicted for various time steps after the start of injection. Figure 4.5and 4.6 show S g, respectively the steam chamber growth, and T for the process of acontinuous injection after 3, 6, 9, 27, 30, 33, 51, 54, and 57 months.Buoyant forces cause the steam to rise upwards from the injection well. Once thelow permeable overburden (indicated by the black horizontal line) is reached, steamaccumulates underneath it and the steam chamber growth is dominated by a horizontalspreading underneath the overburden. To a smaller degree, this horizontal growthis also observed in the middle of the steam chamber. The distribution of the steam

saturation within the steam chamber is rather homogeneous, with a higher steamsaturation around the injection well.For the given injection rate, the development of the temperature front is mainly drivenby convection, and hence, basically follows the steam chamber growth. However,due to conduction, a loss of thermal energy from the reservoir into the overburden isobserved.Figure 4.7 shows the development of S g and T at Node4, directly underneath theoverburden at x = 60 m and y = 34 .5 m. A constant steam saturation and temperatureis observed, with the steam accumulating underneath the low permeable overburden.

A continuous injection rate results in a continuous growth of a steam chamber,characterized by a homogeneous saturation distribution within the chamber, and asimilar development of the temperature front.


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F i g u r e 4 . 5 : S t e a m s a t u r a t i o n S

g , r

e p r e s e n t i n g t h e s t e a m c h a m b e r g r o w t h f o r a c o n t i n u o u s i n j e c t i o n p r o c e s s a t a t i m e o f 3 , 6 ,

9 , 2 7

, 3 0 , 3 3

, 5 1 , 5 4

, a n d 5 7 m o n t h s a f t e r t h e s t a r t o f i n j e c t i o n .


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F i g u r e 4 . 6 : D i s t r i b u t i o n o f t e m p e r a t u r e T f o r a c o n t i n u o u s i n j e c t i o n p r o c e s s a t a t i m e o f 3 , 6 , 9 , 2 7

, 3 0 , 3 3

, 5 1 , 5 4 , a n d 5 7

m o n t h s a f t e r t h e s t a r t o f i n j e c t i o n .


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Figure 4.7: Temperature and steam saturation at Node4, directly underneath the over-burden ( x = 60m and y = 34 .5 m) for a continuous injection process.


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4.3 Cyclic Steam Injection 35

4.3 Cyclic Steam Injection

The objective of the hydrodynamical study of cyclic steam injection into the subsurfaceis the idea, to use solarthermal steam generation plants instead of fossil fuel burningsteam generators. The solarthermal plant would use direct solar radiation to generatesteam, and thus delivering a cyclic steam injection rate, depending on the daily availablehours of direct sunlight (see section 1.3 and 4.1.4).

4.3.1 The Injection Well

The injection rate determines the injection pressure, and consequently the steamtemperature. A cyclic injection routine, due to a solarthermal steam generation

process, thus results in a daily change between an injection and a non-injectionwindow, and the change of the daily injection duration with the seasons (see g-ure 4.3(b) and 4.3(a) ). This injection routine determines the pressure, temperatureand saturation uctuations obtained at the injection well.Figure 4.8 depicts those oscillations at the injection node for one full seasonal cycle(one year) for p, T and S g in the fth year of injection. The broad spectrum of thedata is the result of the daily shift between injection and non-injection phase. In themodel, the actual injection rate is the same for all seasons. The daily injection windowhowever, changes with the seasons, thus does the daily amount of injected steam (seegure 4.3(b) ).It needs to be noticed, that in reality, the actual steam production and injection ratemay vary according to the daily and seasonal variation of the energy of the solarradiation (assumption of sufficient water supply).

As shown in gure 4.8, the change from a short injection window to a long one(e.g. spring to summer), results in more steam being injected into the steam chamber,forcing it to grow faster. This causes a sudden pressure increase, which is reduced witha growing steam chamber. The pressure uctuations are followed by the temperatureoscillations, according to the water saturation pressure-temperature relation.For a shift from a long to a short injection period (e.g. summer to autumn), a suddenpressure decrease, followed by a temperature decline, is observed. This is becausean insufficient amount of steam is injected to obtain the expansion of the steamchamber, causing steam to condense at the front, resulting in a near collapse of thechamber. As water is more dense than steam, less pore volume is needed, resultingin a pressure decline. With a then small, but slowly growing steam chamber, thepressure rises again. The maximum pressure during injection, to which the injectionpressure generally converges, at the given injection rate, is approximately 44 bar.The steam saturation at the injection well basically uctuates within a given range,according to the daily injection cycle, disregarding the change of seasons. An exceptionis observed during the low-injection months of winter (see gure 4.8(c)). This is,


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because the steam chamber diminishes as a consequence of the short injection window,resulting in low steam saturations.

In the model, the steam injection is realised by dening a constant mass andenthalpy ux. Hence, in the case of a cyclic injection process, the described injectionpressure uctuations make it impossible to ensure a certain steam quality at theinjection node. This is, because a change in pressure would be accompanied with achange of the specic steam enthalpy, with respect to a constant steam quality (seegure 3.4). The change of the specic enthalpy is however assumed to be minor for asteam quality of 90 %. Thus, the needed adjustment of the steam enthalpy is neglectedin the model.

4.3.2 Steam Chamber Growth

Using a cyclic injection process, the steam chamber growth varies with time, dependingon the seasons. Figure 4.9 shows the steam saturation within the model domain at 3,6, 9, 27, 30, 33, 51, 54, and 57 months after the start of injection. It indicates a faststeam front propagation during the high-injection months (summer), while during low-injection months (winter), the steam chamber is reduced in volume. This is because thedaily amount of injected steam varies with the seasons. It appears, the steam injectionduring the seasons following summer, is not enough to sustain the steam chamberextension reached during the summer months. The consequence is a hysteresis process,resulting in a circular ush and drainage of the pores.Furthermore, a rather heterogeneous steam saturation establishes within the steamchamber, with layers of different saturations being observed. This layering of differentsaturation areas is a result of the daily injection cycle, as the injected steam rises due tobuoyancy effects, leaving less saturated layers below during the non-injection period.


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F i g u r e 4 . 9 : S t e a m s a t u r a t i o n S

g ,

r e p r e s e n t i n g t h e s t e a m c h a m b e r g r o w t h f o r a c y c l i c i n j e c t i o n p r o c e s s a t a t i m e o f 3 , 6 , 9 ,

2 7 , 3

0 , 3 3

, 5 1 , 5 4

, a n d 5 7 m o n t h s a f t e r t h e s t a r t o f i n j e c t i o n . T h e l e f t c o l u m n i s d u r i n g s u m m e r , t

h e m i d d l e c o l u m n d u r i n g

a u t u m n , a n d t h e r i g h t c o l u m n d u r i n g w i n t e r .


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4.3.3 Temperature Development

In case of a cyclic injection routine, the propagation of the temperature front does notnecessarily follow the steam chamber growth. Figure 4.10 indicates a fast temperaturefront propagation during high-injection months, with large areas of high temperatures.The temperature front propagation is mainly driven by convection, and hence followsthe steam chamber growth. During low-injection months however, the temperaturefront keeps growing even though the steam chamber is reduced in size. The areas of high temperatures are much smaller and restricted to the area close to the injectionwell. The reason for this development is, that the temperature propagation is mainlydriven by conduction in these months. Hence, the thermal energy injected during high-injection months is distributed within the reservoir during low-injection months.

The inuence of conduction during low-injection months is also observed at the transi-tion between the reservoir and the low permeable overburden. In summer months, theheat lost into the overburden, is horizontally less spread than the temperature frontunderneath it. This is, because the heat loss into the overburden is a result of therather slow process of conduction, while the horizontal spreading of the temperaturefront underneath the overburden is driven by convection. In contrast, during wintermonths, the main force driving the temperature propagation is conduction, leaving thetemperature front within the overburden and underneath it equally spread.


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F i g u r e 4 . 1 0 : D i s t r i b u t i o n o f t e m

p e r a t u r e T f o r a c y c l i c i n j e c t i o n p r o c e s s a t a t i m e o f 3 , 6 , 9 , 2 7

, 3 0 , 3 3

, 5 1 , 5 4

, a n d 5 7 m o n t h s

a f t e r t h e s t a r t o f i n j e c t i o n . T h e l e f t c o l u m n i s d u r i n g s u m m e r ,

t h e m i d d l e c o l u m n d u r i n g a u t u m n , a n d t h e r i g h t c o l u m n

d u r i n g w i n t e r .


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4.4 Comparison of the two Injection Routines 41

4.4 Comparison of the two Injection Routines

To analyse the inuence of a cyclic injection on the ow processes in the subsurface,the steam chamber and temperature front propagation of the cyclic and continuoussteam injection routines are checked against each other. The two processes must becompared at a point in time, determined by the same cumulative energy input. Forthe way of injection described in section 4.1.4, this is given after one full seasonal cycle,respectively after every 12 months. The point in time for the following comparison isthus chosen to be after ve full injection cycles, respectively ve years.

4.4.1 Steam Chamber Growth

The propagation of the steam front is not found to be equal for both injectionapproaches at one point in time, which is determined by the same cumulative energyinput. This is because of the varying inuence of condensation in case of a cyclicinjection routine.Figure 4.11 shows the steam saturation for the continuous and cyclic injection processve years after the start of injection. A less horizontal steam chamber expansionunderneath the overburden, and a more heterogeneous steam saturation distributionis observed in case of the cyclic injection. The steam chamber volume at the givenpoint in time is clearly bigger in case of the continuous injection.However, it is pointed out, that with the cyclic injection process, the steam chambervolume is decreasing in the second half of a full seasonal cycle (see gure4.9). Thus,the steam chamber expansion is more similar between the two approaches earlierwithin the full injection cycle. This point in time though, would be characterized bythe cyclic cumulative energy input being higher than the continuous one. Figure 4.12shows the steam saturation for the continuous and cyclic injection routine at the endof the fth summer, at a time of 4 years and 5 months after the start of injection.For the case of a cyclic injection process, it clearly indicates, that the steam chamberexpansion at this point in time is similar to that of the continuous injection.

As the mobilisation of heavy oil is achieved with the reduction of the oils vis-cosity due to the transfer of thermal energy (see section 1.2), it is not solely the steamchamber growth inuencing the enhanced oil recovery. In fact, the temperature frontpropagation and the temperature distribution within the reservoir is assumed to be of main interest for the production of heavy oil.


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(a) Continuous injection

(b) Cyclic injection

Figure 4.11: Steam saturation S g in the model domain for a continuous and cyclicinjection process, ve years after the start of injection (after 5 full seasonal cycles).


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Figure 4.12: Steam saturation S g in the model domain for a continuous and cyclicinjection process, four years and ve months after the start of injection (after summer).


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4.4.2 Temperature Development

It is observed, that the propagation of the temperature front is quite different betweenthe two injection routines. Figure 4.13 shows the temperature for a continuous andcyclic injection process ve years after the start of injection. For the case of a cyclicinjection, a smaller horizontal expansion of the high temperature front underneath theoverburden is observed. The propagation of the temperature front is thus differentbetween the two injection routines.As the energy input is the same for both injection routines, the thermal energy must bedifferently distributed in case of the cyclic process. Therefor, the temperature distribu-tion within the formation is analysed. Figure 4.14 and gure 4.15 show the distributionof low and high temperature areas within the model domain. It is observed, that while

the low temperature front is very similar for both injection routines, as shown in g-ure 4.14(a) and 4.14(b) , the high temperature areas are differently distributed, as shownin gure 4.15(a) and 4.15(b) . In case of the continuous injection process, an increasedaccumulation of thermal energy underneath the overburden is observed, while in caseof cyclic injection, the high temperature areas are more concentrated within the cen-tral area around the injection well, which is also determined by a higher maximumtemperature.The different distribution of high temperature areas between the two injection rou-tines is shown more detailled in gure 4.16. It is observed, that while the depicted245 C front has propagated further for the continuous process, the fronts of higher

temperatures are more developed for the cyclic injection routine, and higher overalltemperatures are reached.


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Figure 4.13: Temperature T in the model domain for a continuous and cyclic injectionprocess, ve years after the start of injection (after 5 full seasonal cycles).


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Figure 4.14: Areas of low temperature T in the model domain for a continuous andcyclic injection process, ve years after the start of injection (after 5 full seasonalcycles).


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Figure 4.15: Areas of high temperature T in the model domain for a continuous andcyclic injection process, ve years after the start of injection (after 5 full seasonalcycles).


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F i g u r e 4 . 1 6 : P r o p a g a t i o n o f t h e t e m p e r a t u r e f r o n t o f 2 4 5

C , 2 4 8 C

, 2 4 9

C

, a n d 2 5 0 C f o r t h e c o n t i n u o u s a n d c y c l i c i n j e c t i o n

p r o c e s s ,

v e y e a r s a f t e r t h e s t a r t o f i n j e c t i o n ( a f t e r 5 f u l l s e a s o n a l c y c l e s ) .


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In summary, a differing temperature front propagation is observed, when comparingthe two injection routines. This is even though the cumulative energy input being the

same at the point of ve years after the start of injection.While the thermal energy is accumulated underneath the overburden in case of contin-uous injection, the heat is more concentrated within the central area of the reservoirin case of cyclic injection. This suggests, that the upward transport of thermal energydue to buoyancy is less with a cyclic injection process. A smaller inuence of buoyantforces in turn, indicates a smaller volume of steam being present.This observation may be explained by the cyclic injection routine itself. On the onehand, as a cyclic injection results in the repetitive heating of the same porous mediaarea. This is, because the thermal energy transferred to the medium during injectionperiods, is distributed throughout the formation during non-injection periods. On theother hand, it seems likely, that the oscillation of the injection pressure, originatingfrom the cyclic injection routine, inuences the propagation of the temperature front.Figure 4.17(a) depicts the injection pressure oscillations of the cyclic injection routinein comparison to the continuous injection, at the injection well. In case of a cyclicprocess, the high pressure of the injection area propagates fast into the reservoir, re-sulting in a higher pressure level within the reservoir for the main injection period (seegure 4.17(b) and 4.18). As described in section 4.1.4, a pressure increase results inan increase of the water saturation temperature according to gure 3.1. Hence, areasof high pressure are characterized by a high water saturation temperatur

solar thermal enhanced oil recovery

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