Cyclic Steam Injection into the Subsurface - … · Diplomarbeit Cyclic Steam Injection into the...

Universitat Stuttgart - Institut fur WasserbauLehrstuhl fur Hydromechanik und Hydrosystemmodellierung

Prof. Dr.-Ing. Rainer Helmig

Diplomarbeit

Cyclic Steam Injection into the Subsurface

- solarthermal steam generation for

enhanced oil recovery

Submitted by

Christoph Klinginger

Matrikelnummer 2195007

Stuttgart, 26th January 2010

Examiners: Prof. Dr.-Ing. Rainer Helmig, Dr.-Ing. Holger Class

Supervisor: Dr.-Ing. Andreas Bielinski

Contents

1 Introduction 1

1.1 Global Energy Demand and the Resource Oil . . . . . . . . . . . . . . 1

1.2 Enhanced Oil Recovery through SAGD . . . . . . . . . . . . . . . . . . 2

1.3 Solarthermal Steam Generation for SAGD . . . . . . . . . . . . . . . . 4

1.4 Scope of this Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 Fundamentals of the Applied Model 6

2.1 Essential Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.1 Phases and Components . . . . . . . . . . . . . . . . . . . . . . 6

2.1.2 Primary Variables . . . . . . . . . . . . . . . . . . . . . . . . . . 6

2.1.3 Secondary Variables . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.4 State of Aggregation and Phase Change . . . . . . . . . . . . . 7

2.2 Flow and Transport Processes . . . . . . . . . . . . . . . . . . . . . . . 8

2.2.1 Advection and Buoyancy . . . . . . . . . . . . . . . . . . . . . . 8

2.2.2 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.3 Mass Transfer Processes . . . . . . . . . . . . . . . . . . . . . . 10

2.2.4 Thermal Convection . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.5 Thermal Conduction . . . . . . . . . . . . . . . . . . . . . . . . 10

2.3 Mathematical Formulations . . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.1 Mass Balance Equation . . . . . . . . . . . . . . . . . . . . . . . 11

2.3.2 Energy Balance Equation . . . . . . . . . . . . . . . . . . . . . 12

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

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

3 System Properties 15

3.1 Physical Properties of Water and Steam . . . . . . . . . . . . . . . . . 15

3.1.1 Density and Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 15

3.1.2 Water Saturation Pressure . . . . . . . . . . . . . . . . . . . . . 15

3.1.3 Enthalpy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Physical Properties of the Porous Medium . . . . . . . . . . . . . . . . 19

3.2.1 Heat Capacity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.2.2 Porosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

I

CONTENTS II

3.2.3 Absolute Permeability . . . . . . . . . . . . . . . . . . . . . . . 20

3.3 Composite Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.1 Relative Permeability . . . . . . . . . . . . . . . . . . . . . . . . 20

3.3.2 Capillary Pressure . . . . . . . . . . . . . . . . . . . . . . . . . 21

3.3.3 Heat Conductivity . . . . . . . . . . . . . . . . . . . . . . . . . 22

4 Simulations 24

4.1 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

4.1.1 Definition of the Model Domain . . . . . . . . . . . . . . . . . . 24

4.1.2 Initial and Boundary Conditions . . . . . . . . . . . . . . . . . . 26

4.1.3 System Property Values . . . . . . . . . . . . . . . . . . . . . . 26

4.1.4 Conditions at the Injection Well . . . . . . . . . . . . . . . . . . 27

4.2 Continuous Steam Injection . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.1 The Injection Well . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.2.2 Steam Chamber and Temperature Development . . . . . . . . . 31

4.3 Cyclic Steam Injection . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.1 The Injection Well . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.3.2 Steam Chamber Growth . . . . . . . . . . . . . . . . . . . . . . 36

4.3.3 Temperature Development . . . . . . . . . . . . . . . . . . . . . 39

4.4 Comparison of the two Injection Routines . . . . . . . . . . . . . . . . 41

4.4.1 Steam Chamber Growth . . . . . . . . . . . . . . . . . . . . . . 41

4.4.2 Temperature Development . . . . . . . . . . . . . . . . . . . . . 44

4.5 Sensitivity Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4.5.1 Absolute Permeability K . . . . . . . . . . . . . . . . . . . . . . 56

4.5.2 Porosity Φ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5.3 Specific Heat Capacity of the Soil Grains csg . . . . . . . . . . . 58

4.5.4 Heat Conductivity λpm . . . . . . . . . . . . . . . . . . . . . . . 59

4.5.5 Capillary Pressure pc and Van Genuchten Parameter α . . . 60

4.5.6 Results of the Sensitivity Study . . . . . . . . . . . . . . . . . . 60

5 Summary 61

5.1 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

5.2 Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

List of Figures

1.1 Schematic sketch of oil sand reservoir and well arrangement . . . . . . . 3

1.2 Schematic sketch of steam chamber growth . . . . . . . . . . . . . . . . 3

2.1 Phase diagram of water . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 Phase states and mass transfer processes considered in the 2p1cni model 13

2.3 The numerical simulator MUFTE-UG . . . . . . . . . . . . . . . . . . . 14

3.1 Water saturation pressure curve . . . . . . . . . . . . . . . . . . . . . . 16

3.2 Specific enthalpy of liquid water . . . . . . . . . . . . . . . . . . . . . . 17

3.3 h-T relation of saturated steam . . . . . . . . . . . . . . . . . . . . . . 18

3.4 h-p relation of saturated steam . . . . . . . . . . . . . . . . . . . . . . 19

3.5 Relative permeability-saturation relation . . . . . . . . . . . . . . . . . 21

3.6 Capillary pressure-saturation relation . . . . . . . . . . . . . . . . . . . 22

3.7 Heat conductivity of a fluid filled porous medium . . . . . . . . . . . . 23

4.1 Model domain for the simulations . . . . . . . . . . . . . . . . . . . . . 25

4.2 Data retrieval nodes within the model grid . . . . . . . . . . . . . . . . 25

4.3 Seasonal and daily injection cycle . . . . . . . . . . . . . . . . . . . . . 29

4.4 p, T and Sg at the injection node for continuous injection . . . . . . . . 30

4.5 Steam chamber growth for continuous injection . . . . . . . . . . . . . 32

4.6 T distribution for continuous injection . . . . . . . . . . . . . . . . . . 33

4.7 T and Sg underneath the overburden for continuous injection . . . . . . 34

4.8 p, T and Sg at the injection node for cyclic injection . . . . . . . . . . . 37

4.9 Steam chamber growth for cyclic injection . . . . . . . . . . . . . . . . 38

4.10 T distribution for cyclic injection . . . . . . . . . . . . . . . . . . . . . 40

4.11 Sg for continuous and cyclic injection after 5 years . . . . . . . . . . . . 42

4.12 Sg for continuous and cyclic injection after 4 years and 5 months . . . . 43

4.13 T for continuous and cyclic injection after 5 years . . . . . . . . . . . . 45

4.14 Low T areas for continuous and cyclic injection after 5 years . . . . . . 46

4.15 High T areas for continuous and cyclic injection after 5 years . . . . . . 47

4.16 Propagation of various T fronts for continuous and cyclic injection . . . 48

4.17 p at Node2 and Node3 for continuous and cyclic injection . . . . . . . . 50

4.18 p distribution for continuous and cyclic injection . . . . . . . . . . . . . 51

III

LIST OF FIGURES IV

4.19 Tsat distribution for continuous and cyclic injection . . . . . . . . . . . 52

4.20 Sg at Node2 and Node3 for continuous and cyclic injection . . . . . . . 53

4.21 Model domain for sensitivity analysis . . . . . . . . . . . . . . . . . . . 54

4.22 Heat conductivity-saturation relation for the sensitivity analysis . . . . 55

4.23 T front propagation for continuous and cyclic injection with varying K 56

4.24 T front propagation for continuous and cyclic injection with varying Φ 57

4.25 T front propagation for continuous and cyclic injection with varying csg 58

4.26 T front propagation for continuous and cyclic injection with varying λpm 59

4.27 T front propagation for continuous and cyclic injection with varying pc 60

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 . . . . . . . . . . . . . . . . 26

4.2 System property values . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

4.3 System property values and range for the sensitivity analysis . . . . . . 55

V

Nomenclature

symbol meaning dimension

∆Q change of heat [J ]

∆U change of internal energy [J ]

∆Wv volume changing work [J ]

E extensive property

Fres resulting force [N ]

Glin linear Gravity number [−]

H enthalpy [J ]

K intrinsic permeability [m2]

Kob intrinsic permeability of overburden [m2]

Kf hydraulic conductivity [m/s]

Re Reynolds number [−]

Sα saturation of phase α [−]

Se effective water saturation [−]

Sw water saturation [−]

Sw,r residual water saturation [−]

T temperature [C]

Tinitial initial temperature [C]

Tsat water saturation temperature [C]

U internal energy [J ]

V volume [m3]

Vpores pore volume [m3]

Vtotal total bulk volume [m3]

csg specific heat capacity solid phase [J/kgK]

cp specific heat capacity at constant pressure [J/kgK]

cv specific 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

Nomenclature VII

g gravitational vector

h piezometric head [m]

h specific enthalpy [J/kg]

hα specific enthalpy of phase α [J/kg]

hg,sat specific enthalpy of saturated steam [J/kg]

hwet specific enthalpy of wet steam [J/kg]

hw,sat specific enthalpy of saturated water [J/kg]

kr relative permeability [−]

kr,α relative permeability of phase α [−]

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]

mliquid mass liquid component [kg]

n Van Genuchten parameter [−]

n outer normal vector

p pressure [Pa]

pα pressure of phase α [Pa]

patm atmospheric pressure [Pa]

pc capillary pressure [Pa]

pg gas phase (steam) pressure [Pa]

pw water phase pressure [Pa]

pw,sat water saturation pressure [Pa]

qc mass source/sink term

qcond conductive heat flux [W/mK]

qh energy source/sink term

qs steam mass flux [kg/sm2]

s entropy [J/K]

t time [s]

u specific internal energy [J/kg]

uα specific internal energy of phase α [J/kg]

v flow velocity [m/s]

v Darcy velocity [m/s]

vα velocity of phase α [m/s]

va,α seepage velocity of phase α [m/s]

vs steam velocity [m/s]

x steam quality [−]

z height [m]

Nomenclature VIII

α Van Genuchten parameter [1/Pa]

α phase α

Γ boundary of control volume domain

λ heat conductivity [W/Km]

λf heat conductivity of fluid phase [W/Km]

λi heat conductivity of material i [W/Km]

λpm equivalent heat conductivity of the porous medium [W/Km]

λs heat conductivity of solid phase [W/Km]

µ dynamic viscosity [kg/ms]

µα dynamic viscosity of phase α [kg/ms]

µs dynamic viscosity of steam [kg/ms]

ν kinematic viscosity [m2/s]

Ω domain of control volume

Φ porosity [−]

Φob porosity of overburden [−]

% mass density [kg/m3]

%α mass density of phase α [kg/m3]

%w mass density of water [kg/m3]

%b mass density of a body b [kg/m3]

%f mass density of a fluid f [kg/m3]

%sg soil grain density [kg/m3]

subscript meaning

α referring to phase α

atm referring to atmospheric conditions

b referring to body b

f referring to fluid f

g referring to gas phase

i referring to material i

initial initial conditions

n referring to non-wetting phase

ob referring to overburden

pm referring to porous media

s referring to steam

sat referring to saturated conditions

sg referring to solid phase

w referring to water phase

wet referring to wet conditions

Nomenclature IX

superscript meaning

c component

h enthalpy

Chapter 1

Introduction

1.1 Global Energy Demand and the Resource Oil

According to the International Energy Agency (IEA), the worldwide economic

downturn since the end of 2008, has lead to a drop in the global energy demand,

accompanied by decreasing CO2 emissions and energy investments. However, this

is assumed to be a short-dated development. On current policies, the global energy

demand would quickly resume its longterm upward trend, once economic recovery is

underway (IEA (2009) [14]). The worldwide primary energy consumption in 2008

was estimated to be 11.29Gt of oil equivalent (BP (2009) [4]), oil being the biggest

primary 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 to

be the dominant source of primary energy in the near future. Oil will thereby remain

the largest single fuel source, although its share is assumed to drop from 34% in

2009 to 30% in 2030. The oil demand is projected to grow 1% per year from 85 mb/d

(million barrels per day) in 2008 to 105 mb/d in 2030 (IEA (2009) [14]). With the

conventional 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-called

non-conventional oil deposits become economically more interesting (the R/P ratio is

an indication for the period the reserve will last assuming a constant consumption rate).

Low viscous oil determined by a relatively good ability to flow, is usually re-

ferred to as conventional oil. While highly viscous oil and oil bound to oil sand and

oil shale, thus being immobile, is defined as non-conventional oil. For this reason, the

oil density can be used to differ between conventional and non-conventional oils. Oil

with a density below 10 API (or above 1 g/cm3) 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 Orinoco

tar belt in Venezuela (Butler (1991) [5]). According to the German Federal

1

1.2 Enhanced Oil Recovery through SAGD 2

Institute for Geosciences and Natural Resources (BGR), reserves are defined as the

deposits geologically detected with a high accuracy and economically and technically

producible. Resources, are the deposits geologically proved but currently economically

not producible, and the deposits which have not been approved but are geologically

expected in a certain region.

The total oil in place of the world’s oil sands alone, is assumed to be 462Gt, with

188 Gt defined as reserves and resources. The estimated total oil in place in the

Canadian oil sands is 272Gt, of which 110 Gt are claimed to be reserves and resources.

The estimated amount of oil in place in the Venezuelan heavy oil fields (which accounts

for more than 97 % of the total heavy oil) is 240Gt. Thereof, 54 Gt are defined as

reserves and resources (BGR (2009) [2]). The total potential, or estimated ultimate

recovery (EUR), of conventional oil is thought to be 400Gt, with a remaining potential

of 249Gt (reserves and resources combined).

These numbers indicate the enormous potential of the described non-conventional

reservoirs, even though one is advised not to directly compare between such numbers.

This is because different authors and institutions use different definitions of the

terms conventional and non-conventional oil deposits or reserves and resources.

Furthermore, the quality of the energy data provided by sources, such as governments

and companies, is not necessarily reliable due to low transparency, economical and

political 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 a

special method of the enhanced oil recovery technologies, called steam-assisted gravity

drainage (SAGD). It was developed, to remove the oil in a systematic manner, in order

to realise a more complete recovery of the reservoirs than achieved in common steam-

flooding processes. The steam-assisted gravity drainage process has since emerged as

the most effective and most promising in-situ technology for the recovery of heavy oil

and 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 to

effect the oil movement. This way, differential fingering, occuring when viscous oils are

moved by pushing with a less viscous fluid, can be avoided (Butler (1991) [5]). The

process 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 10m). The so-called

well pair is drilled to the desired reservoir depth, where it continues horizontically for

500m to 700m. Several such well pairs, lying parallel to each other, are drilled into

the deposit near the reservoir bottom (see figure 1.1).

1.2 Enhanced Oil Recovery through SAGD 3

injection

35m

well length appr. 500 − 700m

production

horizontal distance appr. 100m

vertical distance5m

well pair, consisting of a production and injection well

reservoirthickness

400mreservoir depth

overburden

cross−sectional area for 2d simulations

low permeable

y

xz

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

sand 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 maintained

at a constant value throughout most of the process. The growing steam chamber is

surrounded by colder oil sand. At the interface between the steam front and the porous

medium, 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 figure 1.2). As the oil and steam condensates

drain 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 steaminjection

into 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 and

condensate flow down towards the production well (Butler (1991) [5]).

1.3 Solarthermal Steam Generation for SAGD 4

The most dominant features for a successful SAGD operation are the geology and the

reservoir properties. The reservoir’s average pay zone depth should be above 15 m,

and characterized by a good vertical communication without any thief zones. Often

SAGD operations are compromised by insufficient steam supply. However, as long as

the steam chamber can grow, the ultimate recovery of a SAGD operation can be in

the order of 60% to 70% (Jimenez (2008) [16]).

Reservoir conditions, the production strategy and the depth and quality of the

oil deposit define the steam injection rate, which in turn determines the steam

injection pressure. A steam injection rate of around 180 t/d (tonnes per day) per well

pair is assumed to be realistic. At a steam pressure of around 40 bar and a steam

quality of approximately 90%, this equals an energy amount of 473GJ.

Producing one barrel of oil using the SAGD technology, three barrels of water

and 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 be

increasing, 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, such

as oil sand, has made the depletion of these less traditional reservoirs more interesting.

For instance, bitumen production from the oil sand fields of Alberta, Canada has

almost doubled from the year 2000 to 2007, according to BGR (2009) [2]. This is

followed 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 use

of increasingly large amounts of fossil fuel for steam generation presents a number of

economic and environmental problems. Common steam generators emit large amounts

of greenhouse gases, and the increasing demand for natural gas is feared to influence

the 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) focusing

systems 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 to

produce electricity. While line focusing systems are determined by a concentration

factor of up to 80 and operating temperatures up to 350 C, the concentration achieved

with point focusing systems is higher, and thus is the temperature (Voss (2005) [22]).

Usually, the solar energy is absorbed by a heat storage fluid, such as oil or molten

1.4 Scope of this Work 5

salt. Unlike conventional solarthermal power plants, solarthermal steam generation

for enhanced oil recovery, would require steam at mid-level temperatures, directly

generated with no intermediate heat storage fluid, and thus enhancing the overall

thermal efficiency of the system (Kraemer et al. (2008) [17]).

The result of a solarthermal steam generation process would be an intermittent steam

injection rate, with higher injection rates in comparison to the traditional continuous

injection process (assumption of same total energy input). Assuming the reservoir

formation 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 the

effect of daily and seasonal variations on the average bitumen production is negligible.

Based on this assumption, a feasibility assessment of a solarthermal driven SAGD

process from both, a thermodynamic and economical point of view, is presented in

Kraemer et al. [17].

1.4 Scope of this Work

It needs to be understood, that the work presented here does not describe the influ-

ence of an intermittent steam injection process on the oil production. It is in fact a

hydrodynamical study, analysing and explaining the influence of a cyclic steam injec-

tion process on the steam chamber growth and the temperature distribution in the

geological formation. The component oil is thus neglected in this work.

The fundamentals of the applied model, which are specified in chapter 2, determine

the model, which is used to describe the flow and transport processes for the water

steam system. The system properties, which complement the conceptual model, are

characterized in chapter 3.

As specified in chapter 4, the non-isothermal water steam model is used to simulate a

continuous and, based on the assumption of a solarthermal steam generation, a cyclic

steam injection process into water saturated porous media. The steam chamber and

temperature front propagation within the reservoir is analysed for both injection rou-

tines. To understand the consequences of a cyclic injection routine, its influence on the

flow 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 to

this topic is presented in chapter 5.

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 fluid properties.

Thus, it is possible for several liquid phases to exist in a porous medium, while only

one gaseous phase can be present. The term phase is furthermore used to describe a

substance’s 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-phase

system, 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 as

the sole chemical substances, which influence the physical properties of a phase.

2.1.2 Primary Variables

Primary variables are parameters defining physical properties of a system, and are used

to describe the degrees of freedom of a thermodynamical system. They are needed for

a definite 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 variables

may be chosen for the same system.

The non-isothermal water steam model discussed in this work, is described by two

equations (one mass and one energy balance). The two unknowns pressure p and tem-

perature T or pressure p(T ) and water saturation Sw (see equation 2.11 and 2.12) are

used 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. In

contrast, intensive variables are independent of the system’s size, such as the temper-

ature and the pressure.

6

2.1 Essential Terms 7

2.1.3 Secondary Variables

Secondary variables can be calculated from the primary variables, using constitutive

relationships and equations of state (e.g. Ochs (2006) [20]). These secondary pa-

rameters depend on the primary variables and help to describe the considered system

in detail. Examples are the density %, the viscosity µ, the capillary pressure pc, the

relative permeability kr, the specific enthalpy h, and the heat conductivity λ.

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 component’s 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 phase

diagram shows a substance’s state of aggregation as a function of state variables. Such

a phase diagram is given in figure 2.1, describing the phase state of water, depending

on 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 a

phase 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 a

switch of the primary variables that are necessary to describe the system.

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 phases

within the system, the used set of primary variables consists either of gas phase pressure

pg and water saturation Sw (two-phase system), or gas phase pressure pg and temper-

ature T (single-phase system) (Ochs (2006) [20]). This primary variable switch is

shown in table 2.1.

phase state present phases primary variables

1 water, gas pg(T), Sw

2 water pw, T

3 gas pg, T

Table 2.1: Phase states and corresponding set of primary variables for the 2p1cni

model.

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 the

various flow, transport and energetic processes, that have to be considered, is given in

the following section.

2.2.1 Advection and Buoyancy

The process of advection is associated with the movement of a quantity within the

vector field of a fluid. An example in porous media would be the transport of a compo-

nent’s concentration according to the fluid’s velocity field. Darcy’s Law, emerging from

a series of experiments in a permeameter column, describes the slow linear single-phase

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

v = −Kf grad(h). (2.1)

Here, v is the Darcy velocity, h is the piezometric head and Kf is the hydraulic con-

ductivity of water with

K = Kfµ

%g, (2.2)

where K is the absolute permeability, µ the dynamic fluid viscosity, % the fluid’s density

and g the gravitational constant.

Darcy’s Law is valid for seeping flow with a Reynolds number (Re) smaller than 1. The


dimensionless Reynolds number in a porous medium describes the ratio of inertial to

viscous forces and is given by:

Re =dv

ν. (2.3)

Here, d is the mean pore diameter, v is the typical flow velocity and ν the kinematic

viscosity of the fluid.

To determine the advective flux within a multiphase system, Darcy’s Law has

to be extended for various phases α. The consideration of the phase density %α, the

phase pressure pα, the relative permeability kr,α of the phase, the phase’s dynamic

viscosity µα, the intrinsic permeability K and the gravitational vector g with the

constant g, yields the velocity of the individual phase vα:

vα = −kr,α

µα

K(grad(pα)− %αg

). (2.4)

The so-called Darcy velocity vα of the phase α refers to a flow through the total cross-

sectional area of the porous media. To calculate the actual particle speed, the porosity

Φ of the medium needs to be considered. This yields the seepage velocity va,α of the

phase α:

va,α =vα

Φ. (2.5)

The extended version of Darcy’s Law for multiphase systems, describes fluid flow pro-

cesses due to viscous (advection) and buoyant forces.

Buoyancy flow is caused by density differences within one phase (e.g. cold and hot

water) 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 fluid with density %f yields:

Fres = buoyant forces− gravitational forces = (%b − %f) gV. (2.6)

In the case of steam injection into water saturated porous media this results in a

buoyant flow, driven by the high density difference between liquid water and steam. At

a pressure of 40 bar and a temperature of 250.35 C, the density of water is 798.37 kg/m3,

whereas the density of fully saturated steam is 20.09 kg/m3.

Therefore, buoyancy driven flow is suspected to play an important role in the context

of steam injection into water saturated porous media (Ochs (2006) [20]). Assuming

a hydrostatic pressure distribution in the system (h = p%g

+ z = const.), leads to the

pressure gradient in z-direction:

grad(pw) = %wg. (2.7)

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

velocity:

vs = −kr,s

µs

Kg (%w − %s) . (2.8)


Equation 2.8 describes the buoyant flow 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 between

advection and buoyancy.

2.2.2 Diffusion

The transport process of diffusion occurs continuously, independent of the fluid’s 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 justified, as the influence of diffusion within one-

component systems is very small in comparison to multi-component systems (Corey

et al (2009) [7]).

2.2.3 Mass Transfer Processes

The multiphase one-component model described in this work, contains the two phases

water and steam. Both consist of the one present component water. A mass transport

between the phases, hence only occurs in terms of evaporation and condensation (see

figure 2.2).

2.2.4 Thermal Convection

The transport of thermal energy through bulk motion of a fluid is called thermal or

heat convection. Depending on its origin, it is distinguished between free and forced

convection. Forced convection is characterized by a fluid motion, that is induced by

external forces, such as during steam injection. Free or natural convection occurs

when temperature gradients, and respectively density differences, cause recirculation

processes within the fluid.

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 through

convection is a function of the fluid-flow rate and the thermal properties of the fluid

and the reservoir. This type of thermal convection is described through an energy

balance on the flowing fluid, as the specific phase enthalpy is considered within the

advection term (see equation 2.12).

2.2.5 Thermal Conduction

Another important energy transfer process is thermal or heat conduction. Thermal

conduction is a diffusive process, caused by a temperature gradient. It is the result of

2.3 Mathematical Formulations 11

an energy transfer from high energetic molecules to less energetic ones. During steam

injection 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 important

heat transfer process within the reservoir, when fluid flow velocities are small.

According to Fourier’s Law, one-dimensional stationary conductive heat transfer

is described by the following equation:

qcond = −λi grad(T ). (2.9)

The energy flux related to an area is given by qcond, with the unit J/s m2. The thermal

conductivity λi, 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 fluid dynamics,

the Reynolds Transport Theorem (RTT) is used to formulate these basic conservation

laws (see equation 2.10). It states that the total rate of change of an extensive system

property E equals the rate of change of its corresponding intensive quantity e within a

fixed control volume (CV), plus the net rate change across its boundaries (e.g. Ochs

(2006) [20]).dE

dt=

∫

Ω

∂(%e)

∂tdΩ +

∫

Γ

(%e)(v · n)dΓ. (2.10)

Using the RTT and considering an infinitesimal small CV, a differential formulation

for the conservation of a quantity E (e.g. mass) can be derived. A detailled description

of this process is given in Ochs (2006) [20]. The additional consideration of the pore

space and the phase saturation of the porous multiphase system, yields the balance

equations for each phase.

For the solution of the multiphase problem, the multiphase extension of Darcy’s

Law, as given in equation 2.4, is usually used to calculate the phase velocity vα

(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 balance

of 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]).

2.3 Mathematical Formulations 12

In case of the depicted two-phase one-component model, the formulation of one mass

balance equation, for the one component water is necessary (e.g. Ochs (2006) [20]):

φ

∂∑α

(%αSα)

∂t︸︷︷︸accumulation term

−∑

α

div

%α

kr,α

µα

K(grad(pα)− %αg

)

︸︷︷︸advection term

− qc

︸︷︷︸source/sink term

= 0, α ∈ water, steam (2.11)

with the constant porosity Φ, phase density %α, phase saturation Sα, relative perme-

ability kr,α of phase α, dynamic viscosity µα of phase α, the intrinsic permeability K

and the phase pressure pα.

2.3.2 Energy Balance Equation

The first law of thermodynamics states, that in a physical process, energy can not be

lost but only be transferred from one state to another. In order to describe the energy

transfer in a multiphase system, the balance of energy is formulated, as it is done with

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

The change of a system’s internal energy ∆U equals the change of heat ∆Q across

the system boundaries plus the work ∆Wv done by change in volume. Assuming local

thermodynamic equilibrium, only one single energy balance equation is necessary to

describe the system (e.g. Ochs (2006) [20]).

φ

∂∑α

(%αSαuα)

∂t︸︷︷︸accumulation term fluid

+ (1− φ)∂ (%sgcsgT )

∂t︸︷︷︸accumulation term solid

− div(λpm grad(T )

)

︸︷︷︸conduction term

−∑

α

div

%αhα

kr,α

µα

K(grad(pα)− %αg

)

︸︷︷︸convection term

− qh

︸︷︷︸source/sink term

= 0 α ∈ water, steam (2.12)

2.4 The 2p1cni Model 13

In equation 2.12, radiation is neglected, uα is the specific internal energy of phase

α, hα is the specific enthalpy of phase α, %sg and csg are the soil grain den-

sity and the specific heat capacity of the solid medium, λpm is the equivalent heat

conductivity of the system (porous medium including fluids), and T is the temperature.

To solve the partial differential balance equations, the following closure relationships

are necessary:

− The sum of the phase saturations adds up to one:∑α

Sα = 1.

− The sum of the pressure of the wetting phase and the capillary pressure equals

the 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 heterogeneous

system, containing the two phases liquid water (water phase) and gaseous water (steam

phase), 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 figure 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) model

for 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 Multiphase

Flow Transport and Energy Model on Unstructured Grids. As shown in figure 2.3,

it consists of two parts. The MUFTE part of the simulator describes the physical

problems and the discretisation method of the system (Helmig et al. (1998) [11]).

The UG part with its multigrid data structures, grid refinement techniques and the

numerical 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 flow processes in a geological formation.

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

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 is

a function of temperature and pressure. While the density of the liquid water phase

is assumed to remain constant with changing temperature, the density of the gaseous

water 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 the

viscosity of the liquid water phase, which decreases with increasing temperature, that

of 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 equilibrium

with 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 used

to determine the occurence of a second phase within the model, accompanied by a

primary variable switch (for details see section 2.1.4).

For gas being the only phase present, and pg ≥ pw,sat, the water phase appears. For

water being the only phase present, and pg ≤ pw,sat, the gas phase appears.

15

3.1 Physical Properties of Water and Steam 16

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

the model.

3.1.3 Enthalpy

The amount of energy within a system capable of doing mechanical work, is called

enthalpy H. It is defined as the sum of the system’s internal energy U and the volume

changing work pV (e.g. Helmig (1997) [12]). The division by the system’s mass yields

the specific enthalpy: h = u + p%.

The specific enthalpy of water is implemented after IFC (1967) [15]. While the spe-

cific enthalpy of gaseous water (steam) strongly depends on the volume changing work,

the definition of the specific enthalpy of liquid water often neglects this correlation, as

a result of the low compressibility of water: h ≈ u.

Figure 3.2 shows the specific enthalpy of liquid water depending on temperature (con-

stant pressure) and pressure (constant temperature). It is observed, that the specific

enthalpy of water is more dependent on temperature than on pressure.


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

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

Figure 3.2: Specific enthalpy of liquid water as a function of temperature at constant

pressure, and as a function of pressure at constant temperature. As implemented in

the model.


Defining the specific enthalpy of steam, it is theoretically distinguished between wet

steam, saturated steam and overheated steam. While wet and saturated steam are

determined through the parameters temperature T (p) and steam quality x, the specific

enthalpy of overheated steam is a function of T and p. The steam quality parameter

x is a mass ratio, defined as: x = mgaseous

mliquid+mgaseous.

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 with

a temperature above boiling point is called overheated steam.

For the given process of steam injection into saturated porous media, it is high

quality wet steam occupying the pore space besides water. Overheated steam

would require higher temperatures. The specific enthalpy of wet steam hwet is

calculated, using hw,sat of saturated water and hg,sat of saturated steam at boiling

temperature, and combining it with the steam quality x: hwet = (1−x)·hw,sat+x·hg,sat.

The specific enthalpy of saturated steam as a function of temperature T , as im-

plemented in the model, is shown in figure 3.3. For more details see the Mollier

h,s-Diagram (Langeheinecke et al. (2003) [18]).

Figure 3.3: Specific enthalpy of saturated steam (x = 1.0) as a function of temperature.

As implemented in the model.

3.2 Physical Properties of the Porous Medium 19

Figure 3.3 indicates, that a pressure, respectively temperature increase only results in

an increased specific 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 figure 3.4. It is pointed out here, that the pressure,

respectively temperature to be exceeded for the enthalpy decrease depends on the

steam quality. With lower steam quality, a higher pressure, respectively temperature

is needed to cause the decline of the specific 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

100°C

10

50

1

spec. enthalpy h [kJ/kg]

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

3.2 Physical Properties of the Porous Medium

3.2.1 Heat Capacity

The specific heat capacity of a material, is a measure of how much thermal energy

must be added to heat up 1 kg of the material by one Kelvin. The unit is kJ/kg K. The

heat capacity thus describes a substance’s ability to store heat. A body determined by

a high specific heat capacity stores heat well. In thermodynamics, it is distinguished

between the specific heat capacity cp at constant pressure, and cv at constant volume.

In terms of equation 2.12, the energy content of the fluid phase is calculated using

the specific internal energy u. The energy storage term of the solid phase however, is

calculated using the specific heat capacity of the soil grain material csg. As cp ≈ cv for

solid substances, a constant value, independent of pressure and temperature is used for

csg.

3.3 Composite Properties 20

3.2.2 Porosity

The porosity Φ is defined as the ratio between the pore volume and the total bulk

volume of the porous media: Φ = Vpores

Vtotal.

It is a measure of the volume not filled with soil grains but fluids, such as liquid water

and steam. It is furthermore distinguished between porosity and effective porosity,

which describes the pore space accessible for a fluid entering the porous medium.

3.2.3 Absolute Permeability

The absolute or intrinsic permeability K of a porous medium describes the resistance

that the material opposes to fluid flow. The unit is m2 or D, with 1 D ≈ 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 Kf by including the fluid’s vis-

cosity and density. For the computation of multiphase flow as shown in equation 2.11,

the hydraulic conductivity is extended with the relative permeability kr,α of phase α

(e.g. Helmig (1997) [12]):

Kf = K kr,α%αg

µα

. (3.1)

While the intrinsic permeability K is solely a property of the soil grains, the relative

permeability is dependent on the fluid and the porous medium properties (for details

see section 3.3.1).

3.3 Composite Properties

Along the fluid and soil properties, additional parameters combining fluid and porous

medium properties are needed to describe the multiphase system. As these parameters

can neither be assigned solely to the porous medium, nor to the fluid occupying the

pore space, they are called composite properties here. They result from the interaction

between the fluid and the porous medium and are no conventional system properties.

Composite properties reflect the conceptual model, that is used to reproduce the system

behavior (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 the

intrinsic permeability (see equation 3.1), with the product of K and kr,α being called

the effective permeability of phase α (e.g. Helmig (1997) [12]). The introduction of

kr,α accounts for the fact, that in a multi-phase system, the presence of one phase in a

porous medium influences the flow of the other phase.

In the model, the relative permeability-saturation relations of the two phases water and


steam are implemented after Van Genuchten, as shown in figure 3.5. With water

representing the wetting phase and steam being the non-wetting phase, the relative

permeabilities are calculated as follows:

kr,w =√

Se[1− (1− S1me )m]2

kr,n = (1− Se)13 [1− S

1me ]2m. (3.2)

The parameter m results from the definition of the effective water saturation Se as a

function of the capillary pressure pc after Van Genuchten:

Se(pc) =Sw − Sw,r

1− Sw,r

= [1 + (α · pc)n]m, (3.3)

with the water saturation Sw, the residual water saturation Sw,r, and m, n and α as

the three Van Genuchten parameters (see also section 3.3.2).

Figure 3.5: Relative permeability of the wetting phase (water) and of the non-wetting

phase (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 fluid phases in a state of equilibrium, a pressure difference

at the interface between the wetting and non-wetting phase occurs. It originates from


molecular cohesion effects, which cause a surface tension at the interface. The resulting

pressure 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 Van

Genuchten (e.g. Class (2001) [6]), as depicted in figure 3.6.

pc =1

α(S

− 1m

e − 1)1n . (3.4)

With m = 1 − 1n, the two Van Genuchten paramaters α and n emerge. The pa-

rameter α describes the entry behaviour of the non-wetting phase, and the parameter

n describes the material’s uniformity, with a low value for n being associated with a

non-uniform material. The effective saturation Se is defined as given in equation 3.3.

Figure 3.6: Capillary pressure as a function of the water saturation after the approach

of Van Genuchten, with α set to 0.0028 1/Pa and n set to 4.0 . As implemented in

the model.

3.3.3 Heat Conductivity

The heat conductivity λ is a parameter combining fluid and soil grain properties with

respect to equation 2.12. It describes the averaged ability of the fluid filled porous

media to conduct heat. It is implemented after the approach of Somerton, as shown

in equation 3.5 (e.g. Class (2001) [6]).

λpm = λSw=0pm +

√Sw(λSw=1

pm − λSw=0pm ) (3.5)


In this case, the definition of the effective heat conductivity λSw=1pm for the fully water

saturated and λSw=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 the

needed effective heat conductivities, an average of the heat conductivity λsg for the

soil grains and λf for the fluids (λSw=1pm for water and λSw=0

pm for steam) needs to be

determined. Here, the conservative method of the geometric mean is used:

λpm = λ(1−φ)sg · λφ

f . (3.6)

With λsg assumed to be 2.5 W/m · K (Quartz), the value of λSw=1f (liquid water) being

0.621 W/m K and that of λSw=0f (steam) being 0.051 W/m K . This yields a λpm as a

function of the water saturation calculated after equation 3.5, as shown in figure 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 implemented

in the model.

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 influence of a

cyclic injection routine on the steam chamber growth and the temperature distribution

within the porous medium is analysed, and compared to the process of a continuous

injection.

To determine the influence of the system properties on the simulation results, a

sensitivity study is carried out. Therefor, a set of porous medium and composite

properties, assumed to be most relevant for the depicted process, is chosen. Each

parameter is then seperately examined to determine its influence on the flow processes

in the geological formation.

4.1 The Model

4.1.1 Definition of the Model Domain

The development of the steam and temperature front along the horizontal injection

well, such as described in section 1.2, is assumed to be constant. Therefore, the steam

and temperature front development is depicted using a two-dimensional model, that

represents a vertical y-z slice through the inner reservoir area, with a thickness in x-

direction of 1m (see figure 1.1).

This results in the model domain shown in figure 4.1. The vertical model extension of

40m represents the full assumed reservoir height of 35 m, plus a 5m thick, low perme-

able overburden on top. The horizontal extension is chosen to include an equal area

to the left and right of the well pair, and is set to 120 m. This is, because the distance

between two well pairs of 100m leads to the assumption, that at 50m to the left and

right of the injection well, the steam front would link up with that of a neighbouring

well with the same injection routine.

Only the steam injection well (upper well of a well pair) is implemented in the model.

24

4.1 The Model 25

It is located 8 m above the reservoir bottom, in the middle of the reservoir at x = 60m

(see figure 4.1).

The grid discretization of the model domain is set to 0.5m, 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 the

model domain, seven data nodes are implemented at various locations in the grid (see

figure 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 overburden 5m

p(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: no−flow conditions

T(initial) = 10°C

Figure 4.1: The model domain and its initial and boundary conditions as used for the

simulation 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 information

on the system properties, as given in table 4.1.

4.1 The Model 26

designation x [m] y [m]

Node1 60.0 1.0

Node2 60.0 8.0

Node3 60.0 20.0

Node4 60.0 34.5

Node5 30.0 34.5

Node6 90.0 34.5

Node7 60.0 38.0

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

grid.

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 figure 4.1), and is referring

to conditions found in the Canadian oil sand fields.

− The domain is assumed to be initially fully water saturated: Sw = 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 the

total depth in meter.

− The initial temperature Tinitial is assumed to be 10 C. A vertical temperature

distribution, according to the geothermal temperature gradient (estimated to be

0.03 C/m), is neglected because of the reservoir being only 35m in height.

− The bottom boundary of the domain is determined by a no-flow condition. The

right, left and upper boundary of the domain is characterized by the temperature

and pressure of the initial situation. The definition of the upper boundary con-

dition in combination with the very low permeable overburden, accounts for the

fact, that while thermal energy can be lost from the reservoir into the overburden

by conduction, no relevant flux 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 defined by a constant

value, or as a function of the primary variables, often including empirically derived

parameters. Only those properties, respectively parameters, associated with a constant

value are given in table 4.2. For details on the remaining parameters see chapter 3.

4.1 The Model 27

The porosity Φob and absolute permeability Kob are properties of the overburden and

account for the difference in permeability between the reservoir and overburden.

The values of the porosity and permeability of the reservoir are chosen to be rather

low in comparison to observed field data from Canadian oil sand fields. This is, to

account for the fact, that the presence of an oil phase in reality leads to a decrease

of the relative permeability of water. This procedure is random, but is considered to

be a first good approach to the problem. Furthermore, the sensitivity of the absolute

permeability is discussed in detail in section 4.5.1.

parameter value unit

specific heat capacity csg 850 J/kg K

porosity Φ 0.1 -

porosity Φob 0.05 -

absolute permeability K 40 mD

absolute permeability Kob 0.0001 mD

soil grain density %sg 2650 kg/m3

Van Genuchten parameter α 0.0028 1/Pa

Van Genuchten parameter n 4 -

residual saturation Sw,r of water and Sg,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. Mass

and energy is injected at Node2 (see figure 4.2), and characterized by a mole and en-

thalpy flux (mol/s and J/s).

To analyse the influence of a solarthermal steam generation, respectively cyclic steam

injection, on the temperature and steam development in the subsurface, a cyclic injec-

tion process is compared to a continuous one. Two injection approaches, determined

by 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 injection

routines.

For the continuous injection approach, this simply results in a mass and enthalpy flux

at the injection node of:

− 12.5 kg/hr

− 32875 kJ/hr.

4.1 The Model 28

For the cyclic injection approach based on solarthermal steam generation, the locally

available 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 a

yearly average of approximately 6.3 hrs/d of bright sunshine. Based on an average daily

injection of 0.3 t/m, respectively 109.5 t/m per year, the mass and enthalpy flux for the

cyclic injection process is calculated to be approximately:

− 47.6 kg/hr

− 125238.1 kJ/hr.

A combination of two injection cycles determines the actual injection period for the

cyclic injection process, as a function of time. One describes the different seasons for

the given location of Edmonton (see figure 4.3(a)). The other represents the actual

daily injection window depending on the season (see figure 4.3(b)). As the possible

daily 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 cyclic

injection as for continuous injection, the actual injection rates have been calculated as

described above. It is important to notice, that in case of cyclic injection, it is not the

actual injection rate changing with the seasons, but the duration of injection.

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 by

the 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.

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 (liquified petroleum gas).

Such a steam generation process delivers a continuous steam injection rate, in case the

fossil fuel and water supply is sufficient.

4.2.1 The Injection Well

A constant mass and enthalpy flux 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 time

at the injection node. It indicates, how a high injection pressure during the start-up

phase decreases over time, followed by a similar development of the temperature. The

steam saturation at the injection node is constant over the whole time.

Figure 4.4: Pressure, temperature and steam saturation at Node2 (injection node at

x = 60 m and y = 8 m) for a continuous injection process.


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 and

temperature are depicted for various time steps after the start of injection. Figure 4.5

and 4.6 show Sg, respectively the steam chamber growth, and T for the process of a

continuous 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 the

low permeable overburden (indicated by the black horizontal line) is reached, steam

accumulates underneath it and the steam chamber growth is dominated by a horizontal

spreading underneath the overburden. To a smaller degree, this horizontal growth

is 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 steam

saturation around the injection well.

For the given injection rate, the development of the temperature front is mainly driven

by convection, and hence, basically follows the steam chamber growth. However,

due to conduction, a loss of thermal energy from the reservoir into the overburden is

observed.

Figure 4.7 shows the development of Sg and T at Node4, directly underneath the

overburden at x = 60 m and y = 34.5 m. A constant steam saturation and temperature

is 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 a

similar development of the temperature front.


Fig

ure

4.5:

Ste

amsa

tura

tion

Sg,re

pre

senti

ng

the

stea

mch

amber

grow

thfo

ra

conti

nuou

sin

ject

ion

pro

cess

ata

tim

eof

3,6,

9,27

,30

,33

,51

,54

,an

d57

mon

ths

afte

rth

est

art

ofin

ject

ion.


Fig

ure

4.6:

Dis

trib

uti

onof

tem

per

ature

Tfo

ra

conti

nuou

sin

ject

ion

pro

cess

ata

tim

eof

3,6,

9,27

,30

,33

,51

,54

,an

d57

mon

ths

afte

rth

est

art

ofin

ject

ion.


Figure 4.7: Temperature and steam saturation at Node4, directly underneath the over-

burden (x = 60 m and y = 34.5 m) for a continuous injection process.

4.3 Cyclic Steam Injection 35

4.3 Cyclic Steam Injection

The objective of the hydrodynamical study of cyclic steam injection into the subsurface

is the idea, to use solarthermal steam generation plants instead of fossil fuel burning

steam generators. The solarthermal plant would use direct solar radiation to generate

steam, and thus delivering a cyclic steam injection rate, depending on the daily available

hours 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 steam

temperature. A cyclic injection routine, due to a solarthermal steam generation

process, thus results in a daily change between an injection and a non-injection

window, and the change of the daily injection duration with the seasons (see fig-

ure 4.3(b) and 4.3(a)). This injection routine determines the pressure, temperature

and saturation fluctuations 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 Sg in the fifth year of injection. The broad spectrum of the

data is the result of the daily shift between injection and non-injection phase. In the

model, the actual injection rate is the same for all seasons. The daily injection window

however, changes with the seasons, thus does the daily amount of injected steam (see

figure 4.3(b)).

It needs to be noticed, that in reality, the actual steam production and injection rate

may vary according to the daily and seasonal variation of the energy of the solar

radiation (assumption of sufficient water supply).

As shown in figure 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 with

a growing steam chamber. The pressure fluctuations are followed by the temperature

oscillations, 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 sudden

pressure decrease, followed by a temperature decline, is observed. This is because

an insufficient amount of steam is injected to obtain the expansion of the steam

chamber, causing steam to condense at the front, resulting in a near collapse of the

chamber. As water is more dense than steam, less pore volume is needed, resulting

in a pressure decline. With a then small, but slowly growing steam chamber, the

pressure rises again. The maximum pressure during injection, to which the injection

pressure generally converges, at the given injection rate, is approximately 44 bar.

The steam saturation at the injection well basically fluctuates within a given range,

according to the daily injection cycle, disregarding the change of seasons. An exception

is observed during the low-injection months of winter (see figure 4.8(c)). This is,


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 defining a constant mass and

enthalpy flux. Hence, in the case of a cyclic injection process, the described injection

pressure fluctuations make it impossible to ensure a certain steam quality at the

injection node. This is, because a change in pressure would be accompanied with a

change of the specific steam enthalpy, with respect to a constant steam quality (see

figure 3.4). The change of the specific enthalpy is however assumed to be minor for a

steam quality of 90%. Thus, the needed adjustment of the steam enthalpy is neglected

in the model.

4.3.2 Steam Chamber Growth

Using a cyclic injection process, the steam chamber growth varies with time, depending

on 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 fast

steam front propagation during the high-injection months (summer), while during low-

injection months (winter), the steam chamber is reduced in volume. This is because the

daily amount of injected steam varies with the seasons. It appears, the steam injection

during the seasons following summer, is not enough to sustain the steam chamber

extension reached during the summer months. The consequence is a hysteresis process,

resulting in a circular flush and drainage of the pores.

Furthermore, a rather heterogeneous steam saturation establishes within the steam

chamber, with layers of different saturations being observed. This layering of different

saturation areas is a result of the daily injection cycle, as the injected steam rises due to

buoyancy effects, leaving less saturated layers below during the non-injection period.


(a) p at Node2 (b) T at Node2

(c) Sg at Node2

Figure 4.8: Pressure, temperature and steam saturation at Node2 (injection node at

x = 60 m and y = 8 m) for a cyclic injection process.


Fig

ure

4.9:

Ste

amsa

tura

tion

Sg,

repre

senti

ng

the

stea

mch

amber

grow

thfo

ra

cycl

icin

ject

ion

pro

cess

ata

tim

eof

3,6,

9,

27,30

,33

,51

,54

,an

d57

mon

ths

afte

rth

est

art

ofin

ject

ion.

The

left

colu

mn

isduri

ng

sum

mer

,th

em

iddle

colu

mn

duri

ng

autu

mn,an

dth

eri

ght

colu

mn

duri

ng

win

ter.


4.3.3 Temperature Development

In case of a cyclic injection routine, the propagation of the temperature front does not

necessarily follow the steam chamber growth. Figure 4.10 indicates a fast temperature

front propagation during high-injection months, with large areas of high temperatures.

The temperature front propagation is mainly driven by convection, and hence follows

the steam chamber growth. During low-injection months however, the temperature

front 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 injection

well. The reason for this development is, that the temperature propagation is mainly

driven by conduction in these months. Hence, the thermal energy injected during high-

injection months is distributed within the reservoir during low-injection months.

The influence of conduction during low-injection months is also observed at the transi-

tion between the reservoir and the low permeable overburden. In summer months, the

heat lost into the overburden, is horizontally less spread than the temperature front

underneath it. This is, because the heat loss into the overburden is a result of the

rather slow process of conduction, while the horizontal spreading of the temperature

front underneath the overburden is driven by convection. In contrast, during winter

months, the main force driving the temperature propagation is conduction, leaving the

temperature front within the overburden and underneath it equally spread.


Fig

ure

4.10

:D

istr

ibuti

onof

tem

per

ature

Tfo

ra

cycl

icin

ject

ion

pro

cess

ata

tim

eof

3,6,

9,27

,30

,33

,51

,54

,an

d57

mon

ths

afte

rth

est

art

ofin

ject

ion.

The

left

colu

mn

isduri

ng

sum

mer

,th

em

iddle

colu

mn

duri

ng

autu

mn,

and

the

righ

tco

lum

n

duri

ng

win

ter.

4.4 Comparison of the two Injection Routines 41

4.4 Comparison of the two Injection Routines

To analyse the influence of a cyclic injection on the flow processes in the subsurface,

the steam chamber and temperature front propagation of the cyclic and continuous

steam injection routines are checked against each other. The two processes must be

compared at a point in time, determined by the same cumulative energy input. For

the 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 is

thus chosen to be after five full injection cycles, respectively five years.

4.4.1 Steam Chamber Growth

The propagation of the steam front is not found to be equal for both injection

approaches at one point in time, which is determined by the same cumulative energy

input. This is because of the varying influence of condensation in case of a cyclic

injection routine.

Figure 4.11 shows the steam saturation for the continuous and cyclic injection process

five years after the start of injection. A less horizontal steam chamber expansion

underneath the overburden, and a more heterogeneous steam saturation distribution

is observed in case of the cyclic injection. The steam chamber volume at the given

point in time is clearly bigger in case of the continuous injection.

However, it is pointed out, that with the cyclic injection process, the steam chamber

volume is decreasing in the second half of a full seasonal cycle (see figure 4.9). Thus,

the steam chamber expansion is more similar between the two approaches earlier

within the full injection cycle. This point in time though, would be characterized by

the cyclic cumulative energy input being higher than the continuous one. Figure 4.12

shows the steam saturation for the continuous and cyclic injection routine at the end

of the fifth 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 chamber

expansion 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 oil’s vis-

cosity due to the transfer of thermal energy (see section 1.2), it is not solely the steam

chamber growth influencing the enhanced oil recovery. In fact, the temperature front

propagation and the temperature distribution within the reservoir is assumed to be of

main interest for the production of heavy oil.


(a) Continuous injection

(b) Cyclic injection

Figure 4.11: Steam saturation Sg in the model domain for a continuous and cyclic

injection process, five years after the start of injection (after 5 full seasonal cycles).




Figure 4.12: Steam saturation Sg in the model domain for a continuous and cyclic

injection process, four years and five months after the start of injection (after summer).


4.4.2 Temperature Development

It is observed, that the propagation of the temperature front is quite different between

the two injection routines. Figure 4.13 shows the temperature for a continuous and

cyclic injection process five years after the start of injection. For the case of a cyclic

injection, a smaller horizontal expansion of the high temperature front underneath the

overburden is observed. The propagation of the temperature front is thus different

between the two injection routines.

As the energy input is the same for both injection routines, the thermal energy must be

differently distributed in case of the cyclic process. Therefor, the temperature distribu-

tion within the formation is analysed. Figure 4.14 and figure 4.15 show the distribution

of 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 fig-

ure 4.14(a) and 4.14(b), the high temperature areas are differently distributed, as shown

in figure 4.15(a) and 4.15(b). In case of the continuous injection process, an increased

accumulation of thermal energy underneath the overburden is observed, while in case

of 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 maximum

temperature.

The different distribution of high temperature areas between the two injection rou-

tines is shown more detailled in figure 4.16. It is observed, that while the depicted

245 C front has propagated further for the continuous process, the fronts of higher

temperatures are more developed for the cyclic injection routine, and higher overall

temperatures are reached.




Figure 4.13: Temperature T in the model domain for a continuous and cyclic injection

process, five years after the start of injection (after 5 full seasonal cycles).




Figure 4.14: Areas of low temperature T in the model domain for a continuous and

cyclic injection process, five years after the start of injection (after 5 full seasonal

cycles).




Figure 4.15: Areas of high temperature T in the model domain for a continuous and

cyclic injection process, five years after the start of injection (after 5 full seasonal

cycles).


Fig

ure

4.16

:P

ropag

atio

nof

the

tem

per

ature

fron

tof

245 C

,24

8 C

,24

9 C

,an

d25

0 C

for

the

conti

nuou

san

dcy

clic

inje

ctio

n

pro

cess

,five

year

saf

ter

the

star

tof

inje

ctio

n(a

fter

5fu

llse

ason

alcy

cles

).


In summary, a differing temperature front propagation is observed, when comparing

the two injection routines. This is even though the cumulative energy input being the

same at the point of five 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 reservoir

in case of cyclic injection. This suggests, that the upward transport of thermal energy

due to buoyancy is less with a cyclic injection process. A smaller influence of buoyant

forces in turn, indicates a smaller volume of steam being present.

This observation may be explained by the cyclic injection routine itself. On the one

hand, as a cyclic injection results in the repetitive heating of the same porous media

area. This is, because the thermal energy transferred to the medium during injection

periods, is distributed throughout the formation during non-injection periods. On the

other hand, it seems likely, that the oscillation of the injection pressure, originating

from the cyclic injection routine, influences the propagation of the temperature front.

Figure 4.17(a) depicts the injection pressure oscillations of the cyclic injection routine

in comparison to the continuous injection, at the injection well. In case of a cyclic

process, 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 (see

figure 4.17(b) and 4.18). As described in section 4.1.4, a pressure increase results in

an increase of the water saturation temperature according to figure 3.1. Hence, areas

of high pressure are characterized by a high water saturation temperature, as shown

in figure 4.19. In such areas, the energy needed to evaporate water, filling the pores, is

consequently more in case of the cyclic process relative to the continuous injection case.

As a result, less steam develops, which is indicated by lower steam saturations within

the formation (see figure 4.20). This suggests, that with cyclic injection, the amount

of thermal energy stored and transported with steam is less than with the continu-

ous process. Hence, the thermal energy within the hot water phase is proportionately

more with the cyclic steam injection process, which explains the fact, that the thermal

energy is less accumulated underneath the overburden, but more concentrated in the

central area of the reservoir.


(a) Node2

(b) Node3

Figure 4.17: Pressure at Node2 (x=60 m and y=8m) and Node3 (x=60m and y=20m)

in the fifth year of injection for the continuous and cyclic injection process.


(a)

51m

onth

saf

ter

star

tof

cont

inuo

usin

ject

ion

(b)

51m

onth

saf

ter

star

tof

cycl

icin

ject

ion

(c)

60m

onth

saf

ter

star

tof

cont

inuo

usin

ject

ion

(d)

60m

onth

saf

ter

star

tof

cycl

icin

ject

ion

Fig

ure

4.18

:P

ress

ure

pin

the

model

dom

ain

for

the

conti

nuou

san

dcy

clic

inje

ctio

npro

cess

,at

51m

onth

s(s

um

mer

)an

d60

mon

ths

afte

rth

est

art

ofin

ject

ion.


(a)

51m

onth

saf

ter

star

tof

cont

inuo

usin

ject

ion

(b)

51m

onth

saf

ter

star

tof

cycl

icin

ject

ion

(c)

60m

onth

saf

ter

star

tof

cont

inuo

usin

ject

ion

(d)

60m

onth

saf

ter

star

tof

cycl

icin

ject

ion

Fig

ure

4.19

:W

ater

satu

rati

onte

mper

ature

Tsa

tfo

rth

eco

nti

nuou

san

dcy

clic

inje

ctio

npro

cess

,at

51m

onth

s(s

um

mer

)an

d

60m

onth

saf

ter

the

star

tof

inje

ctio

n.


(a) Node2

(b) Node3

Figure 4.20: Steam saturation Sg at Node2 (x=60m and y=8m) and Node3 (x=60m

and y=20m) in the fifth year of injection for the continuous and cyclic injection process.

4.5 Sensitivity Study 54

4.5 Sensitivity Study

A sensitivity analysis is carried out to obtain an indication for the influence of various

system properties on the development of the temperature front for a steam injection

process. Therefor, five properties listed in table 4.3 are selected, and an upper and

lower boundary value is assumed (high and low value). For each parameter, simulation

runs determined by the high and low value are compared to the reference scenario,

given in table 4.3. The model domain of the sensitivity analysis is a section of the

model domain shown in figure 4.1. As the study only analyses the influence on

a short time scale (thus only the influence on the daily injection oscillation for a

cyclic injection process), the domain is given by a 20 mx20m box around an injection

well, which is located 5m above the reservoir bottom (see figure 4.21). The initial

temperature of the model domain is higher than for the domain given in figure 4.1, to

allow for a proper temperature front development within the short time of simulation

for the sensitivity study. The top, left and right domain boundary conditions are

those of hydrostatic pressure distribution and initial temperature.

The influence of the given parameters on the temperature front 1 C above ini-

tial temperature is analysed for a continuous and cyclic injection process, assuming

an injection rate of 0.5 t/d. For the cyclic injection, an injection window of 12 hrs/d, and

thus an actual injection rate twice that of the continuous process, is assumed. The

propagation of the temperature front is compared between the reference scenario, and

the high and low value scenario for each parameter (see figure 4.23 to 4.27). For the

cyclic injection, the point in time for the comparison is 14.5 d. For the continuous

injection it is 15 d. This allows for a comparison of the parameter’s influence between

the two processes, as the cumulative energy input is the same at these points in time.

low permeable overburden

bottom boundary: no−flow conditions

injection well 5m above bottom boundaryT (initial) = 35°CSw (initial) = 1.0

new model domain for sensitivity analysis (20m x 20m)reservoir

Figure 4.21: Model domain for the sensitivity analysis within the reservoir.


parameter unit reference value high value low value

absolute permeability K mD 75 1000 1

porosity Φ - 0.3 0.5 0.1

specific heat capacity csgJ/kg K 850 1050 650

heat conductivity λpmW/m K see figure 4.22

Van Genuchten parameter α 1/Pa 0.0028 0.01 0.0001

Table 4.3: Reference, upper and lower value for the system properties, chosen to be

analysed in the sensitivity study.

Figure 4.22: Heat conductivity as a function of water saturation. Approach of Somer-

ton, to calculate the effective heat conductivities for the fully water, and fully steam

saturated porous media. For the reference value, the method of the geometric mean is

used. The high and low value is calculated, using the method of the arithmetic mean,

respectively harmonic mean (e.g. Class (2001) [6]).


4.5.1 Absolute Permeability K

For the sensitivity analysis, the absolute permeabilty K is varied within the range

given in table 4.3. Figure 4.23 indicates, that the influence of a change in K is of the

same trend for the continuous and the cyclic injection routine.

A low absolute permeability leads to a more radial distribution of the temperature

front. While a high absolute permeability results in a less radial propagation. The

reason for that is described in detail in Ochs (2006) [20]. The so-called qs/K ratio (ratio

between steam injection rate and absolute permeability) is an indication of the balance

between viscous and buoyant forces. It originates from the linear gravity number

(Grlin), derived by Van Lookeren. Based on this approach, a decrease of the absolute

permeability at a constant injection rate, results in an increasing qs/K ratio. This

increases the influence of the viscous forces, which results in a more radial spreading

and more concentrated distribution of the steam front, respectively temperature front.

A high absolute permeability, on the other hand, increases the influence of the buoyant

forces, hence causing a less radial but more linear spreading, dominated by an upward

movement of the steam, due to density differences. In figure 4.23(b) however, it is

observed, that for this example of a cyclic injection, a high K does not result in

an increased upwards growth of the temperature front. Due to condensation, the

thermal energy sinks with the hot water, resulting in a wider horizontal spreading of

the temperature front near the domain bottom.

(a) Continuous injection (b) Cyclic injection

Figure 4.23: Propagation of the temperature front (T ≥ 36 C), with varying absolute

permeability K. After 15 d for the continuous injection, and 14.5 d for the cyclic

injection.


4.5.2 Porosity Φ

The influence of the Porosity Φ on the temperature front propagation is similar for a

continuous and cyclic injection process (as shown in figure 4.24). The change of poros-

ity basically has two effects relevant for the temperature front propagation. In a fully

water saturated system, a higher porosity results in more volume of water. This on the

one hand, decreases the average specific heat capacity of the system, as cw is smaller

than csg. This in turn would result in a faster temperature front propagation. On the

other hand, more volume of water simply results in the necessity of a higher energy

amount, to heat the water. Hence, with a constant energy input, the time needed to

heat a larger volume of water increases, which would result in a slower temperature

front propagation.

It is observed, that a low porosity results in a faster growth, while a high porosity

slightly slows the temperature front propagation. Thus, the latter of the effects de-

scribed above has the dominating influence.

For both cases, the general shape of the front is similar to that of the reference case.


Figure 4.24: Propagation of the temperature front (T ≥ 36 C) , with varying porosity

Φ. After 15 d for the continuous injection, and 14.5 d for the cyclic injection.


4.5.3 Specific Heat Capacity of the Soil Grains csg

The specific heat capacity csg of the solid phase describes the ability of the soil grains to

store thermal energy. Consequently, a high value for csg, indicating a good heat storage

ability, results in a slow propagation of the temperature front. A low value for csg,

hence accelerates the growth of the temperature front. This is observed in figure 4.25,

which shows the influence of a varying csg on the temperature front development for a

continuous and cyclic injection. The general trend resulting from a change of csg is the

same for both injection processes.


Figure 4.25: Propagation of the temperature front (T ≥ 36 C) , with a varying specific

heat capacity csg of the solid phase. After 15 d for the continuous injection, and 14.5 d

for the cyclic injection.


4.5.4 Heat Conductivity λpm

The heat conductivity λpm is a parameter, describing the average ability of the fluid

filled porous medium to transmit heat. This suggests, that an increasing λpm results in

a faster temperature front propagation and a less concentrated heat distribution. This

is also indicated by figure 4.26. The influence of λpm is rather small here, as the high

and low value has been set up accordingly to table 4.3, respectively figure 4.22.

Instead of changing the method to obtain the effective heat conductivity λpm, the

direct variation of the soil grain heat conductivity λsg may have more influence (see

section 3.3.3). λsg is set to 2.5 W/m K here, although it may be an uncertainty too. This

however is not analysed within this work.


Figure 4.26: Propagation of the temperature front (T ≥ 36 C) , with a varying heat

conductivity λ. After 15 d for the continuous injection, and 14.5 d for the cyclic injec-

tion.


4.5.5 Capillary Pressure pc and Van Genuchten Parameter α

The capillary pressure pc is a function of the residual saturations Sw,r and Sg,r of

the water and steam phase, the water saturation Sw, and the two Van Genuchten

parameters n and α (see section 3.3.2). For the sensitivity study, the latter one of

the two Van Genuchten parameters is changed within the range given in table 4.3.

According to equation 3.4, an increase of α results in a decreasing pc, and vice versa.

As shown in figure 4.27, a change of α within the given range has barely any influence

on the temperature front propagation for the time period analysed. The slightly slower

propagation with an increase of α, respectively decrease of pc, can not be explained

within this work.


Figure 4.27: Propagation of the temperature front (T ≥ 36 C) , with a varying capillary

pressure. After 15 d for the continuous injection, and 14.5 d for the cyclic injection.

4.5.6 Results of the Sensitivity Study

Of the various parameters analysed within the sensitivity study, the absolute permeabil-

ity K is identified as the system property with the biggest influence on the temperature

front propagation. While a low K results in a more radial spreading of the front, a

high K leads to a more linear propagation. The reason for that is described by the

so-called qs/K ratio (see section 4.5.1).

The remaining parameters (see table 4.3) are of small or no influence.

Chapter 5

Summary

The work presented in this thesis, is inspired by the idea to increase the efficiency of

oil production from non-conventional heavy oil deposits in a way less harmful to the

environment.

Oil extraction from non-conventional reservoirs, such as the oil sand fields in Al-

berta, Canada, is increasing, as the demand for oil rises in a manner, production

from conventional deposits is soon expected to fall below. Enhanced oil recovery

technologies, often relying on steam, are usually necessary to produce oil from such

non-conventional reservoirs. The so induced increasing demand for steam, which is

produced by fossil fuel burning steam generators, presents various environmental and

economical problems.

The motivation for the presented work is thus the idea of solarthermal steam

generation plants for the steam assisted gravity drainage technology. Solarthermal

steam generation will lead to a cyclic injection process due to daily and seasonal

variations of solar radiation.

A two-dimensional, non-isothermal water steam model is used to simulate steam

injection into saturated porous media through a single injection well. The applied

model does not include oil, neither as a phase nor as a component. Hence, the

influence of a cyclic injection process on the oil production is not subject of this thesis.

The underlying mathematical model concept and the reservoir properties of the system

are described in chapter 2 and chapter 3 of this work. In chapter 4, the influence of

a cyclic injection routine on the fluid flow and transport processes is analysed and

compared to a continuous injection routine, using the described model. Furthermore,

a sensitivity study identifies the absolute permeability K as the system property,

which influences the temperature front propagation the most amongst the analysed

parameters. This is because of its influence on the balance between viscous and

buoyant forces, as described in detail in Ochs (2006) [20].

61

5.1 Conclusion 62

5.1 Conclusion

The hydrodynamical study of the two different steam injection processes, yields the

conclusion, that there is a difference between the cyclic and continuous injection

routine with respect to the steam chamber and temperature development within the

reservoir.

For the continuous injection process described in this work, the dominant transport

mechanism of thermal energy is convection. Hence, the temperature front development

basically follows the continuous steam chamber growth, as long as the steam front is

propagating.

In contrast, the temperature front development does not necessarily follow the

steam chamber growth in case of cyclic injection. In addition to convection, the

transport of thermal energy due to conduction plays an important role during

non-injection periods. As a result, the temperature propagates continuously within

the reservoir, while due to condensation, the steam chamber volume is reduced during

injection pauses.

Furthermore it is observed, that although the cumulative energy input is the same

for both injection routines, the temperature front develops differently with cyclic

injection. The thermal energy is thus differently distributed. The presented work

suggests, that the reason for the different distribution of thermal energy within the

reservoir, is the cyclic injection routine itself. This is because, based on the assumption

of the same cumulative energy input, a higher injection rate is needed in case of the

cyclic injection routine. The consequence is a higher pressure distribution within the

reservoir. This in turn results in higher temperatures where water and steam are in

equilibrium according to the curve of saturation-vapor pressure over temperature (see

figure 3.1). Hence, less steam develops within the reservoir, resulting in a decline of

buoyant transport.

In summary, two distinct influences of the cyclic injection routine on the steam

flow and energy transport in the subsurface are established in this thesis:

− Vibrant steam chamber growth with a heterogeneous steam saturation distribu-

tion

− Increased concentration of thermal energy within the central area of the reservoir.

The influence of a cyclic injection routine and its consequences on the profitability of

the bitumen and heavy oil business can not be evaluated, based on the work presented

in this thesis.

5.2 Outlook 63

5.2 Outlook

The applied 2D model represents a simplification of the situation in the reservoir and

neglects the component oil. A statement about the influence of a cyclic injection

routine on the oil production rate, respectively the adaptability of solarthermal steam

generation for SAGD, is thus not possible. Open questions remaining are:

− Would the temperature distribution within the reservoir in case of cyclic injec-

tion still differ from continuous injection, if steam and temperature fronts of

neighbouring injection wells link up?

− Would a different temperature distribution within the reservoir influnce the oil

production and if yes, in which way?

− How would the fluctuating steam chamber growth in case of cyclic injection in-

fluence the oil production rate?

Tasks for future work related to this topic may therefore be:

− Implementation of production well to complete well pair

− Model implementation of several well pairs

− Development of a non-isothermal water steam oil model.

Bibliography

[1] Bastian, P., Birken, K., Johannsen, K., Lang, S., Eckstein, K., Neuss, N., Rentz-

Reichert, H., and Wieners, C. UG - A Flexible Software Toolbox for Solving

Partial Differential Equations. Computing and Visualization in Science, 1(1), S.

27-40, 1997.

[2] BGR: Bundesanstalt fur Geowissenschaften und Rohstoffe. Energierohstoffe 2009

- Reserven, Ressourcen, Verfugbarkeit. http://www.bgr.bund.de, 2009.

[3] Birrel, G. E., Aherne, A. L., and Seleshanko, D. J. Cyclic SAGD - economic impli-

cations of manipulating steam injection rates in SAGD projects - re-examination

of the Dover project. Journal of Canadian Petroleum Technology, 44, 2005.

[4] BP. BP Statistical Review of World Energy June 2009 0. bp.com/statisticalreview,

2009.

[5] Butler, R. M. Thermal Recovery of Oil and Bitumen. Prentice Hall, 1991.

[6] Class, H. Theorie und numerische Modellierung nichtisothermer Mehrphasen-

prozesse in NAPL-kontaminierten porosen Medien. Dissertation, Institut fur

Wasserbau, Universitat Stuttgart, 2001.

[7] Corey, A. T., Kemper, W. D., and Dane, J. H. Revised Model for Molecular

Diffusion and Advection. Vadose Zone Journal, 9, 2009.

[8] Darcy, H. P. G. Les Fontaines Publiques de la Ville de Dijon. 1856.

[9] Environment Canada. National Climate Data and Information Archive.

www.climate.weatheroffice.gc.ca, 1971-2000.

[10] Faerber, A. Warmetransport in der ungesattigten Bodenzone: Entwicklung einer

thermischen In-Situ Sanierungstechnologie. Dissertation, Institut fur Wasserbau,

Universitat Stuttgart, 1997.

[11] Helmig, R., Class, H., Huber, R., Sheta, H., Ewing, R., Hinkelmann, R., Jakobs,

H., and Bastian, P. Architecture of the Modular Program System MUFTE-UG

for Simulating Multiphase Flow and Transport Processes in Heterogeneous Porous

Media. Mathematische Geologie, 2:123–131, 1998.

64

BIBLIOGRAPHY 65

[12] Helmig, R. Multiphase Flow and Transport Processes in the Subsurface. Springer,

1997.

[13] Hong, K. C. Steamflood Reservoir Management - Thermal Enhanced Oil Recovery.

Penwell Books, 1994.

[14] IEA: International Energy Agency. World Energy Outlook 2009 - Executive Sum-

mary. http://www.iea.org/ or OECD/IEA in Paris, France, 2009.

[15] IFC: International Formulation Committee. A formulation of the thermody-

namic properties of ordinary water substance. Technical report, IFC Sekretariat,

Dusseldorf, Germany, 1967.

[16] Jimenez, J. The Field Performance of SAGD Projects in Canada. International

Petroleum Technology Conference (IPTC) in Kuala Lumpur, Malaysia, 2008.

[17] Kraemer, D., Bajpayee, A., Muto, A., Berube, V., and Chiesa, M. Solar assisted

method for recovery of bitumen from oil sand. Applied Energy, 2008.

[18] Langeheinecke, K., Jany, P., and Sappert, E. Thermodynamik fur Ingenieure,

Band 4. Auflage. Vieweg Verlag, 2003.

[19] Nasr, T. N., Golbeck, H., Korpany, G., and Pierce, G. SAGD Operating Strategies.

SPE International Conference on Horizontal Well Technology in Calgary, Alberta,

Canada, 1998.

[20] Ochs, S. Steam injection into saturated porous media - process analysis including

experimental and numerical investigations. Dissertation, Institut fur Wasserbau,

Universitat Stuttgart, 2006.

[21] Panday, S., Forsyth, P. A., Falta, R. W., Wu, Y., and Huyakorn, P. S. Consider-

ations for robust compositional simulations of subsurface nonaqueous phase liquid

contamination and remediation, Band 5. Water Resources Research, 1995.

[22] Prof. Dr. Ing. Voss, A. Energiesysteme 1, Band 3. Vorlesungsskript IER, Univer-

sitat Stuttgart, Germany, 2005.

Cyclic Steam Injection into the Subsurface - … · Diplomarbeit Cyclic Steam Injection into the...

Documents

Transcript of Cyclic Steam Injection into the Subsurface - … · Diplomarbeit Cyclic Steam Injection into the...