Thermal recovery by steam injection

The most common method used to enhance oil production over primary rates is water injection, commonly referred to as secondary oil recovery. Common practice in the industry is to refer to all other methods as tertiary enhanced oil recovery. According to Prats, thermal enhanced oil recovery (TEOR) is a family of tertiary processes defined as "any process in which heat is introduced intentionally into a subsurface accumulation of organic compounds for the purpose of recovering fuels through wells." This article provides an introduction to the mechanisms by which steam can enhance oil recovery.

Steam

The most common vehicle used to inject heat is saturated steam. Hot water and heated gasses have been tried, but none are as effective as quality steam. According to a 2000 Oil & Gas Journal survey, steam enhanced oil recovery (EOR) projects accounted for 417,675 barrels of oil per day (BOPD), or 56% of the total for all tertiary enhanced recovery methods. That production rate has been essentially flat for more than 15 years. Hydrocarbon gas injection and CO₂ gas injection are the only other significant contributors and amount to only 17 and 24%, respectively.

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Properties of saturated steam

Like other substances, water can exist in the form of a solid (ice), as a liquid (water), or as a gas (loosely called steam). Steamflood processes are concerned with the liquid and gas phases, and the change from one phase to the other. The phase change region, in which water coexists as liquid and gas, is where our interest lies when considering steam for use in the oil field. The term "steam" is an imprecise designation because it refers to a water liquid/gas system that can exist from 32°F to any higher temperature; from 0.1 psia to any higher pressure; and from nearly all liquid to 100% gas. Steam quality refers to the phase change region of liquid to gas and is defined as

....................(1)

Heat capacity is expressed in units of Btu/(lbm-°F). A "Btu" is defined as the amount of heat required to raise 1 lbm of water from 60 to 61°F. All liquids and solids are compared to pure water, which has the highest heat capacity of any substance at 1 Btu/(lbm-°F). By calculating a ratio of the heat capacity of water divided by that of another substance, a convenient fraction called "specific heat" is obtained. Notice that petroleum has a specific heat of 0.5, or half that of water, and sandstone is only 20% of water on a per pound basis. No other liquid or gas carries as much heat per pound as water. Also, the temperature range at which this high heat carrying performance is achieved, 34 to 700°F, is ideal for many processes, including steamflooding.

Enthalpy is a useful property defined by an arbitrary combination of other properties and is not a true form of energy. The absolute value of enthalpy is of no practical value. Changes in enthalpy are extremely useful, however, and are the basis for steamflood energy calculations. The total enthalpy held by each pound of liquid water at any temperature is called sensible heat, h_f. The heat input, which produces a change of state from liquid to gas without a change of temperature, is called the "latent heat of evaporation" and is shown by h_fv. The total heat, h_v, in each pound of 100% quality or saturated steam is the sum of these two, h_v = h_f + h_fv.

In the phase change or "saturation" region, steam can only exist at one temperature for a given pressure regardless of quality or latent heat content, as shown in Fig. 1 . Steam increases in volume as latent heat increases, as in Fig. 2. This is a useful property in displacing oil in a steamflood process. The volume occupied by 1 lbm of steam at any pressure is its specific volume in ft³/lbm and is represented by υ_s. Values for these thermal properties of water are published widely. Fig. 3 is a chart of the phase change region. Equations have been derived that approximate the values to acceptable accuracy for most steamflood calculations.

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• 

  Fig. 1 – Saturation steam temperature and pressure.

• 

  Fig. 2 – Steam specific volume vs. saturation pressure.

• 

  Fig. 3 – Enthalpy of wet steam as a function of saturation pressure, temperature, and steam quality.

Simple versions that are accurate to within a few percent in the normal pressure ranges encountered in steamflooding projects are

....................(2)

....................(3)

....................(4)

....................(5)

....................(6)

....................(7)

and

....................(8)

These are recommended for hand calculations or simple analytical equations. There are more precise versions in the literature, but for most purposes, Eqs. 2 through 8 are more accurate than any other available information that goes into steamflood calculations and are more than adequate for most calculations. The more accurate equations are cumbersome and lend themselves to computer applications. However, in a computer application, a lookup table is easy to create and is much more accurate than even the advanced analytical equations.

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Reservoir heating

The basis for reservoir heat transfer calculations is traced back to the published solution to a mechanical engineering problem. Marx and Langenheim were the first to publish an adaptation of this solution to a steamflood process. They assumed that the equations for temperature response in a thin plate, backed in perfect contact to a semi-infinite solid after sudden exposure to constant-heat input, were analogous to steam injection into an oil-bearing reservoir.

Fig. 4 shows the temperature distribution anticipated in this model. The entire flood zone is at steam temperature upstream of the steam front, and the reservoir downstream of the steam front is at initial reservoir temperature. The true temperature profile is much less defined.

• 

  Fig. 4 - Temperature profile resulting from convection and conduction caused by piston displacement of steam (after Marx and Langenheim).

Their equation for the heated area, A_t, over time, t, is

....................(9)

G(t_D) from the mechanical engineering problem is a function of dimensionless time, t_D.

....................(10)

where t_D is time of injection, t, multiplied by a few reservoir properties.

....................(11)

and the complementary error function, erfc(x), is common in heat conduction calculations. Several publications have tables of values for G(t_D) vs. time, but van Lookeren offers a simple equation with sufficient accuracy for most calculations, which is written as

....................(12)

Other useful relationships derived from the Marx and Langenheim equations are heat loss to the adjacent formations,

....................(13)

rate of heated zone growth,

....................(14)

heat remaining in the reservoir,

....................(15)

cumulative heat loss to the adjacent formations,

....................(16)

and reservoir efficiency or fraction of injected heat remaining in the reservoir,

....................(17)

Two constants appear in the equations that need definitions. M_R is the volumetric heat capacity of the composite formation including rock and fluids.

....................(18)

Note that there are two gas components: inert gas represented by the volumetric heat capacity, M_g, and steam represented by two terms, one owing to the latent heat of vaporization and one to the sensible heat.

Thermal diffusivity, α, is the ratio of the thermal conductivity to the volumetric heat capacity,

....................(19)

Farouq Ali showed it is appropriate to use average values for M and α when the thermal properties of various layers of formation and over/underburden differ significantly.

Ramey and Prats showed that Eq. 17, reservoir heating efficiency, E_h, is independent of reservoir and steam zone geometry. Further the relationships apply to any form of heat transport (convection, conduction, or even radiation) in the plane of the reservoir and when the heat transport to adjacent formations is three-dimensional (3D). Assuming the reservoir properties are constant and vary little with changing temperature, E_h is solely a function of dimensionless time.

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Steam zone growth

Reservoir heating by steam injection translates into the formation of a swept zone of some shape and an oil bank consisting of a migrating zone containing the displaced oil. Two general concepts have been proposed to describe this process.

Viscous displacement

This is an extension of early water flooding concepts in which the displacement front is considered to be an advancing vertical front, the plane of which is normal to the bedding plane and extending vertically from the top to the bottom of a homogeneous flow section. Displacement of oil in this model is piston-like and is directly proportional to injection rate. The equations in the Reservoir Heating section, have been used to calculate steamfloods as frontal advance floods.

Mandl and Volek, followed by a slight modification by Myhill and Stegemeier, contributed the concept of a critical time beyond which the vapor front stagnates and heat is carried only by hot water traveling through the condensation front. Dimensionless critical time, t_cD, is defined by

....................(20)

where f_hv is the fraction of heat injected as latent heat.

....................(21)

and f_s and h_fv are at reservoir conditions.

....................(22)

The Marx and Langenheim equation (Eq. 10) is an upper bound to Eq. 22, as shown in Fig. 5.

• 

  Fig. 5 – Fraction of injected steam remaining in steam zone.

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Bypass

These models address the severe buoyancy forces that pertain when steam vapor, a gas, is injected into a liquid filled reservoir. In bypass models, the fronts are not vertical; the steam migrates quickly to the top of the reservoir. Van Lookeren describes the severity of this override with a buoyancy factor.

....................(23)

Average steam zone thickness is

....................(24)

The shape of the steam zone is described by

....................(25)

Note that steam zone thickness is not dependent on net zone thickness in Eqs. 24 and 25.

Fig. 6 shows the calculated injector liquid level as a function of time and five values of A_RD. A_RD is normally smaller than 0.6 in field projects; thus, the steam zone does not cover the vertical zone except for very thin reservoirs.

• 

  Fig. 6 – Effect of the ratio of viscous to gravity forces on the location of steam displacement fronts.

Neuman addresses the bypass or steam override concept by basically assuming that injected steam quickly rises to the top of the zone and spreads out evenly. Thickness of the steam zone, h_s, is related to

....................(26)

Combination

Field projects usually include features of both frontal advance and bypass processes. Owens and Ziegler propose an analytical model that calculates the contribution of each process. They calculate total oil rate, q_o, as the sum of gravity drainage oil rate, q_og, after Clossman, and viscous oil rate, q_ov, as

....................(27)

....................(28)

and

....................(29)

where

....................(30)

....................(31)

....................(32)

and

....................(33)

This series of equations can be solved in a computer spreadsheet. The authors report that the viscous component of oil rate in the Kern River Ten-Pattern is significant and varied from 66% early in the project to 53% later. The method is also used to show the effect of operating with (supporting q_ov) and without (inhibiting q_ov) a casing vapor recovery system. Fig. 7 shows the impact of shutting in the casing vapor recovery on a selected project. This is not to say that shutting in casing vapor recovery will have this profound negative impact on every steamflood. Notice that this method does not account for steam injection rate. A project that is significantly over-injected (high-pressure drawdown) would be expected to respond as in Fig. 7, while a project with more controlled steam rate (modest-pressure drawdown) may show little, if any, reduction in production rate.

• 

  Fig. 7 – Effect of shutting in casing vapor recovery system on a selected steamflood project.

Kimber et al. found with a physical model that there is a viscous component of steamflooding that has potential to add significant oil recovery. Fig. 8 shows that there is an optimal steam quality for a steamflood and that some amount of overinjection may be beneficial also. Ward and Sharpe studied the subject at the Kern River field using a numerical simulator and found that shutting in the casing vents resulted in a permanent 18% loss in oil production rate as shown in Fig. 9. Oil production could be restored if either the vents were reopened or a depleted zone in the wellbore were perforated, allowing the excess steam to vent by crossflow.

• 

  Fig. 8 – The effect of latent heat injection rate on strategy economics.

• 

  Fig. 9 – Results of a numerical simulation showing 18% loss in production resulting from shutting in casing vapor recovery.

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Nomenclature

A	=	area, sq ft [m2]
ARD	=	dimensionless buoyancy defined in Eq. 23
At	=	time-dependent heated area, sq ft [m2]
Bo	=	oil formation volume factor, RB/STB [res m3/stock-tank m3]
C	=	isobaric specific heat
Can	=	isobaric specific heat of annular fluid, Btu/(lbm-°F) [kJ/kg•K]
Co	=	isobaric specific heat of oil, Btu/(lbm-°F) [kJ/kg•K]
Cw	=	isobaric specific heat of water, Btu/(lbm-°F) [kJ/kg•K]
D	=	depth below surface, ft [m]
erfc(x)	=	complementary error function
E	=	efficiency
Ec	=	fraction of oil displaced that is produced
Eh	=	heat efficiency—fraction of injected heat remaining in reservoir
f	=	volumetric fraction of noncondensable gas in vapor phase
fhv	=	fraction of heat injected as latent heat
fp	=	fraction of heat injected that is produced
fpD	=	heat loss factor caused by hot fluid production
fR	=	oil recovery factor defined by Eq. 14
fs	=	steam quality
fVr	=	conductive heat loss factor caused by radial conduction
fVz	=	conductive heat loss factor caused by vertical conduction
Ffo	=	ratio of fuel burned to produced oil, B/B [m3/m3]
Fof	=	produce oil/fuel burned ratio, B/B [m3/m3]
Fos	=	produce oil/injected steam ratio, B/B [m3/m3]
g	=	gravity acceleration constant, 32.174 ft/sec2 [9.8067 m/s2]
gc	=	conversion factor in Newton’s second law of motion, 32.174 lbm-ft/lbf-s2 [1.0 kg•m/N•s2]
G (tD)	=	function defined by Eq. 10
h	=	enthalpy per unit mass, Btu/lbm [kJ/kg]
he	=	fluid level in reservoir at external boundary, ft [m]
hf	=	enthalpy of liquid portion of saturated steam, Btu/lbm [kJ/kg]
hfc	=	forced convection coefficient of heat transfer, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hfs	=	enthalpy of < 100% quality saturated steam, Btu/lbm [kJ/kg]
hft	=	film coefficient of heat transfer, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hfv	=	enthalpy of vapor portion of saturated steam, Btu/lbm [kJ/kg]
hh	=	fluid level in stimulated reservoir, ft [m]
hn	=	net reservoir thickness, ft [m]
hpi	=	film coefficient of heat transfer at pipe inner radius, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hpo	=	film coefficient of heat transfer at pipe outer radius, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hr	=	coefficient of radiant heat transfer for the outermost surface, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hrc,an	=	radiant/convection heat transfer coefficient in well annulus, Btu/(sq ft-D-°F) [kJ/m2•d•K]
hs	=	steam zone thickness, ft [m]
ht	=	gross reservoir thickness, ft [m]
hv	=	enthalpy of 100% quality (saturated) saturated steam, Btu/lbm [kJ/kg]
hw	=	fluid level in cold wellbore, ft [m]
iw	=	cold water equivalent steam injection rate, B/D [m3/d]
J	=	productivity of a cold well, B/psi-D [m3/kPa•d]
Jh	=	productivity of a stimulated well, B/psi-D [m3/kPa•d]
k	=	reservoir permeability, md [μm3]
kro	=	relative permeability to oil
krs	=	relative permeability to steam
L	=	distance between wells, ft [m]
m	=	mass, lbm [kg]
m*	=	exponent in Eq. 33
mcasing_blow	=	mass (gas) extracted from system, lbm [kg]
mi	=	mass injection, lbm [kg]
minflux	=	mass exiting system, lbm [kg]
ml	=	mass of liquid, lbm [kg]
m(o/w)influx	=	mass flowing into system, lbm [kg]
m(o/w)prod	=	mass (fluid) extracted from system, lbm [kg]
mv	=	mass of vapor, lbm [kg]
mZ(accum)	=	mass accumulating in system, lbm [kg]
Mg	=	volumetric heat capacity of gas, Btu/(ft3-°F) [kJ/m3•K]
Mo	=	volumetric heat capacity of oil, Btu/(ft3-°F) [kJ/m3•K]
MR	=	volumetric heat capacity of the reservoir, Btu/(ft3-°F) [kJ/m3•K]
Ms	=	volumetric heat capacity of steam zone, Btu/(ft3-°F) [kJ/m3•K]
MS	=	volumetric heat capacity of surrounding formation, Btu/(ft3-°F) [kJ/m3•K]
Mw	=	volumetric heat capacity of water, Btu/(ft3-°F) [kJ/m3•K]
Mσ	=	volumetric heat capacity of reservoir rocks, Btu/(ft3-°F) [kJ/m3•K]
n	=	index of time increment
N	=	initial oil in place, B [m3]
Nd	=	oil displacement rate, B/D [m3/d]
NGr	=	Grashof number
Nm	=	initial mobile oil in place, B [m3]
Np	=	cumulative oil produced, B [m3]
NPr	=	Prandtl number
NRe	=	Reynolds number
p	=	atmospheric pressure, psia [kPa]
pe	=	external boundary pressure, psia [kPa]
ps	=	steam pressure, psia [kPa]
pw	=	wellbore pressure, psia [kPa]
	=	steam injection rate to make up for surface heat losses, B/D [m3/d]
qgh	=	hot gas production rate, Mcf/D [std m3/d]
qis	=	reproduced steam rate, B/D [m3/d]
qiso	=	initial steam injection rate, B/D [m3/d]
qls	=	steam injection rate to make up for reservoir heat losses, B/D [m3/d]
qoc	=	cold oil production rate, B/D [m3/d]
qog	=	oil production rate owing to gravity displacement, B/D [m3/d]
qoh	=	hot oil production rate, B/D [m3/d]
qoi	=	initial oil production rate, B/D [m3/d]
qot	=	total oil production rate, B/D [m3/d]
qov	=	oil production rate because of viscous displacement, B/D [m3/d]
qps	=	steam rate to replace reservoir volume of produced oil, B/D [m3/d]
qwc	=	cold water production rate, B/D [m3/d]
qwh	=	hot water production rate, B/D [m3/d]
Q	=	amount of injected heat remaining in reservoir, Btu [kJ]
Q casing_blow	=	heat removed with produced gas, Btu [kJ]
Qi	=	total heat injected, Btu [kJ]
Q influx	=	heat leaving system, Btu [kJ]
Ql	=	heat lost in reservoir, Btu [kJ]
Qls	=	surface piping heat loss/unit length, Btu/ft [kJ/m]
Qot	=	cumulative oil recovery at time (t), B/D [m3/d]
Q (o/w)influx	=	heat flowing into system, Btu [kJ]
Q(o/w)prod	=	heat removed with produced liquids, Btu [kL]
Qz(accum)	=	heat accumulating in system, Btu [kJ]
	=	heat injection rate, Btu/D [kJ/d]
	=	heat loss rate, Btu/D [kJ/d]
	=	heat removed with produced fluids, Btu/D [kJ/d]
	=	volumetric heat injection rate, MMBtu/D/acre-ft [kJ/m3]
r	=	radius of reservoir, ft [m]
rci	=	casing internal radius, ft [m]
rco	=	outer casing radius, ft [m]
re	=	external radius of heated zone, ft [m]
rEa	=	altered radius in earth around wellbore, ft [m]
rh	=	radius of heated or steam zone, ft [m]
ri	=	inside pipe radius, ft [m]
rins	=	insulation external radius, ft [m]
ro	=	outside pipe radius, ft [m]
rw	=	radius of well, ft [m]
Rh	=	overall specific thermal resistance, °F-ft-D/Btu [K•m•d/kJ]
S	=	skin factor before stimulation
Sg	=	gas saturation fraction
Sh	=	skin factor after stimulation
So	=	oil saturation
Soi	=	initial oil saturation fraction
Som	=	mobile oil saturation fraction
Sor	=	residual oil saturation fraction
Sors	=	residual oil saturation to steam fraction
Sorw	=	residual oil saturation to water fraction
Sw	=	water saturation fraction
t	=	time, D [d]
t*	=	time at which steam injection rate reduction is to begin, D [d]
tcD	=	critical dimensionless time
tD	=	dimensionless time
T	=	average temperature in heated reservoir, °F
T*	=	temperature above which oil saturation is reduced to Sorw, °F
Ta	=	air temperature, °F
TA	=	ambient temperature, °F
Tb	=	bulk fluid temperature, °F
TBHF	=	bottomhole fluid temperature, °F
Tci	=	temperature of casing wall, °F
TE	=	temperature of earth, °F
TFW	=	steam generator feedwater temperature, °F
Th	=	temperature in stimulated zone, °F
Ti	=	influx water temperature, °F
To	=	temperature of outer surface, °F
Tp	=	produced fluid temperature, °F
TR	=	unaffected reservoir temperature, °F
Ts	=	steam temperature, °F
TSZ	=	steam zone temperature, °F
u	=	volumetric flux, ft3/sq ft-D [m/d]
U	=	unit function equals 1 for tD – tcD > 0, 0 for tD – tcD < 0 in Eq. 22
Vs	=	steam zone volume, acre ft [m3]
wst	=	mass flow rate of dry steam, lbm/D [kg/d]
x	=	distance along the x ordinate
X	=	factor defined in Eq. 30
Y	=	factor defined in Eq. 31
α	=	thermal diffusivity of reservoir, ft2/D [m2/d]
αE	=	thermal diffusivity of earth, ft2/D [m2/d]
αs	=	thermal diffusivity of surrounding formation, ft2/D [m2/d]
β1	=	thermal volumetric expansion coefficient, 1/°F [1/K]
βan	=	volumetric thermal expansion coefficient of gas in annulus, 1/°F [1/K]
γ	=	specific gravity
Δ	=	increment or decrement
Δhh	=	change in stimulated zone fluid level, ft [m]
Δt	=	time steps, D [d]
ΔT	=	steam temperature/reservoir temperature, Ts/TR , °F
Δγ	=	oil/steam specific gravity difference
Δρ	=	density difference between water and oil, lbm/ft3 [kg/m 3]
ε	=	emissivity
εci	=	radiant emissivity of casing wall
εins	=	radiant emissivity of insulation outer surface
θc	=	wetting contact angle, deg (°) [rad]
θ	=	formation dip angle, deg (°) [rad]
λ	=	thermal conductivity, Btu/(ft-D-°F) [kJ/m•d•K]
λa	=	thermal conductivity of air, Btu/(ft-D-°F) [kJ/m•d•K]
λa,a	=	thermal conductivity of air in well annulus, Btu/(ft-D-°F) [kJ/m•d•K]
λE	=	thermal conductivity of unaltered earth, cp [Pa•s]
λEa	=	thermal conductivity of altered earth, cp [Pa•s]
λins	=	thermal conductivity of insulation, cp [Pa•s]
λp	=	thermal conductivity of pipe, cp [Pa•s]
λS	=	thermal conductivity of surrounding formation, cp [Pa•s]
μ	=	viscosity, cp [Pa•s]
μa	=	viscosity of air, cp [Pa•s]
μan	=	viscosity of well annulus gas, cp [Pa•s]
μoh	=	hot oil viscosity, cp [Pa•s]
μoi	=	initial oil viscosity, cp [Pa•s]
μs	=	steam viscosity, cp [Pa•s]
π	=	constant pi, 3.141
ρ	=	density, lbm/ft3 [kg/m3]
ρa,sc	=	density of air, lbm/ft3 [kg/m 3]
ρan	=	density of well annulus gas, lbm/ft3 [kg/m3]
ρo	=	density of oil, lbm/ft3 [kg/m3]
ρs	=	density of dry steam, lbm/ft3 [kg/m3]
ρw	=	density of water, lbm/ft3 [kg/m3]
ρw,sc	=	density of water at standard conditions, 62.4 lbm/ft3 [662.69 kg/m3]
σ	=	interfacial tension, oil/water, dyne/cm [mN/m]
τ	=	time since location in reservoir reached steam temperature, D [d]
υs	=	steam specific volume, ft3/lbm [m3/kg]
υw	=	wind velocity, miles/hr [km/h]
Ф	=	porosity

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References

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Noteworthy papers in OnePetro

Morrow, A. W., Mukhametshina, A., Aleksandrov, D., & Hascakir, B. 2014. Environmental Impact of Bitumen Extraction with Thermal Recovery. Society of Petroleum Engineers. http://dx.doi.org/10.2118/170066-MS

Mukhametshina, A., Morrow, A. W., Aleksandrov, D., & Hascakir, B. 2014. Evaluation of Four Thermal Recovery Methods for Bitumen Extraction. Society of Petroleum Engineers. http://dx.doi.org/10.2118/169543-MS

Mukhametshina, Albina, & Hascakir, B. 2014. Bitumen Extraction by Expanding Solvent-Steam Assisted Gravity Drainage (ES-SAGD) with Asphaltene Solvents and Non-Solvents. Society of Petroleum Engineers. http://dx.doi.org/10.2118/170013-MS

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

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See also

Steamflood design

Cyclic steam stimulation design

Horizontal well applications in steamflooding

Facilities for steam generation

In-situ combustion

Steam assisted gravity drainage

Electromagnetic heating of oil

Heavy oil

PEH:Thermal_Recovery_by_Steam_Injection

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