Steamflood design

Designing a successful steamflooding project requires good candidate selection and an excellent understanding of the mechanisms by which recovery is enhanced.

Candidate selection

Screening criteria for identification of steamflood candidates have been published for many years. Table 1 shows the screening guides from five different sources.

• 

  Table 1 - Steamflood project screening criteria

It is obvious from Table 1 that there is a finite envelope of properties that define successful candidates. However, within that envelope there is a relatively wide spread of values for the indicators. The reason for this is that each reservoir is unique and success is a function of a combination of all of the screening criteria plus a myriad of other considerations. The authors of the papers typically offer linear regression equations to generate an indicator for a specific reservoir. The most recent version is by Donaldson, which is written as

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

Doscher and Ghassemi showed that there is an upper oil viscosity barrier that makes economic recovery of very viscous oils very difficult by conventional steamflood methods. Using scaled physical models, they found that for oils with a viscosity much greater than that in the Kern River or Midway Sunset fields in California, the steam/oil ratio for conventional steamflood or cyclic steam stimulation was uneconomic. The 14 and 12° API lines on Fig. 1 show the general upper bound range for oil viscosity in a successful conventional steamflood. They proposed a correlation equation to estimate the limiting viscosity. The correlation is a function of steam and oil viscosities.

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

Other critical requirements exist such as reservoir continuity between injector and producer and barriers to contain steam from uncontrolled migration to nonsteam-bearing intervals. Qualitatively, one looks for relatively shallow, low pressure, low temperature, thick, high porosity, highly permeable reservoirs with medium to high saturation of high viscosity liquid oil.

• 

  Fig. 1 – Temperature dependence on viscosity for crude oils.

All of the following applies to oil sands with mobile oil. The enhanced recovery process in reservoirs that are fractured during the steam injection process are too complicated to be calculated with analytical models.

Analogy

The simplest way to design an steamflood project is by analogy. If there is an analogous project in the same field or in a field with enough similarities to the one in question, simply using the design and results from the former may be adequate. Fig. 2 from a paper by Greaser et al. in the Kern River field, California is an example of the use of analogy. In that project there are thousands of steamflood injection zones. Texaco made good use of the huge amount of steamflood performance data by calculating an "average pattern response" and using that as the standard to design and monitor future flood patterns.

• 

  Fig. 2 – Kern River “average pattern” used as an analogy to evaluate field performance.

Recovery mechanisms

Waterflooding, successful in reservoirs with low viscosity/high mobility crude oil, is extremely inefficient in reservoirs with low mobility/high viscosity crude oil. Three dimensionless flow parameters help us understand the problem.

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

These are, respectively, the ratio of gravity forces to applied pressure; the ratio of capillary forces to applied pressure; and the ratio of applied pressure to viscous forces. The ability to modify the variables in the above relationships is indicative of the potential success of extracting oil from the reservoir.

In the gravity ratio, the main controllable parameter is the distance between the injector and producer. The only other potential variable is density difference between injectant and the crude oil, which is large but does not change appreciably.

σ cosθ_c in the capillary pressure-applied pressure ratio represents the interfacial tension of the crude oil in the rock pore and can be varied. The obvious goal is to reduce it to zero. Several approaches have been tried, including adding emulsified chemicals in the steam to form a single-phase water/oil emulsion, which has lower viscosity and lower interfacial tension than the crude alone. Many field trials have been tried over the years but have yet to prove economical.

The viscosity parameter in the third ratio has been the most important in designing a successful steamflood project. Other methods of reducing oil viscosity, such as miscible solvent injection, have been tried but have proven to be far inferior to heat injection. Fig. 1 shows the viscosity vs. temperature relationship for a few representative crude oils. Raising the temperature of the oil from the typical reservoir temperature of less than 100°F to approximately 300°F gives a viscosity reduction of orders of magnitude. Of all of the potential heat-carrying media, water-based steam is inexpensive and universally available and has the highest heat-carrying capacity of any compound; it exists at the ideal 300 to 500°F temperature range to achieve optimal oil viscosity reduction.

Texaco published a correlation that estimates the residual oil saturation to steam based on the huge database generated over the decades of steamflood in the Kern River field. They found the residual saturation is a function of gross zone thickness and presteam oil viscosity. There appears to be an optimal zone thickness, above and below, where residual oil is less attractive. Residual oil saturation continuously increases for increasing viscosity, reaching a point of immobile oil at some high value. Their data was based on an average initial oil saturation of 55%. Fig. 3 shows their correlation, normalized for any initial oil saturation. Short of actual core or laboratory data, that figure can be used to estimate residual oil saturation by finding the value of the factor for the desired initial oil saturation and zone thickness and then multiplying that factor by initial oil saturation. The equations presented next provide an alternative method for obtaining the same information.

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

where

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

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

and

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

This is instructive as to the qualitative relationships between the parameters, but caution should be used when applying it quantitatively outside of the Kern River field. Also, the authors explain that they had no information for zones thicker than 120 ft or oil viscosity greater than 16,000 cp.

• 

  Fig. 3 – Graph of a dimensionless function F_Sor, which relates residual oil saturation to gross section thickness and presteam oil viscosity.

Other mechanisms include formation compaction, in-situ steam distillation generated solvent banks, and formation and fluid heat-induced swelling, but they are rarely necessary to supplement the previous ones in adequately describing the steamflood process. Of these secondary mechanisms, compaction has had the most significant impact on recovery. The most notable regions to benefit are the Bolivar Coast, western Venezuela, and the Long Beach area near Los Angeles, California. The Bolivar Coast has been using cyclic steam stimulation (CSS) since the early 1960s. Rattia and Farouq Ali published a study that concluded that formation compaction enhanced process efficiency in CSS but harmed process efficiency in steamflood.

Design calculations: viscous displacement models

Marx-Langenheim and Mandl-Volek (M-V) models

These steam zone growth models have often been used to calculate cumulative oil recovery and steam zone size over time. They are a simple way to get a quick estimate of project viability. Volume of steam zone is proportional to the fraction of heat remaining in the steam zone, E_h.

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

It follows that oil displaced from the steam zone is

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

E_c is an arbitrary "capture" factor that is inserted to "scale" invariably optimistic oil volume to realistic values. This factor is best determined by history matching the equation to field project and normally has a value from 0.7 to 1.0. This represents a serious limitation in calculating oil recovery because the calculation predicts the highest oil production rate at the beginning of the project.

This method is most useful in calculating steam zone size and extent. It is less useful for calculating oil rates and recovery because it does not account for the terms in the ratios in Eq. 3.

The calculation allows any value for steam injection rate and calculates oil rate. Information on practical steam rates must be found before practical results can be derived. Either method can be done by hand or in a computer spreadsheet.

Jones model

The Jones  model extended the M-V model by accounting for the third dimensionless factor in Eq. 10 and by honoring the oil in place. The model modifies the former model by calculating the delayed oil response to a growing steam chest using the third term in Eq. 3, which shows that well spacing and oil viscosity are important parameters. Also addressed is the often-present depletion in the form of in-situ gas and depletion gas cap, both of which must be filled with steam before oil can be displaced. M-V steam zone growth rate is converted to an oil production rate by multiplying by three dimensionless factors.

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

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

where

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

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

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

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

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

and

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

The method can be calculated in a spreadsheet by first calculating a displaced oil rate from Eq. 12 for a time period, Δt; 1 ∕12 year is convenient. That volume is then multiplied by the dimensionless modifiers in Eqs. 13 through 15.

A_cD accounts for the viscosity of the oil and the size of the well spacing and has these restrictions: 0 ≤ A_cD ≤ 1.0, and A_cD = 1.0 at μ_oi ≤100 cp.

V_pD accounts for reservoir fill-up that must occur because of in-situ gas saturation or depleted gas zones before steam zone growth can begin to displace oil. Restrictions are 0 ≤ V_pD ≤ 1.0, and V_pD = 1.0 at S_g = 0.

The M-V method allows the steam zone to grow to an indefinite size for an indefinite time. Oil recovery can amount to more than original oil in place. V_oD is used to limit predicted oil recovery to some fraction of the original oil in place with this limit; 0 ≤ V_oD ≤ 1.0.

Fig. 3 shows the results of the M-S viscous displacement model with and without the Jones corrections for a hypothetical steamflood. In this example Kern River California reservoir properties were used. A small pattern size was chosen to illustrate that the M-V displacement rate is independent of oil in place and pattern size. At 75 months, the M-V displacement was 132% of original oil in place, while the Jones model corrected it to 91%. This calculation was done to an unrealistic terminal point, but if the flood were terminated at 48 months when instantaneous oil/steam ratio had fallen to below 0.2 then recovery calculated by Jones would be 77%.

• 

  Fig. 3 – Graphical presentation of Eq. 6.

This method is very good for estimating oil rates, especially early in a steamflood and for incremental recovery. It has been used in many projects worldwide with success. As with the M-V method, this calculation allows any value for steam injection rate and calculates oil rate. Information on practical steam rates must be found before practical results can be derived. Because this method produces best results if calculated in small time steps (i.e., 10 days), it is best programmed on a computer.

Design calculations: gravity drainage models

Neuman model

The Neuman method is very useful for calculating post-steam breakthrough performance and for heat management in calculating required steam injection rates. It does not address the presteam breakthrough period. Van der Knaap shows that the Neuman method can be derived from the Mandl-Volek method, and they are completely compatible. Note that Neuman’s paper contains typographical errors in Eqs. D-2 andD-3. They are corrected next.

Steam-zone thickness is calculated as a function of the time lapse between the time of prediction, t, and the time when the location reached steam temperature, τ.

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

An estimation of the steam-injection rate and the time required to achieve the required complete coverage of the project area with a steam zone is given by

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

Because everything in Eq. 19 is a constant except time (t), an estimate of required rate is easy to derive by simply changing the time. Caution should be used because this time/rate is divorced from reservoir reaction, primarily to viscous forces during these early stages of a flood; therefore, impractical results are easily obtained.

The steam-zone volume is

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

Oil displaced from both the steam zone and the adjacent hot-water zone, heated by condensate convection and by conductive heat lost from the steam zone, is

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

where oil rate from the hot-water zone is expressed as a fraction (f_b) of the oil from the steam zone.

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

and

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

Once steam covers the entire area, steam injection can be reduced by

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

where

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

This method can be done by hand but is easier to use if programmed on a computer spreadsheet.

Vogel model

Similar to the Neuman method, the Vogel  method is very useful for post-steam breakthrough heat-management calculations. It does not address early steamflood performance. Vogel first postulates that a producing well in a California-type reservoir with thick, dipping zones and gas caps that are incapable of maintaining pressure will produce at a maximum rate regardless of excess steam injection over some optimal rate. Thus, the steam rate can be calculated to maintain a steam chest by replacing lost heat and the voidage left by produced fluids. To use this method, a good estimate of a hot well producing rate is necessary, but it is very useful for optimizing existing projects with established producing rates.

A modified interpretation of the M-V method is used to calculate heat necessary to overcome reservoir heat loss. Vogel uses the following equations to calculate the steam injection rate in barrels per day.

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

where

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

and

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

is a value added that accounts for surface and wellbore and miscellaneous heat losses.

Fig. 4 shows the main benefit provided by the Neuman and Vogel methods. They are very useful in managing steam-injection requirements that continuously reduce as the project matures.

• 

  Fig. 4 – Typical steam-injection rate schedule for gravity-dominated steam displacement.

These equations apply only after steam has overlaid the reservoir and oil production has peaked because oil rate is known and steam rate is unknown in the equations. This method is easily done by hand but can also be programmed on a computer spreadsheet.

Steam rate reduction

Kumar and Ziegler investigated the issue of steam rate reduction schedule using a numerical reservoir simulator. The Neuman and Vogel methods previously described are based on analytical heat balances and do not directly predict oil production rates. Fig. 5 shows the effect on oil production rate determined using the simulator as a result of three steam-injection schedules: constant rate, linear constant reduction, and Neuman reduction schedule. Fig. 6 shows the steam injection for each of these schedules. The constant rate schedule results in the highest oil-production rate but at the cost of high late-steam rates. The linear reduction schedule yields nearly the same oil for a lot less steam. Neuman results in arrested steam-zone growth, but the severe early reduction in steam results in an equally severe loss in oil rate.

• 

  Fig. 5 – Effect of steam injection schedule on oil production.

• 

  Fig. 6 – Steam injection schedule.

Table 2 shows that the linear rate-reduction compromise is economically superior to either of the other two schedules. Because the injection rate reduction changes net salable oil at various times in the project life, the authors used discount factors to properly value the oil production stream for each case. They termed this time-weighted oil volume "discounted net present barrels of oil."

• 

  Table 2 - Kumar and Zeiglar discounted net present barrels of oil (confined model)

Design calculations: other models

Gomaa model

Gomaa approached the design problem by first doing a history match on a Kern River field steamflood using a numerical simulator then extracting an analytical solution from the simulator results.

Because the method is totally a function of a history match to the Kern River field, caution must be used in applying it to other projects. However, because it is a graphical method with few calculations, it offers ease in estimating project performance. After achieving a history match, Gomaa did several parametric simulations that allowed generation of several graphs that are, in turn, used to estimate project performance. Important parameters for the method are initial reservoir pressure (< 100 psia); steam injection pressure (< 200 psia); reservoir thickness (10 to 300 ft); mobile oil saturation (0.05 to 0.60); porosity (0.21 to 0.35); and heat injection rate (0.05 to 0.6 MM Btu/D/acre-ft). The steps for the procedure are outlined next.

• Provide downhole steam quality, pressure, and injection rate and determine enthalpy, h_fs.
• Calculate the heat injection rate,

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

• Determine vertical heat loss, Q_l, from Fig. 7.
• Determine the heat utilization factor from

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

For a series of time steps (t, days), calculate the effective heat injection rate and the cumulative heat injected with

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

and

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

• Estimate the mobile oil saturation,

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

• Use Fig. 8 to determine the oil recovery factor, f_R.
• Calculate the initial mobile oil in place with

....................(34)

• Calculate the oil recovery at time (t),

....................(35)

• Calculate the cumulative oil/steam ratio,

....................(36)

Repeat these steps for a period equal to the expected life of a steamflood in convenient time steps (i.e., 365 days) to estimate steamflood performance. This calculation method is easily done by hand but can be programmed in a spreadsheet.

• 

  Fig. 7 – Heat loss to overlying and underlying strata.

• 

  Fig. 8 – Steamflood oil recovery as a function of effective heat injected and mobile oil saturation.

Nomenclature

A	=	area, sq ft [m2]
AcD	=	dimensionless factor defined by Eq. 13
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
fb	=	hot-water zone oil-rate factor defined by Eq. 22
fh	=	heat utilization factor defined by Eq. 23
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
fs	=	steam quality
f(T)	=	temperature function defined in Eq. 24
fVr	=	conductive heat loss factor caused by radial conduction
fVz	=	conductive heat loss factor caused by vertical conduction
F1, F2	=	constants defined in Table 2
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]
FSor	=	residual oil factor used in Eq. 4
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]
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]
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]
qoD	=	displaced oil rate defined in Eq. 17, 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
Sora, Sorb	=	terms used in Eq. 7
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]
VoD	=	dimensionless factor defined by Eq. 9
VpD	=	dimensionless factor defined by Eq. 11
Vs	=	steam zone volume, acre ft [m3]
Vsz	=	steam zone volume per Neuman in Eq. 20, B [m 3]
wst	=	mass flow rate of dry steam, lbm/D [kg/d]
x	=	distance along the x ordinate
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

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

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See also

Thermal recovery by steam injection

Cyclic steam stimulation design

Horizontal well applications in steamflooding

PEH:Thermal_Recovery_by_Steam_Injection