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Cyclic steam stimulation design: Difference between revisions

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m (This modification is inappropriate because it doesn't deal with CSS, but development of tight sand which requires fracturing. It doesn't belong in this section.)
 
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Prats<ref name="r1">Prats, M. 1982. Thermal Recovery, No. 7. Richardson, Texas: Monograph Series, SPE.</ref> defines stimulation as "any operation (not involving perforating or recompleting) carried out with the intent of increasing the post-treatment production rate without changing the driving forces in the reservoir." Periodic injection of steam into a producing well, alternating with a production cycle, has many features of this definition but also has many features that distinguish it as a true enhanced recovery mechanism. (This cyclic process is sometimes referred to as "huff and puff.") The primary benefit of the process is true stimulation—near wellbore reduction of flow resistance, viscosity reduction. However, there are enhanced oil recovery (EOR) benefits of high-temperature gas dissolution, wettability changes, and relative permeability hysteresis (water flows into the reservoir easier than it flows out). Fortunately, calculating the temperature history of the wellbore, tracking the water/oil saturation history and the [[Oil_viscosity|oil viscosity]] reduction is adequate to estimate the oil production response to the process. The design of the cyclic steam stimulation (CSS) process involves constantly changing conditions; this page discusses calculations that give a good representation of what can be expected.
See Creating quality topic pages([http://petrowiki.org/Help:Creating_quality_topic_pages http://petrowiki.org/Help:Creating_quality_topic_pages]) for full details on how to make this a quality topic page
 
== Design calculations ==
 
Steamflood design is simple compared to CSS design. Whereas steamflood reaches equilibrium and can be represented by a set of steady-state equations for much of its life, the CSS process is one of constantly changing conditions. First there is the injection phase, which is relatively so short that it is a total transition period. Then during the soaking period, steam vapor condenses and temperature begins to fall. The producing period is in a constant state of flux as testified by the constantly changing producing rates. [[Relative_permeability_and_capillary_pressure|Relative permeability]] curves, which can typically be ignored in steamflood calculations, become very important to CSS.
 
In spite of these problems, there are several desktop calculations that give a good representation of what can be expected from CSS. Probably the simplest representation of the process is by Owens and Suter,<ref name="r2">Owens, W.D. and Suter, V.E. 1965. Steam Stimulation—Newest Form of Secondary Petroleum Recovery. Oil & Gas J. 90 (April): 82.</ref>
 
[[File:Vol5 page 1333 eq 001.png|RTENOTITLE]]....................(1)
 
This simply indicates the productivity ratio resulting from steam temperature-induced oil-viscosity reduction. No attempt was made to calculate how the reservoir got the peak temperature, but once the well is steamed and placed on production, the authors propose that the operator can simply watch leadline temperature and accurately predict the production history of the production period prior to the next cycle.
 
== Boberg and Lantz<ref name="r3">Boberg, T.C. and Lantz, R.B. 1966. Calculation of the Production Rate of a Thermally Stimulated Well. J Pet Technol 18 (12): 1613–1623. SPE-1578-PA. http://dx.doi.org/10.2118/1578-PA</ref> method ==
 
The referenced paper describes the definitive work that serves as the basis of virtually all subsequent analytical analyses of CSS. They first calculate the reservoir temperature distribution resulting during the injection period. '''Eq. 2''' is used to calculate the area of the processed zone that is heated to ''T''<sub>''i''</sub>.
 
[[File:Vol5 page 1312 eq 001.png|RTENOTITLE]]....................(2)
 
Then, the well is placed on production and temperature of the heated volume, which is assumed to remain constant and begins to fall by conduction to the surrounding cold reservoir rock and by hot fluid production. The average temperature in the hot zone is
 
[[File:Vol5 page 1334 eq 001.png|RTENOTITLE]]....................(3)
 
where ''f''<sub>''Vr''</sub> and ''f''<sub>''Vz''</sub> are unit solutions of component conduction in the radial and vertical directions, respectively. They can be estimated from '''Fig. 1''' or from
 
[[File:Vol5 page 1334 eq 002.png|RTENOTITLE]]....................(4)
 
and
 
[[File:Vol5 page 1334 eq 003.png|RTENOTITLE]]....................(5)
 
The term ''f''<sub>''pD''</sub> accounts for heat removed with produced fluids.
 
[[File:Vol5 page 1334 eq 004.png|RTENOTITLE]]....................(6)
 
and
 
[[File:Vol5 page 1335 eq 001.png|RTENOTITLE]]....................(7)
 
The subscript, ''h'', indicates that the properties should be for fluids from the hot zone at the sand face. The model does not predict steam, gas, or water producing rates, which must be estimated from some other source. Oil production rates are given by a method similar to '''Eq. 1''', which is written as
 
[[File:Vol5 page 1335 eq 002.png|RTENOTITLE]]....................(8)
 
and
 
[[File:Vol5 page 1335 eq 003.png|RTENOTITLE]]....................(9)
 
''F''<sub>1</sub> and ''F''<sub>2</sub> are radial flow factors for which Boberg and Lantz give expressions in '''Table 1'''. Note that the production rate is a function of only two variables—oil viscosity and the heated radius.
 
[[File:Vol5 page 1331 eq 002.png|RTENOTITLE]]....................(10)
 
<gallery widths="300px" heights="200px">
File:vol5 Page 1334 Image 0001.png|'''Fig. 1 – Vertical and radial heat-loss factors for Eq. 10.<ref name="r2" />'''
 
File:Vol5 Page 1335 Image 0001.png|'''Table 1 - Boberg and Lantz<ref name="r3" /> radial flow factors'''
</gallery>
 
 
 
The method can be calculated by hand for a very few time steps, but it is much easier to use if programmed into a spreadsheet.
 
== Towson and Boberg<ref name="r4">Towson, D.E. and Boberg, T.C. 1967. Gravity Drainage in Thermally Stimulated Wells. J. of Canadian Petroleum Technology (October–December): 130.</ref> model ==
 
The Boberg and Lantz method assumes that there is significant reservoir energy to produce oil under primary conditions. Because many CSS candidates have only gravity forces and initial viscosity is high, there is no significant primary production. Many California reservoirs have free liquid surfaces in the oil zones with a gas oil interface at atmospheric pressure. Towson and Boberg extended the former work to cover this situation. '''Eq. 3''' is used to calculate the heated zone temperature from which oil viscosity is estimated. Then, gravity drainage oil rate may be calculated.
 
[[File:Vol5 page 1336 eq 001.png|RTENOTITLE]]....................(11)
 
''h''<sub>h</sub> must be computed for each time step during the production cycle by first calculating the average hot-zone fluid level.
 
[[File:Vol5 page 1336 eq 002.png|RTENOTITLE]]....................(12)
 
Now the fluid level at the heated zone radius is
 
[[File:Vol5 page 1336 eq 003.png|RTENOTITLE]]....................(13)
 
This procedure can be hand calculated but is much easier to use if a computer spreadsheet is used.
 
== Jones<ref name="r5">Jones, J.A. 1992. Why Cyclic Steam Predictive Models Get No Respect. SPE Res Eng 7 (1): 67–74. SPE-20022-PA. http://dx.doi.org/10.2118/20022-PA</ref> method ==
 
Jones took a similar approach to Towson and Boberg<ref name="r4">Towson, D.E. and Boberg, T.C. 1967. Gravity Drainage in Thermally Stimulated Wells. J. of Canadian Petroleum Technology (October–December): 130.</ref> in calculating oil rates as a function of gravity forces alone. He extended the model by also calculating heated-zone water rate. Information on relative permeability is necessary to accomplish this. Further, recognizing that Towson and Boberg and other similar models commonly over-predict oil production, he limited the vertical size of the zone that is invaded with steam using a version of '''Eq. 14'''.
 
[[File:Vol5 page 1315 eq 005.png|RTENOTITLE]]....................(14)
 
This phenomenon is easily demonstrated by running a downhole temperature survey following a steam cycle. Then, because cold oil sand is still exposed in the wellbore, another set of equations similar to '''Eq. 11''' is used to calculate oil and water from the cold zone. Using this modification, fluid rates can be matched quite well without need of a scaling factor to reduce predicted oil rates to realistic levels.
 
A convenient parameter to track, when trying to history-match a field steam cycle with this model, is produced fluid temperature that represents a combination of cold/hot oil and water.
 
[[File:Vol5 page 1336 eq 004.png|RTENOTITLE]]....................(15)
 
This method does not lend itself to hand calculation and should be programmed on a computer.
 
Because steam only enters a small fraction of the sandface in a thick interval as in California oil fields, there is opportunity to improve performance of a steam cycle by using packers or other methods to divert steam into more of the oil zone.
 
== Process optimization ==
 
There are always the operational questions of how much steam should be injected during a cycle; what rate should steam be injected; when should a well be resteamed; etc. Jones<ref name="r5">Jones, J.A. 1992. Why Cyclic Steam Predictive Models Get No Respect. SPE Res Eng 7 (1): 67–74. SPE-20022-PA. http://dx.doi.org/10.2118/20022-PA</ref> reported the results of the use of the model previously described to history-match a massive 20-year, 1,500-well cyclic steam project in the Potter Sand in the Midway Sunset field, California. He then used the history-match information to do a long-life parametric study of the process. '''Table 2''' lists the conclusions for this particular application. This is, however, not a common practice. There are so many variables that the results from a single well or even a small group of wells cannot be used for a meaningful history match. Further, cyclic steam is easy to apply in the field and is relatively inexpensive, so most operators simply start immediately with a field trial. Very little is published on optimizing CSS.
 
<gallery widths="300px" heights="200px">
File:Vol5 Page 1337 Image 0001.png|'''Table 2'''
</gallery>
 
It is generally true of CSS that soak time should be as short as possible and that steam quality should be as high as possible. Further, efforts should be made to divert steam out of depleted zones and gas caps and into as much good oil-saturated sand as possible.
 
There are generally two reasons to apply CSS. First, there is the obvious stimulation of economic oil production immediately from the well. Second, because of the time delay in oil response from the initiation of steam injection into a continuous steam injector in a steamflood project, CSS concentrated in the steamflood zone is often used to accelerate project response.
 
=== Cumulative average daily profit method ===
 
Because process optimization is ultimately an economic decision, a resteaming decision can be based on the Rivero and Heintz<ref name="r6">Rivero, R.T. and Heintz, R.C. 1975. Resteaming Time Determination-Case History Of a Steam-Soak Well in Midway Sunset. J Pet Technol 27 (6): 665-671. SPE-4892-PA. http://dx.doi.org/10.2118/4892-PA</ref> cumulative average daily profit (CADP) method. '''Fig. 2''' shows a graphical representation of how to use this method. When steam is injected into a producer, profits of the cycle are driven negative because of the cost of the steam, costs to prepare the well for steaming, and lost production as a result of the well being shut down. Once the well is put back on production, the oil rate will peak, and daily cash flow will be at a relative high. Concurrently, CADP for the cycle will begin to increase as the daily production begins to pay for the injection costs. As the well continues to produce, the oil rate gradually falls, as does daily profit. CADP hopefully soon becomes positive, then continues to increase until it reaches a value equal to the daily cash flow. It is at this point that the well should be recycled because cash flow for the next day’s production will fall below the CADP.
 
<gallery widths="300px" heights="200px">
File:vol5 Page 1338 Image 0001.png|'''Fig. 2 – Graphical representation of the cumulative average daily profit method of the recycle determination method.<ref name="r6" />'''
</gallery>
 
Although instructive as a concept for picking resteaming time, actual field application of the method is practically impossible because of ever-present problems in gathering precise enough well production gauges and in collecting all of the necessary economic data in a timely manner. Also, because the method is divorced from the reservoir process, it may lead to short-term economic decisions that damage the reservoir.
 
=== Sequential CSS method ===
 
In a large CSS project, one needs a way to decide which well to steam and in what sequence. McBean<ref name="r7">McBean, W.N. 1972. Attic Oil Recovery by Steam Displacement. Presented at the SPE California Regional Meeting, Bakersfield, California, 8-10 November 1972. SPE-4170-MS. http://dx.doi.org/10.2118/4170-MS</ref> and Jones and Cawthon<ref name="r8">Jones, J. and Cawthon, G.J. 1990. Sequential Steam: An Engineered Cyclic Steaming Method. J Pet Technol 42 (7): 848-853, 901. SPE-17421-PA. http://dx.doi.org/10.2118/17421-PA.</ref> presented a sequential CSS method that ensures that all wells will be stimulated in a timely manner and takes advantage of the interwell stimulation often observed.
 
By steaming wells in a sequential manner from downdip to updip as shown in '''Fig. 3''', they observed not only the oil response from the steamed wells but also some response from offset wells caused by a mini-steamflood. Kuo ''et al''.<ref name="r9">Kuo, C.H., Shain, S.A., and Phocas, D.M. 1970. A Gravity Drainage Model for the Steam-Soak Process. SPE J. 10 (2): 119-126. SPE-2329-PA. http://dx.doi.org/10.2118/2329-PA</ref> found in numerical simulations that small cycles in closely spaced wells are preferable in this process. Field experience in the sequential CSS project confirmed that finding with wells drilled on 5/8 acre (0.25 ha) spacing.
 
<gallery widths="300px" heights="200px">
File:vol5 Page 1338 Image 0002.png|'''Fig. 3 – Well steaming schedule for the sequential steam method of cyclic steam design.<ref name="r8" />'''
</gallery>
 
== Nomenclature ==
 
{|
|-
| ''A''
| =
| area, sq ft [m<sup>2</sup>]
|-
| ''A''<sub>''t''</sub>
| =
| time-dependent heated area, sq ft [m<sup>2</sup>]
|-
| ''B''<sub>''o''</sub>
| =
| oil formation volume factor, RB/STB [res m<sup>3</sup>/stock-tank m<sup>3</sup>]
|-
| ''C''
| =
| isobaric specific heat
|-
| ''C''<sub>''an''</sub>
| =
| isobaric specific heat of annular fluid, Btu/(lbm-°F) [kJ/kg•K]
|-
| ''C''<sub>''o''</sub>
| =
| isobaric specific heat of oil, Btu/(lbm-°F) [kJ/kg•K]
|-
| ''C''<sub>''w''</sub>
| =
| isobaric specific heat of water, Btu/(lbm-°F) [kJ/kg•K]
|-
| ''D''
| =
| depth below surface, ft [m]
|-
| ''erfc''(''x'')
| =
| complementary error function
|-
| ''E''
| =
| efficiency
|-
| ''E''<sub>''c''</sub>
| =
| fraction of oil displaced that is produced
|-
| ''E''<sub>''h''</sub>
| =
| heat efficiency—fraction of injected heat remaining in reservoir
|-
| ''f''
| =
| volumetric fraction of noncondensable gas in vapor phase
|-
| ''f''<sub>''hv''</sub>
| =
| fraction of heat injected as latent heat
|-
| ''f''<sub>''p''</sub>
| =
| fraction of heat injected that is produced
|-
| ''f''<sub>''pD''</sub>
| =
| heat loss factor caused by hot fluid production
|-
| ''f''<sub>''s''</sub>
| =
| steam quality
|-
| ''f''<sub>''Vr''</sub>
| =
| conductive heat loss factor caused by radial conduction
|-
| ''f''<sub>''Vz''</sub>
| =
| conductive heat loss factor caused by vertical conduction
|-
| ''F''<sub>''fo''</sub>
| =
| ratio of fuel burned to produced oil, B/B [m<sup>3</sup>/m<sup>3</sup>]
|-
| ''F''<sub>''of''</sub>
| =
| produce oil/fuel burned ratio, B/B [m<sup>3</sup>/m<sup>3</sup>]
|-
| ''F''<sub>''os''</sub>
| =
| produce oil/injected steam ratio, B/B [m<sup>3</sup>/m<sup>3</sup>]
|-
| ''g''
| =
| gravity acceleration constant, 32.174 ft/sec<sup>2</sup> [9.8067 m/s<sup>2</sup>]
|-
| ''g''<sub>''c''</sub>
| =
| conversion factor in Newton’s second law of motion, 32.174 lbm-ft/lbf-s<sup>2</sup> [1.0 kg•m/N•s<sup>2</sup>]
|-
| ''h''
| =
| enthalpy per unit mass, Btu/lbm [kJ/kg]
|-
| ''h''<sub>''f''</sub>
| =
| enthalpy of liquid portion of saturated steam, Btu/lbm [kJ/kg]
|-
| ''h''<sub>''fs''</sub>
| =
| enthalpy of < 100% quality saturated steam, Btu/lbm [kJ/kg]
|-
| ''h''<sub>''fv''</sub>
| =
| enthalpy of vapor portion of saturated steam, Btu/lbm [kJ/kg]
|-
| ''h''<sub>''h''</sub>
| =
| fluid level in stimulated reservoir, ft [m]
|-
| ''h''<sub>''s''</sub>
| =
| steam zone thickness, ft [m]
|-
| ''h''<sub>''t''</sub>
| =
| gross reservoir thickness, ft [m]
|-
| ''h''<sub>''v''</sub>
| =
| enthalpy of 100% quality (saturated) saturated steam, Btu/lbm [kJ/kg]
|-
| ''h''<sub>''w''</sub>
| =
| fluid level in cold wellbore, ft [m]
|-
| ''i''<sub>''w''</sub>
| =
| cold water equivalent steam injection rate, B/D [m<sup>3</sup>/d]
|-
| ''J''
| =
| productivity of a cold well, B/psi-D [m<sup>3</sup>/kPa•d]
|-
| ''J''<sub>''h''</sub>
| =
| productivity of a stimulated well, B/psi-D [m<sup>3</sup>/kPa•d]
|-
| ''k''
| =
| reservoir permeability, md [μm<sup>3</sup>]
|-
| ''k''<sub>''ro''</sub>
| =
| relative permeability to oil
|-
| ''k''<sub>''rs''</sub>
| =
| relative permeability to steam
|-
| ''L''
| =
| distance between wells, ft [m]
|-
| ''M''<sub>''g''</sub>
| =
| volumetric heat capacity of gas, Btu/(ft<sup>3</sup>-°F) [kJ/m<sup>3</sup>•K]
|-
| ''M''<sub>''o''</sub>
| =
| volumetric heat capacity of oil, Btu/(ft<sup>3</sup>-°F) [kJ/m<sup>3</sup>•K]
|-
| ''M''<sub>''R''</sub>
| =
| volumetric heat capacity of the reservoir, Btu/(ft<sup>3</sup>-°F) [kJ/m<sup>3</sup>•K]
|-
| ''M''<sub>''w''</sub>
| =
| volumetric heat capacity of water, Btu/(ft<sup>3</sup>-°F) [kJ/m<sup>3</sup>•K]
|-
| ''n''
| =
| index of time increment
|-
| ''N''
| =
| initial oil in place, B [m<sup>3</sup>]
|-
| ''N''<sub>''d''</sub>
| =
| oil displacement rate, B/D [m<sup>3</sup>/d]
|-
| ''N''<sub>Gr</sub>
| =
| Grashof number
|-
| ''N''<sub>''m''</sub>
| =
| initial mobile oil in place, B [m<sup>3</sup>]
|-
| ''N''<sub>''p''</sub>
| =
| cumulative oil produced, B [m<sup>3</sup>]
|-
| ''N''<sub>Pr</sub>
| =
| Prandtl number
|-
| ''N''<sub>Re</sub>
| =
| Reynolds number
|-
| ''p''
| =
| atmospheric pressure, psia [kPa]
|-
| ''p''<sub>''e''</sub>
| =
| external boundary pressure, psia [kPa]
|-
| ''p''<sub>''s''</sub>
| =
| steam pressure, psia [kPa]
|-
| ''p''<sub>''w''</sub>
| =
| wellbore pressure, psia [kPa]
|-
| [[File:Vol5 page 1328 inline 001.png|RTENOTITLE]]
| =
| steam injection rate to make up for surface heat losses, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''gh''</sub>
| =
| hot gas production rate, Mcf/D [std m<sup>3</sup>/d]
|-
| ''q''<sub>''is''</sub>
| =
| reproduced steam rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''iso''</sub>
| =
| initial steam injection rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''ls''</sub>
| =
| steam injection rate to make up for reservoir heat losses, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''oc''</sub>
| =
| cold oil production rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''og''</sub>
| =
| oil production rate owing to gravity displacement, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''oh''</sub>
| =
| hot oil production rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''oi''</sub>
| =
| initial oil production rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''ot''</sub>
| =
| total oil production rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''ov''</sub>
| =
| oil production rate because of viscous displacement, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''ps''</sub>
| =
| steam rate to replace reservoir volume of produced oil, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''wc''</sub>
| =
| cold water production rate, B/D [m<sup>3</sup>/d]
|-
| ''q''<sub>''wh''</sub>
| =
| hot water production rate, B/D [m<sup>3</sup>/d]
|-
| ''Q''
| =
| amount of injected heat remaining in reservoir, Btu [kJ]
|-
| ''Q''<sub>''i''</sub>
| =
| total heat injected, Btu [kJ]
|-
| ''Q''<sub>''l''</sub>
| =
| heat lost in reservoir, Btu [kJ]
|-
| ''Q''<sub>''ls''</sub>
| =
| surface piping heat loss/unit length, Btu/ft [kJ/m]
|-
| ''Q''<sub>''ot''</sub>
| =
| cumulative oil recovery at time (''t''), B/D [m<sup>3</sup>/d]
|-
| ''Q''(<sub>''o/w''</sub>)<sub>prod</sub>
| =
| heat removed with produced liquids, Btu [kL]
|-
| ''Q''<sub>''z''</sub>(<sub>accum</sub>)
| =
| heat accumulating in system, Btu [kJ]
|-
| [[File:Vol5 page 1360 inline 001.png|RTENOTITLE]]
| =
| heat injection rate, Btu/D [kJ/d]
|-
| [[File:Vol5 page 1360 inline 002.png|RTENOTITLE]]
| =
| heat loss rate, Btu/D [kJ/d]
|-
| [[File:Vol5 page 1360 inline 003.png|RTENOTITLE]]
| =
| heat removed with produced fluids, Btu/D [kJ/d]
|-
| [[File:Vol5 page 1360 inline 004.png|RTENOTITLE]]
| =
| volumetric heat injection rate, MMBtu/D/acre-ft [kJ/m<sup>3</sup>]
|-
| ''r''
| =
| radius of reservoir, ft [m]
|-
| ''r''<sub>''ci''</sub>
| =
| casing internal radius, ft [m]
|-
| ''r''<sub>''co''</sub>
| =
| outer casing radius, ft [m]
|-
| ''r''<sub>''e''</sub>
| =
| external radius of heated zone, ft [m]
|-
| ''r''<sub>''Ea''</sub>
| =
| altered radius in earth around wellbore, ft [m]
|-
| ''r''<sub>''h''</sub>
| =
| radius of heated or steam zone, ft [m]
|-
| ''r''<sub>''i''</sub>
| =
| inside pipe radius, ft [m]
|-
| ''r''<sub>ins</sub>
| =
| insulation external radius, ft [m]
|-
| ''r''<sub>''o''</sub>
| =
| outside pipe radius, ft [m]
|-
| ''r''<sub>''w''</sub>
| =
| radius of well, ft [m]
|-
| ''R''<sub>''h''</sub>
| =
| overall specific thermal resistance, °F-ft-D/Btu [K•m•d/kJ]
|-
| ''S''
| =
| skin factor before stimulation
|-
| ''S''<sub>''g''</sub>
| =
| gas saturation fraction
|-
| ''S''<sub>''h''</sub>
| =
| skin factor after stimulation
|-
| ''S''<sub>''o''</sub>
| =
| oil saturation
|-
| ''S''<sub>''oi''</sub>
| =
| initial oil saturation fraction
|-
| ''S''<sub>''om''</sub>
| =
| mobile oil saturation fraction
|-
| ''S''<sub>''or''</sub>
| =
| residual oil saturation fraction
|-
| ''S''<sub>''ors''</sub>
| =
| residual oil saturation to steam fraction
|-
| ''S''<sub>''orw''</sub>
| =
| residual oil saturation to water fraction
|-
| ''S''<sub>''w''</sub>
| =
| water saturation fraction
|-
| ''t''
| =
| time, D [d]
|-
| ''T''
| =
| average temperature in heated reservoir, °F
|-
| ''T''<sub>''p''</sub>
| =
| produced fluid temperature, °F
|-
| ''T''<sub>''R''</sub>
| =
| unaffected reservoir temperature, °F
|-
| ''T''<sub>''s''</sub>
| =
| steam temperature, °F
|-
| ''T''<sub>''SZ''</sub>
| =
| steam zone temperature, °F
|-
| ''u''
| =
| volumetric flux, ft<sup>3</sup>/sq ft-D [m/d]
|-
| ''V''<sub>''s''</sub>
| =
| steam zone volume, acre ft [m<sup>3</sup>]
|-
| ''w''<sub>''st''</sub>
| =
| mass flow rate of dry steam, lbm/D [kg/d]
|-
| ''x''
| =
| distance along the ''x'' ordinate
|-
| ''α''
| =
| thermal diffusivity of reservoir, ft<sup>2</sup>/D [m<sup>2</sup>/d]
|-
| ''α''<sub>''E''</sub>
| =
| thermal diffusivity of earth, ft<sup>2</sup>/D [m<sup>2</sup>/d]
|-
| ''α''<sub>''s''</sub>
| =
| thermal diffusivity of surrounding formation, ft<sup>2</sup>/D [m<sup>2</sup>/d]
|-
| ''γ''
| =
| specific gravity
|-
| Δ
| =
| increment or decrement
|-
| Δ''h''<sub>''h''</sub>
| =
| change in stimulated zone fluid level, ft [m]
|-
| Δ''t''
| =
| time steps, D [d]
|-
| Δ''T''
| =
| steam temperature/reservoir temperature, ''T''<sub>''s''</sub>/''T''<sub>''R''</sub> , °F
|-
| Δ''γ''
| =
| oil/steam specific gravity difference
|-
| Δ''ρ''
| =
| density difference between water and oil, lbm/ft<sup>3</sup> [kg/m <sup>3</sup>]
|-
| ''ε''
| =
| emissivity
|-
| ''ε''<sub>''ci''</sub>
| =
| radiant emissivity of casing wall
|-
| ''ε''<sub>ins</sub>
| =
| radiant emissivity of insulation outer surface
|-
| ''θ''<sub>''c''</sub>
| =
| wetting contact angle, deg (°) [rad]
|-
| ''θ''
| =
| formation dip angle, deg (°) [rad]
|-
| ''μ<sub>oh</sub>''
| =
| hot oil viscosity, cp [Pa•s]
|-
| ''μ<sub>oi</sub>''
| =
| initial oil viscosity, cp [Pa•s]
|-
| ''π''
| =
| constant pi, 3.141
|-
| ''ρ''
| =
| density, lbm/ft<sup>3</sup> [kg/m<sup>3</sup>]
|-
| ''ρ''<sub>''a,sc''</sub>
| =
| density of air, lbm/ft<sup>3</sup> [kg/m <sup>3</sup>]
|-
| ''ρ''<sub>''an''</sub>
| =
| density of well annulus gas, lbm/ft<sup>3</sup> [kg/m<sup>3</sup>]
|-
| ''ρ''<sub>''o''</sub>
| =
| density of oil, lbm/ft<sup>3</sup> [kg/m<sup>3</sup>]
|-
| ''ρ''<sub>''s''</sub>
| =
| density of dry steam, lbm/ft<sup>3</sup> [kg/m<sup>3</sup>]
|-
| ''ρ''<sub>''w''</sub>
| =
| density of water, lbm/ft<sup>3</sup> [kg/m<sup>3</sup>]
|-
| ''ρ''<sub>''w,sc''</sub>
| =
| density of water at standard conditions, 62.4 lbm/ft<sup>3</sup> [662.69 kg/m<sup>3</sup>]
|-
| ''σ''
| =
| interfacial tension, oil/water, dyne/cm [mN/m]
|-
| ''τ''
| =
| time since location in reservoir reached steam temperature, D [d]
|-
| ''υ''<sub>''s''</sub>
| =
| steam specific volume, ft<sup>3</sup>/lbm [m<sup>3</sup>/kg]
|-
| ''υ''<sub>''w''</sub>
| =
| wind velocity, miles/hr [km/h]
|}
 
== References ==
 
<references />
 
== Noteworthy papers in OnePetro ==
 
Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read
 
Hascakir, B., Kovscek, A., Reservoir Simulation of Cyclic Steam Injection Including the Effects of Temperature Induced Wettability Alteration, SPE Western Regional Meeting, Anaheim, California, USA, 27-29 May 2010, SPE 132608., [https://www.onepetro.org/conference-paper/SPE-132608-MS https://www.onepetro.org/conference-paper/SPE-132608-MS]
 
== External links ==
 
Xiong, Hongjie. 2017. "Optimizing Cluster or Fracture Spacing: An Overview." The Way Ahead. Society of Petroleum Engineers. https://www.spe.org/en/twa/twa-article-detail/?art=3007
 
== See also ==
 
[[Steamflood_design|Steamflood design]]
 
[[Thermal_recovery_by_steam_injection|Thermal recovery by steam injection]]
 
[[Steam_delivery_systems_for_EOR|Steam delivery systems for EOR]]
 
[[Steamflood_heat_management|Steamflood heat management]]
 
[[PEH:Thermal_Recovery_by_Steam_Injection]]
 
== Category ==
[[Category:3.2 Well operations, optimization, and stimulation]] [[Category:YR]]

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