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# 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.^{[1]}^{[2]}^{[3]}^{[4]}^{[5]}

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^{[1]}^{[2]}^{[3]}^{[4]}^{[5]} typically offer linear regression equations to generate an indicator for a specific reservoir. The most recent version is by Donaldson,^{[6]} which is written as

Doscher and Ghassemi^{[7]} 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.

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.

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*.^{[8]} 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.

### 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.

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* cos*θ*_{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^{[9]} 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.

where

and

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.

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^{[10]} 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^{[11]} and Mandl-Volek^{[12]} (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}.

It follows that oil displaced from the steam zone is

*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 ^{[13]} 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.

where

and

The method can be calculated in a spreadsheet by first calculating a displaced oil rate from **Eq. 12** for a time period, Δ*t*; 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%.

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^{[14]} shows that the Neuman method can be derived from the Mandl-Volek method, and they are completely compatible. Note that Neuman’s paper^{[15]} contains typographical errors in **Eqs. D-2 **and**D-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*.

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

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

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

where oil rate from the hot-water zone is expressed as a fraction (*f*_{b}) of the oil from the steam zone.

and

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

where

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 ^{[16]} 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.

where

and

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.

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^{[17]} 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.

**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."

## Design calculations: other models

### Gomaa model

Gomaa^{[18]} 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,

- Determine vertical heat loss,
*Q*_{l}, from**Fig. 7**. - Determine the heat utilization factor from

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

and

- Estimate the mobile oil saturation,

- Use
**Fig. 8**to determine the oil recovery factor,*f*_{R}. - Calculate the initial mobile oil in place with

- Calculate the oil recovery at time (
*t*),

- Calculate the cumulative oil/steam ratio,

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.

## Nomenclature

## References

- ↑
^{1.0}^{1.1}Venkatesh, E.S., Venkatesh, V.E., and Menzie, D.E. 1998. PDS Data Base Aids Selection of EOR Method. Oil & Gas J. 82 (23): 63-66. - ↑
^{2.0}^{2.1}Chu, C. 1985. State-of-the-Art Review of Steamflood Field Projects. J Pet Technol 37 (10): 1887-1902. SPE-11733-PA. http://dx.doi.org/10.2118/11733-PA - ↑
^{3.0}^{3.1}Donaldson, A.B. and Donaldson, J.E. 1997. Dimensional Analysis of the Criteria for Steam Injection. Presented at the SPE Western Regional Meeting, Long Beach, California, 25-27 June 1997. SPE-38303-MS. http://dx.doi.org/10.2118/38303-MS - ↑
^{4.0}^{4.1}Doscher, T.M. and Ghassemi, F. 1984. Limitations on the Oil/Steam Ratio for Truly Viscous Crudes. J Pet Technol 36 (7): 1123-1126. SPE-11681-PA. http://dx.doi.org/10.2118/11681-PA - ↑
^{5.0}^{5.1}Greaser, G.R. and Shore, R.A. 1980. Steamflood Performance in the Kern River Field. Presented at the SPE/DOE Enhanced Oil Recovery Symposium, Tulsa, Oklahoma, 20-23 April 1980. SPE-8834-MS. http://dx.doi.org/10.2118/8834-MS - ↑
^{6.0}^{6.1}Restine, J.L. 1991. On the Effect of Viscosity and Sand Thickness on Kern River Field, Single-Zone, Steamflood Performance. Presented at the SPE International Thermal Operations Symposium, Bakersfield, California, 7-8 February 1991. SPE-21526-MS. http://dx.doi.org/10.2118/21526-MS - ↑ Rattia, A.J. and Farouq Ali, S.M. 1981. Effect of Formation Compaction on Steam Injection Response. Presented at the SPE Annual Technical Conference and Exhibition, San Antonio, Texas, 4-7 October 1981. SPE-10323-MS. http://dx.doi.org/10.2118/10323-MS
- ↑
^{8.0}^{8.1}Marx, J.W. and Langenheim, R.H. 1959. Reservoir Heating by Hot Fluid Injection. In Trans., AIME, 216, 312–314. - ↑ Mandl, G. and Volek, C.W. 1969. Heat and Mass Transport in Steam-Drive Processes. SPE J. 9 (1): 59-79. SPE-2049-PA.
- ↑ Jones, J. 1981. Steam Drive Model for Hand-Held Programmable Calculators. J Pet Technol 33 (9): 1583-1598. SPE-8882-PA. http://dx.doi.org/10.2118/8882-PA
- ↑ Hayes, H.J. et al. 1984. Enhanced Oil Recovery. Washington, DC: National Petroleum Council, Industry and Advisory to the U.S. Department of the Interior.
- ↑ Iyoho, A.W. 1978. Selecting Enhanced Oil Recovery Processes. World Oil (November): 61.
- ↑
^{13.0}^{13.1}Neuman, C.H. 1985. A Gravity Override Model of Steamdrive. J Pet Technol 37 (1): 163-169. SPE-13348-PA. http://dx.doi.org/10.2118/13348-PA - ↑ van der Knaap, W. 1993. Physical Aspects of Some Steam Injection Theories, an Application. Paper SPE 26293 available from SPE, Richardson, Texas.
- ↑ Ali, S.M.F. 1974. Current Status of Steam Injection As a Heavy Oil Recovery Method. J Can Pet Technol 13 (1). PETSOC-74-01-06. http://dx.doi.org/10.2118/74-01-06.
- ↑
^{16.0}^{16.1}Vogel, J.V. 1984. Simplified Heat Calculations for Steamfloods. J Pet Technol 36 (7): 1127–1136. SPE-11219-PA. http://dx.doi.org/10.2118/11219-PA - ↑
^{17.0}^{17.1}^{17.2}^{17.3}Kumar, M. and Ziegler, V.M. 1993. Injection Schedules and Production Strategies for Optimizing Steamflood Performance. SPE Res Eng 8 (2): 101-107. SPE-20763-PA. http://dx.doi.org/10.2118/20763-PA - ↑
^{18.0}^{18.1}^{18.2}Gomaa, E.E. 1980. Correlations for Predicting Oil Recovery by Steamflood. J Pet Technol 32 (2): 325-332. SPE-6169-PA. http://dx.doi.org/10.2118/6169-PA

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## See also

Thermal recovery by steam injection

Cyclic steam stimulation design