Verification of thevenin's theorem for BEEE Lab (1).pptx
Reservoir Heat Requirement During a Steamflood Exhibiting Steam Override
1. 10. Reservoir Heat Requirement During
a Steamflood Exhibiting Steam Override
PTE 582
By: Long Vo
5079449949
2. Outline
• Problem Statement
• Problem Formulation
• Results & Planning Summary
• Solution Methods
• Application and Sensitivity
• Results
• Planning
• Summary & Conclusion
3. Problem Statement
Heat Required for injection to
Grow Steam Zone:
• Gravity Override displacement occur
once steam has broken through to
the producing well
– A steam zone is established that
connect the injector to the producer
• Oil production is primarily gravity
drainage
• Steam injection is independent of
steam rate, but is dependent on the
integrity of the steam zone
4. Problem Formulation
• There are three methods to calculate the heat
required to maintain steam zone:
– Vogel:
• Assume instantaneous steam coverage
• Heat from the steam help drains the oil while also replacing it to
grow steam zone
– Modified Vogel:
• Heat calculation based on measured field observations
– Neuman:
• Provide time to steam coverage
• Heat from steam help drains the oil, does not require oil
displacement to grow steam zone
5. Results & Planning Summary
• Vogel and Neuman yield
similar results at late time
• At early time, Vogel and
Neuman differed
• Modified Vogel yield a low
requirement for steam
injection rate
– This can change based on actual
field observation of steam zone
temperature profile
Total Heat Requirement is converted to
Steam Rate Requirement
6. Results & Planning Summary
• A combination of
Neuman, Vogel, and
Modified Vogel can be
used to plan for heat
injection schedule
• Real time or sequential
sampling of field data can
be used to update the
heat requirement
Updated Design
Initial Design
7. Solution Methods
• Analogous to Gravity Drainage
– Favored by:
• Thick oil column (he)
• Low producing well back pressure (small hw)
• High permeability (large k oil)
• High steam zone temperature (low oil
Viscosity)
• Temperature is not uniform
• Management of steamflood require data
in the vertical direction of the change of
steam-oil contact with time
• Minimize production of steam to
conserve heat.
– Small production is required to observe
steam breakthrough
• Once steam breakthrough occurred,
Steam injected to oil produced is kept
constant.
8. Solution Methods
• Vogel Heat Management:
– Conductive Heat Losses (BTU/Day):
• Rate of heat loss by conduction to an overlying or underlying zone
10. Solution Methods
• Modified Vogel Heat
Management
– Conductive Heat Losses
(BTU/Day):
• Heat is always flowing up or
down
• Lack of a temperature gradient
indicate the steam zone
• Heat flow to the steam zone is
by convection
• Temperature gradient is
measured from observation
well
11. Solution Methods
• Modified Vogel Heat Management
– Heat required for Steam Zone Growth (BTU/Day):
• Steam zone growth measured from observation well
15. Solution Methods
• All Model Heat Management
– Heat Required from Produced Fluid (BTU/Day):
16. Solution Methods
• All Model Heat Management
– Wellbore Heat Losses (BTU/Day):
• Based off Horne, R.N. & Shinohara, K.
• Consider steam as single phase fluid flowing in Injection and
Producing Well
• Modification of Ramey’s heat loss analysis on wellbore heat
transmission of temperature distribution in a well used for
injecting hot fluid.
• Consider Over-all heat transfer coefficients from G. Paul
Willhite
20. Solution Methods
• Wellbore Heat Losses: Over-all Heat Transfer Coefficient
– Four cases:
• General Heat Coefficient
– Non-insulated Tubing
– Insulated Tubing
• Practical Heat Coefficient: Drying of formation and cement
– Non-insulated Tubing
– Insulated Tubing
– Iterative method
21. Solution Methods
• Wellbore Heat Losses: Over-all Heat Transfer Coefficient
– Iterative Method:
1. Guess Uto
2. Calculate f(t)
3. Calculate Th, replace with Td if Practical Model
4. Calculate Tci
5. Calculate Ftci, replace with Ftci’ if Practical Model
6. Calculate hr, replace with hr’ if Practical Model
7. Calculate Pr
8. Calculate Gr
9. Calculate khc
10. Calculate hc, replace with hc’ if Practical Model
11. Calulate Uto
12. If calculated Uto does not agree with Guess Uto repeat step 2 to 10
22. Solution Methods
General Model Practical Model
-Replace Tto with Tins for insulated Tubing
Wellbore Heat Losses: Over-all Heat Transfer Coefficient
29. Application and Sensitivity
• To calculate the required heat injection for each model, assumptions was made for
sensitivity test:
1. Overburden and Underlying zone are equal
2. Vogel heat required to grow steam zone equal modified Vogel
3. Modified Vogel temperature gradient equal 2 F/ft and constant for all time period
4. All oil production forecast equal to Vogel with an initial production rate of 500 bbl/day
5. Tau equals t*
6. Heat from produced oil and water are negligible
7. Surface heat loss is negligible
8. Wellbore heat loss consider single phase steam vapor flow
9. Overall heat transfer coefficient from non-insulated general model
10. Steam production of 100 BCWE/Day
11. Steam quality of 100 %
12. Injection well steam temperature of 400 degree F
13. Producing well steam temperature of 250 degree F at 30 psia
14. All else being equal
30. Application and Sensitivity
• Equal Inputs:
RhoC (BTU/Ft^3-F) RhoW (lbm/ft^3) rto (ft) Can (BTU/lb-F)
Heat Capacity of steam zone Feedwater density Outside radius of tubing
Heat capacity of the fluid in the annulus
at the average annulus temperature
A (ft^2) Lv (Btu/lbm) rh (ft) Man (lbmass/ft-hr)
Project area Heat of vaporization of water Radius of drill hole
Viscosity of the fluid in the annulus at
Tan and P
To (F) fd rco (ft) Kha (BTU/hr-ft-F)
Original formation temperature Downhole steam quality Outside radius of casing
Thermal conductivity of the fluid in the
annulus at the average temperature and
pressure of the annulus
Ts (F) fp kcem (BTU/hr-ft-F) Tan (F)
Steam Temperature
Fraction of Injected Heat
Produced
Thermal conductivity of the cement at
the average cement temperature and
pressure
Average temperature of the fluid in the
annulus
Phi I (ft^3/day) Tf (F) Rhoan (lb/ft^3)
Porosity
Injection rate as volume of
water converted to steam Temperature at flowing fluid Injection
Density of the fluid in the annulus at Tan
and pressure P
Soi Cw (BTU/ft^3-F) Te (F) Tf (F)
Initial oil saturation Heat capacity of water
Undistributed temperature of the
formation Injection Temperature at flowing fluid Producing
Sor c (BTU/lb-F) rci (ft) Te (F)
Irreducible oil saturation Specific Heat of Fluid Producing Inside radius of casing
Undistributed temperature of the
formation Producing
Kh (Btu/ft-day-F) z (ft) kcas (BTU/hr-ft-F) Tto (F)
Thermal conductivity Total depth
Thermal conductivity of the casing
material at the average casing
temperature
Temperature outside tubing surface
Producing
r1 (ft) Eto (dim) Tan (F)
Inside radius of tubing Emissivity of outside tubing surface
Average temperature of the fluid in the
annulus Producing
r2 (ft) Eci (dim)
Outside radius of casing Emissivity of inside casing surface
c (BTU/lb-F) Tto (F)
Specific Heat of Fluid Injection
Temperature outside tubing surface
Injection
b (F)
Surface temperature
35
217800
100
400
0.3
62.1
854
60
0.146
0.5
0.4
0.2
400
100
0.355
500
1
3.5
1.527967417
0.99
0.1
38.4
1
0
10000
0.016029109
1.70
0.9
400
0.245
0.069
0.0255
350
0.0388
250
100
250
235
0.2
0.9
31. Application and Sensitivity
• Each function is iterated based on different time period and
oil production rate
• Iterative Method For Each Model:
1. Calculate Conductive Heat Loss from initial time period
2. Calculate Heat Required to Grow Steam Zone
3. Calculate Heat Removed from Producing Fluids
4. Calculate Wellbore & Surface Heat Loss for Injection and
Producing wells
5. Sum all heat losses
6. Repeat step 1 to 5 for next time period
7. Repeat step 1 to 6 for all time period, if new calculated values
does not agree continue iteration
32. Application and Sensitivity
• Neuman:
– If tau is large, heat required for injection will be greater than Vogel
and Modified Vogel.
– If tau is zero, heat required for injection will be very close to Vogel.
• Modified Vogel:
– Decrease temperature gradient and rate of downward growth of
steam zone will decrease the injection requirement
• Vogel:
– If oil production decrease, steam zone growth requirement will
decrease
• A small steam coverage area will decrease all heat requirement.
33. Results
• Neuman has a higher conductive heat loss than Vogel and Modified Vogel to
compensate for a low heat required to grow steam zone and a later steam
coverage time
– Neuman only consider steam vapor as the primary factor of heat loss, neglecting the production
of oil as a heat loss to grow steam zone
• Vogel has a lower conductive heat loss than Neuman but higher heat required to
grow steam zone due to instantaneous steam coverage
– Vogel consider the production of oil with replacement of steam liquid to grow steam zone
• Modified Vogel has a much less conductive heat loss due to a constant
temperature gradient
• Heat removed with producing fluids are low due to low steam vapor production
• Wellbore and Surface Heat Loss will increase if temperature gradient increase
• SOR Neuman > SOR Vogel > SOR Modified Vogel
34. Results
• Vogel give an impractical infinite injection rate at
start of project.
• Neuman give injection rate after breakthrough of
steam occurred.
• Modified Vogel give accurate rate if field observation
data is use
• At late time, Neuman and Vogel yield similar results
• At early time, Neuman require a slightly higher
injection rate.
40. Planning
• Combining Vogel, Modified Vogel, and Neuman to
minimize steam injection:
– Initial injection heat requirement can be taken from
Neuman model
– Initial injection decline rate can be taken from Vogel model
at early time.
– Verification of field observation can be taken from
Modified Vogel model.
• If real time verification can not be implemented, high sampling
rate can be taken at early time, and low sampling rate at late time
42. Summary & Conclusions
• Main heat loss occur with conductive and heat
require to grow steam zone
• Modified Vogel shows a much less heat required,
however when actual field data is applied.
Modified Vogel will be more accurate.
• The models are each limited by oil production,
time to breakthrough and field observation data.
• A combination of the three can be used to plan
injection schedule of heat required
43. References
• Vogel, J. V. (1984, July 1). Simplified Heat Calculations for Steamfloods. Society of
Petroleum Engineers. doi:10.2118/11219-PA
• Neuman, C. H. (1985, January 1). A Gravity Override Model of Steamdrive.
Society of Petroleum Engineers. doi:10.2118/13348-PA
• Willhite, G. P. (1967, May 1). Over-all Heat Transfer Coefficients in Steam And
Hot Water Injection Wells. Society of Petroleum Engineers. doi:10.2118/1449-PA
• Horne, R. N., & Shinohara, K. (1979, January 1). Wellbore Heat Loss in Production
and Injection Wells. Society of Petroleum Engineers. doi:10.2118/7153-PA
