10. Reservoir Heat Requirement During a Steamflood Exhibiting Steam Override

PTE 582By: Long Vo5079449949

Outline• Problem Statement• Problem Formulation• Results & Planning Summary• Solution Methods• Application and Sensitivity• Results• Planning• Summary & Conclusion

Problem StatementHeat 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

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

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

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

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.

Solution Methods• Vogel Heat Management:

– Conductive Heat Losses (BTU/Day):• Rate of heat loss by conduction to an overlying or underlying zone

Solution Methods

• Vogel Heat Management– Heat required for Steam Zone Growth (BTU/Day):

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

Solution Methods

• Modified Vogel Heat Management– Heat required for Steam Zone Growth (BTU/Day):

• Steam zone growth measured from observation well

Solution Methods• Neuman Heat Management

– t*: time required to cover pattern area with steam

Solution Methods• Neuman Heat Management

– Conductive Heat Losses (BTU/Day):

Solution Methods• Neuman Heat Management

– Heat required for Steam Zone Growth (BTU/Day):

Solution Methods• All Model Heat Management

– Heat Required from Produced Fluid (BTU/Day):

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

Solution Methods

Wellbore Heat Losses: Injection Well

Solution MethodsWellbore Heat Losses: Injection Well

Solution Methods

Wellbore Heat Losses: Producing Well

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

Solution Methods• Wellbore Heat Losses: Over-all Heat Transfer Coefficient

– Iterative Method:1. Guess Uto2. Calculate f(t)3. Calculate Th, replace with Td if Practical Model4. Calculate Tci5. Calculate Ftci, replace with Ftci’ if Practical Model6. Calculate hr, replace with hr’ if Practical Model7. Calculate Pr8. Calculate Gr9. Calculate khc10. Calculate hc, replace with hc’ if Practical Model11. Calulate Uto12. If calculated Uto does not agree with Guess Uto repeat step 2 to 10

Solution Methods

General Model Practical Model

-Replace Tto with Tins for insulated Tubing

Wellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution Methods

General Model Practical Model

Wellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution Methods

General Model Practical Model• Replace Th with Td

Wellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution MethodsInsulated Tubing• Same as Non-Insulated Tubing

Except:– hc’: replace rto with rins.– hr’: replace Tto with Tins.– Ftci’: replace rto with rins.

Non-Insulated TubingWellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution MethodsWellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution MethodsWellbore Heat Losses: Over-all Heat Transfer Coefficient

Solution MethodsWellbore Heat Losses: Over-all Heat Transfer Coefficient

Application and Sensitivity• To calculate the required heat injection for each model, assumptions was made for

sensitivity test:1. Overburden and Underlying zone are equal2. Vogel heat required to grow steam zone equal modified Vogel3. Modified Vogel temperature gradient equal 2 F/ft and constant for all time period4. All oil production forecast equal to Vogel with an initial production rate of 500 bbl/day5. Tau equals t*6. Heat from produced oil and water are negligible7. Surface heat loss is negligible8. Wellbore heat loss consider single phase steam vapor flow9. Overall heat transfer coefficient from non-insulated general model10. Steam production of 100 BCWE/Day11. Steam quality of 100 %12. Injection well steam temperature of 400 degree F13. Producing well steam temperature of 250 degree F at 30 psia14. All else being equal

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 tubingHeat 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 holeViscosity 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 TemperatureFraction 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)

PorosityInjection 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 waterUndistributed 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 casingUndistributed 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 surfaceAverage temperature of the fluid in the annulus Producing

r2 (ft) Eci (dim)Outside radius of casing Emissivity of inside casing surfacec (BTU/lb-F) Tto (F)

Specific Heat of Fluid InjectionTemperature 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

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 period2. Calculate Heat Required to Grow Steam Zone3. Calculate Heat Removed from Producing Fluids4. Calculate Wellbore & Surface Heat Loss for Injection and

Producing wells5. Sum all heat losses6. Repeat step 1 to 5 for next time period7. Repeat step 1 to 6 for all time period, if new calculated values

does not agree continue iteration

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.

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

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.

Results

Results

Results

Results

Results

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

Planning

Updated Design

Initial Design

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

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