A Calculation Method of Stage Division in Steam

Drive Considering Heat Transfer

Bin Hu College of Petroleum Engineering, China University of Petroleum, Beijing, China; 2.The Planning Department, China

National Petroleum Corporation (CNPC), Beijing, China

Email: hubin003@cnpc.com.cn

Tingting Pan Research Centre of Reservoir Geophysics, BGP Inc. of CNPC, Hebei, China

Email: 2254315232@qq.com

Jingwei Bao and Lingbin Lai Petro China Research Institute of Petroleum Exploration & Development, Beijing, China

Email: 173499433@qq.com; lingbin86@163.com

Abstract—Appropriate control measures for different steam

flooding stages is very important to improve the recovery.

Generally, stage division of the steam flooding is based on

dynamic analysis of production curve. By analyzing the heat

transfer and mass transfer in porous media, considering

steam overlap and one-dimensional change for area patterns

to avoid the difference of well spacing in stage division, the

theoretical model of well group stage division of steam drive

is established. When the viscosity of crude oil in production

well bottom is dropped 50 mpa.s, hot inter-well

communication stages completed. when steam front migrate

to the production well bottom, the steam breakthrough

stage begins. The steam stimulation stage is between the hot

inter-well communication and the steam breakthrough.

Example shows that the production bottom temperature

started to maintain original formation temperature, then

had a sharp rise after a period of time, and changed slowly

at last. This calculation result is consistent with the actual

results, the method can be used to divide the stages of steam

flooding.

Index Terms—stage division, one-dimensional change, steam

overlap, bottom temperature

I. INTRODUCTION

The dynamic characteristics and variation of reservoir

are very difference in different stages, and the control

methods are also very difference [1]-[3]. so the division

of steam drive stages will affect the measures of adjusting

of steam drive and ultimate recovery. Jones raised steam

flooding forecasting model in 1981, he think that steam

flood is divided into three stages, cold production,

thermal fluid control phase and steam breakthrough stage

[3]-[13]. Sun Chuansheng subdivided steam flooding into

four stages in 1998, Booster pressure In the early stage,

pressure stability stage, breakthrough stage, and adjusting

stage [2]-[13]. Zhao Hongyan divided it into three stages

Manuscript received February 10, 2015; revised May 20, 2015.

in 2008: effective stage, displacement and breakthroughs

[1]; During the steam flooding in Qi 40, Zhang Jianfeng

divided it into hot connected phase, steam displacement

and steam breakthrough stage [6]. These methods are

difference, but all based on the liquid producing capacity,

oil production and fluid temperature in single well or

multiple well group [1]. Dividing stages behind the

production process, and lack of a reasonable theoretical

[1]-[9]. By means of reservoir porous medium heat and

mass transfer analysis, studies the heat transfer

characteristics and stage division theory in steam flooding.

In considering reservoir steam overlap and the injection-

production well pattern of one dimensional, established

the theoretical model of stage division.

II. BASED ON THE HEAT TRANSFER OF STAGE

DIVISION MECHANISM

Steam flooding is a heat and mass transfer process in

porous media. Heat transfer includes the solid skeleton

and pore fluid; Mass transfer includes molecular diffusion,

spread caused by fluid macroscopic movement and

caused by the pressure gradient [10]. Reservoir steam

heat transfer includes heat conduction and heat

convection. Heat transfer, is no direction, had occurred in

the horizontal direction and vertical direction; Heat

convection can be divided into natural convection and

forced convection. Due to outside pressure driven, steam

migrates to production Wells in horizontal direction. In

vertical direction, the vapor density is far less than the

density of oil and water. Due to gravitational

differentiation, forming the steam overlap phenomenon.

So heat transfer includes forced convective and heat

conduction in horizontal direction. The speed of heat

transfer is equal to the vapor migration and heat

conduction velocity. Heat transfer rate is greater than the

mass transfer velocity in the reservoir. Hot inter-well

communication stages (0~tL) start from steam injection to

heat transfer to the production well. During this stage,

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Journal of Industrial and Intelligent Information Vol. 4, No. 1, January 2016

© 2016 Journal of Industrial and Intelligent Informationdoi: 10.12720/jiii.4.1.56-60

crude oil is mainly controlled by the original viscosity, so

the viscosity of crude oil reduce to the thin oil, fluid

temperature is low in wellhead and daily oil production is

low. The steam stimulation stage (tL~tBT) is between the

hot inter-well communication and the steam breakthrough.

During this stage, daily oil production is high. After

Steam migration to the production well is steam

breakthrough stage ( ＞ tBT). During this stage, steam

channel is formed, fluid temperature rise sharply, daily

oil production drop sharply.

III. STEAM FLOODING STAGE DIVISION MODEL

A. Model Assumptions

B. One Dimension Dispose of Steam Flooding W ell

Pattern

At present, a lot of steam flooding mostly adopt areal

pattern, liaohe oilfield using nine point well pattern. The

well spacing of different wells is different. The time of

steam migration to the bottom of production and other

issues have a direct relationship with the injection-

production well spacing.

In order to do stage division, and to eliminate the

differences of the injection-production well spacing, two-

dimensional area well pattern need to be changed to one-

dimensional pattern.

Reservoir pore volume is derived with reserves

formula:

p o oi o oiV N B S (1)

oN geological reserves, t ; oiB volume coefficient,

fraction; oiS initial oil saturation, fraction; o degassed oil

relative density, 3t m .

Reduced length x is equal to the radius cr of well

group conversion:

2

c pr h V (2)

0.5

c o oi o oix r N B h S (3)

Reduced width rB is exported by well group reduced

area:

2

r c c aB r h r h (4)

r c aB r (5)

a is volume sweep efficiency, raction; h is thicness,

m.

C. Determination of Steam Cavity Volume

When certain quality of saturated steam turn into the

reservoir, due to gravitational differentiation, steam gets

to the top together, which form a steam overlap

phenomenon [11], [12]. Steam is no longer a piston

propulsion in the strata, but to form the bevel edge [11].

According to Chen Yueming derived [13] and Van

Lookeren [5] theory, assuming the steam on the radial

velocity is proportional to the radius, and longitudinally,

steam rate is proportional to the thickness of the steam

zone, vapor liquid interface is formed and achieves

stability after a certain time of steam in jection, and

pseudo mobility ratio is approximately zero at this time.

Equation for the steam front:

22

22

(1 )

2

s eRD

s

rh

h rA

r rh

(6)

9

210

( )

s s b

RD

o s s s

i rA

gh k

(7)

shis the thickness of steam overlap, m; h is the

thickness of reservoir, m; skis the permeability of steam,

3 210 m

; s bi r

is steam injection rate in earth

surface,/kg s

; o , s is the density of oil and steam, 3/kg m ; s is steam radial velocity, kg s .

When er r,

0sh , steam drive front equation can

be obtained by integral:

1

2 2

2

1 1(ln )

2 2

s e

RD e

h r r

A h r r

(8)

When br r , sh h, the relationship of RDA ’ er ’ br can

be obtained by steam drive front equation(8)

2

2 2

1 1 1ln( )

2 2

e b

RD b e

r r

A r r (9)

Order：

( )ee b

b

rx r r

r (10)

Equation (9) can be simplified to

2 2

1 1 1ln ( 1)

2 2RD

x xA x

(11)

2

1( )

RD

x fA

(12)

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Journal of Industrial and Intelligent Information Vol. 4, No. 1, January 2016

There is three-phase flow in the strata, and its

distribution is extremely complex. Several aspects of the

hypothesis must be set up, in order to study steam

flooding stage division model. ①Reservoir thickness is

more than 20 m, homogeneous, not considering cracks;②Reservoir physical property and fluid saturation does not

change with temperature; ③ Injection velocity and

temperature are constant; ④ The temperature of the

steam and hot water in the reservoir zone are equal to the

steam temperature; ⑤ Injecting steam rate is low, so heat

conduction and thermal equilibrium process is

instantaneous; ⑥ Regardless of condensation and

distillation, oil and steam is the only flowing in steam

flooding.

© 2016 Journal of Industrial and Intelligent Information

Making the steam front for a straight line

approximately, steam chamber volume can be similarly

calculated

1

12

s e b or wr aV h r r S S (13)

a is sweep efficiency; orS is residual oil

saturation; wrSis irreducible water saturation.

D. Determination of Steam Migration Velocity

Steam linear velocity in the formation, which can be

treated as equal as steam injection rate, is the ratio the

injected steam volume and seepage cross-sectional area,

namely

s s

f

s r

M xv

B h

(14)

sM is steam injection velocity, t d ; sx is steam quality

of bottom hole, fraction; s is the density of steam in the

strata.

According to Fan Deer gas equation, steam

compression factor of formation can be got

2

3 2

3 3

27 271 1 0

8 64 512

r r r

r r r

p p pZ Z Z

T T T

(15)

rp is reduced pressure, r s cp p p; rT

is reduced

temperature,

273

273

sr

c

TT

T

; spis saturated steam pressure of

formation, MPa ; sT is saturated steam temperature of

formation,oC ,By the empirical formula:

0.25 0.5179.1 0.47s s s sT p p p ; cp

, cT is threshold for the

steam pressure and temperature.

Steam density is derived by the empirical formula

1

3273 10s s sZR T p

(16)

R is ideal gas constant, 8.314R J mol K .

Steam viscosity in different temperature can be

obtained by empirical formula

1.224440.00102 exp(0.0007295 )s sT (17)

E. Determination of Reduced Production Bottom Hole

Temperature

With the continuous steam injection, heat via

convection and conduction, makes the reservoir

temperature continue to rise. According to the existing

classification of crude oil standard, crude oil viscosity is

less than 50mpa.s is not heavy oil [2]. According to

heavy oil viscosity-temperature curve, hot unicom is

finished when the reduced production well bottom hole

temperature rise to the temperature at which the viscosity

of crude oil is to 50.

Reduced production bottom hole temperature can be

got by Lowell method [2].

2x r s r xT T T T erfc U

(18)

0 0

1 0xU

when

when

(19)

2

96 ob

ob

K t

h M (20)

2

96 ob

f f f

K L

h C v

(21)

rT is original formation temperature,oC ; sT

is steam

temperature,oC ; is the ratio of the reservoir heat

capacity and the bottom,

R F

ob

C

C

＝

;

R FC

is reservoir heat

capacity, 3 okcal m C, 1o o o w w wR F R

C C S C S C

;

ob

C is bottom heat capacity, 3 okcal m C ; fC is fluid

heat capacity; 3 okcal m C; is porosity,fraction.

Based on the viscosity-temperature curve, the

temperature when the oil viscosity is 50mpa.s can be got,

and then thermal unicom completion time Lt can be

calculated.

F. Determination of the Steam Breakthrough Time

When steam migrated to the reduced production well

bottom hole, hot steam flooding breakthrough stage

begins. The dimensionless vapor cavity volume and

dimensionless time relationship can be made of the

following approximation [3] in this stage

214

D Dt V

(22)

22

96=

h obD BT

R F

K Ct t

h C

(23)

Dimensionless vapor cavity volume can be defined the

ratio of the steam chamber calculated by Marx-

langenheim method and equation (13)

2

0.096 h s iobD s

s sR F

K C T TV V

h C M H

(24)

sV is steam cavity volume when steam reaches the

bottom hole,3m ; hK is heat conductivity coefficient of

bottom, okcal/ m h C; sH is the unit mass thermal enthalpy

of saturated steam, 0.0148

3 661.5 /s as p MP sH p kcal kg

,

correlation coefficient 0.9986r ;

3 10 681.6 0.9957 /s

s a

p

s p MPH kcal kg , correlation coefficient

0.988r . the steam breakthrough time is obtained by

solving equation (22), (23) and (24)

222

2

0.0961

384

h s iobR FBT s

h s sob R F

K C T Th Ct V

K C h C M H

(25)

IV. EXAMPLE

A. Basic Data

Qi 40 heavy oil block of liaohe oilfield is surrounded

by fault sealing. Reservoir depth is 810m. Putting into

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Journal of Industrial and Intelligent Information Vol. 4, No. 1, January 2016

Dimensionless time in steam Breakthrough

© 2016 Journal of Industrial and Intelligent Information

development in 1987 by steam stimulation, Qi 40 heavy

oil block obtains the good economic benefit. At the end

of 2006 Qi 40 turns to steam flooding. X well group

belongs to Qi 40 and starts to steam flooding in January

2007. Oil viscosity-temperature curve during indoor test

(Fig. 1).

0

50

100

150

200

250

300

350

400

450

0 200 400 600 800 1000

Viscosity（mpa.s）

Tem

pera

ture（

°C）

Figure 1. Oil viscosity-temperature curve

B. Stage Division

Basic physical quantities can be calculated by field

parameters (Table I).

TABLE I. CALCULATED RESULTS

Basic physical

quantities value

Basic physical

quantities value

well spacing(m) 139.64 re(m) when

breakthough 139.64

width(m) 307.59 rb(m) when

breakthough 18.018

steam-saturation temperature

219.8 fluid velocity (m/d) 0.55

steam

density(t/m3) 0.01756

steam enthalpy

(kcal/kg) 670.1

Steam viscosity(mpa.s)

0.00175 shape factor 0.935

Fluid

melt(kcal/m3.°C) 645.808

Steam cavity

volume when breakthough

3997.44

The change of reduced production well bottom hole

temperature along with the time is obtained according to

the equation (18), as shown in the Fig. 2.

0

50

100

150

200

250

0 200 400 600 800 1000 1200

Steam flooding time（d）

Tem

pera

ture（

°C）

Figure 2. The change of reduced production well bottom hole temperature along with the time

By viscosity-temperature curve we can find proper

temperature when crude oil viscosity is 50mpa.s, and the

temperature is 120℃. Then calculated the hot inter-well

communication time is 5 months. During the 120 days of

steam flooding, the heat has not yet reached production

well and the temperature is 50 ℃ in the bottom of

production well. Between 120 days and 220 days of

steam flooding, the temperature has risen sharply. After

steam flooding more than 220 days, Temperature changes

is more smoothly. The steam breakthrough time can be

obtained according to the equation (25), BTt =971.3d=32.4

months.

So, the hot inter-well communication time is 5 months

after steam flooding; the steam stimulation stage is 5 to

32.4 months; steam breakthrough stage is more than 32.4

months.

C. Result Analysis

The X well group in Qi 40 block turned steam flooding

since January 2007 .And its production curve is shown in

the Fig. 3.

0

0.5

1

1.5

2

2.5

3

3.5

4

Jan-07 Aug-07 Feb-08 Sep-08 Mar-09 Oct-09 May-10 Nov-10

Dail

y o

il o

utp

ut（

t）

0

20

40

60

80

100

120

Wate

r cu

t（%）

/Tem

pera

ture（

°C）

Daily oil Water cut Temperature

Figure 3. The production curve of X well group

According to the dynamic production curve, daily oil

output, wellhead temperature is low, between January

2007 and June 2007 (turned steam drive 5 months),

which accords with hot unicom phase characteristic;

Between June 2007 to August 2009 (turned steam drive 5

months to 32 months), daily oil output is

displacement stage; After August 2009, wellhead

temperature rises sharply, oil production declines, the

water cut increases, and this is the thermal break phase.

Model results have a highly conformity degree with the

actual production situation, the method can theoretically

guide the demarcation of steam drive stage.

V. CONCLUSION

Hot unicom phase is from the start of steam injection

to bottom hole temperature which reduces viscosity of

crude oil to 50, steam breakthrough is the time after

steam migrate nto the productionwell bottom; thermal

displacement is for middle stage.

In the process of steam flooding, heat transfer along

the direction of oil layer includes forced convection and

heat transfer, heat transfer is faster than mass transfer in

oil layer; the steam chamber volume is derived under the

influence of the overlap .

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Journal of Industrial and Intelligent Information Vol. 4, No. 1, January 2016

good , temperature rises gently, and this is the thermal

© 2016 Journal of Industrial and Intelligent Information

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Journal of Industrial and Intelligent Information Vol. 4, No. 1, January 2016

The example results show that the temperature of

production well bottom hole remain 50 oC within 120 days,

and it sharply rise to 200 oC when the days from 120 days

to 120 days, and after that temperature changes become

gently; Model results have a highly conformity degree

with the actual production situation, the method can

theoretically guide the demarcation of steam drive stage.

REFERENCES

[1] H. Y. Zhao, “Approach to control methods of steam flooding performance,” Special Gas and Oil Reservoir, vol. 15, pp. 71-72.

Dec. 2008.

[2] W. Z. Liu, Steam Injection for Heavy Oil Thermal Recovery, 1st ed. Beijing, 1997, pp. 23-116.

[3] R. S. Ni, “An approximate one-dimensional, two-phase mode for the estimation of steam front during steam drive,” Petroleum

Exploration and Development, vol. 2, pp. 53-60, 1989.

[4] J. Jones, “Steam drive model for handheld programmable calculators,” JPT, pp. 1583-1598, Sep. 1981.

[5] J. van Lookeren, “Calculation methods for liner and radial steam flow in oil reservoirs,” SPE 6788, 1983.

[6] J. F. Zhang, “Discussion on technical indicators of steam

stimulation of Qi 40 block,” Petroleum Geology and Engineering, vol. 24, pp. 82-84. Apr. 2010.

[7] B. J. Liu, A Study on Steam Drive Course Evaluation and Parameter Optimization Based on QI40 Reservoir, China

University of Petroleum, 2007, pp. 3-50.

[8] B. Liu, “Steam flooding, development, characteristics, shuguang oil field,” Petroleum Exploration and Development, vol. 22, pp.

91-95, Jun 1995.[9] X. W. Xu, “Steam flooding recovery characteristics and steam

flooding conversion program study for heavy oil,” Special Gas

and Oil Reservoir, vol. 5, pp. 24-27, Apr. 1998.[10] R. T. Lin, Introduction to Heat and Mass Transfer in Porous

Medium, 1st ed. Beijing, 1995, pp. 109-112.[11] L. B. Lai, T. T. Pan, and Y. Qin, “A calchlation method for heat

loss considering steam overlap in steam flooding,” Journal of

Northwest University: Natural Science Edition, vol. 44, pp. 103-110, Feb. 2014.

[12] Y. L. Liu and Y. L. Jia, “Three-zone composite reservoir well testing model for heavy oil thermal recovery with consideration

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Daqing, vol. 27, pp. 78-82, Feb. 2008.[13] Y. M. Chen, Thermal Recovery by Steam Injection, 1st ed.

Dongying, 1996, pp. 143-146.

Bin Hu, doctoral student of China University of Petroleum (Beijing),

was born in Heilong River in 1984, Mainly engaged in the Reservoir management and Oil & gas exploration research. (Tel)010-59984615.

(E-mail) hubin003@cnpc.com.cn.

© 2016 Journal of Industrial and Intelligent Information