TWO-PHASE WELLBORE SIMULATOR AND ANALYSIS OF REINJECTION

DATA FROM SVARTSENGI, ICELAND

Mahmut Parlaktuna*,

UNU Geothermal Training Programme,

National Energy Authority,

Grensasvegur 9. 108 Reykjavik.

ICELAND .

• Permanent Address:

Middle East Technical University, Petroleum Engineering Department.

Ankara. TURKEY.

2

3

ABSTRACT

A computer program Is developed for the simulation of flowing geothermal wells. Th e necessary correc t ions of the

salt and C02 concentrations on the thermophysical proper ­ties of the geothermal fluid are included 1n the program.

The program is tested wi th the data from the Svartsengi

geothermal field in Iceland and the Kizl1dere geotherma!

field in Turkey.

The response of the Svartsengl geothermal field to the

injection is also investigated. A lumped model, called "the

steam model" is used to analyze the effect of injection.

and the actual data from th e injection test at the Svarts­

eng! field in 1984 Is used for that purpose.

4

5

TABLE OF CONTENTS

Page

ABSTRAC T ..... ... . . •.. . .. .. •..•..•.. . . .. .. . . ... . ... . . .. . . . . 3

INTRODUCTION

1.1 Purpose of the study

1.2 Statement of the prob l em

2 FLOW PERFORMANCE CALCU LATIONS IN GEOTHE RMAL WELLS

9

9

2 . 1 Introduction........... . . ... . ......... . . . ... . . .. .... , t

2 . 2 De r ivation of the equatio n s for f luid flow In a

vertical pipe . . ....... . .. . ..... .. ........ . .. .. . . ... 1 2

2.2.1 Single - phas e r egion ... ..... .... . . . .... .. . . .. . 14

2 . 2.2 Two-phase region

2 . 3 Wellbore heat transfer

2 . 4

2 . 5 2 . 6

Thermodynamic pro perties of geo t he r mal fluids ..... .

Ef f ect of C02 ...... . . . ... . ...... .. .. . .. ... . ....... . .

Applications of the prog r am

2 . 6 • 1 Svartsengl well No . 4

2.6.2 Svartsengl well No. 1 1

2.6 . 3 Kizl1dere well No . 6

3 RESPONSE OF SV ARTSENG I FIELD TO REINJ ECTION 3 . 1 Ana l ysis of injec t io n data .... .. . . ... .. . .. .... . ... .

3 . 2 Model description ....... . .... .. . .. . ... .... . ...... . .

4 SUMMARY ... . .. .... . . .. .. . . . ... .. .. ........ .. .. . . . .. . ....

ACKNOWLEDGEMENTS

NOMENCLATURE . . . . ... .. .. . ... ..... . ..... . .. . . .. . .. ........ .

REFERENCES .... ...... ... .. .... .. .. ... .......... .. ...... ...

APPENDIX A, Program listing ... .. . ... .. . ..... . . . ... . . . .

APPENDIX B . 1 : Computer outputs fo r Sva r tsengi well No. 4

15

1 9 20

22 24

25 26

27

29 30

33

7

35

48

without calc i te deposi ti o n . . .. .. .......... 53

APPEND I X B.2 : Compu t er o ut puts for Svartse ngi well No. 4

with calcite de position 55

6

LIST OF FIGURES

Fig. Svartsengi well No . 4 output characteristiCS 38

Fig. 2 Svartsengl well No . 4 calcit e deposition accordi ng

to callper log measured 78.12.13 ... . .. . .. .. . .. . . . 39

Fig. 3 Pressure profiles in Svartsengi well No. 4 40

Fig. 4 Change In flashing depth with mass flow rate 41

Fi g . 5 Deliverabl1ity curves for SG - l1 fo r different reservoir pressures 41

Fig. 6 Effect of casing size on the outp ut cu r ves of geothermal wells 42

Fig . 7 Scaling thick ness e s measured by go-devil In

Klzildere well No. 6 43

Fig. 8 Net production and injection rates with time 44

Fig. 9 Drawdown with time 45

Fig . 10 Conceptual model of the Sva r tsengi reservoir •.. . . . 46

Fig . 11 Schematic representation of the steam model for

the Svartsengl reservoir 46

Fig . 12 Measured and fitted drawdown from the steam model.. 47

LIST OF TABLES

1 • Svartsengi well No . 4 output measurements 25

2. Data and comp uter output for Kizildere well No. 6 .. ..• 28

NOMENCLATURE

C

C

Cm o ( d P ) t

(dp)acc

(dp)fri

(dp)pot

dz

E

f

G

g

H

h1

m

P

Ps Pwf P

Q

Q

r

R

Re

Cross - sectional area to flow , (m2)

~low area in water zone. (m 2 )

Flow area in feed zo n e, (m 2 ) Pressure drop factor fo r skin effect and long

term drawdown, (Pa/(kg/s»

Leakage co nstan t for steam model (kg/sec/m)

Turbulence factor, (Pa/(kg/s)2)

Specific heat of the rock matrix, (J/kgK) Diameter of pipe , (m)

Total pressure drop , (Pa)

Pressure drop due to acceleration,

Pressure drop due to friction, ( P a )

Pressure drop due to gravitational I ncremental pipe length. (m)

Energy of fluid. (J/.)

Friction factor

Mass flux, (kg/m 2 s)

Accelerat i on due to gravity. (m/5 2 )

Enthalpy, (kJ/kg)

( P a )

gradient ,

Drawdown between two-phase and liquid phase inter f ace, (m)

Drawdown i n feed zone. (m)

Permeability of the aquifer , (m 2 ) Thermal conductivity of rock, (W/mK)

(Pa)

Molality of the solution, (moles/kg)

Concentration of carbondioxide in liquid phase , ($ by weight)

Pressure. (Pa)

Steam saturation pressure , (Pa)

Bottom hole flowing pressure, (Pa) Wellhead pressure, (Pa)

Heat loss to surroundings, (J/s/m)

Amount of wa t er flowing out of storage in the

water zone, (kg/s)

Radial distanc e, (rn)

Universal gas consta n t, (kJ/krnoleK)

Rey nol ds nurn ber

Well bore radius , (m)

Storage in the liquid zone

Storage in the feed zone

7

8

T

t

V

W

x

Temperature. (OC)

Time, (sec)

Fluid velocity. (m/s)

Mass flow rate . (kg/ s)

Steam quality, (%)

Aquifer depth, (m)

Flashing point in the well, (m)

Greek symbols:

p

P 1

P2 ,

"

K

SUbscripts

L

m

s

Fluid density. (kg/m3)

Density of fluid in water zone, (kg/m 3 )

Density of fluid 1n feed zone, (kg/m 3 ) Absolute roughness factor of the pipe, (m)

Dynamic viscosity of fluld. (Pa 5) Void fraction

Slip factor

Two-phase multiplier

Specific volume of fluid. (m3/kg)

Thermal diffusivity of the rock, (m2/sec)

Liquid phase

Rock matrix

Vapour phase

9

1 INTRODUCTION

1.1 Purpose of the study

This report is the final part of a 6 month training at the UNU Geothermal Training Programme I at the National Energy

Authority 1n Reykjavik, Iceland 1n the summer of 1985.

The author's training programme can be divided into four

main sections, namely introductory lectures in various

disciplines of geothermal technology, lectures on reservoir engineering for the specialized training in this subject.

two weeks field excursion and seminars on the various

geothermal fields of Iceland and the final project on the

subjects of simulation of flowing wells and response of the Svartsengl field to injection.

The experience and knowledge gained will be helpful to

solve not only problems dealt with in this report but a

wide range of problems associated with evaluation and

utilization of geothermal energy in Turkey.

1.2 Statement of the problem

Among the several factors affecting the flow performance of

the wells, diameter of the we ll as well as the reduction in

the diameter due to calcite scaling and the drawdown in the reservoir can be mentioned. It is a common practi ce to develop simulators to study the effects of those factors. Because of the chemical composition of the geothermal

fluid, the thermodynamic properties of pure water should be

corrected for salt concentration . Another factor which

should be taken into account in the two-phase pressure drop

calculations is the effect of non-condensable gases.

Reinjection is increasingly becoming an integral part of

the deSign of geothermal projects. The necessity of

reinjection mainly arises from three factors I disposal of chemically hazardous geothermal waste water, possibility of

pressure recovery of the declining aquifer and more heat extraction from the reservoir rock.

1 0

The main pr o blems encoun t ered

Turkey are the reduction 1n the

1n geoth e rma l fields in

yields of the wells due to

both scaling and drawdown 1n the reservo i r , and the disposal of waste water. These two problems were selected

to provide the writer with a useful experience and knowl ­

edge on the methods of solution.

11

2 FLOW PERFORMANCE CALCULATIONS IN GEOTHERMAL WELLS

2.1 Introduction

Good production wells 1n high temperature fields are characterized by high flowrates which make the downhole

measurement of the flowing wells impractical. This diffi ­

culty makes simulation of the flowing wells important .

Therefore, it is necessary to develop and test the flow

models for geothermal wells by using limite d data which

exists for low flowrates.

Wells 1n high temperature, liquid dominated geothermal

reservoirs generally produce two-phase mixtures . In the

case of liquid water inflow to the wellbore, the drop 1n

pressure during upflow results in flashing of the fluid in the wellbore. Since the thermodynam i c properties of a brine

change with the salt concentration, it is necessary to

correlate the properties of fluid with respect to salt concentration. One of the constituents in geothermal fluid

is non - condensable gas, especially C02, which causes an increase in the flashing pressure. To analyze the behaviour

of flowing wells, a wellbore simulator was developed which

takes the effects of salt and C02 concentration into

account. This simulator was used to estimate the

deliverability curves for two wells in the Svartsengi

geothermal field 1n Iceland. The effect of C02 was studied by using data from the Kizilde r e geothermal field in Turkey . As a final applica t ion, the changes 1n the output

of a wel l as a result of calcite deposition was also

stUdied.

In the following sections, the derivation of flow equations

and corrections for

presented .

salt concentration and C02 are

1 2

2.2 Derivation of the equations for fluid flow in a

vertical pipe

To describe the fluid flow in a vertical pipe, one can use the equations of conservation of mass, momentum and energy.

During the following derivation of equations it is assumed that the flow 1s homogeneous, steady and one - d i mensional.

- Equation for conservation of mass:

w pVA (1)

- Equation for conservation of momentum:

This

pOint

equation of view.

1s generally wr i tten

Total pressure drop

from a pressure

is made up of

individual gradients,

- {dP)t = (dP)fric + (dP)acc + (dP)pot ( 2 )

Let us define each gradient separately.

i) Frictional pressure drop

drop

three

This pressure drop is def ioed by the Darcy-Weisbach

equation as;

(dP)fric pfV2 --dz

2D ( 3 )

The friction factor "f" is a function of the Reynolds

Number, Re, and the relative roughness of pipe and is given

by the modified Colebrook's equation as;

where

< f = [ [ -2 log (--J +

3.7D

pVD Re

7 0.9 2 -1 (-J 1 1

Re ( 4 )

( 5 )

1 3

11) Acceleration pressure drop

(dP)acc = pVdV ( 6 )

If the mass flux ls defined as G - W/A, and from Eg o 1.

V Gip. then the acce l eration pressure drop can be

expressed as;

(dP)acc • G dV

ill) Potential pressure drop

This pressure drop is defined as;

(dP)pot • pgdZ ( 8 )

By using equations 3.7 and 8 the total pressure drop can be

written as;

pfV2 - (dP)t - dZ + GdV + pgdZ

2D ( 9 )

- Energy equation:

The total energy equation can be expressed as;

dE WdH + Wd (':'.:.) 2

- WgdZ - QdZ ( 1 0 )

since there is no energy input for a self-flowing well,

E- O. equation 10 becomes;

o V2 Q

dH + d ( - ) + gdZ - dZ 2 W

( 1 1 )

The total enthalpy ls a function of the enthalpies of each

phase, HI and Ha. and the flowing steam quality. x.

H - xHs + (l - x) HI ( 1 2 )

1 ~

Integration of equation 11 between any two points in the

well 1n an upward direction gives;

Q ( 1 3 )

By introducing equation 12, the steam quality at point 2

can be found as;

H8 .2 - Hl,2 ( 1 ~ )

The heat 10S8 to the surrounding, Q. will be discussed 1n a

later section.

It 1s known that a liquid-dominated geothermal reservoir

will initially produce undersaturated water at the well bore

sand - face. During the upflow of the fluid along the

wellbore. the drop 1n pressure results 1n saturated water

and the flow becomes a two - phase flow. In order to examine

these two different sections, namely single-phase and two - phase, it is necessary to study the above equations at

each section separately.

2 • 2 • 1 Singe - phase region

In this section, the fluid density is almost constant which

corresponds to the density of the inflow temperature . This

constant density results in a constant velocity, V,R V2,

then according to equation 7 (dP)acc - o.

Now, total pressure drop for Single-phase region is reduced

to;

-(dP) -pfV2 --dZ

20 + pgd Z ( 1 5 )

1 5

2.2 . 2 Two-phase region

When the fluid starts flashing 1n the wellbore, it under ­

goes different two - phase flow regimes. namely bubble . slug

and annular. These flow regimes have been studied by several authors (Ros, 1961; Hagedorn , 1964; Orkiszewski.

1967). In these flow regimes , the vapour and liquid phases

travel separately at different velocities. Since the vapour

always "slips " past the liquid 1n vertical flow, equation

9 has to be corrected.

In general the mixture density Is presented 1n terms of

actual void fraction defined f r om the volume occupied by

the vapour phase,

where

o • or Al

(1 - 0) • A

( 1 6 )

( 1 7l

On the other hand the slip factor , '\, Is defined as the

velocity ra t io,

, . ( 1 8 )

Another important definition for the two - phase region is the steam quality. x.

x • Ws

W or (l-x) • ( 1 9 )

Now , let us define individual pressure drops in the two - phase region .

1 6

i) Potential pressure drop

By substituting equation 17 into equation 8

(dP)pot : ( 20 )

11) Acceleration pressure drop

From the equation for conservation of mass, equation 1. the

velocities of each phase can be written as;

xW V . (21 )

PsAs

and

V . (l - x)W ( 22)

P1Al

On the other hand. the acceleration pressure drop in

two- phase region is defined as;

(23)

By substituting the definitions of velocities from equa­

tions 21 and 22

_W_W,,-l..:.( ..:.1 _- ,,-x .c) d(

A P1Al ( 24 )

By making further substitutions for rates of mass flow and

cross - sectional areas for each phase from equations 17 and

19 the final equation is obtained as;

(dP)acc • (l-x)2 --J (I-.)Pl

( 25 )

1 7

111) Frictional pressure drop

If we introduce the definition of mixture dens i ty , equation 16, into eq uation 3 the frictional pressure drop for the two-phase region can be obtained.

( 2 6 )

But the difficulty a r ises here In the evaluation of the

two - phase friction factor and velocity of the fluid,

because oC the definition of the two - phase viscosity and

the difference between the velocities of phases due to

slip. In order to overcome this difficulty several empiri­

cal correlations have been studied.

Martinelli-Nelson (1948) defined an empirical relation to

calculate the friction pressure gradient by assuming a

ratl-o, called two-phase multIplier.

(dP/dZ)rtp - ~21 ors (27 )

where (dP/dz)rtp Is the two - phase frictional pressure gra ­dient, (dP/dz)l and (dP/dz)s are the frictional pr essure gradients for the li quid or gas respectively if they a re flowing alone in the same tube .

Other correlating parameters have been defined if the total mass is flowing with the physical properties of one of the

phases .

(28)

where (dP/dz)lo and (dP/dz)so are the pressure gradients for the total flow of fluid having the liquid or gas physical properties respect i vely .

In this correlation , frictional pressure drop for the single phase is obtai ned by assuming that all the flo wing

fluid is in this phase , then this single phase pressure

drop is multiplied by the two-phase multiplier to obtain

the frictional pressure drop in the two-phase flow.

1 8

In the literature, there are several correlations fo r a

two- phase multip l ier. In this report, the correlation given

by Chisholm (1972) is used.

4> 2= C 1 1 + + 7 X

( 29 )

where

X2 . 1-x 2 vl (-).- (30 )

x Vs

and

C 1 + xVs - a ( 3 1 )

xvs + (1 - xlvl

As can be seen in equation 31 the void fraction, hould

be known to calculate t he two - phase multiplier . In order to

calculate the vo i d fraction the correlation by Ar ma nd and

Teacher (1959) is used .

a = 0 . 833 + 0 . 05 log(P)

(1-x) Vl +

This concludes the equations for

two- phase section . The location of

be calculated as follows.

- (dP)t . (Pwf - Ps) . (d P)fr! +

From equation 1 5 • by substituting dZ

- (dP)t .

z* - Za -

pfV2 pg)( Za - Z*) (""2D +

Pwf - Ps

pfV2 pg +

2D

Pin bar

pressure drop in the

the flashing point can

(dP)pot (33 )

. Za - Z*

(34 )

(35 )

, 9

But. the high flowrates and temperatures in geothermal wells, make it difficult t o run downhole measurements

under normal operati ng conditions. Therefore, in order to get the value o f the bottom hole flowing pressure, Pwf. we

should find a relationship between the conditions of static well and flowing well.

Durlng the flow of fluid 1n the reservoir. the pressure

drops from undisturbed reservoir pressure, Pal to the

bottom hole flowing pressure. Pwf. at the sand-face. This

pressure drop in the reservoir Is due to the skin effect,

the longterm drawdown factor. and the turbulence pressure

drop. (Kjaran , 1983) Therefore, Pwf can be written as;

Pwf • Pa - (SW + Cw2) (36)

where Band C are some factors.

In the high flowrate geothermal wells, initially the pressure drop due to turbulence is the dominant factor and

equation 36 can be rewritten as;

Pwf - Pa - CW2 (37)

Since we have some measurements of Pwf for the low flowrates, equation 39 can be solved analytically by taking

the slope of (Pa-Pwf)/W vs. W graph as turbulence factor C.

Another way of obtaining the C value is the use of

simulators to match the deliverability measurements of the wells since the wellhead pressure is given by,

Po • Pwf - (dP)t • Pa - CW 2 - (dP)t (38 )

In this procedure, Pa is an i nput and C is the variableto match the measured wellhead pressure for a given flowrate.

2.3 Well bore heat transfer

During the flow of fluid in the wellbore, some heat is transferred by conduction through the rock surrounding the

well bore. This heat transfer to the surrounding has been

20

studied by Ramey (1962). By assuming that the conductive

heat flow Is normal to the axis of the well. the equation

for heat conduction can be written as;

1 3 3T K -.-(r. - )

3T PmCm-

3T r ar ar

The boundary conditions are as follows,

where Tr •

T

(r + "').

(r - r w)

undisturbed reservoir temperature, (OK) temperature at the well face, (OK)

<39 )

The conductive heat transfer per unit length of the

well bore Is given by:

(T r - Tw)

f(t)

where let) Is defined as;

2;'](t f(t)-ln( ) - 0.29

rw

( ~ 0 )

( ~ 1 )

In fact. the boundary condition given for undisturbed

reservoir temperature occurrs at a certain distance from

the wellbore instead of infinity. By introducing this new

boundary condition, the solution of the problem becomes

more complicated and is given by Carslaw and Jaeger (1959).

2 . ~ Thermodynamic properties of geothermal fluids

Geothermal fluids are solutions of various types of salts.

These are primarily NaCl, KC1, and CaC12, but it is a

common practice to use the "equivalent NaCl content" to

define the salinity of a geothermal fluid. The "equivalent

NaCl content" is the amount of NaCl in solution that will

bring the same effect on the properties as the amount of

all the salts combined.

21

For the model ling of the geotherma! well, it is necessary

to know some thermophysical properties accurately. such as

the density, the enthalpy, the entropy. the viscosity and the saturation pressure at a given temperature. To make the

corrections on the pure water properties, Michaelides

(19Bl) presented some formulas which are based on "equiva­lent NaCl content".

One of the effective changes in the properties of pure

water wi th salt content is the depression of saturation

pressure at a given temperature,

1 .8R(T + 273.15) m OF -

Vs - VI 55.56 ( 4 2 )

where R - (8.314/18) - 0.4619 kJ/kgK. 55.56 15 the moles of

water in 1 kg of the substance

Salinity of water in pprn and m -

Molecular weight of NaCl

The saturation pressure of pure water Is given by the

following simplified correlation;

P(T) • exp(0.21913E - 6T3- 0.17816E-3T 2

+ 0.0653665T - 4.96087) (43)

In his paper Michaelides gives the gas constant as 8 . 314

kJ/kgK for equation 42, but if the unit analysis is done

carefully, it is found that the actual gas constant is the

ratio of universal gas constant (8.314 kJ/kmoleK) to the

molecular weight of water ('8 kg/kmole). The reader should

give attention to this change in the formula.

Let us take an example to show the effect of salt on the

depression of saturation pressure. If we take the common

values from the Svartsengi geothermal field in Iceland,

T • 240DC and salinity - 20.000 ppm

by using equation 43, P(T) - 32 .93 bar

22

20.000 mg/kg m = = 0.342 mol/kg

58.500 mg/mol

and Vs 0.0595 m3/kg . vI 0.0012 m3/kg from the steam

tables for pure water.

By substituting the above values into equatIon 42

6P - 45.05 kPa = 0.45 bar

The true saturation pressure therefore reduces to.

P P(T) - 6P - 32.93 - 0.45 - 32.48 bar

For the correlations of densIty. enthalpy. viscosity,

entropy and elevation of saturation temperature, the reader is referred to Michaelldes (198 1 ).

2.5 Effect of C02

C02 provides an Important component to the total pressure

of geothermal fluid. Presence of C02 causes the transition between single-phase and two-phase flow to happen deep er in

the well bore than one would expect by ignoring C02.

The pressure of the vapour phase Is the sum of steam and

gas partIal pressures,

p - Ps + Pg ( 4 4 )

The partial pressure of gas can be expressed in terms of

the concentration o f gas in liquid phase and solubility.

The solubility data for C02 was fitted to an equation by

Sutton (1976).

a(T) - {5.4-3.5(T/IOO)+1.2(T/IOO)2IE - 9. (I/Pa) (45)

The partial pressure of C02 i s given by the following

formula,

( 45)

23

In order to show the effect of C02 on the flashing pressure

of the fluid I let us take an example from the Kizildere geothermal field in Turkey.

The well number KD-6 is producing 15% C02 by weight in the

steam phase and the wellhead steam quality is measured as

9.47%. The inflow temperature of fluid is 201°C.

In order to get the flashing pressure, the steam saturation

pressure and C02 partial pressure should be calculated separately.

By using equation 45 the steam pressure can be found.

Ps(T) • 15.79 bar

Now,first of all we should convert the wellhead C02 meas­

urement to downhole concentration. By assuming all the C02

was in the vapour phase at the wellhead,

n1 • 0.15·9.47 • 1.42 % by weight

By using equation 45. a(T) - 3.21E-9

0.0142

3.21E-9 4.42E6, Pa

l/Pa

1i4.2 bar

Therefore, the flashing pressure of this system 1s;

P • 15.8 + 44.2 • 60 bar

which is far beyond the steam saturation pressure.

After flashing, the C02 pressure in the vapour diminishes

from its inl tial value as flashing progresses. Most of the

mass of C02 is exsolved in the first few weight percent of flashing. Mlchels (1981) developed a relationship for the

C02 pressure in a developing vapour phase.

The partial pressure of C02 is given accurately enough by

the real gas equation, PV = znRT, and the final form can be

expressed as a function of three factors, namely initial

24

CO 2 partial system. and

developed.

pressure, the present temperature of the the weight percent of flashing that has

Pc(O) {l 44 \lsx -1

+ .(T)R(T+273.15)1 (47)

where pc{o) Initial C02 partial pressure and 42 is molecular weight of C02.

2.6 Applications of the program

The developed computer program can find the main applica­

tions in the follow i ng subjects:

i. Prediction of flowing well pressure and temperature

profiles.

11. Development of deliverability curves for a certain

well for different aquifer pressures.

iil. Determination of the effect of salt and C02 concentra ­

tion on the flashing point of the fluid.

iv. Determination of the e ff ect of calcite deposition and plugging on production .

These four items were analyzed for two wells in the

Svartsengi the effect

During the

field in Iceland

of CO 2 from the applicatio n of

a nd one exampl e is gi ven for

Kizildere field in Turkey. the computer program , the

relative roughness coefficients of the slotted liner,

casing and calcite deposition were taken as 1.37 E- 4, 4.57

E- 5 and 3.041 E- 4 m respectively.

The listing of the program is presented in Appendix A.

25

2.6.1 Svartsengl Well No. q

This well was initially drilled to 1113 m depth, and it was used as a production well until a casing damage occurred 1n

the well in 1980. Presently it Is used as an observation

well.

The depth of the aquifer Is found from the temperature

profiles as 1024 m, initial temperature and pressure values

were 240 0 C and 88 bars respectively.

During the application

deliverability curves of

of the computer program. the

the well, with or without calcite

deposition, and the pressure profile of the well were

obtained. These results are compared with the actual

measurements. The output measurements for well 4 In

Svartsengi are given in Table t. As can be seen from

Fig. 1, the deliverability curves for the cases with or

without calcite are in good agreement with the measured

ones. This fit was obtained by using the turbulence

coefficient as 0.0035 bar/(kg/s)2.

TABLE 1 Svartsengi well no 4 output measurements

WHP(bara) Flow(kg/s) WHP(bara) Flow(kg/s) Without calcite With calcite

19.0 33.0 18.9 28.0 17.1 59.0 1 6.8 39.0 1 4 . 0 75.0 1 3. 5 49.0 1 3.2 80.0 1 1 .2 50.0 1 1 . 7 85.0 9.2 51 .0

8.9 52.0

Data derived from Fig. 2 was used to see the ef fect of

calcite deposition. The length of deposition was taken as

60 m between the interval 350-410 m and the best fit was

obtained by using 11.5 cm as the average diameter of the

calcite section. The calcite deposition causes a very high

in high flowrates and the chang e in pressure drop

deliverability curve

flowrate. In Svartsengi

Is very abrupt at a parti cular

kg/S and with a flowrate

choked.

51 4, this flowrate is found as

higher than this value the flow is

26

The measured and calculated pressure profiles were also

compared at Fig. 3. The calculated pressure profUe at 30

kg/s flowrates gives a good fit with the measured one.

As a final application, mass flowrate vs. flashing depth

from wellhead was plotted. and the caliper log of the well,

Fig. 2, was compared with this plot (Fig . 4) . By taking the

flashing depth as 410 m from Fig. 2, the corresponding

f!owrate Is found as 31 kg/a from Fig. 4 which was the

actual average flowrate of the well before callper log.

The computer outputs for Svartsengl Appendix B.

are given in

2.6.2 Svartsengi Well No. 11

This well was used as an example for the effect of reser­

voir pressure and casing size on the dellverabl11ty curves.

The family curves for different reservoir pressures are

shown on Fig. 5. The pressure drawdown causes a reduction

in the wellhead pressure but this reduction is not of the

magnitude as the reduction of reservoir

the other hand, the shape of the

same order of

pressure. On

deliverability curves are almost the same for all reservoir

pressures, therefore it is possible to find a common

formula depending on the reservoir pressure, wellhead

pressure and mass flowrate by knowing

deliverability curve for a reservoir pressure.

only o n e

As a part of this study, three production tests were

carried out and the data is used in the program. The lip

pressure method developed by James (1970) was use to test

the well. A V-notch was used to measure the low mass

flowrates and

James's formula

area, en thal py

the enthalpy of fluid is calculated from

which relates mass flow, discharge pipe

of fluid, and lip pressure. For a higher

mass flowrate, the well was discharged vertically, direct

to the atmosphere. The enthalpy value obtained from low

flowrates is used to get the flowrate from James ' s formula.

The results of the test are given in Fig. 5. Since there is

about 12 bar pressure reduction in the field from the

initial reservoir pressure, due to the production, the

27

reservoir pressure is taken as 76 bar. The best fit is

obtained by using zero turbulence factor.

The effect of casing size on the output curves was also

studied and the results obtained for two different wells

are plotted in Fig. 6 . The main effect of the casing size

on the output characteristics of the wells is the decrease

1n the turbulence pressure drop in the wider wells. The

dellverabl11ty curve for Svartsengi 11 was obtained by

using zero turbulence factor and as can be seen from Fig.

6. the change in flowrate does not affect the wellhead

pressure in the wider well as in the narrower wel l .

2.6.3 Kizildere Well No. 6

To see the effect of C02 on the output curves, data from

Kizildere geothermal field in Turkey was used. The

Kizildere field is a hot-water type geothermal field which

is producing through six wells. One of the important problems in this field is CaCO scaling in wells which is

related not only to the calcium but also to the C02 content of the geothermal fluid. High percentage of C02 in the geothermal fluid of Kizildere causes early flashing of

the fluid because of higher C02 partial press ure . The data from Kizildere Well no 6 (KD-6) was used in the program and

the flashing depth and the wellhead pressure were examined. The actual data (Tan, 1982) and computer output for this

well are given in Table 2. Fig. 7 shows the configuration

of casing string and flashing point.

By using zero turbulence pressure drop, the wellhead pressure was obtained as 3.14 bar and the flashing point is at 576 m which shows a good agreement with the measure­

ments.

28

TABLE 2: Data and computer output for Kiz1!dere well No. 6

NME or FII:r.n ~

W~tL fl\'l~

DAtE OF CALe ,

KIll LOr.nE KP· 6

17·0'-8~

~!N~t£ · I'H."'':;r.(W!1'Efl) !iECTI9N·

r~ (aAAS) (llp)tu!b (W,S) . I'wr (RA.1S) CC02 (p~~)

C!l.a..CL (p~)

D~rIH! !I ) rf ba! )

1100 . 000 7'1 .H4 7 !10.l!O ~ 70 .1!2 fj 6~ . ~OO ~1.750 61j; . fj~O 67 .7U Gao .OOG 62 .o"

84.0 00 !I.eo!!

QUOD 14204.0 1200.0

VeW )

J,034 3.oJ4 3. 034 2. 366 2.36'

1.'\ (K'J /~ ) .. '!G .O!!O I'w t (MlI.:; J 84.000 B (tJ/~'.I) , Oj6.617 rna!lh (S,,,'S) 5' , '85

O!'!'Ti! , re ore

~7) . 1 j, .!, 1~ . 21 !I .aao ~ O!! . O n.'-9 2.79 · 41.421 ~ O ~ . !! 11.26 1.21 ·U~9

~ ~~ . ~ o .~~ U, · 0.~4 2

200 . 0 6. 12 0. 40 - 0. 288 leO . D 3.'0 0. 22 - 0. 178

' . 0 l . 12 US · 0.0 39

WII r (AAJl. ) .. l.12

Ka~:; nOM taLe

Oepth

»,

Sall >:ontcnl

Haclor

0.018 O.O!! O. OIB O. !lt4 0.014

0 %01

24.~5 D.' 2U~ 2.1 '- U5 U 14.45 '-' 2U~ I . ' 1.4. 4512.1 24.45 \3 . 5

96 k1J/ ~

851 •

3. 0 bi[

1200 p~lII

O{ru~AT . DrM! QPFIlIC W(ku/51 f(CJ

21.5'0 -4.406 - 4.242 · 0.164 ' !i.!!!! 201. !I 2\.5'0 . B.B\2 - g. 4S~ -o. m '6 .00 201.0 2U'O -l.m -2.,n -0. lt3 '5.00 20U 14.448 0 .1102 0. 000 O . O~!I 96 . 0(1 201.!! 14 . 448 -5.Ii56 -5.5" -0 .0'0 ",00 201 .0

0" OrIl?! OrACe DPrRIC I!fJt~!l Hq F!

o.lloa C . ~~~ ~ . OoO 0 .000 B~6 . 6 2et . O ~ . OlH . H .700 · J. OIJ4 ·o.m; ~!I . I 12 e~~ . 9 I" . B O . ~t41

~4.m ·2.l72 ·U170 - O.!!!! 8~4. 9 179 .9 O. OW . 2. ~13 . L7~J · 0.057 - 0.3 \7 a~1 .0 m.9 o.om -2.l31 · 1.508 · 0. !!7!! · 0.466 952 . 7 m.B 0.0141 ·2 .m · 1.267 · 0.204 -0 .776 m .2 140 . 1 0. 0141 - !l .771 -o.m -a . 105 -11 .334 B~a . 5 132 . 5 0. 0141

Boll~ hole P(C~5U(£ B4 b~[ , T\!:IIpl! [atull: 201 C

CO2 content of I lea. 15 t by lidyhl

SICiU. qUllity 'U7 ~

Tabl\! 2. D~la and to~puLc( out pul fer I:i:iltkrl! Wdl no 6

f'F!.AS1I

5' .'85 ~ ~ . '95 H . ~m S, .,R5 5' . 985

Stf t-1QIJl.!Y

1. !!O ~ . a, S!! 1.56 0. 70 ;":1 Ut ~.7!' M 3.17 !I.8) /Ill 4.S! 0.84 11:1 6. I! ~.89 AI{ 6.71 !! . 90 A!l

29

3 RESPONSE OF THE SVARTSENGI GEOTHERMAL FIELD TO INJECTION

The Svartsengl geothermal field is a high temperature

liquid dominated field with a temperature range 235-2400C

and the fluid produced is in composition of two-thirds sea water and one - third fresh water. The geology of the

Svartsengl field has been deseri bed by Franzson ('983).

Res e rvoir engineering studies in Svartseng l are discussed

by Kj aran et al . (1979) and Gudmundsson et al. (, 985a.

1985b). The fluid production in Svartsengl has resulted 1n

a draw down of 135 m, after a fluid production of about 41

E9 kg. The rap i d drawdown in the field may affect the

following items of the future performance of the field, i) cold water

cooling of

production

encroachment from surrounding

the formation, i1) decline in

wells with falling reservoir

aqu ifers, and

the output of pressure, iii)

migration of the flashing zone down the wells and into the formation, iv) sealing of the producing fractures by

calcite deposition if the fluid flashes in the formation.

Injection would be a solution to the pressure recovery of

the field as well as the efficient disposal of waste brine and condensate.

To study the effects of injection in the field two injec­tion and tracer tests were carried out in 1982 and 1984.

These tests are discussed by Gudmundsson (1983) and Hauksson (1985). The purpose of this study is to investi ­

gate the pressure response of the field to injection and match one year production history of the field by using a

lumped-parameter model.

3.1 Analysis of injection data

In the Svartsengi injection test, a brine - condensate

mixture was injected for 72 days between 25th July to 4th October, 1984. The mixture was 80 percent flashed brine and 20 percent steam condensate and the injection flowrate

was kept at 50 kg/so The mixture had a pH close to 6.7 and the temperature 80°C. During the injection test, the

drawdown was measured as water level in a monitoring well . The critical problem encountered during the injection was

the silica scaling in the i njection well. It was tried to

30

avoid this by controlling the pH of the injected fluid and by dilution of the

plant. During the

brine with the condensate of the

test the condensate concentration

power

could

not be kept constant because of the unavailability of

adequate amount of condensate from the power plant. As a

resul t the concentration of the condensate decreased down

to 10 percent which caused an increase in the rate of

silica deposition. One of the proposed solutions to

decrease the rate of silica deposition Is the injection of

CO 2 with the condensate, which produces a weak acid to lower the pH down to 5.5 (Hauksson, T. personal communi ca­t 1 on) •

To see the effect of injection on the drawdown of the

field. the rate of production and drawdown data are used

for the time period of October 1983 to January 1985. The

total rate of production and injection data are shown in

Fig. 8 with time, and the net production is the difference

between production and injection rates. The water level

drawdown is shown in Fig. 9 with time.

The drawdown data shows a linear trend for the first seven

months in which the net production rate is almost constant.

But after a decrease in production. the rate of drawdown

also decreases and during the time of injection the water

level starts to increase. The effect of reinjection can

also be seen from the late portion of the data when the

production rate reaches the initial value. During this

period, the change in drawdown shows the similar trend as

of the early data. By using these two graphs it can be

concluded that the injection can be helpful to recover

pressure .

3.2 Model description

Fluid extraction and reservoir drawdown in the Svartsengi

field developed an increased steam zone after a few years

of fluid production. This is evident from Well 10 which

changed from being liquid-fed to producing steam only which

is the shallowest well among the six main producing wells

(424 m deep). Other wells in the field are still liquid­

fed. A conceptual model of the Svartsengi reservoir is

31

shown in Fig. 1 0 • The liquid dominated reservoir Is

overlaln with a steam zone, which increases in size with

drawdown (Hauksson, 1985).

Based on the above conceptual model Vatnaskil (1983)

developed a lumped parameter model of the field. The schematic representation of the model Is given In Fig. 11.

The boundaries of the reservoir are impermeable and there

Is a slightly impermeable barrier between the feed zone and the liquid dominated zone. The drawdown In the feed zone

leads to a leakage from the water zone. This leakage

results in an increase In the size of the two-phase zone.

The balance equations for this model can be written as;

W "" q +

where c is a constant .

If we solve these equations for h, and h2 we get;

t

h1 (t) • Cdm(t-tle-t/kdt o

t

h2(t) - Cl(t) - C2 fm(t-t)e-t/kdt o

where;

C

( 4 8 )

( 49)

( 5 0 )

(51 )

(52)

( 5 3 )

( 5 4 )

32

c C3 •

A, " S, A2'2S2 ( 5 5 )

A, " S, A2'2S2 K • ( 5 6 )

C A, P, S, +A2P2S2

and

k

M (t ) • fW(T)dT (57)

0

The same set of production and drawdown data given In Figs . 8 and 9 were used to test the proposed model. The produc­

tion rate of Well 10 was subtracted from the total field

product i on. because it i s producing from the two" phase

region. For the best fit of dr a w-down, the variables in Eq.

54 are found as;

K '" 125 days, C = 5.1 E- 9 m/kg, C = 2.5 E- l1 m/kg/day

A good fit is obtained for the long term behavio r of t he

drawdown (Fig. ' .2). but the model was not able to produce

the sharp changes In the draw-down . This is due to the

nature of the model, which assumes the storage is given by

the free surface effect at the boiling surface. which is

the long term effect thus neglecting the short term elastic

storage. The model also assumes that all the introduced

change in the flowrate should reach to the boundaries to be

effecti ve on the drawdown, The time required to see the

boundary effects in the Svartsengi field was found to be

10 " 30 days by Kjaran e t .al. (1979) , Therefore, it is not

possible to simulate any changes

time less than 30 days.

in the flowrate for a

33

4 SUMMARY

Simulation of flowing wells can be a useful tool for geothermal well analysis. Using the flow model, It Is still possible to get information for the conditions where the

actual measurements failed. The following parameters can be deduced by the application of a well bore simulator.

1. The temperature and pressure profiles of flowing wells

can be obtained.

2. The change In the performance of the well after scaling

development In the well can be simulated.

3. The magnitude of decline In wellhead pressure with aquifer pressure can be found

4. The wellbores with wider production casings give higher

flowrates than those with smaller sized wells .

The practical use of the model presented here can be listed as follows:

a. The flash level of the geothermal fluid can be found

within a good accuracy. therefore it gives a valuable data

for the cleaning operations of the wells.

b. The wellhead pressure and mass flowrate history of the

wells can be forecasted by using the predicted drawdown of

the reservoir itself. This Information is used for the

planning of the operational life of a geothermal power

plant, since it requires some minimum values for both mass

flowrate and pressure values in the turbine.

It is found that the decline in the drawdown can be reduced

by injection. Reinjection also has merits for the waste

disposal problems of geofluid which causes pollution

problems. To fit the immediate response of the Svartsengi

field to injection, a new model should be developed which

can respond to changes in the

less than a month. In order to

steam model the flowrate of

constant for a longer time.

flowrate over a period of

see the validity of the

injection should be kept

34

ACKNOWLEDGEMENTS

It is a great pleasure for me to express my appreaciatlons

to Dr. Snorri Pall Kjaran for his helpful and patient

guidance during this study.

I would like to extend my thanks to Mr. Sigurdur Larus Holm

who provided the field data and helped in the computer work of this study.

Thanks are due to Mr. Trausti Hauksson who conducted the

well test and supplied his experience about the practical

aspects of the injection test.

Special acknowledgements are also due to Dr. Ingvar 8irgir

Fridleifsson for critical reading of this report.

I also wish to extend my gratitude to the United Nations

University for the Fellowship. the National Energy Author­

ity of Iceland in the use of the computer and other facilities and the Middle East Technical University for the

leave of absence which made this work possible.

35

REFERENCES

Armand, A.A., Teacher, C.G. (1959): Investigation of the

Resistance During the Movement of Steam-Water Mixtures In

a Heated Boiler Pipe at High Pressures. Atomic Energy

Research Establishments. Hartwell. Berkshire.

Bjarnason, J.O •• Stelngrlmsson. B., and Gudmundsson,

G. ,(1983), I. Drawdown In the Geothermal Reservoir. 11. The

Chemistry of the brine and Steam 1980-1983. Ill. Tempera-

ture and Pressure in the Reservoir: National Energy

Authority of Iceland, Report OS 83086-JHD-17.

Carslaw, H.S. and Jaeger, J.S. (1959): Conduction of Heat

In Solids. Oxford Press. London, 386 pp.

Chlsholm. D. (1972): Pressure Gradients Due to Friction

During the Flow of Evaporating Two-Phase Mixtures in Smooth

Tubes and Cha nnels. Int. Jo u. Heat and Mass Trans., 16,

347-358.

Franzson, H. (1983):The Svartsengi High-Temperature Field,

Iceland, Subsurface Geology and Alteration. Geothermal

Resources Counsil, Trans., Vol. 7, 75-78.

Gudmundsson, J.S. (1983): Injection Testing in 1982 at the

Svartsengi High-Temperature Field in Iceland. Geothermal

Resources Counsil, Trans., Vol 7 ,423-428.

Gudmundsson, J.S ., Olsen, G.

Sva rtsengi Field Production

and Thorhallsson, S. (1985a) :

Data and Depletion Analysis .

Proc., Tenth Workshop Geoth. Reservoir Engineering, Report

SGP -TR-84 ,45-51, Stanford, California .

Gudmundsson, J.S. and Olsen , G. (1985b) : Water Influx

Modeling of Svartsengi Geothermal Field, Iceland. paper SPE

13615 presented at the California Regional Meeting,

Bakersfield, March 27 - 29.

Hagedorn, A.R. and Brown. K.E. (1964): The Effect of Liquid

Viscosity in Vertical Two-Phase Flow. Jour. of Pet. Tech.,

203-210.

36

Hauksson, T. and Gudmundsson, J.S. (1985) : Tracer Survey 1n

Svartsengl Field 1984 . Geothermal Resources Couns!l.

Trans . , Val 9, part 11, 307-315 .

Jarnes, R . (1970): Factors Cont r olling Well bore Performance .

Proe. of UN Symposium on the Development and Utilization of Geotherrnal Resources, Val 2, Part 2, 22 Sept-l Oct., Pisa,

1502-1515.

Kjaran,

Eliasson,

s . P • •

J.

Halldorsson, G . K ••

(1979), Reservoir

Thorhallsson, S.

Engineering Aspects

and

of

Svartsengi Geothermal Area . Geothermal Recources Couns!l,

Trans . , Val 3. 337-339.

Kjaran, S.P . and Eliasson, S . (1983): Geothermal Reservoir

Engineering Lecture Notes. UNU Geothermal Training

Programme, Iceland, Report 1983-2, 250 pages.

Martinell! , R.e . and Nelson, D.B . (19118): Prediction of

Pressure Drop Duri n g Forced Circulation Boiling of Water.

ASME Trans •• 70. 695-702.

Michaelides, E. E. (1981) , Thermodynamic Properties of

Geothermal Fluids.

Vol 5. 361 - 36~.

Geothermal Resources Counsil, Trans.,

Michels, D.E. (1981), C02 and

to Geothermal Engineering .

Lawrence Berkeley Laboratory,

Carbonate Chem i stry Applied

Rep. LBL - 11509(GREMP - 15).

Berkeley, California .

Orkiszewski, J. (1967): Predicting Two-Phase Pressure Drop

in Vertical pipe. Jour. of Pet. Tech., 829 - 838.

Ramey, H.J.Jr. (1962): Well bore Heat Transmission . Jour. of

Pet. Tech . , 1127-1135 .

ROS, N.C.J. (1961): Simultaneous Flow of Gas - Liquid as

Encountered in Well Tubing. Jour. of Pet . Tech., 1037 - 10119.

Sutton, F.M . (1976) : Pressure-Temperature Curves for a

Two-Phase Mixture of Water and Carbon Dioxide. N.Z . J.Sci.,

19. 297-301.

37

Tan, E. (1982): Reservoir Characteristics of the Kizildere Geothermal Field. First Turkish-Italian Geothermal Energy

Seminar, Vcl 11, Comparative

and Cesano Geotherrnal Fields, Examination of the Kizildere (6-28 Sept.), Ankara.

38

•

2 • • • %

~ .

O~-------;,--------;,--------;o,-------~c-------co~ · o g ~ or g

~~ · , -. , -· , · . ·0 'u •

• • · !: .!! •

~'--------"o<' --------"O'"'-------;~------~'-------Co~= 8 \0 <D ~ ~

5. "S o

39

Diome!er

__ -,0_" __ -,-' '_' _ _ 2~" __ -,3~" __ -,4_' _ _ 5-,-" _ __ 6~" __ -,7_" __ ~8'_' __ ,-~"-=-(inche3]

<OE- C.::Ising (0.0 . 9~le")

Fig.2

, , , , 0" " 2" 3"

Svartsengi Well nO.4 Calcite deposi tion according to caliper log measured· 78.12 ,13

, , 4" ," 6" 7"

19.01 .2"-

3~O-

4~O

, , [inches] 8" 9"

B.SI1S J·S~Q,ts ... o;; "'18019

40

~JHD·HSb - 2300 - MP L.J::J 85.09.1180-00

o

100

200

300

E

-= 400 <> m

'" 500

600

700

800

10

Pressure (kg/cmZ)

o 30 40 50 60

o Measured

~ Calculated

. Figure 3. Pressure Profile in Svartsengi 'Well no. 4

70

.. • • ;; • ! ii:

• 0 •

r;T"=tJHD-HSI:J -230Q-MP ~85.09 . IIBI-'OD

'00

.0

60

"Or 31 kg/s

20

01 1

300 ' 40U 000 600

FlashlnQ Oepih rroll'! Wellhtad(lfI)

"-:: • 0 • • ~ · · 0 •

700

Figure 4. Change in Flashing Depth with Mass Flow Rale

200 •

060

020

.0

· \" • 0 • ~ • • •

o

\~ \;

..

o Calculated

.. Measured

Meo , ,,,red Value '

W(h / . )

32 . 6

53. " 2 01.0

WtlP{ba r)

16 . 8

14 .2 12. 8

0~1--r--r--r-~~'-~~--.---------6 • '0 .. '4 ,. " 20 22

WHP (bar)

Figure 5. Deliverabilily curves for SG- Il for different reservoir pressures

=

42

~JHD'HS~'2300'MP ~85.09.1182·OD

!! o 0:

~ ...

200~

160~

: 80 o ,.

40

.... SG-II 9 5/S"cosi rq

O~~--~--~--~~---r--~---------6 8 10 12 14 16 18 20

. WHP (ber)

Figure 6. Effect of Casing Size an the Output Curves af geathermal Wells

KO-6

Om 8"

40m 7" 47m 6"

112 m 5"

575 m 4"

~Flashing depth

655.63m ...

50m I--

Fig.7 Scaling thicknesses measured by go-devil in kizildere well no 6

~3

280 Net

260

240

220

200

180

160

140

120

100

80

60

40

20

o -o

. . production role (kg/s)

Production rate of We ll no. 10

1 -

-

- - . - - - - -N 0 J F M A M

1983

.

In jection --l

, -- , -J J

1984

. .

, -A s

. . . I NJECTION RATE

II -

. JUt I - , o N

Figure 8. Net Production and In jeclion ra tes with time

I

(kg/ s)

-- -

-o J

1985

~

~

45

-, ~

'" en ~

-,

) • •

" '" E -~ -~ • c: ~ 0

g • "0 ~ 0

z >-

'" 0 D D • oi '" " "' a:

~ " " '" ::J

"' Z <D

'" a: en ~ ;:) ~

'" • "' "' " "

<D '" ~ N 0 <D '" " N 0 <D '" ~ N 0 N N N N N ~ ~ ~ ~

~ JHO-HStl-2 30Q-MP ~ 95. 09. 1I05-'OD

Well, 4- 9, 11,12:

Two-phou

(OC) o ISO soo

or '00 ,. n

'. , '. r

r~

1000

1000

Figure 10. Conceptual Model of the Svorlsengl Reservoir

"

i~~~~~~I@ TWO-PHASE

~~~It ~~~ur\ 111 1111111 1 111 111111111 r I 11 I I I I lWO-PHASE WATER

INTERFACE

WATER

.,.-BOREHOLE

f-::.----=--=------~ :: :::-= !.E.!~~I.!.E_:" __ :

Figure 11. Schematic Representollon of Steam Model of the Svorlsenol Reservoir

c

'"

28 DRAWDOWN IHI

26

2.

22

20

18

16

,. 12

10

8

6

• 2

0 0 N

1983 0 J F H

+ MEASURED 6 CALCULATED

"I,,!,"" +

~ *'-"""'~> ....;:;;:; : ~ K' 125 da,. ~ + C - 51 E-9 m/ko # .~ c~; 2:5E- 1I m/kg/day

A H J J A s o N o 1984

J 1985

Figure. 12. Measured and Fitted Oro wdown from steam Model

~ ....,

48

"

:c= " -0 -

•

, , , , " . " " , 0

f , . ,g , ~

" < '~ ," ~ . g

E f

~

, , , , UUu

00 _ N

::: , " , . '. :f :.

g '" ' il " I f

," ,~ ,. '. • , " , " • '.

W N ~~~ ~. ~_N ~

~~~ ~ ~~~<~o~g!89~ ~~~ ~N~<~~ NQ_<N~%~~~2~_o _~ -~~H~ ~ ZHC~~CUUU~_CQ~UC~

o o

a­-. g~ o· % •

~ ; f : -­>--: =:= w­o-

g : .­.­> -" ­w _

"­w _ --ii: .-

..............

"

.. .. .. .. .. uuuuuuuuuuuuuuuuuvuuuuuuuuuuvuuuuuuuuuuuuu

: ,

, , , , , , , , i· , , , , ,

, UuU

, , , ,

, , , ,

" '-, ~ , . ," .. ,.

w , 0

'. • .. E

' " ,. .. :2 ,~ '. :~ , , , , uuu

. :; " . ~ " U

" -N

;t . , ;..: ~ ' <, w w,

t

w ..

, uu

, , , , , , , , , , , , , , , , , , , , , , , , , , ,

1 ~: I, : e '" ,

• •

0 :8' : ~ : .... ... ::;;:g i:ti~

! ~ : ~ ~:!& : :. (j . ... , '" , ,

: ( , , , , uuu uu

, , , , , , , , , , , , , , ' u ,

'~ : e " ' 8' : -' I :;; 1 ~ i ~ g : 1if ~ I ...

",tif ~ > c:. ' ~ • , >

, , , , uuu

:~ " '. ' f ,~ " ,. " I ~

:~ u ' M ,. ,

' U ~ •

, , uuu

, , , , , '. :~ e

, " '" ': ,g lE ,~

o I f ~ w . •

· " · • ~ w u e

" e ~ Q

~ ~ " ~ , . . ,. '~: ... ". .., .. ; !:>

uz ,~ , '" a~ I .... : ::l ~~ '~ : f ... ... : .. :"'" ;:;~ . e ! ~ <o:~ I ~ : ;

:;8 Cl ' ''' , ' ,

~uu.:. ,!, ... .:,

· •

· · · ;:; •

• . 0 ,,~

;:.=-· , ,. "-0, '. _u wU ;;' 6 :i~

, , , ,

~ i ,~' c , ' U , ... , Go 00 '" . , ,,,,e. , ~~ , c • .., I ,

,'" ,'" , Co I Co.

" , '" , at . v: ... ' '''i ' '' j ;: l!

, , , , , uuu

,

.. t ,N • ,~ . ' ~

uu

-"

• • • o ~

• •

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