Determination of reservoir properties at Wairakei Geothermal Field using gravity change measurements

Juumalof volcanoh~D' and geolhermal research ELSEVIER

Journal of Volcanology and Geothermal Research 63 ( 1994 ) 129-143

Determination of reservoir properties at Wairakei Geothermal Field using gravity change measurements Trevor M. Hunt a, Warwick M. Kissling b alnstitute (),/'Geological and Nuclear Sciences, 1~"airakei Research Centre, Private Bag 2000. Taupo, New Zealand blnstitutejor Industrial Research and Development, P.O. Box 31 310, Lower Hurt, New Zealand

Received 1 April 1993; accepted 6 April 1994

Abstract

Exploitation of a liquid-dominated geothermal system generally results in the transfer of mass within, or out or', the system and causes measurable changes in gravity. When the rate of mass transfer is controlled by the permeability of the reservoir rocks, then the analysis of measured gravity changes can yield values for reservoir properties. For two such cases we derive permeability or permeability-thickness (transmissivity) and storativity. One case is during the early stages of exploitation when a two-phase zone is rapidly' expanding. Calculations using a numerical reservoir simulation model show that for Wairakei the gravity changes associated with permeabilities of 50 and 100 md would be clearly distinguishable ( > 50/zGal) in less than 2 years. A measured gravity change of - 4 1 5 ,uGa! between 1950 and 1961 suggests a permeability of 100 md, which is consistent with values obtained from well tests. The second case is during reinjection into a deep-liquid zone overlain by a two-phase zone. Gravity changes of up to 120/~Gal associated with reinjection at Wairakei are analysed using analytical models (Theis solution). The measured gravity changes are matched by those of a model with isotropic permeability having a permeability'thickness (kh) of 9.9 d-m and a storativity of 9.2× 10 .6 m Pa -~. If a model having anisotropic (horizontal) permeability is used the derived values for kh are 18.2 and 5.4 d-m, and the storativity is 8.7)< 10 .6 m Pa -1.

I. Introduction

T h e u p p e r parts of volcanic g e o t h e r m a l syst e m s in m a n y places are exploited to generate electricity. M a n y o f these systems are liquid d o m i n a t e d : wells exploiting the u p p e r part o f the system ( r e s e r v o i r ) generally discharge a m i x t u r e of water and steam, but liquid water is the pressure-controlling m e d i u m in m o s t parts o f the system. The s t e a m and water are separated, a n d the s t e a m is passed through turbines in similar m a n n e r to a c o n v e n t i o n a l t h e r m a l (coal, gas) power station. The separated water, together with

c o n d e n s e d steam f r o m the p o w e r station, is considered waste and either reinjected into the edges o f the system or r e m o v e d completely f r o m the system by surface drainage. Exploitation involves withdrawal of large masses and v o l u m e s of fluid. At Wairakei G e o t h e r m a l Field, N e w Zealand, the total mass withdrawn f r o m the borefield between 1958 and 1990 was a b o u t 1600 Mt, equivalent to a b o u t 2 k m 3 of water at 250°C, and in addition, a b o u t 250 Mt of fluid was discharged f r o m natural thermal features such as hot springs, geysers a n d fumaroles. W i t h d r a w a l o f such large a m o u n t s o f fluid causes m a j o r hydro-

0377-0273/94/$07.00 © 1994 Elsevier Science B.V. All rights reserved SSD10377-0273( 94 )OOO33-D

130

T.M. Hunt, W.M. Kissling / Journal of Volcanology and Geothermal Research 63 (1994) 129-143

logical changes, and consequently it is important to understand the physical properties of the system, both in the natural and exploited state, if energy is to be extracted from the system in a rational, economic and environmentally responsible manner. Probably the best documented behaviour of a liquid-dominated geothermal system during exploitation is that at Wairakei Geothermal Field (Fig. 1 ), where continuous production for base load electricity generation has taken place since 1958. In its natural (unexploited) state, the Wairakei geothermal system is believed to have contained a thin liquid-dominated two-phase zone overlying a single-phase deep-liquid zone (Grant and Home, 1980; Donaldson et al., 1983 ). The nomenclature we use here is the same as that used by Allis and Hunt (1986) and is shown in Table 1. When exploitation began, production was mainly from the deep-liquid zone beneath a small area ( 1 km 2 ) known as the Main Production Bo-

Table 1 Nomenclature used for fluid zones at Wairakei Geothermal Field (after Allis and Hunt, 1986). Depths are approximate, Zone

Relativt permeabiiity

Vadose zone Dry or partly saturated rock (0-15 m depth)

High

Groundwater zone Saturated rock with m i n o r stream in thermal areas ( 15-100 m depth)

High ~upper) Low ( lowe~ )

Reservoir." two-phase zone Steam zone: vapour-dominated. but large amounts of immobile hot water are present. Fractures contain steam and minor hot water; pores contain various a m o u n t s of hot water and steam. ( 100-400 m depth) Liquid-dominated zone: liquiddominated, but small amounts of steam are present. Fractures contain hot water and m i n o r steam; pores contain hot water. ( 4 0 0 - 6 0 0 m depth)

High

High

............................. Deep liquid level ...............................

Reservoir: single-phase zone Deep-liquid zone: liquid dominated. Fractures and pores contain hot water; no steam present ( > 600 m depth)

Fig. 1. Map of Wairakei Geothermal Field showing the location of the Main Production Borefield and its parts. E B = E a s t e r n Borefield; W B = W e s t e r n Borefield; TF=Taupo Fundamental benchmark; P S = geothermal power station.

High

refield (Fig. 1 ), hereafter referred to simply as the 'borefield'. Removal of fluid resulted in a pressure drop which caused boiling to occur in the upper part of the reservoir. The two-phase zone expanded both laterally and vertically, and by the early 1970's was about 500 m thick. The two-phase zone also divided into two parts: an upper zone called the 'steam zone' or 'vapourdominated zone' in which steam is the main pressure-controlling phase; and a lower zone called the 'liquid-dominated zone' in which liquid water is the continuous phase but boiling conditions exist and some steam is present (Allis and Hunt, 1986). The boundary between these

72M. tlunt, W,M. Kissling /Journal of! olcanology and Geothermal Research 63 (I 994) 129- I43

zones is believed to be gradational, but there is little information available about the vertical distance over which the changes occur. The steam and liquid-dominated zones may not be homogeneous; liquid saturation in the steam zone may be smaller at the top of the zone than at the bottom (Hunt, 1988). Pressures in the deep-liquid zone beneath the two-phase zone fell by up to 2.5 MPa (25 bar), but have been relatively stable in most parts of the field since the early 1970's. However, gravity and pressure data suggest that in one part of the borefield, the Eastern Borefield (Fig. I ), the deep-liquid level has risen by nearly 100 m since the early 1980's (Hunt, 1988 ). The behaviour of the Wairakei system during exploitation was deduced from pressure and temperature change data, assisted by precise gravity (microgravity) change measurements. Measured gravity changes have been used at Wairakei and Ohaaki geothermal fields to: determine recharge over the whole field (Hunt, 1977; Allis and Hunt, 1986); estimate changes in saturation in the steam zone in different parts of the field (Blakeley and O'Sullivan, 1985; Allis and Hunt, 1986); check the validity of numerical reservoir simulation models for exploitation (Hunt et al., 1990a); and to determine the path ofreinjected fluid (Hunt et al., 1990b). In this paper we extend the application of gravity change measurements further by showing how, under certain circumstances, they can be used to determine the permeability (k) or permeability-thickness (kh) of reservoir rocks and parameters of the system such as storativity (Och). It is acknowledged that the examples of observational data given are not as good as we would have liked, but they are the best currently available, and we believe they suffice to demonstrate the validity of the technique.

2. Permeability 2.1. Permeability in geothermal systems Permeability is an important property of rocks in both groundwater aquifers and geothermal systems. It is much more complex in geothermal

13i

systems because two phases (liquid = water; vap o u r = s t e a m ) may be present and the interchangeability of the phases means that they behave differently from a simple two-phase system containing immiscible components (e.g., oil and water). The permeability of small rock specimens, measured in the laborato~-, is generally much smaller than the permeability determined from well tests, indicating that permeability arises mainly from flow in fractures, rather than through pores (Elder, 1981 ). A minimum representative sample of a geothermal system max. therefore be tens or hundreds of metres in size, and it is not possible to make meaningful measurements of permeability in the laboratory,; any technique which can determine directly the permeability of a sample of this size is therefore very valuable. Permeability in geothermal systems is generally anisotropic: fluid withdrawn or injected often flows preferentially in certain directions, usually (but not always) along the strike of the dominant active faults. An example of this was during a reinjection test at Wairakei where microgravity measurements showed that fluid flowed away from the reinjection well mainly in two directions (Hunt et al., 1990b ). The unit of permeability in S.I. is m ~, but a more commonly used unit (and that used here 1 is the millidarcy (md) which is equivalent to 10-15 m ~"

2.2. Permeability measurements at Wairakei The response of pressure in wells in the outer parts of the Wairakei field to changes in discharge from wells in the borefield is very rapid, and pressure changes over most of the field have been uniform (Bolton, 1970). This indicates v e ~ high values for horizontal permeability. Values of permeability (k) and permeabilitythickness (kh) at Wairakei (Table 2) have previously been determined in three ways (in approximate order of reliability) from: (a) Well tests such as interference and injection tests. Most of the published values are for the Eastern Borefield and the results are poorly

T.M. Hunt, W.M. Kissling / Journal of Volcanology and Geothermal Research 63 (1994) 129-143

132

Table 2 Summary o f published values o f permeability (k) and permeability-thickness (kh) of reservoir rocks at Wairakei Geothermal Field

k

kh

(md)

(d-m)

Details

Reference

Well test values 100-500 4h 4h -

50-500 -

15-75 14-33 3 10-100

-

1 0 0 - 1 5 0

-

100-170

Pressure response at WK223 to borefield production changes Pressure transients at WK33 and WK36 Pressure buildup test on 4 dry steam wells Steam fed wells W K 4 / 2 , 36, 42 (Eastern Borefield) Injection test on impermeable well WK301 Interference tests during initial development Measurements in monitor wells, Eastern Borefield, 1988-89 Injection test in Eastern Borefield

Elder, 1966 McNabb et al., 1975 McNabb et al., 1975 Grant, 1978 Grant, 1980 Elder, 1981 Allis et al., 1985 Electricorp, 1990 Electricorp, 1990 Hunt et al., 1990b

Values determined from reservoir simulation models 25 v

-

I 1

-

12

v

4 7h 8v 25 50 50

-

-

25 40 45

18 -

27 35 h 20-300 h 20 v 5v

30-35 -

Simple 1-D model Simple I-D steady state flow model From model for natural discharge Calculated from temperature decrease due to production From pressure drop in field Calculated from natural output of whole field Gross permeability from single-phase model Simple single-phase model of whole field Lumped parameter model with instantaneous drainage; pressure match Lumped parameter model with slow drainage; pressure match Unconfined aquifer model Lumped parameter model with instantaneous drainage; pressure match Lumped parameter model with slow drainage; pressure match Confined aquifer model, based on effects at Tauhara Distributed parameter, 2D model; pressure, enthalpy, recharge match Calculated from natural output of field and pressure gradient

Marshall, 1966 Donaldson, 1968 Grant, 1970 McNabb et al., 1975 McNabb et al., 1975 McNabb et al., 1975 Grant, 1977 Robinson, 1977 Sorey and Fradkin, 1979 Sorey and Fradkin, 1979 Zais and Bodvarsson~ 1980 Fradkin et al., 1981 Fradkin et al., 1981 Wooding, 1981 Blakeley and O'Sullivan, 1982 Donaldson et al., 1983

Valuesfrom laboratory measurements t

0.01-0.05

-

-

30 specimens o f various rock types, using water Cores from WK37 ( Eastern Borefield), pore pressure 100 bar, confining pressure 150-250 bar; using water

Elder., 1966 Pritchett et al., 1978

v=vertical, h=horizontal, 1 m d = 10 -15 m 2,

documented. Values for permeability range from 4 to 500 md, and for permeability-thickness from 10 to 170 d-m. (b) Reservoir simulation models which match response of the field to exploitation. Early models were simple 1-D models but later models were 2.5 or 3-D models; early models were matched only to pressure changes for a 5-I 0-year period, but later models matched pressure, temperature,

recharge and enthalpy data over more than 20 years. Most of the later models suggest values of 20-50 md for horizontal permeability and 1020 md for vertical permeability. Other modelling studies at Wairakei (Mercer et al., 1975; O'Sullivan et al., 1983) have assumed values for permeability, and adjusted other parameters such as recharge coefficient and reservoir area. (c) Laboratory measurements on core sam-

T.M. Hunt. H: M. Kissling / Journal of Volcanology and Geothermal Research 63 (I 994) I29-I43

ples. All these measurements showed permeabilities much less than 1 md, however, they measure only pore permeability and do not take into account fracture permeability which is of much greater significance.

3. Gravity changes

3.1. Measurement of gravity changes Repeat gravity surveys covering the Wairakei Geothermal Field were made in 1961, 1962, 1967, 1968, 1971, 1974, 1983 and 1991; additional surveys of limited areal extent were made in 1987, 1988 and 1989. The measurements were made on concrete benchmarks using a LaCoste and Romberg G-type gravity meter (except 1961, 1962 surveys, which used a North American type meter). Gravity values were computed relative to a base on Taupo Fundamental benchmark lo-. cated about 6 km south of the borefield and well outside the field boundary (Fig. 1 ). Details of the measurement and data reduction techniques have been given by Hunt (1984). The mean standard errors of the gravity values for each sur.. vey were between 6 and 15 #Gal ( 1 #Gal=0.01 /~N kg- I = 10- * m s- 2). However, a better estimate of the significance level of the gravity changes is the standard deviation of the mean of gravity changes at benchmarks located well outside the field (Hunt, 1984). Values of the standard deviation for several repeat surveys (Table 3) suggest that the significance level of the changes is about 20 ILGal. To isolate the gravity changes associated with

133

mass changes within the upper part of the reservoir, the gravity effects of vertical ground movement (subsidence) and changes in groundwater level have to be determined and removed from the gravity differences between surveys. The effects of ground subsidence are calculated from the results of repeated levelling surveys and the vertical gravity gradient ( 3 0 2 / , G a l / m of subsidence; Hunt et al., 1990b). The gravity effects of changes in groundwater level are determined from regular measurements in shallow ( < 30 m ) monitor holes. Over most of the field the groundwater level varies by only + 1 m as a result of seasonal changes in the amount of rainfall and the gravity effects of such changes are less than 10/zGal (Allis and Hunt, 1986). The gravity effects of changes in topography, regional gravity changes, groundwater temperature variations and errors in gravity meter calibration are small (~< 30/~Gal) and can be neglected (Hunt 1977, 1984). The measured gravity differences, between surveys, corrected for the effects of ground subsidence and changes in groundwater level are called gravity changes. We use the term 'change' in this paper to denote change with time.

3.2. Causes of gravity changes The main causes of gravity changes resulting from mass changes in the reservoir are (in approximate order of importance): --Liquid drawdown in the two-phase zone. --Saturation changes in the two-phase zone (dry out due to boiling and steam loss, or cooling and condensation from invading groundwater).

Table 3 Values for the mean and standard deviation (s.d.) of gravity changes at benchmarks well outside (/> 1 k m ) the Wairakei field Surve~

t7

Mean

s.d.

Data source

1961-67 1967-v4 1974-83 1983-01 1988-89

5a 1O 12 11 8

- 16 - 14 +3 - 23 -- 1

17 18 23 22 17

Allis and H u n t ( 1986 ) Allis and Hunt (1986) Allis and Hunt (1986) Unpublished H u n t et al. (1990b)

n u m b e r of benchmarks outside field. Values ( > 100 #Gal ) at benchmarks northwest of field neglected.

n = a

134

T.M. Hunt, W.M. Kissling / Journal of Volcanology and Geothermal Research 63 (1994) t29-143

--Changes in deep-liquid density due to temperature changes. The gravity effects of changes in deep-liquid density due to pressure changes, pore compaction and silica precipitation are generally negligible (Allis and Hunt, 1986). The first two causes are associated with the transfer of large amounts of mass into or out of the two-phase zone. In some cases (but not all) the rate of transfer of this mass is controlled, or at least significantly influenced, by the permeability of the rock in the two-phase zone. The rate of mass transfer, together with fluid density and geometric factors, determine the rate of gravity change. Hence from the rate of gravity change, fluid density change and the geometry of the twophase zone it is possible to determine the permeability in the vicinity of the region of mass change. We will now examine two cases at Wairakei in which it has been possible to estimate permeabilities from gravity change measurements.

4. Case 1 - - Gravity changes during development of the two-phase zone

4.1. The conceptual model The conceptual model we have for Wairakei consists of an initially liquid-dominated reservoir at boiling point for depth conditions for a vertical extent of several hundred metres. When production from the borefield began, the deepliquid pressures dropped, and this led to increased boiling in the upper part of the reservoir. High horizontal permeability resulted in rapid lateral pressure transmission, and so as production continued a boiling front developed, which moved slowly downward. Little information is available about the lateral extent of the front because few wells were drilled outside the borefield prior to 1962. Deep-liquid pressures in drillhole WK211 (drilled in 1958), located about 1 km south of the borefield (Fig. 1 ), began to decline in 1960 (Grant, 1981). Boiling conditions had reached the far western part of the field, about 3 km from the centre of the borefield, by 1962 (AI-

lis and Hunt, 1986). Deep-liquid pressures had fallen by about 250 psi (1.7 MPa) across most of the field by 1964 (Bolton, 1970). The shape and rate of movement of this front was controlled mainly by the horizontal permeability of the rocks near the top of the deep-liquid zone. Large density changes are associated with this development of the two-phase zone as liquid water is converted to steam and these density changes give rise to measureable gravity changes.

4.2. The numerical model It is possible to determine the rate of movement of the front, and the permeability, from gravity change measurements. To demonstrate this we set up a simple numerical reservoir simulation model for the initial exploitation of the Wairakei field and computed the resultant gravity changes for different values of permeability. To perform the calculations we used the numerical geothermal simulator MULKOM (Pruess, 1983 ). To minimise computational time we chose for the model a homogeneous reservoir having radial geometry, thus saving a large number of model elements. The radial extent of the reservoir model was initially taken as 3 km, with element dimensions ranging from 100 m at the centre to 200 m near the boundary; each element in the model was 10 m thick and the total thickness was taken to be 500 m. The production zone representing the region from which fluid was withdrawn was taken to be a region 200 m thick and 900 m in diameter, located at the bottom centre of the model. The discharge rate was assumed to be 1200 kg s- 1; actually, mass output at Wairakei rose from about 460 kg s-T in early 1958 to 1620 kg s -~ at the end of 1960 (Electricorp, 1990). The temperature of the liquid was taken (initially) to be 200°C, the (connected) porosity of the reservoir rocks to be 0.2, and pressures to be hydrostatic. To simplify the calculations, we assumed that natural mass discharges from surface features (hot springs, fumaroles) and recharge balanced each other: according to Allis ( 1981 ) the natural discharge rate at Wairakei for the period 1958-1962 was about 400 kg s- I and mass inflow into the two-

TM.

Hunt, W.M. Kissling /Journal of Volcanology and Geothermal Research 63 (I 994) 129-143

formulation given in Arnold ( 1970 ). Efficient computation of the gravity effect of an arbitrary distribution of mass is essential for the modelling described in this paper. Traditional methods using layers of horizontal polygonal lamina (Talwani and Ewing, 1960) were not used. In the MULKOM model the computed density differences are complicated functions of position, and the problem is already naturally discretised in a manner which makes the integration very simple. Hence, direct evaluation of the integral defining the gravity effect is the best way to proceed. The gravity effect (zig) of a change in mass is the vertical component of the total gravitational attraction of that mass change. The effect at a particular observation point is defined by the integral:

phase zone was 200-700 kg s- ~. Permeability was assumed to be isotropic. Saturation changes in the two-phase zone were allowed to develop in the model with the residual liquid saturation set at 0.3 (Blakeley and O'Sullivan, 1985). The modelling suggests that the boiling front had the shape of a cone of depression, centred on the borefield where it deepened at a rate of about 5 0 m y r -~ (Fig. 2).

4.3. Gravity change computations The output from MULKOM consists of values of pressure, temperature and liquid saturation for each element in the model at specified times after production commences. From these values the density change (dp) in each element for different periods of time can be determined (Hunt et al., 1990a):

Ap={)ziSpw_s

.

(1)

,

fGAp(z-zo), ~ oV

Agtxo,Yo,Zo)=J

where ~ is the porosity, AS is the change in vapour saturation and Pw-s is the difference in density between liquid water and steam at the temperature and pressure in the element. The densities are calculated in MULKOM using the

(2)

L'

where G is the Universal Gravitational constant ( G = 6 . 6 7 X 10 - ~ Nm 2 kg-2), zip is the density change and L is the distance from the observa-

~ \ \ ~.

:_ --,°° F 150~

/'//>/

~-

I

MODEL A

-'/7

\ae / 42

200 2 -250

135

(Radius

q, I

= ,3 k i n )

~-2

-3

1

0

Distance O V

__ ~-.&~

3

/.~_

F

MODE'"

~ -200~ -250

2

. . . . . . . .

-50:-

;-is°

1

D (km)

._i~:6~ ±

-2

(R= 2 km)

t

-1

i

0 Distance

1

2

D (km)

Fig. 2. Development of the two-phase zone (liquid saturation = 0.9 ) at Wairakei according to MU LKOM models for k = 100 rod. Values in italics (9, 18, ...) indicate months after start of production. Depths indicate thickness of zone beneath the top of the reservoir; vertical exaggeration is 8 X.

136

T.M. Hunt, W.M. Kissling / Journal o/ l,blcanology and Geothermal Research 63 (1994) 129-143

tion point (Xo,Yo,Zo) to the volume element dV at ( x,y,z ).

4.4. Results Theoretical gravity changes with time at the centre of the borefield were computed using the MULKOM model for reservoir permeabilities of 50, 100 and 200 md, for a period of 42 months from the start of production. The results (Fig. 3A) clearly show that gravity changes of greater than 100 pGal would be expected in the area above the production zone in 3-6 months from the start of production. More importantly, the size of the changes differs greatly for the assumed values of permeability. For example, after only 12 months the gravity change at the centre of the borefield is predicted to be nearly - 3 3 0 /iGal for a permeability of 50 md, and - 180/~Gal for a permeability of 200 md. After 36 months of production the difference in predicted gravity changes in the centre of the borefield, for permeabilities of 50 and 200 md, is about 300 pGal. The size of the theoretical changes, after a relatively short time, clearly exceed the errors in gravity change measurement and gravity changes that might occur as a result of shallow groundwater level changes, topographic changes, or other influences. This shows that measurements of gravity change in the borefield area during the early stages of production may be a powerful tool for estimating reservoir permeability. To check if the results were strongly model dependent we repeated the calculations for a model with radius 2 km (Model B, Fig. 2 ), and at points 1 and 2 km from the centre (Fig. 3B, C). These data suggest that the gravity changes are most

Fig. 3. Theoretical gravity changes for the two-phase zone development at Wairakei for various values of permeability calculated using the MULKOM models (A, B). D=distance from centre of the model. Solid lines indicate gravity changes calculated for Model A ( R = 3 km); broken lines for Model B ( R = 2 km). For clarity, only the lines for Model A are labelled with the values of permeability used. Note how quickly the difference between the lines exceed the significance level of the gravity measurements (approx. 20/~Gal) for a point at the centre of the model.

o

o~ o o '~ --,

D=Okm" _

"--,

I

t

0

I .

.

.

.

.

.....

,5-0

.

.

.......... .

.

.

.

.

.

_~_-;J .

.

.

.

en ~" 8 eO >, .~ ,~

m,

_ t~ .o 0

i

C

x: o

o

10

Time

20

(months)

30

40

.

T.M. Hunt, W.M. Kissling / Journal of Volcanology and Geothermal Research 63 (1994) 129-I43

sensitive to differences in reservoir permeability at points close to the centre of the model, and here are not particularly dependent on the radius of the model. At distances of more than 1 km from the centre, however, discrimination is poor and the theoretical gravity values are influenced by the radius. Let us now compare these theoretical gravity changes with gravity changes measured at Wairakei. Unfortunately, no precise gravity surveys were made before production began and the first such survey was not made until August 1961, about 3.5 years after production had commenced. The only data available in the borefield area spanning the period of two-phase zone development is a gravity change of - 415 ( + 100) /zGal between 1950 and 1961 at benchmark A97 (Fig. 1) near the eastern end of the borefield (Hunt, 1977). This benchmark is located close to the centre of production in the early 1960s. If it is assumed that there was no significant mass withdrawal before 1958, and the value of - 415 /zGal is plotted on Fig. 3, the point lies close to the theoretical gravity change curve for a permeability of 100 md. In view of the simplifications and assumptions made in setting up the model and the large error in the measured gravity change, this value for permeability must be considered only approximate. The value of 100 md is, however, consistent with values obtained by well tests and some previous simulation models (Table 2 ) and suggests that the method is viable. If gravity values at a few selected points in the borefield area had been measured immediately before production started and the measurements repeated at 6-12-month intervals for several years after production had begun, then a much better estimate of permeability could have been made.

5. Case 2 m Gravity changes associated with reinjection

5. I. 7"he conceptual model Let us consider the case of a significant thickness of two-phase zone overlying a single-phase

1~7

zone, and that fluid is reinjected at a constant flowrate (simplest case) deep into the singlephase zone. Experience shows that this reinjection may cause the deep-liquid level and possibly also the bottom of the steam zone, in the vicinity of the reinjection well, to be raised in a cone of impression as the lower part of the two-phase zone becomes resaturated. The replacement of vapour in the pores by liquid, in the lower part of the twophase zone, results in measurable increases in gravity at benchmarks adjacent to the reinjection well (Hunt et al., 1990b). The rate of growth (height) of the cone will be related to the horizontal permeability of the rocks near the bottom of the two-phase zone. If the horizontal permeability is significantly greater than the vertical permeability then a cone will not form; the reinjected fluid will merely flow laterally out into the single-phase zone and the deep-liquid level would rise uniformly. From gravity change measurements at the surface, the change in size of the cone can be determined, subject to knowledge of the original depth of the deep-liquid level, the porosity of the rocks and the average liquid saturation near the bottom of the two-phase zone. From the rate of change in size (increase) of the cone of impression, the permeability can be determined, neglecting minor amounts of boiling from the cone due to non-steam static conditions. If the period of time during which reinjection takes place is relatively short (1-2 years), then the gravity effects of changes in deep-liquid temperature and changes in saturation in the two-phase zone (apart from formation of the cone) can also be neglected. If the reinjection is terminated abruptly (simplest case) the cone of impression will subside at a rate determined by the horizontal permeability in the vicinity of the deep-liquid level. The rate of change in size (decrease) of the cone can similarly be determined from measured changes in gravity at the surface, and the permeability determined. The same techniques can also be applied to deep-liquid pressure measurements in monitor wells around the reinjection well. In practise, however, it is rarely possible to have sufficient

138

T.M. Hunt, W.M. Kissling I Journal of Volcanology and Geothermal Research 63 (1994) 129-143

5.3. Analytical models

suitable monitor wells available. This is the advantage of using gravity measurements which are relatively easy and cheap to make in large numbers.

A 'Theis' or 'line source' solution for the pressure in a radial, homogeneous, reservoir of infinite extent, subject to a constant reinjection flowrate is a model commonly and successfully used in the analysis of pressure transients (Bodvarsson and Witherspoon, 1989), giving confidence that it can also be used to analyse gravity data. The pressure P(r,t) at a particular radius r and time t is:

5.2. Gravity changes associated with a reinjection trial at Wairakei During a 13-month test in 1988-1989, separated water from Hash Plant 10 (Fig. 4) having a temperature of 130°C was reinjected at a near constant rate (570 t / h ) , at a depth of about 450 m, into the deep-liquid zone near the centre of the Eastern Borefield using the defunct production well WK62 (Fig. 4). Before and after the trial, precise gravity measurements were made at about 100 benchmarks around the reinjection well and gravity changes associated with the test of up to 100 ( _+20)/tGal were determined (Fig. 4; Hunt et al., 1990b). The gravity changes were interpreted as being caused by displacement of the deep-liquid level (originally 310 m depth) in a cone of impression, about 50 m high. The data suggested that the cone was not symmetrical about the well, but extended about 1.5 km westwards towards the Western Borefield, and about 1 km northeastwards towards an area of ground subsidence (Fig. 4). To investigate the gravity changes that occuffed during this trial we have used two separate modelling techniques.

I !

' • . •

i

"l.

FI,iI~ P i n t 10

/'"

' • !"l

"

\\~

r2

e(r,t) =Po + qBEI 4Dt

where Po is the initial (uniform) pressure, q is the volume flowrate, and the function E1 is the Exponential Integral. The unknown parameters B (the mobility ratio) and D (the diffusivity) can be determined separately from the pressure and gravity data, and contain the permeabilitythickness (kh) and storativity (0ch) (Grant et al., 1982). Since the spatial distribution of the gravity changes suggests that the flow from the reinjection well was not isotropic, we have also considered the (horizontal) anisotropic case of the Theis solution: x2

-t |

• \\1 -" \\1

Fig. 4. Gravity changes associated with the reinjection trial at Wairakei (taken from Hunt et al., 1990b). S=centre of the region of ground subsidence; WB=Western Borefield. Dots indicate benchmarks used in the surveys.

y2

P( x,y,t ) = Po + qBE, (~-~xt+~ffftvt )

1

\

( 3)

(4)

where Dx and Dy are the principal diffusivities, and an angle 0 (which does not appear explicitly in Eq. 4) that defines the alignment of the principal directions of diffusivity (x,y) with respect to the geographic coordinate system. For simplicity, the direction of greatest and least diffusivity in this solution were assumed to be perpendicular. The derived parameters of interest are then (kh )x, (kh )y and Och. Because there is a free water surface at the top of the deep-liquid level, the pressure difference in the deep-liquid P( r,t ) - Po (or P (x,y,t ) - Po for the anisotropic case) is related to the change in elevation of this level h (r,t) by:

Po =P(r,t) +pwgh(r,t)

(5)

where Pw is the liquid density and g is the accel-

T.M. tf unt, It i M. Kissling / Journal of Volcanology and Geothermal Research 63 (1994) 129-143

eration due to gravity (9.81 m s-2). The gravity effect of the change in deep-liquid level (cone of impression) is calculated by direct integration over the fluid volume defined by h(r,t) [or

:/.

For the Theis models we assume that water in the deep-liquid zone is displaced into the twophase zone according to Eqs. ( 3 ) - (5). In this case Ap will be approximately:

Ap~O(1-S)pw

A

•

h(x,y,t) ].

139

:

"5 li

@:

(6)

The homogeneous and anisotropic models described here contain free parameters which were adjusted to best match the observed gravity data; the best fit in each case was obtained by minimising the sum of squares of the residual gravity changes (observed-computed) over all the benchmarks. The 'best-fit' model for the Theis solution using the homogeneous (isotropic) model (Fig. 5) gives values of 9.9 d-m for permeability-thickness (kh) and 9.2X 10 - 6 m Pa -I for storativity (Och). The best fit for the anisotropic model (Fig. 6) gives values of 18.2 and 5.4 d-m for kh, 8.7 X 10 -6 m P a - 1 for Och, and 82 ° for the strike of the axis of greatest permeability (Table 5). The gravity data is reasonably matched by the theory. The sum of squares of the residual gravity changes for the isotropic model is about 43,000 /tGal 2, corresponding to a root mean square (rms) residual of about 24 #Gal per data point. For the anisotropic model, the sum of squares of residuals falls to about 39,000/~Gal 2.

I

~ ....

~

I

°1

,,9

I

Fig. 6. Calculated gravity changes for the best-fit anisotropic

model. Table 4 Physical parameters adopted for models of the Eastern

Borefield Parameter

Value

Two-phase zone Porosity

Units

0.2

Saturation Temperature

0.5 l 75

:C

Deep-liquid zone Depth of deep-liquid level Density Dynamic viscosity

310 900 1.5 X

m kg m 3 Nsm 2

Temperature

200-210

10 - 4

C

Table 5 Summary of derived parameters

Model/data

kh (d-m)

0eh (m Pa-~ )

Homogeneousgravity Anisotropic gravity WK53 pressure WK60 pressure

9.9 18.2, 5.4 69 232

9.2x 10 6 8.7 X 10-° 6.2 × 10- 7 8.3 × 10 7

Although the decrease in goodness of fit between the models is relatively small, the data are quite noisy, and we are confident that the anisotropic solution represents a real effect in the data. •1

5.4. The numerical model o

Fig. 5 Calculated gravity changes for the best-fit isotropic model

To provide a more complete physical concept of the reinjection we constructed a MULKOM

T.M. Hunt, VV..M.Kissling /Journal of Volcanology and Geothermal Research 63 (I 994) 129-143

140

o~

2

el t" 0

I

0

I

I

500 1000 1500 Distance from WK62 (m)

I

2001

Fig. 7. Plot of gravity change against distance from WK62 at the end of the reinjection test. The solid line is from the bestfit radial "Theis" solution; the dashed line is from the MUI_KOM model.

model which describes the injection of fluid into a reservoir with properties as listed in Table 4. To minimise computational time we again chose to model a homogeneous reservoir having radial geometry; the vertical resolution of the model was restricted to 10 m, in order to adequately cover the combined 500 m vertical extent of the deepliquid and two-phase zones. The radial extent of the reservoir was taken as 1500 m, with element dimensions ranging from 10 m at the centre to 100 m near the boundary; the 1500 m extent is almost certainly too large, but was chosen so that boundary effects would not influence the comparison with the analytical model (which assumes no boundary). The Eastern Borefleld was assumed to be in an almost 'static' state prior to reinjection, with a fixed water level and constant saturation in the two-phase zone. To achieve this state, the residual relative permeabilities were chosen so that the liquid water in the zone remained immobile; this fixed the pressure to be steam static, close to what is observed. There is also a requirement that the upper and lower boundaries of the model do not influence the fluid flow. Experiments with the model showed that the total thickness of 500 m (200 m two-phase zone, 300 m deep-liquid zone) taken was adequate to meet this condition. In the M U L K O M model, the density change

(dp) is calculated for each element from the conditions in that element. For the values of ~ (porosity), Pw (liquid density) and s (steam zone saturation ) listed in Table 4, zip has a value of 90 kg m - 3 ; uncertainties in these parameters mean that Ap might lie in the range 50-120 kg m 3. The gravity effects at the measurement points were calculated by direct evaluation of the integral defining the gravity effect (Eq. 2 ). The gravity changes computed from the M U L K O M model at the end of the reinjection trial are shown by the dashed line in Fig. 7. The agreement with the Theis solution (solid line ) is satisfactory, given that rough estimates of the reservoir parameters have been used, and that no attempt has been made to match the M U L K O M model to the gravity data.

5.5. Density models To obtain an estimate of the distribution of density changes associated with the reinjection trial, the density differences at the end of the reinjection period have been computed as a function of position using the M U L K O M model (Fig. 8 ). These calculations showed that there are two regions of increased density associated with the reinjection. The first region (A), surrounding the injection point, is due to the cooler temperature of the injected fluid. The second region (B) is where the deep-liquid level has been displaced upwards into the two-phase zone: it represents a much larger density change (up to 90 kg m - 3 ) , is closer to the surface, and therelbre dominates the gravity signal. A third region (C) represents a very small decrease in density ( < 2 kg m - 3 ) due to the deep hot fluid displacing the cooler water near the free surface, which in turn is displaced into the two-phase zone. The modelling confirms that most of the gravity changes measured at the surface are associated with region (B), and that the values for kh and Och, determined from the gravity changes, relate to this region of the reservoir. Although not well defined in this plot, it is this region that is represented by the analytical models.

T.M. Hunt, ~: M. Kissling / Journal of Volcanology and Geothermal Research 63 (I 994) 129-143

¢ 200 o e=

15~

5 ~ 0

C

400

141

0

-

-

®

600

-[ 0

I

[

I

I

I

I

I

200

400

600

800

1000

1200

1400

Distance from WK62 (m)

Fig. 8. Regions of density change (A, B, C-see text) at the end of the reinjection trial, computed using the MULKOM model. Contour values are in kg m - 3. Contours between 15 and 80 kg m - 3 in region B have been omitted for clarity.

5.6. Pressure transient analysis For comparison with the gravity data, best-fit Theis solutions to the main pressure transient (end of test) at WK53 and WK60 were determined. The fit between the calculated and measured pressure values is excellent (Fig. 9 ). The solution for transients at WK53 gave a value of 69 d-m for kh, and 6.2X 10 - 7 m Pa -~ for Och; that for WK60 gave 232 d-m and 8.3 X 1 0 - 7 m Pa-1, respectively (Table 5 ). These kh values differ slightly from those of 100 d-m for WK53, and 170 d-m for WK60 given by Hunt et al. (1990b) for solutions to a different set of pressure transients. The parameters derived from the pressure data are consistent with those of a fractured reservoir,

ai

O

@

[ 38O

385

3go

3gG

400

I

I

4O5

4tO

Time (days since 1914188)

Fig. 9. Fitted pressure responses at WK53 and WK60. The measured pressure changes are taken from Hunt et al. ( 1990b ); pressure scale is arbitrary.

i.e., kh is high and Och is very small. This is perhaps not surprising given that WK53 and WK60 are both very close ( 150 and 200 m) to the injection well WK62. The parameters derived from the gravity data on the other hand refer to a much wider area, and are more characteristic of a homogeneous reservoir with lower permeability but higher average porosity. The gravity and pressure data then, taken together, suggest a highly permeable fractured central region surrounded by a much larger region of uniform lower permeability.

5.7. Gravity monitoring The expected variation in gravity as a result of decay of the cone of impression was computed using the best-fit anisotropic model (Fig. 10). This shows that the maximum value of gravity change declines to the estimated significance level of 20/~Gal after about 4 years. Unfortunately, gravity measurements were made only before and immediately after the reinjection test. It was not realised until well after the end of the test that monitoring of the gravity effects associated with the growth and decay of the cone of impression could lead to better determinations of reservoir parameters. Therefore, it would have been profitable to have monitored the gravity changes at a few selected benchmarks around the injection well, at about three monthly intervals, for several years after the end of the test.

142

T.M. Hunt, HdM. Kissling /Journal of Volcanology and Geothermal Research 63 (1994) 129-14.4

References Eo

Oo

4

0

I

I

I

500

1000

1500

-'-'-'1

2000

Distance from WK62 (m) Fig. 10. Transient behaviour of the gravity changes computed from the Theis model. Times for each curve, from top to bottom, are about 0, 0.1,0.25, 0.5, 1.2, 3 and 4 years, from the end of the reinjection test.

6. Conclusions Measured gravity changes associated with the transfer of mass within, or out of a geothermal system during exploitation can, in conjunction with numerical and analytical reservoir modelling, be used to determine values for permeability, permeability-thickness (transmissivity) and storativity. If sufficient microgravity data and a valid reservoir model are available it is possible to determine values for permeability anisotropy. The results described here further demonstrate the usefulness of microgravity data in assisting the management of exploitation of geothermal reservoirs by providing reservoir parameter data.

Acknowledgements We acknowledge some stimulus to write this paper from reading an unpublished manuscript on gravity changes at Kawerau Geothermal Field by Peter Whiteford. We are grateful to R.G. AIlis, H.M. Bibby and S.P. White for constructive criticism of the manuscript. Funding for this work was provided by the New Zealand Foundation for Research, Science and Technology.

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