PROCEEDINGS, Twenty-Seventh Workshop on Geothermal Reservoir EngineeringStanford University, Stanford, California, January 28-30, 2002SGP-TR-171

LARGE-SCALE MICROSIESMIC/ERT LABORATORY EXPERIMENTS TO DETERMINEEGS RESPONSE TO WATER INJECTION

Steven D. Glaser, Jeffrey Moore, Hee-Joon Kim1, Mark Talesnick2

University of California440 Davis Hall

Berkeley, CA 94720, USAe-mail: glaser@ce.berkeley.edu

1 Pukyong University, Pusan, Korea; 2 The Technion, Haifa, Israel

ABSTRACT

We present a large-scale testing system fordetermining the precise physical mechanisms at workwhen ambient temperature water is injected into ahigh temperature geothermal reservoir. The poly-axial testing chamber can apply up to 14 MPa loadson 3 independent axes using flat-jacks as the loadingmechanism. The chamber can be flooded by up to300° C steam, so that the rock can be brought to insitu equilibrium. Heat can also be applied by four 2kW heaters around the block perimeter, with theadditional application of modeling hot dry rocksystems. Steam at an appropriate quality is used asthe pore fluid so that field electro-resistive behaviorand in situ effective stresses can be accuratelymodeled. To account for the actual fractured natureof the in situ rock mass, size effects of fracturetoughness, and to undo averaging of electro-resistiveproperties, the specimens will be 260 mm cubicassemblages made up of outcrop rock representativeof reservoir rock. Fracturing of the sample will bemonitored by a dense array of resistivity sensors,which will be used to create a real-time tomograph.The paper describes the full system and givesexamples of the suitability of using electro-resistivetomography for forward and inverse imaging.

PROJECT PURPOSE

The Geysers Geothermal field in northern Californiais currently undergoing enhanced thermal recoveryby injection of local wastewater. This process isillustrated by the cartoon shown in Figure 1. Wewant to determine what physical mechanisms are atwork when ambient temperature water is injected intoa high temperature geothermal reservoir, and theattainment of certainty as to which mechanismscontrol behavior. We want to image the actualdamage mechanics at work, the geo-hydrology atwork, and how these (or other) mechanisms affectfield measurements. We make use of laboratoryresistivity measurements and permeability estimates

of matrix rock at reservoir conditions to aidinterpretation of our electro-resistive tomography(ERT) measurements. Scaling issues associated withthe time evolution of resistivity anomalies withexperiments and flow modeling will be addressed.This fundamental understanding of the injection-resistivity process will allow quantitativeinterpretation of the upcoming cross-wellelectromagnetic imaging to be conducted byElectromagnetic Instruments Inc. under DOEfunding.

Figure 1 Recharge of The Geysers geothermal fieldby wastewater injection (San FranciscoChronicle, 10 July, 2001.

Project Objective(s)• Providing a basis for improved interpretation ofmicroseismic and electrical data to identify, image,

and characterize fluid flow paths in geothermalreservoirs;

• Demonstration of how routine measurement ofphysical properties, combined with acoustic andelectromagnetic emission data interpretation, can beused to improve conventional geothermal reservoirsimulation; and finally

• Providing a quantitative and objective approach formanaging the increasing injection rates in ageothermal field, including enhanced recoverytechniques.

The project combines microseismic imaging ofdamage kinematics and electro-resistive tomographylaboratory experiments with in situ data to define thereaction of enhances geothermal systems to waterinjection. From these predictions, a set of guidelineswill be developed to optimize theproduction/injection strategy.

Plans and ApproachOur experiment isolates the physical processes ofinterest in as realistic an environment as possible. Toaccount for the actual fractured nature of the in siturock mass, size effects of fracture toughness, andundo averaging of electro-resistive properties, thespecimens will be 260 mm cubic assemblages madeup of outcrop graywacke representative of reservoirconditions. The polyaxial testing chamber can applyup to 14 MPa loads on 3 independent axes using flat-jacks as the loading mechanism. The chamber can beflooded by up to 300° C steam, so that the rock canbe brought to in situ equilibrium. Heat can also beapplied by four 2 kw heaters around the blockperimeter. Steam with an appropriate quality is usedas the pore fluid so that field electroresistive behaviorand in situ effective stresses can be accuratelymodeled.

Passive acoustic monitoring during injection of waterthrough a small wellbore will localize andcharacterize dislocation sources from natural andinduced crack interfaces, using an approach based onfundamental physical principles. The challenge is todevelop a methodology to interpret those signals, firstin the laboratory under controlled and knownconditions, and then to migrate this understanding tothe field. Given the fine microseismic surveys madeby previous DOE contractors at a variety of thermalfields such as the Geysers (e.g. Stark, 1990),operators will be able to better utilize microseismicdata after we provide correlations with knownmechanics.

Our approach involves the location of events, andcharacterization of source kinematics through asecond-order time domain moment tensor calculated

from full waveforms rather than first P-wave arrivals(e.g. Stump and Johnson, 1969). This methodcompletely describes the equivalent force-timehistories that make up an event, from analysis of theeigenvalues and eigenvectors. The resulting vectorsform a parametric model that captures time andfrequency characteristics of the original data, andidentifies critical features extracted from each sensorsignal.

A major objective of the resistivity experiment willbe to energize current-voltage configurations that willfacilitate measurement of resistivity anisotropiesinduced by fracture and stress anisotropies. Thesystem will directly measure the resistivitiesassociated with the changing water-steam phases inthe sample and the anisotropy brought about bypreferential flows/fluid content in the fractures. Thesame low-noise electrode arrays will also measure thevoltages generated by fluid or steam flow.

Arrays of electrodes are installed on the rock faces tosimultaneously monitor the resistivity changes andstreaming potentials. Small contact area non-polarizing electrodes have been developed forinjecting current and measuring voltages on thesurface of rock or concrete.

Testing DeviceThe insides of the testing device, shown in Fig. 2,contains a cubical sample with a centered boreholeextending to a depth of half the sample height. Thepolyaxial in situ stress is modeled by the stressesapplied via hydraulic pressure in 20-gauge steel flatjacks.

Figure 2 The inside of the high-pressure testchamber, showing the 260 mm cubicspecimen with a 9 mm diameter injectionwell-point. From the specimen out arelayers of PEEK, aluminum with integralheaters, flat jack, and cell wall.

Once the in situ thermal and stress equilibrium isattained, cool water is injected into the borehole

through the top of the testing device. The amount ofwater injected will be either a constant volume, or ata constant rate, depending on the application.Fracturing of the sample will be monitored by adense array of resistivity sensors, which will be usedto create a real-time tomograph. The hydraulic forceis generated by three independently controlledair/hydraulic intensifiers which can be seen at theright side of Fig. 3.

The sample is surrounded by plate assemblies whichhave a dense machined grid to allow for unimpededmovement of steam and condensate around thesample. On the back of each plate is a machinedgroove holding a 2000W coil heater, which can beused simultaneously with the steam, orindependently, as in modeling a hot-dry-rock system.A 6 mm grooved PEEK plate is the contact layer withthe specimen (so that current flows through the rockrather than short-circuiting through the device).

Steam (126 lb/hr) is produced in a Lattner 480V, 2MPa electric boiler fed by pre-heated water.Furthermore, the sample will be preheated using the2000W coil heaters previously described (preheatingmay also be necessary to deactivate the clays in thesample, as in field conditions).

The system is overseen by computer controlled servoloops. In addition to the ERT and microseismicmeasurements, Table 1 lists process variables that arebeing continuously monitored, controlled, andrecorded.

Figure 3 Overview of the testing device. From theleft of the picture: boiler, pressure cellwith insulation jacket, pressureintensifiers, computer control station(Talesnick in command).

Table 1 Process variables monitored, controlled,and recorded during a test.

Boiler energy consumption Inlet steam pressure

3-D "in situ" stress Hydraulic oil temperature

Water volume into system Water volume out of system

Injection volume Injection temperature

Injection pressure Inlet steam temperature

Rock internal temperature Superheat energy

ELECTROMAGNETIC IMAGING

The advancing injection fluid front will change insitu resistivity which can be mapped, possibly fromthe surface, but certainly using new techniques ofcross hole and surface to bore hole electricalresistivity tomography (ERT) or electromagnetic(EM) imaging. Streaming potentials associated withthese kinematics will provide an independentmeasure of the locations of principal flow paths.

None of the geophysical techniques suggested hereare themselves new. There have been many studiesin which acoustic emissions have been used toidentify dynamic portions of a geothermal reservoirduring normal production, but without absolutephysical calibration of the actual mechanisms andwithout ERT. Resistivity and EM methods have beenused to define high temperature regions and tomonitor long term changes as production continues.Recently ERT and EM imaging have been used inbore holes and a high temperature EM system hasbeen used to map fractures in a hot reservoir in Japan.Streaming potentials are routinely used to monitorleakage paths from reservoirs and dams. In a sensethe field methodology is in place to monitorquantitatively the cold water injection process.

The more fundamental issue is to determine thenature of the physical changes that occur when coldwater is injected into a fractured hot rock formation.This problem does not appear to have received verymuch attention and yet it lies at the core of anyquantitative interpretation of geophysical monitoringof the injection process.

ERT forward modelingApplication of the finite-element method to a three-dimensional (3-D) resistivity problem is thoroughlydiscussed in Pridmore et al. (1981). Forcompleteness, the method is briefly outlined here.

The partial differential equation governing thebehavior of electric potential is described by thePoisson’s equation

sJ⋅∇=∇⋅∇− φσ , (1)

where σ is the conductivity (S/m), φ the potential (V),and Js the impressed current source (A). Thevariational integral derived from the partialdifferential equation (1) is

∫ ⋅∇−∇= dvs ]2)([ 2 Jφφσχ . (2)

The solution to equation (2) corresponds to thefunction φ, which makes the integral χ stationary.

In practice, the 3-D region is divided into a largenumber of bricks (or hexahedras) that can beassembled from five tetrahedral elements. The(unknown) potential is approximated in each elementby a linear polynomial that is defined using the nodalvalues of φ. By substituting the linear polynomialinto equation (2) and integrating over the volume ofthe element, we obtain the element integral that isdependent upon the nodal values of φ. The overallintegral χ is the sum of these element integrals. Theminimum of the integral χ can be found by setting thefirst derivative of χ with respect to the nodal valuesto zero. This leads to the finite-element matrixequation

Ku = s, (3)

where K is a large, sparse, banded system matrix, u isa vector consisting of the unknown solutions of thenodal potentials at all nodes, and s represents theimpressed source.

The incomplete Cholesky-conjugate gradient (ICCG)method is used to solve equation (3). Theconvergence of the iterative process can beaccelerated by implementing in the source vector apair of current sources (or the source and sink) ratherthan a current pole. However, iterative methods suchas ICCG may require more computation time thandirect methods when the solutions need to beobtained for a large number of source locations. Insuch cases a direct method would be preferable if thestorage requirement can be met.

Numerical exampleFigure 4 shows a cubic model containing a thin plate-like conductor. The conductor of 10 Ω-m is buried atthe center of host medium of 100 Ω-m. Both sourceand receiving dipoles are set on the surface of thecube, as shown in Fig. 5. Results of resistivitymodeling are shown in Figs. 6 through 11, in whichunit is apparent resistivity (Ω-m):

I

Ia

φφ

ρ ∆∆

=100

100100, (4)

where ∆φ and ∆φ100 are the potential differences, andI and I100 the impressed currents for theinhomogeneous and homogeneous (100 Ω-m) cubes,

respectively. Here, the factor (100I100/∆φ100) can beregarded as a geometric factor.

Figure 5 A simple model of a water injection zone ina field: a Plate-like conductor in a cube

Figure 6 Locations of the 16 electrodes on the cubicspecimen. Tx are transmitters and Rx arereceivers.

Least-squares inversion for injection imagingThe dc resistivity inverse problem can be expressedas

∆d = G∆m, (5)

where ∆d is the vector of differences betweenmeasured and modeled data, ∆m the correctionvector to the initial model m0, and G the Jacobianmatrix (or the matrix of partial derivatives of themodeled response with respect to the modelparameters). A common approach for the modelparameterization is to divide a model into manyblocks of unknown resistivity. To scale bothparameters and data so that Jacobians will have astable inverse, the logarithms of model resistivitiesand measured apparent resistivities are used.

Z

Y

X

100 -mΩ

40 cm40

cm

40 cm

3.2 x 24 x 16 cm

10 -mΩ

12 Rx dipoles on left face

8 cm

A Tx dipole on front face

8 cm

As in most geophysical inverse problems, aroughness (the reciprocal of smoothness) term shouldbe introduced to stabilize the inversion process (5)(Tikhonov and Arsenin, 1977). For the smoothestinversion, our objective function to be minimized is

22rmGd λ+∆−∆=U , (6)

where ||•|| denotes the Euclidean norm and the secondterm on the right-hand side is the roughness weightedby the Lagrange multiplier λ. Here, the roughness isusually written as

r = C∆m, (7)

where C is a second difference smoothing operator.

Minimization of equation (7) produces the system oflinear equations

(GTG + λ CTC)∆m = GT∆d. (8)

This solution is equivalent to the least-squaressolution of the system

0

dm

C

G ∆=∆

λ. (9)

Equation (9) can be solved using singular-valuedecomposition or the modified Gram-Schmidtmethod. The solution obtained from equation (9) isknown to be more accurate than the solution obtainedvia equation (8) (e.g., Lines and Treitel, 1984). Thevector ∆m is added to the initial vector m0 to obtainupdated parameters. The procedure is repeated until amisfit between the measured and modeled data isreduced to an acceptable rms level. The rms misfit isgiven by

NS

dd ∆∆=T

, (10)

where N is the number of data.

CONCLUSIONS

In this paper we have outlined large-scale physicalmodeling being undertaken to duplicate the in situconditions of geothermal fields, such as The Geysersin Northern California. Field steam, superheat, 3-Dconfining stresses, and injection conditions can nowbe duplicated. Imaging of the injection process andassociated rock damage will be imaged byquantitative microseismics and ERT. The forwardand inverse ERT is described and the results from anumerical simulation is given.

REFERENCES

Lines, L. R., and Treitel, S. (1984), "Tutorial: Areview of least-squares inversion and its applicationto geophysical problems," Geophys. Prosp., 32, 159-186.

Pridmore, D. F., Hohmann, G. W., Ward, S. H., andSill, W. R. (1981), "An investigation of finite-element modeling for electrical and electromagneticdata in three dimensions," Geophysics, 46, 1009-1024.

Stark, M.A. (1990), "Imaging Injected Water in TheGeysers reservoir Using Microearthquake Data,"Trans. Geother. Resour. Counc., 14, 1697-1704.

Stump, B. W., and L. R. Johnson, (1969), "Higher-degree moment tensors - the importance of sourcefiniteness and rupture propagation on seismograms'"Geophysics Journal of the Royal AstronomicalSociety, 69, 721-743.

Tikhonov, A.N., and Arsenin, V.Y. (1977), Solutionsto Ill-Posed Problems, John Wiley and Sons, Inc.

Figure 6 View of back face, Tx on front face

Figure 7 View of left face, Tx on front face

Figure 8 View of bottom face, Tx on front face

Figure 9 View of back face, Tx on right face

Figure 10 View of left face, Tx on right face

Figure 11 View of bottom face, Tx on right face

0 8 16 24 32 40

x (cm)

0

8

16

24

32

40z

(cm

)

82

83

84

85

86

87

88

89

90

(ohm-m)

0 8 16 24 32 40

y (cm)

0

8

16

24

32

40

z(c

m)

92

93

94

95

96

97

98

99

100

(ohm-m)

0 8 16 24 32 40

x (cm)

0

8

16

24

32

40

y(c

m)

88

89

90

91

92

93

94

95

96

(ohm-m)

0 8 16 24 32 40

x (cm)

0

8

16

24

32

40

z(c

m)

70

75

80

85

90

95

100

105

110

(ohm-m)

0 8 16 24 32 40

x (cm)

0

8

16

24

32

40

y(c

m)

84

86.5

89

91.5

94

96.5

99

101.5

104

(ohm-m)

0 8 16 24 32 40

y (cm)

0

8

16

24

32

40

z(c

m)

73

73.5

74

74.5

75

75.5

76

76.5

77

(ohm-m)