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    PROCEEDINGS, Thirty-Sixth Workshop on Geothermal Reservoir EngineeringStanford University, Stanford, California, January 31 - February 2, 2011SGP-TR-191

    A CONCEPTUAL MODEL FOR GEOTHERMAL ENERGY INVESTIGATION WITHEMPHASIS ON THE CARIBBEAN

    *Indra Haraksingh** Randy Koon Koon

    Department of PhysicsThe University of the West Indies

    Trinidad*[email protected]

    **[email protected]

    ABSTRACT

    Some of the Caribbean islands have great potentialfor Geothermal Energy. These islands have beenformed partially by the subduction of the AtlanticCrustal plate beneath the Caribbean plate, formingvolcanic island chains. The North-Eastern islands areolder, extinct volcanoes while the Western arccontains younger more active volcanoes. These giverise to volcanic eruptions resulting in geothermalactivity, lending huge potential for geothermalenergy.

    The only operating geothermal plant in the Caribbeanis at Bouillante in Guadeloupe with a 15 MWcapacity. The island Governments of Dominica andNevis have initiated exploration work for geothermalenergy. Nevis has a potential of 700 MW and theGovernment is in the process of setting up ageothermal power plant to develop 24 MW of energyfor domestic use as well as to sell to neighboringislands.

    Geophysical surveys, resistivity and seismic, arebeing investigated to identify fault lines, thusenhancing the possibility of identification ofhydrothermal systems. The use of shear-wavesplitting (SWS) as a tool for identifying fracturedreservoirs is also being investigated. A conceptualmodel is being developed with the view of betterenabling the investigation of hydrothermal systems.This model would be able to describe the fractureddensity and orientation of the reservoir.

    INTRODUCTION

    Geothermal energy is present beneath the Earthssurface with the most desirable, high temperaturesources being concentrated in regions of active or

    geologically young volcanoes. This is the situationwith the younger more active Western arc of the

    volcanic islands of the Eastern Caribbean chain asshown in Figure 1.

    Figure 1: Interaction of North American andCaribbean plates. (Source: Seismic Research Centre, TheUniversity of the West Indies .)

    Developments are being made to exploit theseresources in the Caribbean. In particular, exploratorywork is being undertaken in the islands of Nevis,Dominica and Saba to develop their geothermalresources for commercial use. This paper focuses on

    the island of Nevis.

    The objective of this paper is to theoretically andmathematically develop a conceptual representationof the fractured zones and the relevant physicalprocesses occurring within them. The geothermalinvestigations are presented specifically with respectto fluid flow and how it behaves in porousboundaries. Hence the fluid flow and transportprocesses within the reservoir are conceptuallymodeled to better understand these hydrothermal

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    systems thereby making it possible to more easilyidentify the fracture zones for exploitation of thegeothermal energy.

    THEORY

    Geothermal energy refers to the stored thermalenergy in, or heat produced from, the Earths interior.The geothermal gradient is defined as the rate ofincrease in temperature per unit depth in the Earth.Although this gradient varies from place to place, itaverages 25 to 30C/km in most regions, but can beseveral times greater in high-grade geothermalregions. Any fluid produced from a geothermal wellis termed a geofluid. Geothermal fluids may be dry orsuperheated steam, pressurized liquid, or a mixture ofliquid and vapor, usually accompanied by dissolvedsolids and non-condensable gases.

    Large quantities of heat that are economicallyextractable tend to be concentrated in places wherehot or even molten rock (magma) exists at relativelyshallow depths (

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    these minerals and also enhances their cohesion.These processes lead to the periodic permeabilityenhancement associated with reactivation ofoptimally oriented and critically stressed fractures,which has been shown to be an important mechanismin maintaining high reservoir permeability in somegeothermal systems (Hickman et al ., 1998; Barton etal ., 1998).

    On the contrary, dissolution of crystalline rock byhydrothermal fluids reduces the strength of graincontacts and increases porosity in fracture walls(Boitnott, 2002). Furthermore, chemical alterationyields an increase in proportions of clay and otherphyllosilicates, which promotes ductile behavior andreduces frictional strength (Lockner and Beeler,2002) and which also reduces fault permeability(Crawford et al ., 2002; Tembe et al., in press). Henceincreased ductility of fault rocks that minimizesdilation accompanying slip and the mitigation offracture regeneration is potentially an outcome ofthese processes.

    In low porosity crystalline rocks where brittlefracture and frictional slip exist, there is dilationowing to surface roughness along fracture walls,brecciation, and micro-cracking. Rapid sealing isevident for fractures that are generated by activeprecipitation and alteration in geothermal system.The brittle dilatant behavior responsible forpermeability generation as revealed by crack-sealtextures and brecciated cements are facilitated byprecipitated calcite and silica.

    Figure 4 is a map of the mineralogy of Nevis. It canbe observed that the mineralogy of the island isdiverse. The North North West region of the island atRound Hill is concentrated with hornblende-pyroxeneand phyric dacite. At Hurricane Hill, Cades Bay,Saddle Hill Red Cliff, Butlers Mountain, and NevisPeak there are pyroxene-phyric dacite, porphyriticdacite, pyroxene-phyric dacite, volcanic breccias,porphyritic and orthopyroxene-phyric daciterespectively (Hutton and Nockolds 1978, Petrologyof Nevis). This mineralogy is evident of geothermalresources in Nevis.

    Figure 4: Mineralogy of Nevis (Source: Hutton andNockholds 1978 )

    GEOLOGY OF NEVIS

    The island of Nevis is one of particular interest to theCaribbean when it comes to geothermal energydevelopment. Nevis is an ellipsoidal island which issituated at the Northern end of the Lesser Antillesarchipelago. The island consists of a single volcaniccomplex comprised of a series of volcanic domes orcentres. The oldest outcropping rock on the island isa conglomerate containing blocks of crystallizedlimestone that contain fossils of mid-Eocene age(Hutton 1965). The majority of the island is

    composed of Upper Pliocene to Lower Pleistocenevolcanic rocks, dominated by ash and block flowdeposits. The volcanic rocks of Nevis are classifiedaccording to the composition of silicon oxideconcentration that they are comprised of. The threevolcanic rocks are dacite, andesite and basalt. Sevenvolcanic centres have been identified on Nevis:Hurricane Hill, Cades Bay, Saddle Hill, Red Cliff,Butlers Mountain and Nevis Peak (Hutton 1965;Hutton and Nockolds 1978) .

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    Figure 5. This represents a simple illustration of thelocations of the seven volcanic centres along the NWto SE of the island of Nevis.

    The main volcanic centre on the island is Nevis peak.It is a single volcanic complex, comprising of a seriesof other volcanic centres and domes. This is the onlypotentially active centre, as it is a Peleen typevolcano- andesite to dacite (58-65wt%; Hutton andNockolds 1978). The formation of Nevis peak is dueto effusive eruptions of lava that also produced thenumerous other nested lava domes which form thebulk of the main cone.

    There exists a 1000 m-wide, semi-circular depressionthat is open to the west and northwest, of the

    northwestern quadrant of Nevis Peak. This wasreferred to as a breached crater by previousresearchers (Martin-Kaye 1959; Hutton and Nockolds1978). The cause of this depression is unclear;however, its formation is credited to the collapse ofthe northwestern summit of the volcano during domecollapse events.

    Violent eruptions at these centres have displayedremnants of lava domes. Saddle Hill and ButlersMountain have radiometric ages of 1.80 and 1.10Marespectively, and are therefore somewhat younger.The Nevis peak volcanic centre is believed to be the

    youngest on the island, based on its youthfulappearance and an age estimate of 0.98 0.10 Ma(Hutton and Nockolds 1978; Geothermica Italiana1991).

    Table 1: The relative ages of the seven volcaniccentres on the island of Nevis.

    Volcanic Centres Relative ages/ MaHurricane Hill 3.43 0.17Cades Bay 3.22 0.16

    Round Hill 2.70 0.50Saddle Hill 1.80 0.30Butlers Mountain 1.10 0.16Nevis Peak 0.98 0.10Red Cliff 1.00

    GEOTHERMAL ACTIVITY IN NEVIS

    Large areas of pervasively hydrothermally alteredrock present throughout the island (e.g. Clarks Ghut)are interpreted as areas of past/extinct fumarolicactivity. Presently geothermal activity is heavilyconcentrated on the Western half of the island ofNevis. In the nineteen fifties the two areas of maininterest in Nevis were Cades bay Soufriere and Farmestate Soufriere.

    Cades bay Soufriere is an area of warm,hydrothermally altered ground approximately 900square metres. Soil temperatures of up to 100C werereported for these early stages (Robson and Willmore1955). As a result of the response to localreadjustments in the groundwater system broughtabout by severe earthquakes between 1950 and 1951,it is likely to have formed Cades bay Soufriere. Farm

    estate Soufriere on the other hand, is also ahydrothermally altered ground (part of the SulphurGhut stream valley). Temperatures of up to 100Cwere also obtained from within small crevices atFarm estate Soufriere when visited by Robson andWillmore in 1953.

    1.0 Fractured ReservoirsA natural geological system can be described ashighly complex when the geological structure andphysical processes occurring within them areconsidered. For investigation into such a system, it isvital to understand the natural processes, and the

    interactions with geological structures. The systemstructure and the processes occurring within it aretherefore represented by conceptual models, designedto meet the requirements of certain types of problemson a given scale Dietrich, P et al. 2005The level of complexity is inversely related to thelevel of simplicity when moving from a naturalsystem to a numerical model that describes thissystem. Specifically a conceptual model is satisfiedby the following three areas:

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    Conceptual representation of the structure.

    Selection of relevant physical processes

    Conceptual representation of the physicalprocesses.

    It is essential to note when model results are beinginterpreted, that model is merely an approximation ofnature.A hydrothermal system or reservoir can beconsidered as one in which the rock matrix is highlyfractured, to facilitate the ease of fluid flowthroughout the system. Fractured porous rock isgenerally divided into three components, theseinclude: (1) a fractured network - a system ofpartially intersecting single fractures. Its hydraulicproperties are typically characterized by thedistribution of fracture size, permeability, orientation,

    distance and density, (2) fractured filled networks -filling material consisting of mineral deposits can befound at these fractures, and (3) the matrix blocksbetween the fractures these have a spatially varyingtexture and porosity. The permeability contrastbetween fractures and matrix is important for theflow and transport processes. It is not possible to generate a model that is an exactrepresentation of reality; however, conceptual modelsare developed to describe the relevant structures andphysical processes of a problem. The choice of amodel concept for the description of fractured mediastrongly depends on the scale of the problem, thegeological characteristics of the area of investigation,and the purpose of the simulation.It is a necessity to have different model concepts ofvarying characteristics, in order to generate models ofsystems. According to Helmig (1993), two principalapproaches are possible:

    1. Provided that the scale of the investigationarea is sufficiently large and that the conceptof representative elementary volume (REV)is valid the model can then be described as aheterogeneous, anisotropic continuum.

    2. If shear zones dominate the flow and

    transport processes in the fractured media,the rock matrix can be neglected and thefeatures specifically described, using adiscrete fracture network model. (Dietrich P.et al., 2005)

    The size of a potential REV is linked to the reliabilityof hydraulic properties of fractured reservoirs (Bear,1972; De Marsily, 1986), and is fundamental to the

    mathematical description of fluid flow and transportin porous media. It is the smallest volume over whicha measurement can be made yielding a valuerepresentative of the whole (Blocher, M. G. 2010).

    1.1 Mathematical considerations of fluid flowThe main concepts of the stress and strain tensor arefundamental in approaching more useful forms of theNavier-Stokes equation, continuity equation, parallelplate concepts of fractured systems, and Darcys law.The fluids under discussion can be assumed to haveno internal forces between the fluid particles,therefore for these inviscid fluids, the equation ofmotion is given by Eulers equation

    where the external force , the density, pressure andrate of fluid flow are represented by , , and

    respectively . The associated fluids are known as Newtonian or viscous fluids. A further property ofthese inviscid fluids is the stress tensor , sometimesreferred to as the traction or Cauchy stress tensor.A general case where S can be any surface with unitnormal, , ( and are thedirection cosines of ) can be considered. Thetraction can be represented by

    Hence the traction on any surface with unitnormal can be expressed as a linear combination ofthe three basic tractions and . Inaddition by considering an infinitesimal part of a

    fluid as a cuboid the stress components can beobserved:

    ;where is a second order tensor as shown below

    If then is called the normal component ofthe stress tensor i.e. , when thenis called the shear stress component of the stresstensor i.e. .Furthermore, a useful form of Eulers equation isshown below:

    Using,and, ,equation (2) can be written as

    1.2 Strain TensorThe strain tensor, otherwise known as the Rate of

    Deformation tensor, is established when the stress

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    forces have the effect of deforming a volume of fluid.A measure of this deformation is given by thedeformation tensor D .It is defined by

    Here it is observed that is a second ordersymmetric tensor which is dependent on the fluid

    velocity gradients of the fluid.Let then

    The trace of , is the summation of all theelements of along the leading diagonal of amatrix containing all the elements of .A particular medium is characterized by theconstitutive equation , which is the relationshipbetween stress and strain . This stress-strainrelationship is given by:

    When this relationship is linear, the fluid is said to beviscous, classical and Newtonian, and is shown by

    where A and B are constants (tensors), and is theidentity matrix.

    By further analysis of the equation and using the factsthat both are symmetric, and that the frame-indifference principle, (the constitutive equation doesnot depend on the orientation of the frame ofreference), the eventual field equation, known as

    Navier-Stokes equation, is obtained as stated below.

    where the viscous coefficient is represented by .Thisequation is very useful when investigating fluidflows, since it is solved together with the continuityequation for incompressible flow, i.e.

    1.3 Special case: Parallel Plate ConceptThe rock matrix bounds naturally occurring fractureson all sides. An identical profile does not exist for thefracture walls, hence the normal tension is carried bycontact zones between the walls. A frequently usedmodel for frature representation is the parallel plate

    concept.Tsang and Tsang 1987 showed that preferential flowpaths exist, hence channeling effects may havesignificant influence on the flow and therefore alsoon the transport processes.For the application of the parallel plate concept it isassumed that the length scale, l, of the plates is muchlarger than the distance between them b (l>>b). Furthermore, hydraulically smooth walls and laminar

    flow are assumed, corresponding to the POISEUILLE fluid model (Wollrath, 1990).Between the parallel plates the velocity profile has aparabolic shape,indicating laminar flow. The upperand lower plates have values of

    , respectively, whilst thevertical distance between , the plates, b, can beconsidered to have a value ofThe NAVIER-STOKES equation(NSE) for thelaminar single-phase flow of an incompressibleNewtonian fluid yields the following equation for thevelocity profile between two parallel plates (Snow1969; White 1999).

    where is the acceleration due to gravity. The meanthree-dimensional velocity can be determined bystating that the maximum velocity , is reached at

    , and for parabolic shaped profiles, the mean

    velocity is given as . (Dietrich P et al.,2005) therefore,

    It can then be seen that the hydraulic conductivity ,and the permeability , have the followingrelationship:

    andNow the flow field can be determined by assumingthere is steady flow between the parallel plates andno external forces act on the plates. We can nowintroduce Cartesian co-ordinate system, where theplates can be taken to be and .Allow the lower plate to be fixed while the upperplate moves with a velocity .Hence we need to solve the NSE and the Continuityequation, respectively. These are given by:

    where

    Equations & simplify to

    The above equation are then subjected to thefollowing boundary conditions

    where is the velocity field of thefluid at any point in the flow field.It is then assumed that

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    Where is a function of .Substituting into yields

    sinceFrom further simplification it is shown that

    where is a constant, from it is seen that thevelocity profile is parabolic.The stress field is finally determined from thefollowing:

    Solutions show that .The only other two non-zero components are

    Hence the stress on the plates is:For the lower plate . Hence

    For the upper plate , yielding

    2.0 Representation of the Physical GeometryA conceptual model can be used to simplify theunderstanding and prediction of physical processesoccurring in a complex fractured geological system.With the use of COMSOL Multiphysics software, itprovides solutions for multiphysics modeling. A clearrepresentation of the geometry and conceptualizedmodels of the different processes within the fracturedsystem can be achieved using COMSOLMultiphysics 4.0.The model represented in this paper is the discretefracture model. Fluids travel through tiny poreswithin the rock matrix and the fracture; furthermore,fluid exchange can occur between them. Hence withthis method the fractures are represented asboundaries between adjacent matrix blocks, and areconsidered as an interior boundary. This model takesinto account that the fractures may not be perfectlyparallel to each other, hence some vertical variationor inclination is possible for the path of the fracture.A representation of such a fracture is shown below.

    Figure [6] : Geometry of a discrete fracturerepresented by COMSOL Multiphysics 4.0

    2.1 Model Definition, coefficients and parametersThe block of porous material illustrated by Figure7[b] can be considered to have a 1m measurement on

    each side. The fracture thickness has a standard valueof 0.1mm, with the fracture being more permeablethan the matrix block. Ideally the walls of the blockare impermeable except for the fracture edges, hencethe fluid flows along the fracture path with minimumto no leakage to the matrix block. Darcys lawgoverns velocities in the system from which thevelocity paths (arrow heads) can be shown to beideally perpendicular to the fluid field.Coefficient and parameters include: porosity of thematrix block , compressibility of the fluid and ofthe solid , permeability of the matrix block ,thickness , storage coefficient and permeability

    of the fracture , viscosity , fluid density , inletand outlet , pressures.

    Within the matrix block the fluid flow is describedtime-dependently (simulation period), throughDarcys law as shown below:

    where the linearized storage model

    In the matrix block, the predefined velocity variable,, gives the Darcy velocity, which can be described

    as the volume flow rate per unit area of the porousmaterial:

    Parallel to all faces of the block the zero flowboundary is applied where

    The outward-pointing normal to the boundary isgiven as , hence this means no flow across theboundary. (COMSOL Multiphysics 4.0 Modellibrary)

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    The fluid flow within the fracture is then observed asa model in which it is a sequence of interiorboundaries. The velocity in the fracture is modified tothat within the matrix block. This is achieved byaltering the equation coefficient of the time-dependent fluid flow Darcys law, to account for therelatively small resistance to flow on the fracture.(COMSOL Multiphysics 4.0 Model library) Hence equations and becomes

    where denotes the gradient operator restricted tothe fractures tangential plane, is the fracture-storage coefficient, is the fractures permeabilityand is the fractures thickness.2.2 Model representation using COMSOL 4.0The conductive heat flow of the fluid can berepresented by Figure 7[a], where at the inlet of thefracture there exists high pressure and temperatureshown in red, and at the outlet there exist a lowerpressure and temperature illustrated in blue.In Figure 7[b] the fracture is represented by fourparallel slabs along the y-z axes. Furthermore, itshows discrete vertical decrease in temperature as thefluid travels from the inlet to outlet of the fracture.This decrease in temperature does not significantlyaffect the overall fluid temperature. It does assist toillustrate thermal distribution vertically across theparallel slabs.Figures 7[c] and 7[d] illustrate isosurfaces which

    show the contours of fluid pressure throughout therock matrix. As mentioned before, Darcys lawgoverns velocities in the block. The fluid moves fromthe inlet to the outlet along the fracture with avelocity field that is uniform across the block.Figure 7[d] in particular illustrates the velocity fieldof the fluid at an instantaneous point along the paththat is perpendicular to the isosurfaces. The contourlines follow the fluid flow and are highly dense at theinlet and outlet of the discrete fracture, in addition,illustrating the parabolic shaped velocity field.

    Figure 7[a]: The conductive heat flow of the fluidthroughout the rock matrix.

    Figure7[b]: Parallel slabs along the y-z axes acrossthe rock fracture.

    Figure7[c]: The isosurfaces with contours of fluidpressure.

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    Figure 7[d] Illustrates the velocity field of the fluidflow.

    Through the use of COMSOL Multiphysics 4.0 arational understanding and appreciation of thefractured system is achieved. Furthermore, byperforming the necessary field and experimental

    studies to determine the required model parameters aslist in 2.1, multiple simplistic models of the researchareas can be developed. As Darcys velocity can bedetermined and modeled to illustrate highlyprospective regions for fluid flow with the reservoir.The most efficient site location for drilling aspectsand further geophysical surveys will then beidentified through this manner.

    LIMITATIONS

    A key assumption made into the investigation of thefluid flow along the geometry shown by Figure [1],was laminar flow through the discrete fracture path.However, turbulent flow was not considered inparticular at the junctions from the horizontal tovertical fractured plates. Furthermore, COMSOLMultiphysics 4.0a did not take into account atemperature component as this can generatesignificant knowledge into the thermal distribution ofheat transfer along the fracture path.

    CONCLUSION

    Many uncertainties about future energy supplies inthe world are being faced presently. Most of the

    energy currently used comes from fossil-fuelresources such as coal, oil and gas. Thecharacterization of a fractured rock system is one ofthe most challenging problems faced byhydrogeologists. The prediction of hydraulicbehavior of fractured porous geological systems isdeterminant upon the assessment of fractures asbarriers or hydraulic conductors. Furthermore,mathematical models are critical for detailed

    understanding and to determine fluid flow behavior.Therefore, as a result of this conceptual model anunderstanding of the geometry and mathematicalflow processes occurring within the fracturedreservoir is attained. This fundamental step is crucial,for more advanced approaches towards fullydescribing an understanding the complex nature ofthe system. Hence through field and laboratorystudies on the mineralogy of research areas on Nevis,this conceptual model can be developed to fullygenerate a mathematical and numerical model. Dueto the diverse nature of the rock mineralogy of Nevis,specific models can be produced to represent thecharacteristic of that individual location. Future workinto the fluid flow and its characteristics can beinvestigated to further enhance this model to fullydevelop a better understanding of the flow with thefracture path.

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