Physical property relationships of the Rotokawa Andesite, a significant geothermal reservoir rock in the Taupo Volcanic Zone, New Zealand

Previous studies of relevance

The study of the core from geothermal systems can yield valuable information to assist their modeling and understanding. For example, Stimac et al. ([2004]) present a study detailing the relationship between permeability and porosity from continuous core from Tiwi geothermal field, Philippines. Their data show that permeability and porosity decrease with depth, with occasional deviations attributed to alteration and compaction. However, the authors are careful to note that their work does not consider the influence of microfractures and their effect on relevant reservoir parameters. Lutz et al. ([2010]) present a case history of the well core from the Desert Peak field (NV, USA) in preparation for the stimulation of an enhanced geothermal system (EGS) by a thorough evaluation of petrological strength and elastic moduli. The results of their study elucidate relationships between clay mineralogy, rock fabric, and permeability increases as a result of mechanical shearing which support proposed hydraulic fracture operations in Well 27-15 at Desert Peak.

The effect of hydrothermal alteration on the physical properties of geothermal core is also a very significant area of research. Hydrothermal alteration can drastically change the elastic wave velocities and permeabilities of rock in both the natural and laboratory environment (Jaya et al. [2010]; Kristinsdóttir et al. [2010]; Pola et al. [2014]). However, coupled studies of physical properties such as porosity, permeability, and strength on geothermal reservoir rocks have not been extensively presented. A detailed study of the impact of a complex microstructure (microfractures and hydrothermal alteration) on the rock physical properties of a geothermal system such as Rotokawa could serve to greatly improve the understanding of reservoir processes at multiple scales.

Geothermal systems are more often than not associated with volcanic systems and are often hosted in rocks sourced from extinct volcanic systems. By proxy, the study of rocks from volcanic edifices can help to boost the understanding of processes within geothermal reservoirs especially with regard to microfractures, which play an essential role in controlling strength, porosity, permeability, elastic wave velocities, and elastic moduli of rocks (Wu et al. [2000]; Guéguen and Schubnel [2003]; Pereira and Arson [2013]; Faoro et al. [2013]; Pola et al. [2014]; Heap et al. [2014]). For example, Vinciguerra et al. ([2005]) studied the influence of thermal stressing on basaltic samples. They show, using elastic wave velocities, that the response of microstructurally variable basalts to thermal stressing can be quite different. While fresh microlitic basalt exhibited severe reductions in P-wave velocity after exposure to 900°C, the P-wave velocity of porphyritic basalt with a pervasive microcrack network did not change.

Similar dependence on the effect of microfractures on strength (Smith et al. [2009]) and permeability (Nara et al. [2011]) has been investigated, with microfractures proving to be deleterious to strength and to enhance permeability. Heap et al. ([2014]) showed, for a suite of pervasively fractured andesites, that an increase in porosity from 8 to 29 vol% decreases strength by a factor of 8 and increases permeability by 4 orders of magnitude. David et al. ([1999]) showed that mechanical and thermal microcracking in granites results in significant changes to permeability and elastic wave velocities. Mechanical microcracking resulted in the development of P-wave velocity anisotropy, while thermally microcracked samples showed little P-wave anisotropy. Additionally, permeability was much more varied in mechanically microcracked rocks than those induced thermally, suggesting that thermal microcracks develop isotropically. Chaki et al. ([2008]) investigated the role of thermal microcracking in granites and showed that elastic wave propagation is attenuated by microcracks and the orientation of these thermal microcracks (with regard to the original microstructure) plays a critical role in the propagation and attenuation of the waves. Faoro et al. ([2013]) provide a model for how microcrack density within an isotropically microcracked sample can be modeled as a function of aspect ratio and microcrack connectivity. Elastic moduli and elastic wave velocities are strongly influenced by the morphology, distribution, and shape of pore space in rocks and are substantially attenuated by the presence of microcracks (Stanchits et al. [2006] and references therein).

The relationship between porosity and strength has been observed by many authors, with general agreement that as the porosity of a sample (both rock and other engineering materials) increases, the strength decreases (e.g., Al-Harthi et al. [1999]; Li and Aubertin [2003]; Kahraman et al. [2005]; Chang et al. [2006]; Diamantis et al. [2009]; Ju et al. [2013]; Baud et al. [2014]; Heap et al. [2014]). The geometry of the pores also has a significant role in the strength of the materials both intrinsically and with respect to the direction of stress (Luping [1986]). The microstructure of rocks can be changed by increasing the crack damage (by mechanical and/or thermal stresses) as well as hydrothermal alteration (Heap et al. [2009]; Nara et al. [2011]; Pola et al. [2014]); these changes can be observed through the evaluation of destructive and nondestructive physical property measurements (Pola et al. [2012] and references therein; Sousa et al. [2005]). Further, Pola et al. ([2014]) also show that hydrothermal alteration of volcanic rocks can either strengthen or weaken rocks by decreasing or increasing their porosity, respectively.

Geological significance of the Rotokawa Andesite

The TVZ is a rifted arc associated with the Hikurangi subduction system in which the Pacific plate descends beneath the Australasian plate (Cole [1990]; Wilson et al. [1995]), and hosts active volcanism and multiple associated hydrothermal systems (Bibby et al. [1995]; Rowland and Sibson [2004]; Rowland et al. [2010]). The Rotokawa field is one of these active hydrothermal systems and has been the subject of exploration for mineral resources (sulfur and gold deposits) and, for many years, was the subject of detailed investigation into its use as a commercial geothermal resource (Collar and Browne [1985]; Krupp and Seward [1987]; Hedenquist et al. [1988]). More recently, electricity generation has been realized at Rotokawa following the installations of the Rotokawa I (1997) and Nga Awa Purua (2010) generation stations (Legmann and Sullivan [2003]; Bloomberg et al. [2012]). The more recent of these installations, the Nga Awa Purua power station, hosts the single largest geothermal turbine installation in the world and has a generation capacity >140 MWe which is approximately 3 % of New Zealand’s electricity consumption (Horie and Muto [2010]).

The main production zone for the installations at Rotokawa is from that of the Rotokawa Andesite, a series of lavas, pseudo-breccias, and breccias. The movement of fluid through the andesite is predominantly along fracture networks (Rae [2007]; Massiot et al. [2012]). The andesite overlies basement of Miocene greywacke and is capped by a sequence of volcaniclastic and sedimentary units: Reporoa Group, Wairakei Ignimbrite, Waiora Formation, and Huka Falls Formation (Krupp and Seward [1987]; Rae [2007]). The andesite is gray to green and occasionally purple in color, depending on alteration within the reservoir; alteration is less intense in the lavas and more intense in the breccia and pseudo-breccia (Ramirez and Hitchcock [2010]). Production of reservoir fluids is sourced from the Rotokawa Andesite by 12 wells in the central part of the field (Figure 2), and re-injection of spent fluids is done through 5 wells along the southeastern margin of the field (Powell [2011]).

Study source material

At the University of Canterbury (UC), the cores were catalogued and cut into workable cylinders approximately 100 mm in length. These smaller sections were over-cored to obtain smaller cylindrical samples 40 mm in diameter and ranging from 80 to 100 mm in length. All samples were machined so that their end faces were flat and parallel in accordance with ISRM standards (Ulusay and Hudson [2007]).

Microstructural characterization

Density and porosity measurements

Once the samples were cut and ground flat and parallel, they were washed with water to remove any debris from sample preparation. They were then immersed in distilled water under vacuum of about 100 kPa for 24 h. Samples were taken out of the water and were weighed after their surface water had been removed. The samples were then placed into a laboratory oven at 105°C and dried until a constant mass was observed. Subsequently, they were removed from the oven and held in a dessicator until further characterization was implemented. Sample lengths and diameters were measured to within 0.01 mm. The connected porosity and dry bulk density of the samples were calculated following the methods recommended by Ulusay and Hudson ([2007]).

Characterization of elastic wave velocities and dynamic elastic moduli

The compressional wave (Vp) and shear wave (Vs) velocities and dynamic elastic moduli were measured using a GCTS (Geotechnical Consulting and Testing Systems, Tempe, AZ, USA) Computer Aided Ultrasonic Velocity Testing System (CATS ULT-100) apparatus with axial P- and S-wave piezoelectric transducers (Figure 3). The resonance frequency of the transducers was 900 kHz, pulse acquisition rate was 20 MHz, and 108 waveforms were captured for each sample. The velocities were collected under a constant uniaxial stress of 10 MPa via a Tecnotest servo-controlled 3,000 kN loading frame (Technotest, Modena, Italy) (Figure 3). The stress of 10 MPa was used to ensure a consistent waveform across the specimens and that applied stress was consistent for all measurement cycles. This was determined to be below microcrack closure and opening stress by analyzing the change in axial strain as the sample was loaded to 10 MPa (Eberhardt et al. [1998]). There was no change in axial strain and absence of acoustic emissions (AEs) during the initial loading (Brace et al. [1966]; Martin and Chandler [1994]; Lion et al. [2005]; Nicksiar and Martin [2012]); this ensured a good quality interpretation of the first arrival time of elastic wave pulses. Using these data, we determined the dynamic Poisson’s ratio and Young’s modulus using Equations 3 and 4 (Guéguen and Palciauskas [1994]), respectively:

${\mathit{V}}_{\mathrm{d}}=\left({\mathrm{Vp}}^2-2{\mathrm{Vs}}^2\right)/2\left({\mathrm{Vp}}^2-{\mathrm{Vs}}^2\right)$

(3)

${\mathit{E}}_{\mathrm{d}}=\left(\mathit{\rho }{\mathrm{Vs}}^2\left(3{\mathrm{Vp}}^2-4{\mathrm{Vs}}^2\right)\right)/\left({\mathrm{Vp}}^2-{\mathrm{Vs}}^2\right)$

(4)

Uniaxial compressive strength testing and static elastic moduli

where E_s is the static Young’s modulus (Pa), v_s is the static Poisson’s Ratio, σa is the differential axial stress (Pa), εa is the axial strain, and εr is the radial strain.

Permeability measurements

where k_gas is the gas permeability, η is the viscosity of the pore fluid, A is the cross-sectional area of the sample, V_up is the volume of the upstream pore pressure circuit (approximately 7 cm³), P_up is the upstream pore pressure, P_down is the downstream pore pressure, and t is the time. By plotting ΔP_up as a function of time, the local slope of the curve is computed to determine the temporal variation of the permeability k_gas. To check whether our data should be corrected for Klinkenberg’s ‘slip flow’ (Klinkenberg [1941]), we plotted the measured gas permeability as a function of the inverse of the mean pore fluid pressure, P_mean. For the transient method, since P_down is constant, the decay of P_up through time corresponds to the decay of the mean pore pressure P_mean. We found that, in all cases, the Klinkenberg correction should be applied:

${\mathit{k}}_{\mathrm{true}}={\mathit{k}}_{\mathrm{gas}}\left(1+\mathit{b}/{\mathit{P}}_{\mathrm{mean}}\right)$

(9)

where k_true is the true gas permeability, b is Klinkenberg slip factor, and P_mean is the mean pore fluid pressure.

Petrology

The Rotokawa Andesite shows moderate to intense hydrothermal alteration with the groundmass and phenocrysts showing replacement of original mineralogy. Fractures and occasional veins of quartz, calcite, anhydrite, and epidote occur, and amygdales within the sample are often filled with chlorite, calcite, hematite, pyrite, and chalcedony, often with quartz rims (Figure 6). Alteration is pervasive with the original mineral assemblages typically replaced by secondary hydrothermal alteration species, with some specimens showing very little original mineralogical texture. Plagioclase feldspars have been altered to albite, adularia, occasional calcite, and rare pyrite, and ferromagnesian minerals have been replaced by chlorite, quartz, calcite, and occasional epidote. Microfractured phenocrysts (Figures 6 and 7) are abundant and many relict phenocrysts retain original texture are but replaced by secondary mineralization. The average phenocryst size is 0.5 to 1 mm with occasional plagioclase near 1.5 to 2 mm; amygdales also range from 1 to 1.5 mm in size. The alteration chemistry of the samples indicates that this portion of the reservoir is dominated by chlorite/epidote alteration. The degree of alteration is relatively consistent across the core we have sampled with most primary mineralogies replaced by secondary alteration products. Microfracture mineralization indicates that these networks may have been conductive pathways for fluid migration (i.e., the presence of chlorite clays, adularization of plagioclase, calcite, and quartz rimming of fractured matrix); we typically observe chlorite, calcite, and quartz as alteration mineralogies with occasional epidote centers within the fractures. Backscatter scanning electron microscopy (SEM) was utilized to further reiterate the complex interaction of fractures and vesicles in the specimens (Figure 7). At several different magnifications, we see an abundance of microfractures in the samples as well as a clear depiction of the complex alteration mineralogy displayed by the andesite.

Quantitative two-dimensional microstructural analysis

We evaluated the microfracture density of 10 specimens as a function of crack surface area per unit volume (Table 2). These samples were selected to represent the range of connected porosities observed within the sample set. We found that the crack area per unit volume in our samples ranges from 3.77 to 13.06 mm²/mm³ and appears to be independent of the alteration and mineralogy of the specimens. The calculated anisotropy factor (Ω_2,3), indicates that the microcracks are isotropic (Table 2).

Porosity and bulk density

Bulk density decreases as connected porosity increases, as expected for samples of similar composition (Figure 8A). Bulk dry densities of the samples range from 2.29 to 2.65 g/cm³, with a mean value of 2.49 g/cm³. The connected porosities range from 4.37 to 16.3 vol%, with a mean value of 8.44 vol%. While there is some variation in the distribution of pores/vesicles in the samples, we observe that the microcrack density exerts an important control on the porosity and density, as illustrated by the correlation between crack area per unit volume and connected porosity presented as Figure 8B.

Ultrasonic wave velocities, dynamic elastic moduli, and spatial attenuation

Measurements made on dry samples under ambient (pressure and temperature) conditions yielded axial P-wave velocities from 3,627 to 4,556 m/s with a mean value of 4,106 m/s, and axial S-wave velocities between 2,160 to 2,752 m/s with a mean value of 2,510 m/s (Table 3). Porosity and P-wave velocities show moderate correlation: samples with higher porosities have slower elastic wave velocities, as seen in Figure 8C. The crack area per unit volume also correlates well with P-wave velocity (Figure 8D). The axial spatial attenuation for the andesites ranges from 8.39 to 28.74 dB/cm (Figure 9). Figure 9 shows that there is no clear trend between spatial attenuation and P-wave velocity. Dynamic Poisson’s ratio and dynamic Young’s modulus were in the range of 0.13 to 0.23 and 24.6 to 45.9 GPa, respectively (Table 3).

Sample source_well sample name	Bulk dry density (g/cm3)	Connected porosity (vol%)	Vp (m/s)	Vs (m/s)	Spatial attenuation (dB/cm)	UCS (MPa)	Static Young’s modulus (GPa)	Dynamic Young’s modulus (GPa)	Static Poisson’s ratio	Dynamic Poisson’s ratio
RK_27_L2_21.5B	2.44	10.72	4,005	2,443	14.63	85.99	19.9	35.1	0.24	0.2
RK_27_L2_21.8A	2.33	13.49	3,850	2,363	16.47	79.91	25.2	31.2	0.26	0.2
RK_27_L2_23.2A	2.56	6.61	4,182	2,490	22.48	105.26	31.2	38.9	0.19	0.23
RK_27_L2_20.4B	2.65	4.37	4,556	2,752	22.53	211.05	37.7	45.9	0.25	0.21
RK_27_L2_21.1C	2.37	13.1	3,877	2,405	23.6	69.53	21.5	32.5	0.18	0.19
RK_27_L2_3.3B	2.45	9.81	3,937	2,331	23.51	95.78	32.4	29.9	0.13	0.18
RK_27_L2_21.0B	2.34	14.91	3,752	2,337	8.4	60.13	28.1	30.6	0.12	0.17
RK_27_L2_21.3A	2.29	16.3	3,627	2,160	15.13	70.57	30.4	24.6	0.16	0.17
RK_28_10.6C	2.5	5.97	4,350	2,652	18.27	146.2	43.7	42.4	0.27	0.2
RK_28_10.8C	2.53	6.72	4,147	2,537	11.67	109.91	27.2	39.1	0.34	0.2
RK_28_10.9B	2.51	7.42	4,285	2,615	14.67	137.31	32.4	41.5	0.2	0.2
RK_28_13.2A	2.55	6.97	4,013	2,531	18.53	146.21	38.3	37.2	0.24	0.19
RK_28_10.5A	2.45	7.47	4,220	2,578	14.83	130.71	27.4	38.8	0.25	0.21
RK_28_11.5A	2.51	7.62	4,403	2,555	10.06	152.76	35.6	37.4	0.27	0.13
RK_28_12.1	2.49	7.89	4,010	2,460	12.23	115.01	29.3	36.2	0.22	0.14
RK_30_20.4A	2.57	5.3	4,002	2,495	10.39	140.97	33.6	36.9	0.09	0.15
RK_30_21.0A	2.55	6.84	4,070	2,508	11.17	126.53	26.4	39.8	0.14	0.15
RK_30_21.1B	2.54	7.47	4,352	2,659	28.75	157.93	25.8	43.2	0.17	0.2
RK_30_21.7B	2.56	6.28	4,154	2,588	19.91	162.71	28.3	41.1	0.22	0.18
RK_30_22.3B	2.53	7.51	4,133	2,550	21.72	137.97	31.5	39.2	0.23	0.19
RK_30_22.4A	2.56	6.49	4,181	2,582	20.27	148.44	34.4	40.7	0.18	0.19
RK_30_22.5B	2.56	6.41	4,236	2,628	23.43	150.71	33.6	42.1	0.09	0.16
Mean	2.49	8.44	4,106	2,510	17.39	124.62	30.6	37.5	0.2	0.18
Standard deviation	0.09	3.23	221	133	5.512	37.01	5.5	5.1	0.06	0.03

Uniaxial compressive strength and static elastic moduli

In order to characterize the mechanical behavior of the Rotokawa Andesite, the 22 samples of Table 3 were loaded in compression to failure. The dataset shows a large range of UCS (as observed for the other physical properties), from 60 to 211 MPa. The stress-strain behavior of the andesites is very similar across the range of strengths, as shown in Figure 10, which reports curves that best represent the dataset and behavior of the Rotokawa Andesite under uniaxial compression. All specimens in the dataset show brittle behavior as evidenced by the stress-strain relationships and bolstered by analysis of the AE activity. An increase of AE between dilatancy (σ_cd) and failure is a benchmark of brittle failure (e.g., Brace and Bombolakis [1963]; Rutter [1986]; Ashby and Sammis [1990]; Heap and Faulkner [2008]), as seen in Figure 10. Weaker specimens showed lower overall AE energy output than higher strength specimens. Static Young’s moduli range between 19.9 and 43.7 GPa and static Poisson’s ratio between 0.09 and 0.34. Our data shows that as porosity and crack surface area increases, the UCS of the rock decreases (Figure 11A,B). Further, the UCS increases as axial P-wave velocity increases (Figure 11C).

Permeability

Micromechanical interpretation

We have shown that the Rotokawa Andesite contains a pervasive network of isotropic microcracks. Due to their isotropic distribution, the majority of these microcracks are consistent with the results of thermal stressing (Fredrich and Wong [1986]; Reuschlé et al. [2006]; Wang et al. [1989]; David et al. [1999]; Heap et al. [2014]). Indeed, the Rotokawa Andesite has experienced several cycles of heating and cooling: the initial eruption of the andesite, burial in a faulted graben, hydrothermal alteration, and the eventual exhumation during core recovery (Rae [2007]; Lim et al. [2012]). Our microstructural analysis has highlighted that the pervasive microcracking appears independent of lithology, original mineralogy, and secondary (hydrothermal alteration) mineralogy.

The intense microcracking in our samples has shown to be a significant factor in all of the measured physical properties. First, microcracking has greatly reduced the propagation velocity of elastic waves through the andesite. We see a clear correlation of crack area per unit volume (Sv) to the observed compressional wave velocities (Figure 8D) and interpret this to be attenuation of the compressional wave through the cracked intracrystalline and intercrystalline boundaries that are abundant in the andesite (e.g., Figures 3 and 4). Many authors (e.g., Vinciguerra et al. [2005]; Keshavarz et al. [2010]; Blake et al. [2012]; Heap et al. [2014]) have also shown that the elastic wave velocities can be highly attenuated by the presence of microcracks.

Second, the crack surface area and UCS have yielded an excellent correlation (Figure 11B). As noted by Walsh ([1965a], [b]), David et al. ([1999]), and Chaki et al. ([2008]), the density of the cracks within a specimen is critical in dictating its strength. The development of microcracks during uniaxial compression, and the coalescence of these cracks (newly formed and pre-existing), leads to the failure of the sample (Brace et al. [1966]; Bieniawski [1967]). In samples that already show relatively high crack densities, less energy is required to coalesce existing cracks and thus they are inherently weaker (David et al. [1999]; Ferrero and Marini [2001]; Keshavarz et al. [2010]). By utilizing AE monitoring during our UCS testing, we observe that fewer events occur during uniaxial compression in weaker samples than those with higher strength (Figure 10), indicating that there are far more pre-existing cracks in the weaker samples (Hardy [1981]; Eberhardt et al. [1998]; Nicksiar and Martin [2012]). Thus, the presence of pre-existing microcracks in the Rotokawa Andesite is shown to exert a strong control on their uniaxial compressive strength.

Permeability is one of the most important properties of a geothermal system. In this study, we have seen that porosity (and bulk sample density) and strength are related to the extent of the microcracking in the andesite. We did not measure the crack surface area in the samples used for our permeability measurements (the samples will be used for future studies; calculating crack surface area required destructive thin section preparation). However, we can, by proxy, assume a correlation between permeability and the extent of the microfracture network. We show that there is a clear inverse relationship between the sample’s permeability and P-wave velocity such that as permeability increases, compressional wave velocity decreases (Figure 11F). These results are consistent with the many investigations have shown a clear link between reduced elastic wave velocities and increased permeability (David et al. [1999]; Vinciguerra et al. [2005]; Chaki et al. [2008]; Nara et al. [2011]; Faoro et al. [2013]; Heap et al. [2014]). While we have not measured the relationship of crack density to permeability directly in our dataset, we show that Sv and Vp are inversely related (Figure 8D), and a similar relationship exists between Vp and permeability. Therefore, we can infer that those samples with higher crack surface areas will be inherently more permeable.

Key empirical relationships

In this section, we present relationships of singular variables that could be readily and easily measured either using photomicrography or geophysical logging tools and their correlation to more complicated and pertinent physical properties. All of these parameters are singularly measurable variables that do not rely on complex formulae for their derivation (such as dynamic Young’s Modulus or Poisson’s ratio) and so have been selected to be the key relationships that we present with relevance to the Rotokawa Andesite.

Porosity and UCS

An exponential correlation between sample porosity and UCS exists (Figure 11A). Such correlations have been utilized by several authors (e.g., Vernik et al. [1993]; Li and Aubertin [2003]; Palchik and Hatzor [2002]; Kahraman et al. [2005]; Chang et al. [2006]; Palchik [2013]; Pola et al. [2014]) for a variety of clastic and volcanic rocks and concrete materials. These authors present empirical fits for the correlation of physical properties versus UCS and show a wide range of correlation within their respective datasets with R² values from near 0.6 to as high as 0.95. We propose that our empirical fit between porosity and UCS (an exponential fit with a correlation factor of 0.82, Figure 11A) can provide useful estimations of the strength of the reservoir rocks within the Rotokawa Andesite reservoir. By utilizing estimations of UCS derived from the correlation of porosity, the minimum strength of the rocks can be applied to important engineering issues such as wellbore stability (Chang et al. [2006]; Schöpfer et al. [2009]).

Vp and UCS

There is an exponential correlation between strength and Vp with an R² value of 0.74 (Figure 11C). As noted by Kahraman ([2001]), the relationship between Vp and UCS is generally nonlinear and the higher the strength of the material, the more scattered the data points. Heap et al. ([2014]) came to similar conclusions following measurements on andesitic rocks from Volcán de Colima (Mexico). In our study, there is an increasing trend of strength with increasing Vp but, as shown in Figure 9, there is a high degree of spatial anisotropy with respect to Vp such that a robust correlation of strength to elastic wave velocity is difficult to obtain. However, Vp is a widely utilized logging tool in borehole geophysics (Chang et al. [2006]), and using the correlation that we have obtained, a minimum strength criteria could be established from the response of the logging tool. This is an important correlation as geophysical logging is much easier, faster, and more efficient than cutting spot cores (as the core for this study was obtained), and so the development of empirical correlations to constrain strength such as that seen in Figure 11B can help mitigate risk and reduce the cost associated with geothermal drilling programs.

Vp and porosity

Correlations between Vp and porosity show an increasing trend of porosity with decreasing Vp (Figure 11D, also observed by Al-Harthi et al. [1999]; Rajabzadeh et al. [2011]; Tugrul and Gurpinar [1997]; Heap et al. [2014]). This can be attributed to both the pore structure distribution and the degree of microcracking within the andesites. It is clear from microstructural analysis (using both optical and scanning electron microscope analyses) that a large proportion of the porosity in the Rotokawa Andesite is likely to be composed of (macro- and mesoscale) fractures and microcracks (e.g., Figures 6 and 7).

An explanation for the variation and wide distribution of the elastic wave velocity data for samples with similar porosities (specifically with regard to those data that range from 4,000 to 4,400 m/s) is that there must be a variable pore (vug/vesicle) content or hydrothermal alteration between the samples. The presence of pores will greatly augment the porosity (due to their aspect ratio) but will have comparatively little influence, compared to the microcracks, on the P-wave velocity. The application of our exponential relationship (Figure 11D) can give a rough approximation for seismic velocities derived from connected porosity, or vice versa. This may be useful during the drilling of additional wells at Rotokawa where porosity can be measured at the wellsite and yield a rough approximation for P-wave velocities and, as such, tie back to our empirical correlations of strength (Figure 11C).

Permeability and porosity

Our permeability and porosity data show that there is a clear trend of increasing porosity with increased permeability for the Rotokawa Andesite (Figure 11E), a common observation in multiple lithologies (e.g., Heard and Page [1982]; Géraud [1994]; Stimac et al. [2004]; Chaki et al. [2008]; Watanabe et al. [2008]; Heap et al. [2014]). We observe that our relationship between porosity and permeability can be described by a power law correlation and is consistent with the Kozeny-Carman relation (Guéguen and Palciauskas [1994], see the ‘Application of micromechanical and geometrical permeability models’ section). The dependence of permeability on porosity is generally explained by the assumption that a more connected pore space (cracks and pores) provides more efficient pathways for fluid migration (e.g., Costa [2006]; Chaki et al. [2008]). We do however need to consider those data points that have a very similar value of permeability (approximately 3.2 × 10⁻¹⁷ m², Table 4), with a porosity range of 7.6 to 10.3 vol% that indicate that there is variability of the samples with respect to permeability that may be reflected in the tortuosity of the porous network. This is consistent with the findings of Bernard et al. ([2007]) and Heap et al. ([2014]) such that the permeability in volcanic rocks is highly dependent upon connectivity of the microstructure.

With respect to microstructure, we have shown that the porosity is very closely linked to crack surface area (Figure 8D) and, thus, that increasing crack density corresponds to a sample with a higher permeability. The three samples that lie slightly outside the trend of the dataset display distinct mesofractures (black stars in Figure 11E,F) and that these mesofractures greatly enhance the permeability of the samples without significantly increasing their porosity. These specimens show higher than average permeability for their porosity, which supports the conclusions of Stimac et al. ([2008]) that meso- and macrofractures are critical in controlling the permeability of geothermal reservoir systems. On the large scale, macrofractures are necessary for fluid production from geothermal reservoirs, but the microstructural characteristics of the host rocks cannot be neglected when considering fluid flow, storage capacity, and total permeability of the reservoir (Jafari and Babadagli [2011]).

The robust relationship between porosity and permeability has wider-scale reservoir applications where the need to understand reservoir rock permeability (the mass itself, not those portions with highly macroscopic fractures e.g., Massiot et al. [2012]) is important for reservoir forecasting and modeling. Measurements of porosity can then yield a good approximation of the permeability of the intact reservoir rock at Rotokawa through our power law correlation (Figure 11E). However, we urge caution if the porosity falls outside our measured range. As porosity is a readily measureable property by geophysical logging tools (Ellis and Singer [2008]), the response from such a tool, together with our empirical fit, can give engineers and geoscientists an approximation of the matrix permeabilities in the Rotokawa Andesite.

Permeability and acoustic velocities

There is a clear inverse relationship between our measurements of permeability and P-wave velocity (Figure 11F) such that the more permeable the sample, the slower the compressional wave velocity. These findings are consistent with the findings of many other authors (e.g., Vinciguerra et al. [2005]; Chaki et al. [2008]; Nara et al. [2011]; Heap et al. [2014]). The correlation of such properties is an excellent tool for understanding the micro- and mesoscopic fracture networks and their relation to permeability in the Rotokawa Andesite as follows: (1) we have shown that the porosity and crack density are closely linked (Figure 8A), (2) acoustic velocity and crack density are closely linked (Figure 8D), and (3) there is a power law correlation of Vp and permeability (Figure 11F). Thus, there is a direct link of P-wave velocity to permeability that is reliant on the crack densities of the samples. The relationship we present in Figure 11F shows a power-law fit which would indicate that the hydraulic radii of the pore space (pore and cracks) are similar in size but that the higher the concentration of cracks, the higher the permeability we observe (Bourbie and Zinszner [1985]).

Similarly, there are occasional mesofractures (with apertures less than 1-mm width; we note that these fractures are much smaller than those described in Massiot et al. [2012]) in the samples that deviate from the rest of the dataset (black stars, Figure 11F). The presence of these macrofractures increases permeability (by a factor of 2) and also appears deleterious to elastic wave propagation (all the three samples containing mesofractures have low elastic wave velocities, although we cannot separate the influence of meso- and microcracks on the velocities of these samples). Further, elastic waves are useful for the detection of cracks in rock and concrete (Chaki et al. [2008]; Heap et al. [2013]), and a decreased elastic wave velocity correlates well to more permeable media which is observed by the three outlying, higher permeability, lower elastic wave velocity samples.

The correlation between elastic wave velocity and permeability outside the laboratory has potentially far-reaching value for the prediction of reservoir permeability interactions from wireline logging and larger-scale seismic and microseismic surveys. There is a complex microseismic network installed at Rotokawa, and the location of earthquake activity has been closely linked to macroscopic permeability within the reservoir (Sewell et al. [2013]; Sherburn et al. [2013]). The existing model of the velocity structure at depth could then be further refined using our acoustic velocity and permeability data for reservoir rock matrix. This may allow a deeper and more accurate understanding of the distribution of permeability at depth.

Additionally, the data we have presented can also be used to infer values of matrix permeability from acoustic wireline logs (dipole sonic) used during exploration at nearby Ngatamariki Geothermal Field (Wallis et al. [2009]). Should similar geophysical logging be used in future wells drilled at Rotokawa, the matrix permeability may be estimated using the relationship we present here. In addition, the coupling of these data with microseismic data could allow a significant increase in understanding the complexity of the Rotokawa Andesite reservoir. While we are aware that macrofractures augment the elastic wave velocity during routine acoustic profiling (e.g., Barton and Zoback [1992]), our laboratory data show that although samples containing mesofractures (i.e., on the sample scale) are shifted to higher permeabilities and elastic wave velocities, they do not stray too far away from the trend extrapolated from our power-law relationship. Despite this, we urge a certain degree of caution, based on the potential presence of large-scale fractures, when estimating permeability using our derived permeability-elastic wave velocity relationship.

Application of micromechanical and geometrical permeability models

Extracting empirical relationships between laboratory-derived rock properties is useful; however, the parameters are not easily related to independently measurable quantities (i.e., they lack a physical basis). Micromechanical (e.g., the wing-crack model of Ashby and Sammis [1990]) and geometrical permeability models (e.g., the Kozeny-Carman relation, Guéguen and Palciauskas [1994]) can be better constrained as the parameters used in such models have a clear physical meaning. In this section, we attempt both sliding wing-crack modeling and Kozeny-Carman permeability modeling to investigate the microstructural controls on deformation and fluid flow, respectively.

Micromechanical modeling

The analytical solution (that assumes an initial crack angle of 45°) presented above contains five parameters. We have, through experimental data and observations, a good handle on three of the parameters: (1) we have measured the UCS of 22 samples (Table 3), (2) μ rarely deviates from 0.6 to 0.7 (Byerlee [1978]), and (3) c can be determined from optical microscopy (we determined c by measuring the approximate average length of the microcracks under the microscope). We do not have a laboratory-determined value for K_IC. While the K_IC of andesite has been previously measured to be about 1.5 MPam^0.5 (Ouchterlony [1990]; Obara et al. [1992]; Tutluoglu and Keles [2011]; Nara et al. [2012]), there is no guarantee that this value is representative of the Rotokawa Andesite, which is likely to be lower than these values due to hydrothermal alteration. We therefore have chosen a slightly lower K_IC of 1.0 MPam^0.5 for our analysis. Using our UCS data, we can solve Equation 10 to assign a value of D₀ to each experiment (using μ = 0.6; K_IC = 1.0; c = 0.001 m). The goal of such analysis, assuming that the other parameters remain roughly constant between different samples/cores, is to estimate D₀ using an easily measured physical property, such as Vp (therefore allowing us to predict rock strength, using the micromechanical model, from Vp measurements alone). Our analysis shows that D₀ ranges from 0.0019 to 0.26 for the 22 measured samples (with average of 0.039). D₀ is plotted against the crack area per unit volume (Sv) and Vp in Figure 12 and indicates that D₀ increases as Sv increases (Figure 12A). While this may appear logical (D₀ is a function of the initial crack density), it serves as an encouraging proof of the concept. The increase in D₀ with crack density is not linear; D₀ increases more rapidly beyond 10 mm⁻¹ (Figure 12A). We also see that Vp decreases with increasing D₀; in detail, Vp decreases rapidly as D₀ increases from 0 to 0.05 and then decreases more gradually above 0.05. Unfortunately, the relationship between D₀ and Vp is a little more clouded (the data are more scattered, Figure 12B) and probably represents variable vesicle density (the model assumes that vesicles do not play a role in failure in compression) and hydrothermal alteration (we assume that K_IC and the average crack lengths are constant). The conclusion of this pilot analysis is that the variability within the Rotokawa Andesite is potentially too large to permit meaningful microstructural wing-crack modeling, but greater success could be achieved with laboratory-determined values for K_IC. Therefore, if micromechanical modeling is to be deployed as a feasible method to predict the strength of Rotokawa Andesite reservoir rocks, the samples/cores should be grouped by their alteration, and K_IC measured for each alteration group.

Permeability modeling

Application of results to geothermal exploration and utilization

The relationships between porosity, acoustic wave velocities, strength, and permeability are valuable for understanding a geothermal reservoir. Our data indicate strong correlations between these parameters, as observed by Stimac et al. ([2004], [2008]) amongst others. The data we have obtained are from cores sourced from three production wells. Such materials are very expensive to obtain, time consuming, and, if coring did not go as planned, can pose great risk of losing the well (Finger and Blankenship [2010]; Hole [2013]). The microstructural and empirical correlations presented in this study can be applied to new wells drilled in geothermal environments and can help refine studies on pre-existing wells, if our correlations hold true at the reservoir scale. Some physical parameters, such as porosity and elastic wave velocities, are easily obtainable through the use of down-hole geophysical logging suites. The empirical correlations shown in this study (bolstered by our application of classical models) show that readily measurable physical properties may therefore be used to predict more complex and pertinent properties such as strength and permeability. Such correlations and calibrations are common in the hydrocarbon industry especially during exploration drilling (e.g., Vernik et al. [1993] and references therein), and we consider that our dataset can help improve the understanding of the Rotokawa reservoir while minimizing the risk to future drilling operations.

A clear understanding of the factors that control reservoir rock permeability is fundamental for the planning of stimulation and enhancement operations that may be necessary as the Rotokawa field and reservoir dynamics change with continued production. The need to drill additional wells or re-work pre-existing wells may become apparent and the ease at which the reservoir can accept and deliver fluids (i.e., its permeability) will be of utmost importance. The thermal stimulation of injection wells has taken place at Rotokawa for some time by the injection of power-plant condensates and spent brines (Siega et al. [2009]), but the technique may play a significant role in enhancing production wells at some future stage.

Therefore, a deeper understanding of how permeability may be increased through stimulation is important. The application of models such as the Kozeny-Carman may provide insight to permeability enhancement. An increase in the porosity of reservoir rock by 1 vol%, according to the geometrical model, should increase the permeability by a factor of 1.5. In the case of an aging field and aging wellbores, such an increase could greatly extend the life of the field. In the interests of keeping geothermal projects commercially economic, the fundamental understanding of the reservoir rock properties become essential to the continued utilization and management of the field.