Fracture properties, structural heterogeneity, and permeability in the Þeistareykir geothermal system, NE Iceland

The complexity of the Krafla volcano and its geothermal system(s) has puzzled geoscientists for decades. New and old geoscientific studies are reviewed in order to shed some light on this complexity. The geological structure and history of the volcano is more complex than hitherto believed. The visible 110 ka caldera hosts, now buried, an 80 ka inner caldera. Both calderas are bisected by an ESE-WNW transverse low-density structure. Resistivity surveys show that geothermal activity has mainly been within the inner caldera but cut through by the ESE-WNW structure. The complexity of the geothermal system in the main drill field can be understood by considering the tectonic history. Isotope composition of the thermal fluids strongly suggests at least three different geothermal systems. Silicic magma encountered in wells K-39 and IDDP-1 indicates a hitherto overlooked heat transport mechanism in evolved volcanos. Basaltic intrusions into subsided hydrothermally altered basalt melt the hydrated parts, producing a buoyant silicic melt which migrates upwards forming sills at shallow crustal levels which are heat sources for the geothermal system above. This can explain the bimodal behavior of evolved volcanos like Krafla and Askja, with occasional silicic, often phreatic, eruptions but purely basaltic in-between. When substantial amounts of silicic intrusions/magma have accumulated, major basalt intrusion(s) may “ignite” them causing a silicic eruption.

Fracture analysis, hydrothermal mineralization and fluid pathways in the Neogene Geitafell central volcano: insights for the Krafla active geothermal system, Iceland

Volcanoes generate complex seismic wavefields due to their heterogeneous geological structure, making it challenging to obtain accurate reflection images of their interiors. However, understanding the internal structure and dynamics of volcanoes is essential for enhancing monitoring capabilities and improving eruption forecasting. In this study, we apply controlled-source seismic techniques to passive reflection imaging at Krafla volcano, NE Iceland. Krafla is globally recognised as one of the few sites where magma was directly encountered during drilling at the IDDP-1 borehole at a depth of 2.1 km. Using the known magma location as a reference, we employ common-depth-point binning and stacking for preconditioned seismic data from over 300 earthquakes recorded by more than 100 short-period (5 Hz) seismic nodes. At first, we computed theoretical arrival times for various P- and S-wave reflections, including both primary and multiple reflections, using a ray-tracing algorithm and local 1D velocity models. The computational domain was discretized between the surface and a depth of 6 km, using a grid of 80x80x20 m cells. For each grid cell, common-depth-point gathers were generated, and amplitudes were stacked along the reflection trajectories. We further use synthetic waveforms to systematically evaluate the challenges and limitations of this approach in our study area. We observe that the specific distribution of earthquakes and stations causes direct waves (e.g., P- and S-waves) to constructively interfere, creating spurious reflectors in the imaging results. To mitigate this effect, we exclude time windows corresponding to the arrival of direct waves. We also investigate the effect of various waveform attributes—such as absolute amplitudes, envelopes, and their derivatives—on the stacking process and the final imaging results. Preliminary results indicate that the second derivative of seismic trace envelopes might be particularly useful in complex environments characterized by a high degree of incoherent scattering and diverse earthquake source mechanisms. This approach has successfully revealed several discontinuities at shallow depths, offering new insights into the local structure of the Krafla geothermal system.

Natural fracture compressibility and permeability estimation is important for evaluating well performance for wells completed in unconventional hydrocarbon and enhanced geothermal energy systems exhibiting a complex fracture geometry where unpropped and natural fractures contribute to flow. This experimental study compares liquid and gas natural fracture compressibility and permeability hysteresis in low-permeability rocks, with examples from the Montney and Duvernay formations. A diverse suite of core plugs (horizontal), differing in lithology (siltstones/sandstones, organic/clay-rich shales), mineralogy (quartz/clay-rich), helium porosity (2-9%), and permeability (~0.0001-0.001 md) were analyzed. Core plugs were fractured under differential stress inside a biaxial core holder. Gas and liquid fracture permeability measurements were then performed at varying stress (500-4000 psi) under loading and unloading conditions representative of fluid depletion and injection, respectively. Assuming a planar fracture geometry and that the cubic law applies, fracture width and compressibility were then calculated using fracture permeability, stress data, and core plug dimensions. Water and liquid hydrocarbons were used for liquid permeability measurements. Natural fracture compressibility (gas: 5·10−5-5·10−4 psi−1; liquid: 1·10−5-7·10−4 psi−1), permeability (gas: >30 darcy; liquid: <30 darcy), and porosity (gas >8.5%; liquid: >8.5%) were consistently larger for gas than liquid. Interestingly, however, the hysteresis in fracture attributes (compressibility, permeability, and porosity) caused by loading/unloading was consistently larger for liquid than gas. Larger hysteresis for liquids is presumably due to the ‘softening’ effect on fracture asperities under stress, and elevated inelastic reduction in (fracture) roughness for liquids compared to gases. Notably, the average empirical (natural) fracture compressibility value commonly assumed in fracture modeling (~1·10−4 psi−1) falls within the range of measured fracture compressibility values (1·10−5-7·10−4 psi−1). However, experimental fracture compressibility values covered a broad range, as opposed to the widely accepted assumption of ‘average’ fracture compressibility adopted for modeling. Interestingly, for loading and unloading, fracture compressibility followed two distinct paths, regardless of fluid type. Fracture compressibility was consistently larger for loading than unloading. The latter observations suggest that larger degrees of hysteresis in complex fracture regions may occur for liquids than gases, and for injection versus production. Natural (and induced) fracture compressibility and permeability, while important controls on well performance for complex fracture cases, are challenging and time-consuming to measure for low-permeability rocks in the laboratory, particularly over multiple stress cycles. As a result, natural fracture compressibility and permeability hysteresis data are sparse in the literature. For low-permeability rocks, these data have been primarily measured with gas. The developed workflows and provided examples are beneficial for verifying empirical and analytical correlations used for evaluation of fracture compressibility and permeability, and their hysteresis in low-permeability sedimentary rocks.

A fractal discrete fracture network based model was proposed for the gas production prediction from a fractured shale reservoir. Firstly, this model was established based on the fractal distribution of fracture length and a fractal permeability model of shale matrix which coupled the multiple flow mechanisms of slip flow, Knudsen diffusion, surface diffusion, and multilayer adsorption. Then, a numerical model was formulated with the governing equations of gas transport in both a shale matrix and fracture network system and the deformation equation of the fractured shale reservoir. Thirdly, this numerical model was solved within the platform of COMSOL Multiphysics (a finite element software) and verified through three fractal discrete fracture networks and the field data of gas production from two shale wells. Finally, the sensitivity analysis was conducted on fracture length fractal dimension, pore size distribution, and fracture permeability. This study found that cumulative gas production increases up to 113% when the fracture fractal length dimension increases from 1.5 to the critical value of 1.7. The gas production rate declines more rapidly for a larger fractal dimension (up to 1.7). Wider distribution of pore sizes (either bigger maximum pore size or smaller minimum pore size or both) can increase the matrix permeability and is beneficial to cumulative gas production. A linear relationship is observed between the fracture permeability and the cumulative gas production. Thus, the fracture permeability can significantly impact shale gas production.

Reservoir modelling of a fractured reservoir with any dual porosity/permeability simulator requires three basic fracture properties – fracture porosity, permeability, and average fracture spacing – to be provided as part of the reservoir description. Theoretically, any two of these are sufficient to determine the remaining third. In many instances, however, direct measurements on these properties or good pressure test data are missing or unreliable, making it virtually impossible to infer the fracture properties. In a recently completed study on the Raman reservoir in Turkey, the spatial variations of the fracture system properties were estimated using a method developed for this purpose. The technique utilizes reservoir structure and layer net thickness data, production information, and some qualitative geological input on the nature of the fractures. The generated fracture system description was later used in successfully history matching close to 40 years of reservoir performance with a fractured reservoir simulator. This paper presents the principles involved and the methodology that was developed to estimate the required fracture description. Fracture data before and after the history match are compared to show the extent of the modifications that were needed. The proposed technique is suitable for the Raman reservoir and others like it. Its application to another situation may require appropriate modifications.

Synergetic mechanism of fracture properties and system configuration on techno-economic performance of enhanced geothermal system for power generation during life cycle

Summary We propose a new semianalytical method for analyzing flowback water and gas production data to estimate hydraulic fracture (HF) properties and to quantify HF dynamics. The method includes a semianalytical flowback model, a set of two-phase diagnostic plots, and a workflow to evaluate initial fracture volume and permeability, as well as fracture compressibility and permeability modulus. The flowback model incorporates two-phase water and gas flow in both HF and matrix domains and considers variations of fluid and rock properties with pressure. The HF domain is modeled by boundary-dominated flow, whereas an infinite-acting linear flow is assumed for the matrix domain. The flowback model is developed by assigning the variable average pressure in the fracture as the inner boundary condition for matrix according to Duhamel's principle. The average pressure in the fracture and distance of investigation (DOI) in the matrix are calculated from a modified material-balance equation by updating the matrix DOI as well as phase saturation and relative permeability in both the fracture and matrix domains. A modified DOI equation is used for two-phase flow in the matrix, which considers the pressure-dependent fluid and rock properties in pseudotime. The diagnostic plots shed light on the identification of flow regimes during the coupled two-phase flow in both fracture and matrix. The proposed workflow quantifies the HF dynamics through the loss of both fracture volume and fracture permeability by reconciling flowback and long-term production data. The accuracy of the new method is tested against numerical simulations conducted by a commercial numerical simulator. The validation results confirm that the proposed method accurately predicts initial fracture volume, permeability, and permeability modulus. Further, we use production data from a multifractured horizontal well (MFHW) drilled in Marcellus Shale to test the practicality of the proposed method. The results show a significant reduction in fracture volume and permeability during production attributable to the HF closure.

Abstract:To better understand the characteristics of coal pores and their influence on coal reservoirs, coal pores in eight main coalfields of North China were analyzed by mercury porosimetry and scanning electron microscopy (SEM). Fractal characteristics of coal pores (size distribution and structure) were researched using two fractal models: classic geometry and thermodynamics. These two models establish the relationship between fractal dimensions and coal pores characteristics. New results include: (1) SEM imaging and fractal analysis show that coal reservoirs generally have very high heterogeneity; (2) coal pore structures have fractal characteristics and fractal dimensions characteristic of pore structures are controlled by the composition (e.g., ash, moisture, volatile component) and pore parameters (e.g., pore diameter, micro pores content) of coals; (3) the fractal dimensions (D1 and D2) of coal pores have good correlations with the heterogeneity of coal pore structures. Larger fractal dimensions correlate to higher heterogeneity of pore structures. The fractal dimensions (D1 and D2) have strong negative linear correlations with the sorted coefficient of coals (R2=0.719 and 0.639, respectively) that shows the heterogeneity of coal pores; (4) fractal dimension D1 and petrologic permeability of coals have a strong negative exponential correlation (R2=0.82). However, fractal dimension D2 and petrologic permeability of coals have no obvious correlation; and (5) the model of classic geometry is more accurate for fractal characterization of coal pores in coal reservoirs than that of thermodynamics by optimization.

Pore structure heterogeneity is present in reservoir rocks at multiple length scales, which makes it a challenge to optimally assess and integrate into digital rock and pore-scale models, especially for complex reservoir rocks. The fractal nature of reservoir rocks causes variation in their physical properties over multiple length scales. The fractal dimension governs the power law scaling of fractals and has been estimated from experimental measurements and rock images of the pore space to quantify pore structure heterogeneity. Each experimental technique and imaging modality has limitations on the pore structure characteristics and the level of detail it can provide, necessitating combining them for comprehensive pore structure characterization. However, challenges in spatially correlating pore structure heterogeneity at multiple length scales remain. An Apparatus for Pore Examination (APEX), with the highest known pressure and volumetric resolutions (5E-6 psi and 1.3E-10 cc), is proposed to make high-resolution rate-controlled capillary pressure measurements, which reflect comprehensive pore structure and fractal characteristics of the rock. Detrended fluctuation analysis (DFA) of the APEX capillary pressure curve estimates a fractal dimension to describe the spatial correlation in pore structure heterogeneity quantitatively. The rock samples analyzed were approximately 0.5-inch in diameter and 0.5-inch long right circular cylindrical core plugs of the Berea sandstone and Indiana limestone. Amplitude spectra of the APEX capillary pressure curves indicated they were "1/fβ" scaling signals (fractional noises) with self- affine fractal properties and power law correlated statistics. Fractal dimension estimates for the pore structure of both rock samples from the APEX capillary pressure curves and thin section images showed agreement, with lesser than 10% relative differences. Additionally, the fractal dimension estimates agreed (within a 10 % relative difference) with published Berea sandstone and Indiana limestone results from SEM and thin section images. Detrended fluctuation analysis (DFA) of the APEX capillary pressure curves showed that the Berea sandstone had a single pore system with short-range power-law correlated pore structure statistics, indicated by a fractal dimension, D = 2.533. The fractal dimension and amplitude spectrum showed a relatively well-connected pore space with mild pore structure heterogeneity at the pore scale. The Indiana limestone had two pore systems with short-range power-law correlated pore structure statistics indicated by two fractal dimensions, D= 2.735 and D = 2.911. The fractal dimension and amplitude spectrum indicated a poorly connected pore space with smaller pores connecting the larger pores. The results presented in this study showed that high-resolution APEX capillary pressure measurements reflect the fractal characteristics of a reservoir rock's pore structure. In this context, fractal dimensions can be estimated from high-resolution APEX capillary pressure measurements to describe spatial correlation in pore structure heterogeneity quantitatively. The stochastic fractal functions, fractional Brownian motion (fBm) and Lévy Flights can describe the spatial correlation in pore structure heterogeneity of the Berea sandstone and Indiana limestone, respectively. The results can be used to integrate spatially correlated pore structure heterogeneity at the pore and core scales in computational rock models to enhance their predictive capabilities. They can also complement the results from techniques of quantifying heterogeneity in reservoir properties with significant pore structure dependencies, which do not account for their spatial correlation.

The continental shale oil resource in China exhibits significant potential and serves as a crucial strategic alternative to the country’s conventional oil and gas reserves. The efficacy of shale oil exploration and production is heavily contingent upon the heterogeneity of the pore structure within the reservoir. However, there remains a scarcity of research pertaining to the pore structure of continental shale and the factors that influence it. The objective of this study is to provide a quantitative characterization of the heterogeneity exhibited by the continental shale of the Funing Formation in the Gaoyou Sag. In this study, the research focus is directed toward the continental shale of the Funing Formation located in the Gaoyou Sag of the Subei Basin. This paper examines the correlation between the fractal dimension of nuclear magnetic resonance (NMR) and various factors including the total organic carbon (TOC), mineral composition, geochemical parameters, and physical properties, utilizing the principles of fractal dimension theory. The findings indicate that the primary pore types observed in the Funing Formation continental shale are inorganic matrix pores, which encompass dissolution pores, clay mineral intergranular pores, and a limited number of pyrite intergranular pores. By employing a relaxation time cutoff, the NMR fractal dimension can be categorized into two distinct dimensions: the bound-fluid-pore fractal dimension (0.5795~1.3813) and the movable-fluid-pore fractal dimension (2.9592~2.9793). The correlation between mineral composition and the fractal dimension indicates a negative relationship between the fractal dimensions of bound-fluid pores and movable-fluid pores and the content of quartz. The correlation between clay minerals and the fractal dimension indicates a significant negative relationship between the fractal dimensions of bound-fluid pores and movable-fluid pores with illite. There exists a negative correlation between the pore fractal dimension of bound fluid and the content of organic matter, whereas a positive correlation is observed between the pore fractal dimension of mobile fluid and the content of organic matter. The range of maturity of organic matter within the Funing Formation exhibits a relatively limited span, as indicated by the vitrinite reflectance (Ro) values falling between 0.8% and 0.9%. This narrow range of maturity does not exert a substantial influence on the two fractal dimensions. The NMR fractal dimension exhibits a negative correlation with permeability in relation to reservoir physical properties, while the bound-fluid-pore fractal dimension demonstrates a negative correlation with the total porosity. The findings suggest that the NMR fractal dimension can serve as a valuable indicator for evaluating the physical characteristics of reservoirs. The present study successfully examined the pore structure of continental shale through the utilization of nuclear magnetic resonance technology. This innovative technique provides a novel avenue for the assessment of continental shale reservoirs and the investigation of pore heterogeneity on a global scale.

Malignant tumor essentially implies structural heterogeneity. Fractal analysis of medical imaging has a potential to quantify this structural heterogeneity in the tumor AIMS: The purpose of this study is to quantify this structural abnormality in the tumor applying fractal analysis to contrast-enhanced computed tomography (CE-CT) image and to evaluate its biomarker value for predicting survival of surgically treated gastric cancer patients. A total of 108 gastric cancer patients (77 men and 31 women; mean age: 69.1years), who received curative surgery without any neoadjuvant therapy, were retrospectively investigated. Portal-phase CE-CT images were analyzed with use of a plug-in tool for ImageJ (NIH, Bethesda, USA), and the fractal dimension (FD) in the tumor was calculated using a differential box-counting method to quantify structural heterogeneity in the tumor. Tumor FD was compared with clinicopathologic features and disease-specific survival (DSS). High FD value of the tumor significantly associated with high T stage and high pathological stage (P = 0.009, 0.007, respectively). In Kaplan-Meier analysis, patients with higher FD tumors (FD > 0.9746) showed a significantly worse DSS (P = 0.009, log rank). Multivariate analysis demonstrated that tumor FD, T stage, and N stage were independent prognostic factors for DSS. In subset analysis of lymph-node positive gastric cancers, only tumor FD was an independent prognostic factor for DSS. CT fractal analysis can be a useful biomarker for gastric cancer patients, reflecting survival and clinicopathologic features.

The long-term sustainability of fracture conductivity in a geothermal system using proppant will be affected by crushing pressure and geothermal fluids. Previous experiments have shown that for short-term periods, field testing results have indicated some performance improvements and a few experiments for long-term periods have shown that different types of proppants and the crushing test results suggest probable geomechanical degradation of the proppants under the test conditions. So, some proppants, such as ceramics and kryptospheres, showed a significant degree of mechanical strength degradation after exposure to high temperatures and geothermal water formation. In addition, the crushing test does not replicate downhole conditions because the crush test compares the conductivity test and downhole conditions. So, all types of proppants do not crush in the same manner. Sand-based proppants tend to shatter, ceramics tend to cleave, and resin-coated proppant deform as the internal substrate breaks. Moreover, according to the literature review, the EGS projects have used proppants such as quartz sand, ceramic LT, and ceramic HSP. However, in recent years, new types of proppants have been designed to face these challenging conditions. For that reason, supplementary testing is required to comprehensively understand the long-term behavior of the proppants in geothermal reservoirs with low permeability, which we want to use proppants. This investigation analyzes the long-term proppant behavior under high-temperature reservoir conditions and shows that some types of proppants can improve fracture conductivity and support long-term performance in harsh aqueous environments with many thermal cycles on fields such as Utah FORGE or other locations with similar characteristics. So, proppants should work for long-term conductivity and thermal pressurization cycles, between 15000 to 500°F and 5000 to 15000 Psi, respectively. This study presents the results of experimental investigations of crushing tests for different proppants at 9000, 12000, and 15000 psi and the development of a numerical model for hydraulic fracturing design to compare how it affects the fracture permeability with a permanent fracture permeability and variable fracture permeability. Also, it is developed water analyzed to compare the chemical properties before and after combining the proppants with water formation at 260 oC after two weeks. The study focuses on evaluating the permeability drop of the artificially generated fracture throughout its lifetime. The artificial fracture permeability is affected by high reservoir temperature, lithostatic pressure, and chemical components of the water formation. According to previous studies, closure stress and geothermal fluids affect proppants reducing the fracture conductivity for long-term sustainability; instead of keeping the area generated and the high permeability in the artificial fractures. Moreover, the fracture permeability is diminished, and the fracture conductivity and width are reduced, affecting the flow rate and heat extraction. So, different kinds of proppants were evaluated under different closure pressure with a crushing test to determine the percentage of destruction after two weeks under high temperatures (260 °C); new proppants have a high crush resistance and withstand stress cycling to ensure that fracture conductivity and connectivity are sustained long-term to optimize production. Hence, a numerical simulation model was developed to compare economically different scenarios of fracture permeability (permanent and variable), fracture length, fracture width, flow rate, and reservoir temperature to determine the feasibility of developing an EGS project stimulated by HF.

Estimation of wave propagation characteristics around fracture using simulation techniques: T. Kikuchi & M. Abe, Geothermal Science & Technology, 5(1–2), 1995, pp 53–62

Coupled thermo-hydro-mechanical modelling for geothermal doublet system with 3D fractal fracture