Fluid substitution in heavy oil rocks

Heavy oils are defined as having high densities and extremely high viscosities. Due to their viscoelastic behavior the traditional rock physics based on Gassmann theory becomes inapplicable. In this paper, we use effective-medium approach known as coherent potential approximation or CPA as an alternative fluid substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modelled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in the fluid when the solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and allows one to model both sandstones and unconsolidated sands. We test the approach against known solutions. First, we apply CPA to fluid-solid mixtures and compare the obtained estimates with Gassmann results. Second, we compare CPA predictions for solid-solid mixtures with numerical simulations. Good match between the results confirms the applicability of the CPA scheme. We extend the scheme to predict the effective frequency- and temperature-dependent properties of heavy oil rocks. CPA scheme reproduces frequency-dependent attenuation and dispersion which are qualitatively consistent with laboratory measurements and numerical simulations. This confirms that the proposed scheme provides realistic estimates of the properties of rocks saturated with heavy oil

An analytic model for the stress-induced anisotropy of dry rocks

One of the main causes of azimuthal anisotropy in sedimentary rocks is anisotropy of tectonic stresses in the earth's crust. We have developed an analytic model for seismic anisotropy caused by the application of a small anisotropic stress. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behavior is defined by a ratio B of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modeled using the Sayers-Kachanov noninteractive approximation. The model predicts that such anisotropic crack closure yields elliptical anisotropy, regardless of the value of the compliance ratio B. It also predicts the ratio of Thomsen's anisotropy parameters epsilon/gamma as a function of the compliance ratio B and Poisson's ratio of the unstressed rock. A comparison of the model predictions with the results of laboratory measurements indicates a reasonable agreement for moderate magnitudes of uniaxial stress (as high as 30 MPa).These results can be used for differentiating stress-induced anisotropy from that caused by aligned fractures. Conversely, if the cause of anisotropy is known, then the anisotropy pattern allows one to estimate P-wave anisotropy from S-wave anisotropy

Bounds for seismic dispersion and attenuation in poroelastic rocks

Recently, Hashin-Shtrikman bounds for bulk and shear moduli of elastic composites have been extended to the moduli of composite viscoelastic media. Since viscoelastic moduli are complex, the viscoelastic bounds form a closed curve on a complex plane. We apply these general viscoelastic bounds to a particular case of a porous solid saturated with a Newtonian fluid. Our analysis shows that for poroelastic media, the viscoelastic bounds for the bulk modulus are represented by a semi-circle and a segment of the real axis, connecting formal HS bounds (computed for an inviscid fluid). Furthermore, these bounds are independent of frequency and realizable. We also show that these viscoelastic bounds account for viscous shear relaxation and squirt-flow dispersion, but do not account for Biot's global flow dispersion

A new model for squirt-flow attenuation and dispersion in fluid-saturated rocks

We develop a new simple model of squirt-flow model attenuation and dispersion, in which most parameters can be independently measured or estimated from measurements. The pore space of the rock is assumed to consist of stiff porosity and compliant (or soft) pores present at grain contacts. The effect of isotropically distributed soft pores is modeled by considering pressure relaxation in a disk-shaped gap between adjacent grains. This derivation gives the complex and frequency-dependent effective bulk and shear moduli of a rock, in which the soft pores are liquid-saturated and stiff pores are dry. The resulting squirt model is consistent with Gassmann s and Mavko-Jizba equations at low and high frequencies, respectively

Finite element modelling of the effective elastic properties of partially saturated rocks

Simulation of effective physical properties from microtomographic 3D images of porous structures allows one to relate properties of rocks directly to their microstructure. A static FEM code has been previously used to estimate effective elastic properties of fully saturated monomineralic (quartz) rock under wet and dry conditions. We use the code to calculate elastic properties under partially saturated conditions. The numerical predictions are compared to the Gassmann theory combined with Wood's formula (GW) for a mixture of pore fluids, which is exact for a monomineralic macroscopically homogeneous porous medium. Results of the numerical simulations performed for two Boolean sphere pack distributions show significant deviation from the GW limit and depend on the spatial distribution of fluids. This is shown to be a numerical artefact caused by incomplete equilibration of fluid pressure, which is primarily due to insufficient spatial resolution. To investigate the effect of pore-size and pore geometry, we perform FEM simulations for a model with regular pore geometry, where all pore channels have the same size and shape. Accuracy of these simulations increases with the total cross-section area of the channels and the size of individual channels. For the case where the total cross-section of the channels is large enough (on the same order as total porosity), there is a minimum of 4 voxels per channel diameter required for adequate fluid pressure equilibration throughout the pore space. Increasing the spatial resolution of the digital models reduces the discrepancy between the simulations and theory, but unfortunately increases the memory and CPU requirements of the simulations

Developing an integrated long-term monitoring program for Darwin Harbour - Water quality pilot project WP2: Intra-annual water quality variability

The main purpose of the Intra-annual Water Quality Variability project is to examine temporal variability of surface water quality in Darwin Harbour to determine whether the current May and October survey periods are suitably representative to summarise Darwin Harbour water quality as well as to explore other design options to improve the capacity of the monitoring program to detect long-term changes in water quality. A project-specific field campaign was developed to collect surface water quality data over the period from May 2017 to October 2018 during neap tidal events along transect lines in the key areas of the Harbour: (1) Elizabeth River and East Arm (EA), (2) Blackmore River and Middle Arm (MA) and (3) Outer Harbour (OH). Physico-chemical parameters and chlorophyll fluorescence were measured along each transect using flow cell monitoring method that produced approximately 500 data points per 100 m. Additionally, intermittent grab sampling was undertaken for nutrients and chlorophyll a at density of approximately one per 2.5 km. Overall, the study produced 85 transects for each of 18 water quality parameters on 44 dates. To identify trends in spatial variation, the EA and MA transects were further subdivided into three polygons resulting in a total of 210 sub-transects for each parameter. Detailed parameter-specific assessments of surface water quality focussed on variability between consecutive days, months and four seasons. Hypothesis tests of similar means (ANOVA) and similar medians (Kruskal-Wallis) were conducted to investigate the difference in variability patterns for each parameter and each spatial area within neap tide periods.1 Summary -- 2 Introduction -- 2.1 Background -- 2.1.1 Darwin Harbour: physical characteristics -- 2.1.2 Water quality in Darwin Harbour -- 2.1.3 DENR WQMP -- 2.2 Study Objectives -- 3 Method. -- 3.1 General approach -- 3.2 Field stations and monitoring dates -- 3.3 Measured parameters -- 3.4 Seasons -- 3.5 Field techniques -- 3.5.1 In-situ field measurements -- 3.5.2 Sample collection and analysis -- 3.6 Data analysis and visualisation -- 3.6.1 Data visualising techniques -- 3.6.2 Statistical parameters -- 3.6.3 Hypothesis testing -- 4 Results and discussion -- 4.1 ...... Depth -- 4.2 ...... Physico-chemical results -- 4.2.1 ........ Water temperature -- 4.2.1.1 ....... East Arm -- 4.2.1.2 Middle Arm -- 4.2.1.3 Outer Harbour -- 4.2.2 ........ Salinity and electrical conductivity -- 4.2.2.1 East Arm -- 4.2.2.2 Middle Arm -- 4.2.2.3 Outer Harbour -- 4.2.3 pH -- 4.2.3.1 East Arm -- 4.2.3.2 Middle Arm -- 4.2.3.3 Outer Harbour -- 4.2.4 Turbidity -- 4.2.4.1 East Arm -- 4.2.4.2 Middle Arm -- 4.2.4.3 Outer Harbour -- 4.2.5 Dissolved oxygen -- 4.2.5.1 East Arm -- 4.2.5.2 Middle Arm -- 4.2.5.3 Outer Harbour -- 4.3 .Nutrients - Nitrogen and Phosphorus -- 4.3.1 Summary statistics -- 4.3.2 Ammonia -- 4.3.2.1 East Arm -- 4.3.2.2 Middle Arm -- 4.3.2.3 Outer Harbour -- 4.3.3 Oxides of nitrogen -- 4.3.3.1 East Arm -- 4.3.3.2 .Middle Arm -- 4.3.3.3 Outer Harbour -- 4.3.4 Total filterable (dissolved) nitrogen -- 4.3.4.1 East Arm -- 4.3.4.2 Middle Arm -- 4.3.4.3 Outer Harbour -- 4.3.5 Total nitrogen -- 4.3.5.1 East Arm -- 4.3.5.2 Middle Arm -- 4.3.5.3 Outer Harbour -- 4.3.6 Soluble reactive phosphorus -- 4.3.6.1 East Arm -- 4.3.6.2 Middle Arm -- 4.3.6.3 Outer Harbour -- 4.3.7 Total filterable (dissolved) phosphorus -- 4.3.7.1 East Arm -- 4.3.7.2 Middle Arm -- 4.3.7.3 Outer Harbour -- 4.3.8 Total phosphorus -- 4.3.8.1 East Arm -- 4.3.8.2 Middle Arm -- 4.3.8.3 Outer Harbour -- 4.4 Phytoplankton biomass -- 4.4.1 Summary statistics -- 4.4.2 Chlorophyll -- 4.4.2.1 East Arm -- 4.4.2.2 Middle Arm -- 4.4.2.3 Outer Harbour -- 5 Summary of results -- 5.1 Parameter-specific trends -- 5.1.1 Physico-chemical parameters -- 5.1.2 Nutrients -- 5.1.3 Algal biomass -- 5.1.4 Coefficient of variation -- 5.1.4.1 Consecutive days -- 5.1.4.2 Monthly and seasonal variation -- 5.2 Trends for combined water quality -- 5.2.1 Monthly and seasonal variation -- 5.2.2 Spatial variability -- 5.3 Variability in natural factors controlling water quality -- 5.4 Study limitations -- 6 Conclusions and recommendations -- Recommendations -- 7 References -- 8 Acknowledgement -- 9 Appendix A: Metocean and hydrological conditions -- 9.1 Data sources -- 9.2 Rainfall -- 9.3 River discharge -- 9.4 Wind -- 9.5 Tides -- 9.6 Water temperature -- 10 Appendix B: Parameters vs downstream distance -- 10.1 Water temperature -- 10.2 Salinity -- 10.3 Turbidity -- 10.4 Dissolved oxygen -- 10.5 Ammonia -- 10.6 Oxides of nitrogen -- 10.7 Soluble reactive phosphorus -- 10.8 Chlorophyll a -- 11 Appendix C: Statistical tests-monthly variation -- 11.1 Water temperature -- 11.2 Salinity and electrical conductivity -- 11.3 pH -- 11.4 Turbidity -- 11.5 Dissolved oxygen -- 11.6 Ammonia -- 11.7 Oxides of nitrogen -- 11.8 Total filterable nitrogen -- 11.9 Total nitrogen -- 11.10 Soluble reactive phosphorus -- 11.11 Total filterable phosphorus -- 11.12 Total phosphorus -- 11.13 ChlorophyllMade available via the Publications (Legal Deposit) Act 2004 (NT

Theoretical and numerical modelling of the effect of viscous and viscoelastic fluids on elastic properties of saturated rocks

Rock physics is an essential link connecting seismic data to the properties of rocks and fluids in the subsurface. One of the most fundamental questions of rock physics is how to model the effects of pore fluids on rock velocity and density. Contemporary scientific computing allows geophysicists to conduct extremely complex virtual (computational) experiments on realistic digital representations of complex porous media, and thus directly relate the measurable properties of the media to their microstructure and saturation. Computational (digital) rock physics can also serve as an effective tool in examining new and existing rock physics models. The finite element method (FEM) has been proved effective in simulations of the linear elastic properties of porous rock under static conditions. In this thesis, FEM is used to study the effect of patchy saturation on elastic velocities of digital images of rocks. However, FEM belongs to a group of grid methods, and its accuracy is limited by discretization errors. This can cause errors in rock property predictions and needs to be thoroughly examined. In this thesis, a test scenario based on rigorous theories for grid-based methods such as FEM is developed, which allows establishing optimal computational parameters in terms of accuracy of the results and time cost of computations.Gassmann’s equations are the most widely used relations to predict velocity changes resulting from different pore fluid saturations. This problem is also known as fluid substitution. Despite the popularity of Gassmann’s equations and their incorporation in most software packages for seismic reservoir interpretation, important aspects of these equations such as sensitivity to microheterogeneity has not been thoroughly examined. In this thesis, the sensitivity of Gassmann’s equations to microheterogeneity is estimated for different quartz/clay porous mixtures using computational (FEM) simulations. The results of this study suggest that the accuracy of Gassmann’s fluid substitution remains adequate for a wide variety of highly porous rocks even if the contrast between the elastic properties of mineral constituents is large.While Gassmann’s fluid substitution is robust for rocks saturated with Newtonian fluids (brine, gas, light oil), it breaks down for viscoelastic fluids such as heavy oils. An alternative fluid substitution scheme for rocks saturated with viscoelastic fluids based on self-consistent effective medium theory is proposed in this thesis. Comparison with laboratory measurements shows that the scheme realistically estimates the frequency- and temperature dependent properties of heavyoil rocks and can be used for practical applications.A useful tool for modelling and estimation of properties of rocks with arbitrary or unknown microstructure are rigorous bounds on elastic moduli. The common elastic bounding methods such as Hashin-Shtrikman bounds are not applicable for heavy-oil rocks because of viscoelastic rheology of heavy oils. In this work, it is demonstrated that the viscoelastic bounding method of Milton and Berryman for the effective shear modulus of a two phase three-dimensional isotropic composite provides rigorous bounds for dispersion and attenuation of elastic waves in heavy-oil rocks. In particular, computation of these bounds shows that dispersion and attenuation in a rock saturated with a fluid (viscous or viscoelastic) can be much stronger than in the free fluid. This phenomenon is caused by wave-induced fluid flow relative to the solid. At sonic and ultrasonic frequencies, dispersion and attenuation appears to be dominated by the local (pore-scale) flow between pores of different shapes and orientations. The Mavko and Jizba expressions for the so-called unrelaxed frame bulk and shear moduli are one of the most popular quantitative models of squirt dispersion. However, these expressions are limited to liquidsaturated rocks and high frequency. In this thesis, The Mavko-Jizba relations are generalized to gas-saturated rocks. Furthermore, dispersion and attenuation is computed using a new squirt flow model, presented in this thesis. All the parameters in this model can be independently measured or estimated from measurements. The model gives complex frequency- and pressure-dependent effective bulk and shear moduli of a rock consistent with laboratory measurements.Variation of elastic properties of rocks with pressure is often modelled using penny-shaped or spheroidal cracks as idealization of real crack/pore geometry. In this doctorate, the validity of this approach is analysed by extracting the ratios of shear to bulk stress sensitivity coefficients, and normal to tangential compliances from ultrasonic measurements on a number of dry sandstone samples. The ratios show large scatter and, for a large number of dry sandstone samples, are not consistent with spheroidal crack theory. This inconsistency results in significantly different estimates of crack density from bulk and shear moduli, and in deviation of predicted pressure variation of Poisson’s ratio from the measured data

Developing an integrated long-term monitoring program for Darwin Harbour - Water Quality Pilot Project WP1 - Neap Tide Trial

The main purpose of WP1 is to determine the optimal tide-based sampling conditions for long-term surface water quality monitoring, and thereby improve the capacity of the monitoring program to detect changes in water quality stressor and response parameters that are caused by anthropogenic pressures. This includes testing the suitability of the existing monitoring protocol used by the DENR WQMP, which assumes that monitoring over a 3-hour window centred on dry season high neap tide (<3 m) is an effective approach for collecting consistent long-term data sets for detection of long-term change in water quality in Darwin Harbour. A project-specific field campaign was developed to collect surface water quality data during three discrete periods coinciding with neap tides in the 2017 dry season months (June, August and September), at four monitoring sites, along the natural estuarine gradient in the area of East Arm and the Elizabeth River estuary. The data were collected over six hours at time intervals between 1 to 30 minutes. A total of 20 parameters were collected at each site and on three discrete dates. The collected data sets included physico-chemical parameters, nutrients and parameters representing algal biomass. Detailed parameter-specific assessments of neap tide surface water quality were undertaken using project-specific data analysis methodology. Data analyses focused on the effects of intra-seasonal variability and tidal range, spatial variability, monitoring window size and tidal flows (flood/ebb) on water quality variability.1 Summary -- 2 Introduction -- 2.1 Background -- 2.1.1 Darwin Harbour: physical characteristics -- 2.1.2 Water quality in Darwin Harbour -- 2.1.3 DENR WQMP -- 2.2 Study Objectives -- 3 Method -- 3.1 General approach -- 3.2 Field stations and neap tide dates -- 3.2.1 Measured parameters -- 3.3 Tidal range -- 3.4 Field techniques -- 3.4.1 .In-situ field measurements -- 3.4.2 Sample collection and analysis -- 3.5 Data analysis and visualisation -- 3.5.1 Monitoring windows -- 3.5.2 Data visualising techniques -- 3.5.3 Statistical parameters -- 3.5.3.1 Coefficient of variation and mean -- 3.5.3.2 Standard errors -- 3.5.4 Hypothesis testing -- 3.5.4.1 Wilcoxon rank sum test -- 3.5.4.2 Ansari-Bradley test -- 3.5.4.3 Analysis of variance -- 3.5.5 Principal component analysis -- 3.5.6 Generalised linear mixed modelling -- 4 Results and discussion -- 4.1 Explanatory parameters -- 4.1.1 Depth -- 4.1.2 Current speed -- 4.2 Physico-chemical results -- 4.2.1 Summary statistics -- 4.2.2 Surface water temperature -- 4.2.2.1 Intra-seasonal variability -- 4.2.2.2 Spatial trend -- 4.2.2.3 Monitoring window assessment -- 4.2.2.3.1 Tidal (flood/ebb) variability -- 4.2.3 Salinity and electrical conductivity -- 4.2.3.1 Intra-seasonal variability -- 4.2.3.2 Spatial trend -- 4.2.3.3 Monitoring window assessment -- 4.2.3.3.1 Tidal (flood/ebb) variability -- 4.2.4 pH -- 4.2.4.1 Intra-seasonal variability -- 4.2.4.2 Spatial trend -- 4.2.4.3 Monitoring window assessment -- 4.2.4.3.1 Tidal (flood/ebb) variability -- 4.2.5 Turbidity -- 4.2.5.1 Intra-seasonal variability -- 4.2.5.2 Spatial trend -- 4.2.5.3 Monitoring window assessment -- 4.2.5.3.1 Tidal (flood/ebb) variability -- 4.2.6 Dissolved oxygen -- 4.2.6.1 Intra-seasonal variability -- 4.2.6.2 Spatial trend -- 4.2.6.3 Monitoring window assessment -- 4.2.6.3.1 Tidal (flood/ebb) variability -- 4.3 Nutrients ? Nitrogen and Phosphorus -- 4.3.1 Anthropogenic sources of nutrients in the study area -- 4.3.2 Summary statistics -- 4.3.3 Ammonia -- 4.3.3.1 Intra-seasonal variability -- 4.3.3.2 Spatial trend -- 4.3.3.3 Monitoring window assessment -- 4.3.3.3.1Tidal (flood/ebb) variability -- 4.3.4 Oxides of nitrogen -- 4.3.4.1 Intra-seasonal variability -- 4.3.4.2 Spatial trend -- 4.3.4.3 Monitoring window assessment -- 4.3.4.3.1 Tidal (flood/ebb) variability -- 4.3.5 Total filterable (dissolved) nitrogen -- 4.3.5.1 Intra-seasonal variability -- 4.3.5.2 Spatial trend -- 4.3.5.3 Monitoring window assessment -- 4.3.5.3.1 Tidal (flood/ebb) variability -- 4.3.6 Total nitrogen -- 4.3.6.1 Intra-seasonal variability -- 4.3.6.2 Spatial trend -- 4.3.6.3 Monitoring window assessment -- 4.3.6.3.1 Tidal (flood/ebb) variability -- 4.3.7 Soluble reactive phosphorus as P -- 4.3.7.1 Intra-seasonal variability -- 4.3.7.2 Spatial trend -- 4.3.7.3 Monitoring window assessment -- 4.3.7.3.1 Tidal (flood/ebb) variability -- 4.3.8 Total filterable (dissolved) phosphorus -- 4.3.8.1 Intra-seasonal variability -- 4.3.8.2 Spatial trend -- 4.3.8.3 Monitoring window assessment -- 4.3.8.3.1. Tidal (flood/ebb) variability -- 4.3.9 Total phosphorus -- 4.3.9.1 Intra-seasonal variability -- 4.3.9.2 Spatial trend -- 4.3.9.3 Monitoring window assessment -- 4.3.9.3.1 Tidal (flood/ebb) variability -- 4.4 Phytoplankton biomass -- 4.4.1 Summary statistics -- 4.4.2 Chlorophyll -- 4.4.2.1 Intra-seasonal variability -- 4.4.2.2 Spatial trend -- 4.4.2.3 Monitoring window assessment -- 4.4.2.3.1 Tidal (flood/ebb) variability -- 4.4.3 Euphotic depth -- 4.4.3.1 Intra-seasonal variability -- 4.4.3.2 Spatial trend -- 4.4.3.3 Monitoring window assessment -- 4.4.3.3.1 Tidal (flood/ebb) variability -- 5 Summary of results -- 5.1 Coefficient of variation -- 5.2 Variability trends -- 5.2.1 Physico-chemical parameters -- 5.2.2 Nutrients -- 5.2.3 Algal biomass -- 5.3 Principal component analysis -- 5.3.1 Intra-seasonal variability -- 5.3.2 Spatial variability -- 5.3.3 Windows -- 5.3.4 Windows-tides -- 5.4 Study limitations -- 6 Conclusions and recommendations -- 7 References -- 8 Acknowledgement -- 9 Appendix A: Current speed analyses for nutrients -- 9.1 Ammonia -- 9.2 Oxides of nitrogen -- 9.3 Total dissolved (filterable) nitrogen -- 9.4 Total nitrogen -- 9.5 Soluble reactive phosphorus -- 9.6 Total dissolved (filterable) phosphorus -- 9.7 Total phosphorus -- 10 Appendix B: Generalised linear mixed model results for nutrients -- 10.1 Ammonia -- 10.2 Oxides of nitrogen -- 10.3 Total dissolved (filterable) nitrogen -- 10.4 Total nitrogen -- 10.5 Soluble reactive phosphorus -- 10.6 Total dissolved (filterable) phosphorus -- 10.7 Total phosphate -- 11 Appendix C: Dry season 2017 -- 12 Appendix D: Elizabeth river stream discharge dataMade available by the Library & Archives NT via the Publications (Legal Deposit) Act 2004 (NT)

Finite element modelling of Gassmann fluid substitution of heterogeneous rocks

The traditional method of fluid substitution requires the rock to be microhomogeneous with a fully connected porespace that ensures hydraulic equilibrium of the pore fluid. These assumptions may be violated for multimineral rocks, such as shaley sediments, due to a large contrast in elastic properties of the host mineral and shale, and due to the ability of clay to inhibit the movement of fluids. In this paper, we investigate the sensitivity of Gassmann’s equation to microheterogeneity for different quartz/clay mixtures using a numerical approach. In order to test the accuracy of Gassmann’s predictions, we utilize a scheme, which combines Gassmann’s equation in its traditional and generalized form with numerical experiments. For a simple double shell model, we show that the accuracy of Gassmann’s equation depends significantly on contrast in elastic properties of the solid constituents. With larger contrast, the common mineral-mixing rules introduce larger errors into the predictions. However, verification of Gassmann’s theory for periodic spheres models with different shape and location of clay show that the theory remains adequate for these more realistic high porous structures with a large contrast between the elastic properties of mineral phases