Fluid sensitivity study of elastic parameters in low-medium porosity and permeability reservoir rocks

In this article, based on the acoustic measurements of core samples obtained from the low to medium porosity and permeability reservoirs in the WXS Depression, the densities and P and S wave velocities of these core samples were obtained. Then based on these data, a series of elastic parameters were computed. From the basic theory and previous pore fluid research results, we derived a new fluid identification factor (F). Using the relative variations, A_g/w and A_o/w, of the elastic parameters between gas and water saturated samples and between oil and water saturated samples, λρ, σ _HSFIF, Kρ, λρ − 2μρ, and F as quantitative indicators, we evaluate the sensitivity of the different fluid identification factors to identify reservoir fluids and validate the effects by crossplots. These confirm that the new fluid identification factor (F) is more sensitive for distinguishing oil and water than the traditional method and is more favorable for fliud identification in low to medium porosity and permeability reservoirs.     

Quantitative detection of fluid distribution using time-lapse seismic

Although previous seismic monitoring studies have revealed several relationships between seismic responses and changes in reservoir rock properties, the quantitative evaluation of time‐lapse seismic data remains a challenge. In most cases of time‐lapse seismic analysis, fluid and/or pressure changes are detected qualitatively by changes in amplitude strength, traveltime and/or Poisson's ratio. We present the steps for time‐lapse seismic analysis, considering the pressure effect and the saturation scale of fluids. We then demonstrate a deterministic workflow for computing the fluid saturation in a reservoir in order to evaluate time‐lapse seismic data. In this approach, we derive the physical properties of the water‐saturated sandstone reservoir, based on the following inputs: V_P, V_S, ρ and the shale volume from seismic analysis, the average properties of sand grains, and formation‐water properties. Next, by comparing the in‐situ fluid‐saturated properties with the 100% formation‐water‐saturated reservoir properties, we determine the bulk modulus and density of the in‐situ fluid. Solving three simultaneous equations (relating the saturations of water, oil and gas in terms of the bulk modulus, density and the total saturation), we compute the saturation of each fluid. We use a real time‐lapse seismic data set from an oilfield in the North Sea for a case study.     

Correlation of vertical electrical sounding and electrical borehole log data for groundwater exploration

We have correlated the longitudinal unit conductance CL obtained from interpreted vertical electrical sounding data with the formation resistivity R_t and the formation resistivity factor F, obtained by carrying out electrical borehole logging. Interpreted geophysical data of eleven soundings and two electrical borehole log records are used for the analysis. The geophysical data used were acquired in a sedimentary basin. The study area is called Lower Maner Basin located in the province of Andhra Pradesh, India. Vertical electrical soundings were carried out using a Schlumberger configuration with half current electrode separation varying from 600–1000 m. For logging the two boreholes, a Widco logger‐model 3200 PLS was used. True formation resistivity R_t was calculated from a resistivity log. Formation resistivity factor F was also calculated at various depths using R_t values. An appreciable inverse relation exists between the correlated parameters. The borehole resistivity R_t and the formation resistivity factor F decrease with the increase in the longitudinal unit conductance CL. We have shown the use of such a relation in computing borehole resistivity R_t and formation resistivity factor F at sites that posses only vertical electrical sounding data, with a fair degree of accuracy. Validation of the correlation is satisfactory. Scope for updating the correlation is discussed. Significance and applications of the relation for exploration of groundwater, namely to update the vertical electrical sounding data interpretation by translating the vertical electrical sounding data into electrical borehole log parameters, to facilitate correlations studies and to estimate the porosity (φ), permeability (K) and water saturation S_w of water bearing zones are discussed.     

Lattice-Boltzmann simulations of the capillary pressure–saturation–interfacial area relationship for porous media

Hysteresis in the relationship between capillary pressure (P_c), wetting phase saturation (S_w) and nonwetting–wetting interfacial area per volume (a_nw) is investigated using multiphase lattice-Boltzmann simulations of drainage and imbibition in a glass bead porous system. In order to validate the simulations, the P_c–S_w and a_nw–S_w main hysteresis loops were compared to experimental data reported by Culligan et al. [Culligan KA, Wildenschild D, Christensen BS, Gray WG, Rivers ML, Tompson AB. Interfacial area measurements for unsaturated flow through porous media. Water Resour Res 2004;40:W12413]. In general, the comparison shows that the simulations are reliable and capture the important physical processes in the experimental system. P_c–S_w curves, a_nw–S_w curves and phase distributions (within the pores) show good agreement during drainage, but less satisfactory agreement during imbibition. Drainage and imbibition scanning curves were simulated in order to construct P_c–S_w–a_nw surfaces. The root mean squared error (RMSE) and mean absolute error (MAE) between drainage and imbibition surfaces was 0.10 mm⁻¹ and 0.03 mm⁻¹, respectively. This small difference indicates that hysteresis is virtually nonexistent in the P_c–S_w–a_nw relationship for the multiphase system studied here. Additionally, a surface was fit to the main loop (excluding scanning curves) of the drainage and imbibition P_c–S_w–a_nw data and compared to the surface fit to all of the data. The differences between these two surfaces were small (RMSE = 0.05 mm⁻¹ and MAE = 0.01 mm⁻¹) indicating that the P_c–S_w–a_nw surface is adequately represented without the need for the scanning curve data, which greatly reduces the amount of data required to construct the non-hysteretic P_c–S_w–a_nw surface for this data.     

Recharge,upflux and water table response for shallow water table conditions in southwest Florida

A disproportionate increase or decrease in water table in response to minor water input or drainage is observed in shallow water table conditions inside drainage lysimeters. This increase happens because the capillary fringe of the shallow water table reaches up to or near the surface (Wieringermeer effect). The correlations between water table level changes and rainfall, seepage irrigation, drip irrigation, and drainage were analysed. Correlations with rainfall, seepage irrigation, and drainage were high (R² ranged from 0·46 to 0·97). Drip irrigation had low correlations due to the low rates of application (R² ranged from 0·26 to 0·44). Conventional methods of calculating recharge, such as multiplying the specific yield with the water table fluctuations, cannot be used for Wieringermeer effect situations. A method using water balance data and soil moisture at different depths in the lysimeters was developed to estimate recharge and upflux. The recharge results were used to develop the apparent specific yield S_ya, which could be used to calculate consequent recharge events from water table fluctuation data. Combining the water table fluctuation relationships developed with the S_ya value will allow the prediction of recharge from rainfall and irrigation events without the need for soil moisture equipment. Copyright © 2005 John Wiley & Sons, Ltd.     

Estimation of LNAPL saturation in fine sand using time-domain reflectometry / Estimation de la saturation en LPNAL dans du sable fin grâce à la réflectométrie en domaine temporel

Abstract

Abstract Recently, substantial progress has been made in detection and observation of non-aqueous phase liquids (NAPLs) in the subsurface using different experimental techniques. However, there is still a lack of appropriate direct methods to measure the saturation of NAPL (θ_NAPL). This paper provides a guide for estimating θ_NAPL and water content (θ _w ) in unsaturated and saturated sand based on direct measurements of soil dielectric constant (K_a ) and electrical conductivity (σ _a ) using time domain reflectometry (TDR). The results show that the previously used dielectric mixing model fails to predict θ_NAPL in the case of a four-phase system. A new methodology is suggested and exemplified by showing that the measured K_a gives accurate estimation of θ_NAPL for a three-phase system while in a four-phase system, both θ _a and K_a need to be measured. The results show that using the suggested methodology, accurate predictions of θ _w (R ² = 0.9998) and θ_NAPL lower than 0.20 m³ m^-3 (average R ² = 0.9756) are possible.     

Dimensional analysis of two-phase flow including a rate-dependent capillary pressure–saturation relationship

The macroscopic modelling of two-phase flow processes in subsurface hydrosystems or industrial applications on the Darcy scale usually requires a constitutive relationship between capillary pressure and saturation, the P_c(S_w) relationship. Traditionally, it is assumed that a unique relation between P_c and S_w exists independently of the flow conditions as long as hysteretic effects can be neglected. Recently, this assumption has been questioned and alternative formulations have been suggested. For example, the extended P_c(S_w) relationship by Hassanizadeh and Gray [Hassanizadeh SM, Gray WG. Mechanics and thermodynamics of multiphase flow in porous media including interphase boundaries. Adv Water Resources 1990;13(4):169–86] proposes that the difference between the phase pressures to the equilibrium capillary pressure is a linear function of the rate of change of saturation, thereby introducing a constant of proportionality, the coefficient τ. It is desirable to identify cases where the extended relationship needs to be considered. Consequently, a dimensional analysis is performed on the basis of the two-phase balance equations. In addition to the well-known capillary and gravitational number, the dimensional analysis yields a new dimensionless number. The dynamic number Dy quantifies the ratio of dynamic capillary to viscous forces. Relating the dynamic to the capillary as well as the gravitational number gives the new numbers DyC and DyG, respectively. For given sets of fluid and porous medium parameters, the dimensionless numbers Dy and DyC are interpreted as functions of the characteristic length and flow velocity. The simulation of an imbibition process provides insight into the interpretation of the characteristic length scale. The most promising choice for this length scale seems to be the front width. We conclude that consideration of the extended P_c(S_w) relationship may be important for porous media with high permeability, small entry pressure and high coefficient τ when systems with a small characteristic length (e.g. steep front) and small characteristic time scale are under investigation.     

Kinematic stationary geodynamo models with separated toroidal and poloidal motions

Abstract

This paper is concerned with a three-dimensional spherical model of a stationary dynamo that consists of a convective layer with a simple poloidal flow of the S^2c ₂ kind between a rotating inner body core and solid outer shell. The rotation of the inner core and the outer shell means that there are regions of concentrated shear or differential rotation at the convective layer boundaries. The induction equation for the inside of the convective layer was solved numerically by the Bullard-Gellman method, the eigenvalue of the problem being the magnetic Reynolds number of the poloidal flow (R _M2) and it was assumed that the magnetic Reynolds number of the core (R _M1) and of the shell (R _M3) were prescribed parameters. Hence R _M2 was studied as a function of R _M1 and R _M3, along with the orientation of the rotation axis, the radial dependence of the poloidal velocity and the relative thickness of the layers for the three different situations, (i) the core alone rotating, (ii) the shell alone rotating and (iii) the core and the shell rotating together. In all three cases it was found that, at definite orientations of the rotation axis, there is a good convergence of both the eigenvalues and the eigenfunctions of the problem as the number of spherical harmonics used to represent the problem increases. For R _M1 =R _M3= 10³, corresponding to the westward drift velocity and the parameters of the Earth's core, the critical values of R _M2 are found to be three orders of magnitude lower than R _M1, R _M3 so that the poloidal flow velocity sufficient for maintaining the dynamo process is 10-20 m/yr. With only the core or the shell rotating, the velocity field generally differs little from the axially symmetric case. However, for R _M2 (or R _M3) lying in the range 10² to 10⁵, the self-excitation condition is found to be of the form R _M2˙R ^½ _M1=constant (or R _M2˙R^½ _M3=constant) and the solution does not possess the properties of the Braginsky near-axisymmetric dynamo. We should expect this, in particular, in the Braginsky limit R _M2˙R^?½; _M1=constant.

An analysis of known three-dimensional dynamo models indicates the importance of the absence of mirror symmetry planes for the efficient generation of magnetic fields.     

Alternative analysis of transient infiltration experiment to estimate soil water repellency

The repellency index (RI) defined as the adjusted ratio between soil‐ethanol, S_e, and soil‐water, S_w, sorptivities estimated from minidisk infiltrometer experiments has been used instead of the widely used water drop penetration time and molarity of ethanol drop tests to assess soil water repellency. However, sorptivity calculated by the usual early‐time infiltration equation may be overestimated as the effects of gravity and lateral capillary are neglected. With the aim to establish the best applicative procedure to assess RI, different approaches to estimate S_e and S_w were compared that make use of both the early‐time infiltration equation (namely, the 1 min, S1, and the short‐time linearization approaches), and the two‐term axisymmetric infiltration equation, valid for early to intermediate times (namely, the cumulative linearization and differentiated linearization approaches). The dataset included 85 minidisk infiltrometer tests conducted in three sites in Italy and Spain under different vegetation habitats (forest of Pinus pinaster and Pinus halepensis, burned pine forest, and annual grasses), soil horizons (organic and mineral), postfire treatments, and initial soil water contents. The S1 approach was inapplicable in 42% of experiments as water infiltration did not start in the first minute. The short‐time linearization approach yielded a systematic overestimation of S_e and S_w that resulted in an overestimation of RI by a factor of 1.57 and 1.23 as compared with the cumulative linearization and differentiated linearization approaches. A new repellency index, RI_s, was proposed as the ratio between the slopes of the linearized data for the wettable and hydrophobic stages obtained by a single water infiltration test. For the experimental conditions considered, RI_s was significantly correlated with RI and WDPT. Compared with RI, RI_s includes information on both soil sorptivity and hydraulic conductivity and, therefore, it can be considered more physically linked to the hydrological processes affected by soil water repellency.     

The moment magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> and the energy magnitude <Emphasis Type="Italic">M</Emphasis><Subscript>e</Subscript>: common roots and differences

Starting from the classical empirical magnitude-energy relationships, in this article, the derivation of the modern scales for moment magnitude M _w and energy magnitude M _e is outlined and critically discussed. The formulas for M _w and M _e calculation are presented in a way that reveals, besides the contributions of the physically defined measurement parameters seismic moment M ₀ and radiated seismic energy E _S, the role of the constants in the classical Gutenberg–Richter magnitude–energy relationship. Further, it is shown that M _w and M _e are linked via the parameter Θ = log(E _S/M ₀), and the formula for M _e can be written as M _e = M _w + (Θ + 4.7)/1.5. This relationship directly links M _e with M _w via their common scaling to classical magnitudes and, at the same time, highlights the reason why M _w and M _e can significantly differ. In fact, Θ is assumed to be constant when calculating M _w. However, variations over three to four orders of magnitude in stress drop Δσ (as well as related variations in rupture velocity V _R and seismic wave radiation efficiency η _R) are responsible for the large variability of actual Θ values of earthquakes. As a result, for the same earthquake, M _e may sometimes differ by more than one magnitude unit from M _w. Such a difference is highly relevant when assessing the actual damage potential associated with a given earthquake, because it expresses rather different static and dynamic source properties. While M _w is most appropriate for estimating the earthquake size (i.e., the product of rupture area times average displacement) and thus the potential tsunami hazard posed by strong and great earthquakes in marine environs, M _e is more suitable than M _w for assessing the potential hazard of damage due to strong ground shaking, i.e., the earthquake strength. Therefore, whenever possible, these two magnitudes should be both independently determined and jointly considered. Usually, only M _w is taken as a unified magnitude in many seismological applications (ShakeMap, seismic hazard studies, etc.) since procedures to calculate it are well developed and accepted to be stable with small uncertainty. For many reasons, procedures for E _S and M _e calculation are affected by a larger uncertainty and are currently not yet available for all global earthquakes. Thus, despite the physical importance of E _S in characterizing the seismic source, the use of M _e has been limited so far to the detriment of quicker and more complete rough estimates of both earthquake size and strength and their causal relationships. Further studies are needed to improve E _S estimations in order to allow M _e to be extensively used as an important complement to M _w in common seismological practice and its applications.     

On the magnetic flux linkage of an electrically-conducting fluid

Abstract

A method has recently been proposed for finding the radius r_c of the electrically-conducting fluid core of a planet of outer radius r_s from observations of the magnetic field B in the accessible region near or well above the surface of the planet (Hide, 1978). The method is based on the supposition that when the magnetic field is produced by hydromagnetic dynamo action in the core, implying that the magnetic Reynolds number R there is large, (a) fluctuations in B can occur everywhere on the comparatively short advective time-scale τ _A associated with fluid motions in the core and so can fluctuations in the quantity N, defined for any closed surface S as the total number of intersection of magnetic lines of force with S, provided that S lies well outside the core, but (b) at the surface of the core, where lines of magnetic force emerge from their region of origin, concomitant fluctuations in N are negligibly small, of the order of τ _A/τ_O where τ _O (= Rτ_A ) is the Ohmic decay time of the core.

A proof of this supposition follows directly from the general expression derived in the present paper showing that when S is a material surface the time rate of change of N is equal to minus twice the line integral of the current density divided by the electrical conductivity around all the lines on S where the magnetic field is tangential to S. This expression (which Palmer in an accompanying paper rederives and extends to the relativistic case using the mathematical formalism of Cartan’s exterior calculus) also provides a direct demonstration of the well-known result that although high electrical conductivity, sufficient to make R ? 1, is a necessary condition for hydromagnetic dynamo action, such action is impossible in a perfect conductor, when R→ ∞.     

Statistical features of aftershock distribution size for moderate and large earthquakes in Chinese mainland

Based on data of earthquake sequences with MS≥5.0 in Chinese mainland from 1970 to 2004,for different se-quence types and different rupture modes of the main shock,the relationship between aftershock distribution size Rand the magnitude of the main shock M0 has been studied statistically.Considering the rupture mode of the mainshock,we give the quantitative statistical relationships between R and M0 under 95%confidence level for differentsequence types.Qualitatively,lgR,the logarithm of the aftershock distribution size,is positively correlative to theM0,but the data distribution is dispersed.Viewing from different sequence types,the correlation between R and M0is very weak for isolated earthquake type(IET)sequence,R distributes in the range from 5 to 60 km;For main-shock-aftershock type(MAT),lgR is positively correlative to M0;For multiple main shock type(MMT),the core-lation between lgR and M0 is not very obvious when M0≤6.2 and R distributes in the range from 5 to 70 km,whileit shows a linear correlation when M0≥6.3.The statistical results also show that the occupational ratios of differentsequence types for strike-slip and oblique slip are almost the same.But for dip-slip(mostly are thrust mechanisms),the ratio of MAT is higher than that of IET and MMT.Comparing with previous results,it indicates that,when M0is large enough,R is mainly determined by M0 and there is almost no relationship with the rupture mode of themain shock.     

An insightful parametrization for the flatlander's interpretation of time‐lapsed seismic data

An approximation is developed that allows mapped 4D seismic amplitudes and time‐shifts to be related directly to the weighted linear sum of pore pressure and saturation changes. The weights in this relation are identified as key groups of parameters from a petroelastic model and include the reservoir porosity. This dependence on groups of parameters explains the inherent non‐uniqueness of this problem experienced by previous researchers. The proposed relation is of use in 4D seismic data feasibility studies and inversion and interpretation of the 4D seismic response in terms of pore pressure and water saturation changes. A further result is drawn from analysis of data from the North Sea and West Africa, which reveals that the relative interplay between the effects of pore pressure and saturation changes on the seismic data can be simplified to the control of a single, spatially variant parameter C_S/C_P. Combining these results with those from published literature, we find that C_S/C_P = 8 appears to be a generality across a range of clastic reservoirs with a similar mean porosity. Using this C_S/C_P value, an in situ seismic‐scale constraint for the rock stress sensitivity component of the petroelastic model is constructed considering this component carries the largest uncertainty.     

Field study on flow structures within aquatic vegetation under combined currents and small-scale waves

Field measurements were conducted to study the influence of aquatic vegetation on flow structures in floodplains under combined currents and wind-driven waves. Wave and turbulent velocities were decomposed from the time series of instantaneous velocity and analysed separately. In the present study, the wind waves were small, leading to the ratios of wave excursion (E_w) to stem spacing (S) for all cases tested here were less than 0.5. This caused the vertical distributions of time-averaged velocity (U_horiz) and turbulent kinetic energy (TKE) impacted by vegetation similar with the vegetated flow structures under pure current conditions. For emergent vegetation, U_horiz and TKE distributed uniformly through the entire water column or increased slightly from bed to water surface. Similar distributions were present in the lower part of submerged vegetation. In the upper part of submerged vegetation, U_horiz and TKE increased rapidly toward water surface and TKE reached its maximum near the top of vegetation. The measured wave orbital velocity (U_w) fitted linear wave theory well through the entire water depth for both the emergent and submerged cases, so that with small E_w/S the wave velocity was not attenuated within vegetation and U_w within canopy can be predicted by the linear wave theory under combined currents and waves. However, wind-driven waves made the turbulence generated near the top of canopy penetrate a deeper depth into vegetation than predictions under pure current conditions.     

First approximations of soil moisture retention curves using the filter‐paper method

Relationships between gravimetric soil moisture content (w) and matric potential (ϕ), and between volumetric soil moisture content (θ_v) and pressure head (h) were approximated for the unsaturated zone on Long Island, New York. Soil samples were collected from two sites using a hand auger. The soil moisture content was determined using the filter‐paper (w_f) and gravimetric (w) methods, respectively. The w_f was then used in an empirical equation to estimate ϕ_m. Each set of ϕ_m and w was combined with a straight‐line empirical model to obtain a w(ϕ_m) relationship. Soil ϕ_m was converted to h, and w to the volumetric moisture content θ_v, in order to produce a θ_v(h) curve. Graphical and statistical comparison showed that the resulting θ_v(h) curves fell within one order of magnitude of similar curves generated by a more sophisticated non‐linear model developed previously. The simplicity and low cost of the filter‐paper approach described in this study recommends it for preliminary studies of hydraulic properties in the unsaturated zone. Copyright © 2000 John Wiley & Sons, Ltd.     

Chi-square regression for seismic strength parameter relations, and their uncertainties, with applications to an M w based earthquake catalogue for central, northern and northwestern Europe

A generalized chi-square regression approach to establishempirical relations between different types of seismic strengthparameters with uncertainties in all input data is presented anddiscussed in comparison with standard least-squares techniques.The chi-square technique can consider errors of individual entriesbut can also be applied when errors are not exactly known and onlyweaker quantitative constraints can be made. It can preserve thesymmetry of the derived relations and is preferred for complexregression models. Results for three types of regression modelsare presented for (1) a linear relation between M _Sand m _bfor events in the North Atlantic Ocean; (2) a quadratic relationbetween M _w and M _L forevents in central Europe; (3) linearrelations between M _L and I ₀,with logarithmic dependency ofthe focal depth, for several regions in central and northernEurope.     

Using neural networks for calibration of time-domain reflectometry measurements

Abstract

Time-domain reflectometry (TDR) is an electromagnetic technique for measurements of water and solute transport in soils. The relationship between the TDR-measured dielectric constant (K_a ) and bulk soil electrical conductivity ([sgrave]_a) to water content (θ_W) and solute concentration is difficult to describe physically due to the complex dielectric response of wet soil. This has led to the development of mostly empirical calibration models. In the present study, artificial neural networks (ANNs) are utilized for calculations of θ_w and soil solution electrical conductivity ([sgrave]_w) from TDR-measured K_a and [sgrave]_a in sand. The ANN model performance is compared to other existing models. The results show that the ANN performs consistently better than all other models, suggesting the suitability of ANNs for accurate TDR calibrations.     

A concise parameterization of the hydraulic conductivity of unsaturated soils

The parameter n in the well-known expression for hydraulic conductivity K=K₀S_eⁿ (where K₀ is its value at satiation and S_e the effective saturation) is determined as a function of the exponent in the power form of the soil–water retention relationship. The result is validated with an extensive experimental database comprising some 43 soils, collected by Mualem.     

豫01井地下水位模糊分维值的变化与地震的关系

采用了模糊集理论与分形理论相结合的模糊分维方法，计算了河南范县豫01井水位动态的模糊分维值，并分析了与1981年河北宁晋Ms 5.8、1983年山东菏泽Ms 5.9、1985年河北任县Ms 5.0地震的关系。结果显示，模糊分维值在这3次地震前都明显地出现了小于0．75的降维低值异常特征。且震级越大，震中距越小，异常时间越长；反之则相反。