An effective medium algorithm for calculating water saturations at any salinity or frequency

Geophysics ◽  
2007 ◽  
Vol 72 (2) ◽  
pp. E59-E67 ◽  
Author(s):  
Charles Berg
Keyword(s):  
Water Saturation ◽  
Low Frequency ◽  
Dielectric Constants ◽  
Data Sets ◽  
Formation Water ◽  
Water Conductivity ◽  
Low Frequencies ◽  
Incremental Model ◽  
Geometric Factors ◽  
Coated Sand

An algorithmic approach is used to mix the conductivities and geometric factors of the disperse components (the rock and hydrocarbon particles) with the host conductivity (formation water). The theoretical basis for the algorithm is the Hanai-Bruggeman (HB) equation, which itself incorporates only one disperse component. The new approach, the incremental model, accommodates geometric factors such as sand and shale porosity exponents, saturation exponent, and also accommodates the associated grain conductivities. Its advantage over previous methods is that it works at any water salinity or tool frequency while allowing saturation and porosity exponents to have values other than 1.5. The algorithm is general and is written to accommodate simultaneous mixing of up to three disperse components and the formation water, but it can be extended to accommodate any number of disperse components. In its application to shaley sands, hydrocarbon and sand elements are set to zero conductivity at low frequency, but they can be nonzero for calculating saturations at higher frequencies. The reason for this is that hydrocarbon and sand conductivities are real and very close to zero at low frequencies, but at high frequencies the dielectric constants become significant, making the complex conductivities nonzero. The incremental model compared well with the Waxman-Smits model on multiple water-conductivity saturation data from two published experimental data sets. The model is adaptable to other rock conductivity problems such as vuggy porosity, vuggy water saturation, and clay-coated sand grains. The potential exists for the algorithm to be part of a comprehensive computer program for calculating rock conductivities and saturations using many different combinations of rock fabrics and compositions.

Petrophysical Type Curves for Identifying the Electrical Character of Petroleum Reservoirs

2007 ◽  
Vol 10 (06) ◽  
pp. 711-729 ◽  
Author(s):  
Paul Francis Worthington
Keyword(s):  
Water Saturation ◽  
Early Stage ◽  
Well Logs ◽  
Log Analysis ◽  
Well Log ◽  
Formation Water ◽  
Water Conductivity ◽  
Core Data ◽  
Water Saturated ◽  
Petrophysical Evaluation

Summary A user-friendly type chart has been constructed as an aid to the evaluation of water saturation from well logs. It provides a basis for the inter-reservoir comparison of electrical character in terms of adherence to, or departures from, Archie conditions in the presence of significant shaliness and/or low formation-water salinity. Therefore, it constitutes an analog facility. The deliverables include reservoir classification to guide well-log analysis, a protocol for optimizing the acquisition of special core data in support of log analysis, and reservoir characterization in terms of an (analog) porosity exponent and saturation exponent. The type chart describes a continuum of electrical behavior for both water and hydrocarbon zones. This is important because some reservoir rocks can conform to Archie conditions in the fully water-saturated state, but show pronounced departures from Archie conditions in the partially water-saturated state. In this respect, the chart is an extension of earlier approaches that were restricted to the water zone. This extension is achieved by adopting a generalized geometric factor—the ratio of water conductivity to formation conductivity—regardless of the degree of hydrocarbon saturation. The type chart relates a normalized form of this geometric factor to formation-water conductivity, a "shale" conductivity term, and (irreducible) water saturation. The chart has been validated using core data from comprehensively studied reservoirs. A workflow details the application of the type chart to core and/or log data. The analog role of the chart is illustrated for reservoir units that show different levels of non-Archie effects. The application of the method should take rock types, scale effects, the degree of core sampling, and net reservoir criteria into account. The principal benefit is a reduced uncertainty in the choice of a procedure for the petrophysical evaluation of water saturation, especially at an early stage in the appraisal/development process, when adequate characterizing data may not be available. Introduction One of the ever-present problems in petrophysics is how to carry out a meaningful evaluation of well logs in situations where characterizing information from quality-assured core analysis is either unavailable or is insufficient to satisfactorily support the log interpretation. This problem is especially pertinent at an early stage in the life of a field, when reservoir data are relatively sparse. Data shortfalls could be mitigated if there was a means of identifying petrophysical analogs of reservoir character, so that the broader experience of the hydrocarbon industry could be utilized in constructing reservoir models and thence be brought to bear on current appraisal and development decisions. Here, a principal requirement calls for type charts of petrophysical character, on which data from different reservoirs can be plotted and compared, as a basis for aligning approaches to future data acquisition and interpretation. This need manifests itself strongly in the petrophysical evaluation of water saturation, a process that traditionally uses the electrical properties of a reservoir rock to deliver key building blocks for an integrated reservoir model. The solution to this problem calls for an analog facility through which the electrical character of a subject reservoir can be compared with others that have been more comprehensively studied. In this way, the degree of confidence in log-derived water saturation might be reinforced. At the limit, the log analyst needs a reference basis for recourse to capillary pressure data in cases where the well-log evaluation of water saturation turns out to be prohibitively uncertain.

Theoretical and Experimental Bases for the Dual-Water Model for Interpretation of Shaly Sands

1984 ◽  
Vol 24 (02) ◽  
pp. 153-168 ◽  
Author(s):  
C. Clavier ◽  
G. Coates ◽  
J. Dumanoir
Keyword(s):  
Volume Fraction ◽  
Water Saturation ◽  
Free Water ◽  
Total Porosity ◽  
Water Model ◽  
Implicit Assumption ◽  
Formation Water ◽  
Formation Factor ◽  
Water Conductivity ◽  
Clayey Sand

Abstract A simple petrophysical model proposed by Waxman and Smits (WS)1 in 1968 and Waxman and Thomas (WT)2 in 1972 accounts for the results of an extensive experimental study on the effects of clays on the resistivity of shaly sands. This model has been well accepted by the industry despite a few inconsistencies with experimental results. It is proposed that these inconsistencies resulted from the unaccounted presence of salt-free water at the clay/water interface. Electrochemistry indicates that this water should exist, but is there enough to influence the results? Both a theoretical study and reinterpretation of Waxman-Smits-Thomas data show that there is. The corresponding new model starts from the Waxman and Smits concept of supplementing the water conductivity with a conductivity from the clay counterions. The crucial step, however, is equating each of these conductivity terms to a particular type of water, each occupying a representative volume of the total porosity. This approach has been named the "dual-water" (DW) model because of these two water types - the conductivity and volume fraction of each being predicted by the model. The DW model has been tested on most of the core data reported in Refs. 1 and 2. The DW concept is also supported by log data3 and has been successfully applied to the interpretation of thousands of wells. However, the scope of this paper remains limited to the theoretical and experimental bases of the DW model. The Petrophysical DW Model The purpose of this model is to account for the resistivity behavior of clayey sands. For petrophysical considerations, a clayey formation is characterized by its total porosity, ft; its formation factor, F0; its water saturation, SwT; its bulk conductivity, Ct; and its concentration per unit PV of clay counterions, Qv. The formation behaves like a clean formation with identical parameters ft, F0, and Swt but containing a water whose conductivity, Cwe, differs from the bulk formation water. Neither the type of clays nor their distribution influences the results. Since the formation obeys Archie's laws,Equation 1 The clayey sand equivalent water conductivity, Cwe, can be considered a mixture of two waters. 1. A clay water surrounds the clay particles but has a conductivity independent of the type and amount of clay. Its conductivity, Ccw, comes exclusively from the clay counterions. The volume fraction of clay water, Vcw, is directly proportional to the counterion concentration, QvEquation 2 where vQ is the amount of clay water associated with 1 unit (meq) of clay counterions. 2. The water further away from the clay is called far water. Its conductivity, Cw, and ionic concentration correspond to the salinity of bulk-formation water. The volume fraction of this water, Vfw, is the balance between the total water content and the clay water.Equation 3 The implicit assumption is that the far water is displaced preferentially by hydrocarbons.

Multiparameter waveform inversion of a large wide-azimuth low-frequency land data set in Oman

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. WA69-WA77 ◽  
Author(s):  
Alexandre Stopin ◽  
René-Édouard Plessix ◽  
Said Al Abri
Keyword(s):  
Waveform Inversion ◽  
Low Frequency ◽  
Large Data ◽  
Earth Model ◽  
Data Sets ◽  
Anisotropic Parameter ◽  
Data Set ◽  
Low Frequencies ◽  
Reflected Waves ◽  
Simultaneous Inversion

Several 3D seismic acoustic full-waveform inversions (FWIs) of offshore data sets have been reported over the last five years. A successful updating of the long-to-intermediate wavelengths of the earth model by FWI requires good-quality wide-angle, long-offset, low-frequency data. Recent improvements in acquisition make such data sets available on land, too. We evaluated a 3D application on a data set recorded in North Oman. The data contain low frequencies down to 1.5 Hz, long-offsets, and wide azimuths. The application of acoustic FWI on land remains complicated because of the elastic effects, notably the strong ground-roll and many acquisition and human-activity-related noises. The presence of fast carbonate layers in this region induces velocity inversions, difficult to recover from diving or postcritical waves. We accounted for anisotropic effects as we include FWI in a classical structural imaging workflow. With a dedicated processing of the data and a simultaneous inversion of the NMO velocity and the anelliptic-anisotropic parameter, we succeeded to interpret the kinematics of transmitted and reflected waves, although in the waveform inversion we included only the diving and postcritical waves. This approach has some limitations because of the acoustic assumption. We could not obtain a high-resolution image, especially at the shale-carbonate interfaces. There is also a trade-off between the NMO velocity and the anelliptic anisotropic parameter. However, the image improvements after acoustic FWI and the ability to handle the large data volume make this technique attractive in an imaging workflow.

Radio and Electrical Measurements on Glacial Streams

1987 ◽  
Vol 33 (114) ◽  
pp. 239-242
Author(s):  
M. E. R. Walford
Keyword(s):  
Electrical Conductivity ◽  
Water Channel ◽  
Water System ◽  
Low Frequency ◽  
Water Channels ◽  
Radiative Loss ◽  
Radio Waves ◽  
Electrical Measurements ◽  
Water Conductivity ◽  
Glacier Surface

AbstractWe discuss the suggestion that small underwater transmitters might be used to illuminate the interior of major englacial water channels with radio waves. Once launched, the radio waves would naturally tend to be guided along the channels until attenuated by absorption and by radiative loss. Receivers placed within the channels or at the glacier surface could be used to detect the signals. They would provide valuable information about the connectivity of the water system. The electrical conductivity of the water is of crucial importance. A surface stream on Storglaciären, in Sweden, was found, using a low-frequency technique, to have a conductivity of approximately 4 × 10−4 S m−1. Although this is several hundred times higher than the conductivity of the surrounding glacier ice, the contrast is not sufficient to permit us simply to use electrical conductivity measurements to establish the connectivity of englacial water channels. However, the water conductivity is sufficiently small that, under favourable circumstances, radio signals should be detectable after travelling as much as a few hundred metres along an englacial water channel. In a preliminary field experiment, we demonstrated semi quantitatively that radio waves do indeed propagate as expected, at least in surface streams. We conclude that under-water radio transmitters could be of real practical value in the study of the englacial water system, provided that sufficiently robust devices can be constructed. In a subglacial channel, however, we expect the radio range would be much smaller, the environment much harsher, and the technique of less practical value.

scholarly journals On Time Scales of Intrinsic Oscillations in the Climate System

Entropy ◽  
2021 ◽  
Vol 23 (4) ◽  
pp. 459
Author(s):  
Anastasios A. Tsonis ◽  
Geli Wang ◽  
Wenxu Lu ◽  
Sergey Kravtsov ◽  
Christopher Essex ◽  
...  
Keyword(s):  
Low Frequency ◽  
Milankovitch Cycles ◽  
Data Sets ◽  
External Forcing ◽  
Natural Oscillations ◽  
Climatic Oscillations ◽  
Slow Feature Analysis ◽  
Limited Length ◽  
Past Data ◽  
Cumulative Evidence

Proxy temperature data records featuring local time series, regional averages from areas all around the globe, as well as global averages, are analyzed using the Slow Feature Analysis (SFA) method. As explained in the paper, SFA is much more effective than the traditional Fourier analysis in identifying slow-varying (low-frequency) signals in data sets of a limited length. We find the existence of a striking gap from ~1000 to about ~20,000 years, which separates intrinsic climatic oscillations with periods ranging from ~ 60 years to ~1000 years, from the longer time-scale periodicities (20,000 yr +) involving external forcing associated with Milankovitch cycles. The absence of natural oscillations with periods within the gap is consistent with cumulative evidence based on past data analyses, as well as with earlier theoretical and modeling studies.

scholarly journals Estimation of permeability and saturation based on imaginary component of complex resistivity spectra: A laboratory study

2020 ◽  
Vol 12 (1) ◽  
pp. 299-306
Author(s):  
Jiang Jia ◽  
Shizhen Ke ◽  
Junjian Li ◽  
Zhengming Kang ◽  
Xuerui Ma ◽  
...  
Keyword(s):  
Water Saturation ◽  
Pore Space ◽  
Evaluation Model ◽  
Low Frequency ◽  
Petroleum Exploration ◽  
Western China ◽  
Imaginary Component ◽  
Estimation Model ◽  
Complex Resistivity ◽  
Linear Relationships

AbstractLow-frequency resistivity logging plays an important role in the field of petroleum exploration, but the complex resistivity spectrum of rock also contains a large amount of information about reservoir parameters. The complex resistivity spectra of 15 natural sandstone cores from western China, with different water saturations, were measured with an impedance analyzer. The pore space of each core was saturated with NaCl solution, and measurements were collected at a frequency range of 40–15 MHz. The results showed a linear relationship between the real resistivity at 1 kHz and the maximum values of imaginary resistivity for each core with different water saturations. The slopes of the linear best-fit lines had good linear relationships with the porosity and the permeability of cores. Based on this, a permeability estimation model was proposed and tested. In addition, the maxima of imaginary resistivity had power exponential relationships with the porosity and the water saturation of the cores. A saturation evaluation model based on the maxima of imaginary resistivity was established by imitating Archie’s formula. The new models were found to be feasible for determining the permeability and saturation of sandstone based on complex resistivity spectrum measurements. These models advance the application of complex resistivity spectrum in petrophysics.

scholarly journals Dielectric Properties of Wood-Polymer Composites: Effects of Frequency, Fiber Nature, Proportion, and Chemical Composition

2021 ◽  
Vol 5 (6) ◽  
pp. 141
Author(s):  
Imen Elloumi ◽  
Ahmed Koubaa ◽  
Wassim Kharrat ◽  
Chedly Bradai ◽  
Ahmed Elloumi
Keyword(s):  
Dielectric Properties ◽  
Polymer Composites ◽  
Wide Frequency Range ◽  
Dielectric Constants ◽  
Cellulose Content ◽  
Wood Fibers ◽  
Low Frequencies ◽  
Wood Polymer ◽  
Wood Polymer Composites ◽  
New Applications

The characterization of the dielectric properties of wood–polymer composites (WPCs) is essential to understand their interaction with electromagnetic fields and evaluate their potential use for new applications. Thus, dielectric spectroscopy monitored the evolution of the dielectric properties of WPCs over a wide frequency range of 1 MHz to 1 GHz. WPCs were prepared using mixtures of different proportions (40%, 50%, and 60%) of wood and bark fibers from various species, high-density polyethylene, and maleated polyethylene (3%) by a two-step process, extrusion and compression molding. Results indicated that wood fibers modify the resistivity of polyethylene at low frequencies but have no effect at microwave frequencies. Increasing the fiber content increases the composites’ dielectric properties. The fibers’ cellulose content explains the variation in the dielectric properties of composites reinforced with fibers from different wood species. Indeed, composites with high cellulose content show higher dielectric constants.

scholarly journals Earless toads sense low frequencies but miss the high notes

2017 ◽  
Vol 284 (1864) ◽  
pp. 20171670 ◽  
Author(s):  
Molly C. Womack ◽  
Jakob Christensen-Dalsgaard ◽  
Luis A. Coloma ◽  
Juan C. Chaparro ◽  
Kim L. Hoke
Keyword(s):  
High Frequency ◽  
Species Differences ◽  
Low Frequency ◽  
Auditory Brainstem ◽  
Low Frequencies ◽  
Hearing Sensitivity ◽  
Sensory Pathways ◽  
Airborne Sound ◽  
Vibrational Sensitivity ◽  
Species Specific

Sensory losses or reductions are frequently attributed to relaxed selection. However, anuran species have lost tympanic middle ears many times, despite anurans' use of acoustic communication and the benefit of middle ears for hearing airborne sound. Here we determine whether pre-existing alternative sensory pathways enable anurans lacking tympanic middle ears (termed earless anurans) to hear airborne sound as well as eared species or to better sense vibrations in the environment. We used auditory brainstem recordings to compare hearing and vibrational sensitivity among 10 species (six eared, four earless) within the Neotropical true toad family (Bufonidae). We found that species lacking middle ears are less sensitive to high-frequency sounds, however, low-frequency hearing and vibrational sensitivity are equivalent between eared and earless species. Furthermore, extratympanic hearing sensitivity varies among earless species, highlighting potential species differences in extratympanic hearing mechanisms. We argue that ancestral bufonids may have sufficient extratympanic hearing and vibrational sensitivity such that earless lineages tolerated the loss of high frequency hearing sensitivity by adopting species-specific behavioural strategies to detect conspecifics, predators and prey.

scholarly journals The Sampling Distribution of Disease-Associated Alleles

Genetics ◽  
1997 ◽  
Vol 147 (4) ◽  
pp. 1855-1861 ◽  
Author(s):  
Montgomery Slatkin ◽  
Bruce Rannala
Keyword(s):  
Low Frequency ◽  
Null Model ◽  
Sampling Distribution ◽  
Death Process ◽  
Published Data ◽  
Data Sets ◽  
Likelihood Functions ◽  
Alternative Hypotheses ◽  
Size Standard ◽  
Birth Death

Abstract A theory is developed that provides the sampling distribution of low frequency alleles at a single locus under the assumption that each allele is the result of a unique mutation. The numbers of copies of each allele is assumed to follow a linear birth-death process with sampling. If the population is of constant size, standard results from theory of birth-death processes show that the distribution of numbers of copies of each allele is logarithmic and that the joint distribution of numbers of copies of k alleles found in a sample of size n follows the Ewens sampling distribution. If the population from which the sample was obtained was increasing in size, if there are different selective classes of alleles, or if there are differences in penetrance among alleles, the Ewens distribution no longer applies. Likelihood functions for a given set of observations are obtained under different alternative hypotheses. These results are applied to published data from the BRCA1 locus (associated with early onset breast cancer) and the factor VIII locus (associated with hemophilia A) in humans. In both cases, the sampling distribution of alleles allows rejection of the null hypothesis, but relatively small deviations from the null model can account for the data. In particular, roughly the same population growth rate appears consistent with both data sets.

A waveform inversion technique for measuring elastic wave attenuation in cylindrical bars

Geophysics ◽  
1992 ◽  
Vol 57 (6) ◽  
pp. 854-859 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Elastic Wave ◽  
Wave Attenuation ◽  
Waveform Inversion ◽  
Finite Size ◽  
Low Frequency ◽  
Frequency Range ◽  
Multiple Reflections ◽  
Low Frequencies ◽  
The Time Domain ◽  
Attenuation Values

A new technique for measuring elastic wave attenuation in the frequency range of 10–150 kHz consists of measuring low‐frequency waveforms using two cylindrical bars of the same material but of different lengths. The attenuation is obtained through two steps. In the first, the waveform measured within the shorter bar is propagated to the length of the longer bar, and the distortion of the waveform due to the dispersion effect of the cylindrical waveguide is compensated. The second step is the inversion for the attenuation or Q of the bar material by minimizing the difference between the waveform propagated from the shorter bar and the waveform measured within the longer bar. The waveform inversion is performed in the time domain, and the waveforms can be appropriately truncated to avoid multiple reflections due to the finite size of the (shorter) sample, allowing attenuation to be measured at long wavelengths or low frequencies. The frequency range in which this technique operates fills the gap between the resonant bar measurement (∼10 kHz) and ultrasonic measurement (∼100–1000 kHz). By using the technique, attenuation values in a PVC (a highly attenuative) material and in Sierra White granite were measured in the frequency range of 40–140 kHz. The obtained attenuation values for the two materials are found to be reliable and consistent.

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