Thermal effective stress in shales

2019 ◽  
Vol 38 (5) ◽  
pp. 374-378
Author(s):  
Jeremy Gallop
Keyword(s):  
Effective Stress ◽  
Reservoir Characterization ◽  
Time Lapse ◽  
Forward Modeling ◽  
Calibration Data ◽  
S Wave ◽  
Wave Velocities ◽  
Proposed Model ◽  
Stress Coefficient ◽  
The Matrix

Calculating velocities in shales in thermal production settings is important to refine time-lapse reservoir characterization from seismic. The effective stress concept is attractive to potentially reduce the amount of expensive core calibration data required. We propose a formulation for thermal effective stress in shales based on the idea of balancing undrained pore pressure increments from thermal expansion with an increase in the matrix stress to minimize pore deformation. This formulation is motivated by a desire to simplify forward modeling, reduce the number of dimensions that must be experimentally calibrated through core testing, and to leverage existing velocity-stress relations for thermal applications. The concept was tested on data from a well-known set of experiments consisting of two North Sea Kimmeridge shale core samples, which displayed a linear dependence of velocity on pressure and temperature. These data were found to be consistent with the proposed thermal effective stress model with a constant effective stress coefficient when considering elastic changes but do not prove that the concept is universally valid. Thermal effective stress coefficients were calculated for P- and S-wave velocities from the data and were found to lie from 0.66 to 1.22, demonstrating reasonable scaling for the proposed model.

Experimental efforts to access 4D feasibility and interpretation issues of Brazilian presalt carbonate reservoirs

2019 ◽  
Vol 7 (4) ◽  
pp. SH1-SH18
Author(s):  
Guilherme Fernandes Vasquez ◽  
Marcio Jose Morschbacher ◽  
Julio Cesar Ramos Justen
Keyword(s):  
Pore Pressure ◽  
Effective Stress ◽  
Carbonate Rocks ◽  
Time Lapse ◽  
Carbonate Reservoirs ◽  
Fluid Replacement ◽  
S Wave ◽  
Confining Stress ◽  
Reservoir Properties ◽  
Stress Coefficient

Brazilian presalt reservoirs comprise carbonate rocks saturated with light oil with different amounts of [Formula: see text] and excellent productivity. The occurrence of giant-size accumulations with such productivity generates the interest in production monitoring tools, such as time-lapse seismic. However, time-lapse seismic may present several challenges, such as imaging difficulties, repeatability, and detectability of small variations of reservoir properties. In addition, when assessing time-lapse seismic feasibility, the validity of Gassmann’s modeling for complex, heterogeneous carbonate rocks is arguable. Other questions include the pressure variation effects on the seismic properties of competent rocks. The effective stress is a linear combination of confining stress and pore pressure that governs the behavior of physical properties of rocks. Many applications assume that the effective stress for elastic-wave velocity is given by the difference between confining stress and pore pressure, whereas another common approach uses the Biot-Willis coefficient as a weight applied to the pore pressure to estimate the effective stress. Through a series of experiments involving ultrasonic pulse transmission on saturated core plugs in the laboratory, we verified the applicability of Gassmann’s fluid substitution and estimated the empirical effective stress coefficients related to the P- and S-wave velocities for rock samples from two offshore carbonate reservoirs from the presalt section, Santos Basin. We observed that Gassmann’s equation predicts quite well the effects of fluid replacement, and we found that the effective stress coefficient is less than one and not equal to the Biot-Willis coefficient. Moreover, there is a good agreement between the static and dynamic Biot-Willis coefficient, which is a suggestion that the presalt rocks behave as a poroelastic media. These observations suggest that more accurate time-lapse studies require the estimation of the effective stress coefficient for the particular reservoir of interest.

Derivation of seismic cone interval velocities utilizing forward modeling and the downhill simplex method

2002 ◽  
Vol 39 (5) ◽  
pp. 1181-1192 ◽  
Author(s):  
Erick J Baziw
Keyword(s):  
Elastic Constants ◽  
Simplex Method ◽  
Forward Modeling ◽  
S Wave ◽  
Cone Penetration ◽  
Interval Velocity ◽  
Wave Velocities ◽  
Downhill Simplex Method ◽  
Downhill Simplex ◽  
Interval Velocities

The seismic cone penetration test (SCPT) has proven to be a very valuable geotechnical tool in facilitating the determination of low strain (<10–4%) in situ compression (P) and shear (S) wave velocities. The P- and S-wave velocities are directly related to the soil elastic constants of Poisson's ratio, shear modulus, bulk modulus, and Young's modulus. The accurate determination of P- and S-wave velocities from the recorded seismic cone time series is of paramount importance to the evaluation of reliable elastic constants. Furthermore, since the shear and compression wave velocities are squared in deriving the elastic constants, small variations in the estimated velocities can cause appreciable errors. The standard techniques implemented in deriving SCPT interval velocities rely upon obtaining reference P- and S-wave arrival times as the probe is advanced into the soil profile. By assuming a straight ray travel path from the source to the SCPT seismic receiver and calculating the relative reference arrival time differences, interval SCPT velocities are obtained. The forward modeling – downhill simplex method (FMDSM) outlined in this paper offers distinct advantages over conventional SCPT velocity profile estimation methods. Some of these advantages consist of the allowance of ray path refraction, greater sophistication in interval velocity determination, incorporation of measurement weights, and meaningful interval velocity accuracy estimators.Key words: seismic cone penetration testing (SCPT), downhill simplex method (DSM), forward modeling, Fermat's principle, weighted least squares (l2 norm), cost function.

The influence of pore fluids and frequency on apparent effective stress behavior of seismic velocities

Geophysics ◽  
2010 ◽  
Vol 75 (1) ◽  
pp. N1-N7 ◽  
Author(s):  
Gary Mavko ◽  
Tiziana Vanorio
Keyword(s):  
Elastic Wave ◽  
Bulk Modulus ◽  
Effective Stress ◽  
High Frequency ◽  
Laboratory Data ◽  
Pore Fluids ◽  
Wave Velocities ◽  
Stress Behavior ◽  
Stress Coefficient ◽  
The Impact

Although poroelastic theory predicts that the effective stress coefficient equals unity for elastic moduli in monomineralic rocks, some rock elastic wave velocities measured at ultrasonic frequencies have effective stress coefficients less than one. Laboratory effective stress behavior for P-waves is often different than S-waves. Furthermore, laboratory ultrasonic velocities almost always reflect high-frequency artifacts associated with pore fluids, including an increase in velocities and flattening of velocity-versus-pressure curves. We have investigated the impact of pore fluids and frequency on the observed effective stress coefficient for elastic wave velocities by developing a model that calculates pore-fluid effects on velocity, including high-frequency squirt dispersion, and we have compared the model’s predictions with laboratory data. We modeled a rock frame with penny-shaped cracks for three situations: vacuum dry, saturated with helium, and saturated with brine. Even if the frame modulus depends only on the differential stress, the saturated-rock effective stress coefficient is predicted to be significantly less than one at ultrasonic frequencies because of two effects: an increase in the fluid bulk modulus with increasing pressure and the contribution of high-frequency squirt dispersion. The latter effect is most significant in soft fluids (helium in this experiment) in which the fluid-bulk modulus is less than or comparable to the thin-crack pore stiffness.

AVO inversion of Troll Field data

Geophysics ◽  
1996 ◽  
Vol 61 (6) ◽  
pp. 1589-1602 ◽  
Author(s):  
Arild Buland ◽  
Martin Landrø ◽  
Mona Andersen ◽  
Terje Dahl
Keyword(s):  
Least Squares ◽  
Field Data ◽  
Forward Modeling ◽  
S Wave ◽  
Data Set ◽  
Wave Velocities ◽  
Avo Inversion ◽  
Common Depth Point ◽  
Elastic Inversion ◽  
Water Bottom

A stratigraphic elastic inversion scheme has been applied to a data set from the Troll East Field, offshore Norway. The objective of the present work is to obtain estimates of the P‐ and S‐wave velocities and densities of the subsurface. The inversion is carried out on τ − p transformed common depth‐point (CMP) gathers. The forward modeling is performed by convolving a wavelet with the reflectivity that includes water‐bottom multiples, transmission effects, and absorption and array effects. A damped Gauss‐Newton algorithm is used to minimize a least‐squares misfit function. Inversion results show good correlation between the estimated [Formula: see text] ratios and the lithologies in the wells. The [Formula: see text] ratio is estimated to 2.1–3.0 for shale and 1.6–2.0 for sandstones. In the reservoir, the [Formula: see text] ratio is estimated to 1.55 in the gas sand and to 1.62 below the fluid contact.

scholarly journals Influence of microheterogeneity on effective stress law for elastic properties of rocks

Geophysics ◽  
2008 ◽  
Vol 73 (1) ◽  
pp. E7-E14 ◽  
Author(s):  
Radim Ciz ◽  
Anthony F. Siggins ◽  
Boris Gurevich ◽  
Jack Dvorkin
Keyword(s):  
Effective Stress ◽  
Seismic Data ◽  
Elastic Moduli ◽  
Seismic Velocity ◽  
Time Lapse ◽  
Seismic Velocities ◽  
Laboratory Measurements ◽  
Hydrocarbon Production ◽  
Stress Coefficient ◽  
Seismic Measurements

Understanding the effective stress coefficient for seismic velocity is important for geophysical applications such as overpressure prediction from seismic data as well as for hydrocarbon production and monitoring using time-lapse seismic measurements. This quantity is still not completely understood. Laboratory measurements show that the seismic velocities as a function of effective stress yield effective stress coefficients less than one and usually vary between 0.5 and 1. At the same time, theoretical analysis shows that for an idealized monomineral rock, the effective stress coefficient for elastic moduli (and therefore also for seismic velocities) will always equal one. We explore whether this deviation of the effective stress coefficient from unity can be caused by the spatial microheterogeneity of the rock. The results show that only a small amount (less than 1%) of a very soft component is sufficient to cause this effect. Such soft material may be present in grain contact areas of many rocks and may explain the variation observed experimentally.

Predicting subsurface CO2 movement: From laboratory to field scale

Geophysics ◽  
2012 ◽  
Vol 77 (3) ◽  
pp. M27-M37 ◽  
Author(s):  
Ranjana Ghosh ◽  
Mrinal K. Sen
Keyword(s):  
Elastic Properties ◽  
Carbonate Rocks ◽  
Water Saturation ◽  
Time Lapse ◽  
Carbonate Reservoir ◽  
S Wave ◽  
Permeability Enhancement ◽  
Proposed Model ◽  
Porosity And Permeability ◽  
Frequency Dependent Model

Finding an appropriate model for time-lapse seismic monitoring of [Formula: see text]-sequestered carbonate reservoir poses a great challenge because carbonate-rocks have varying textures and highly reactive rock-fluid system. We introduced a frequency-dependent model based on Eshelby’s inclusion and differential effective medium (DEM) theory that can account for heterogeneity in microstructure of rocks and squirt flow. We showed that the estimated velocities from the modified DEM theory match well with the laboratory measurements (ultrasonic) of velocities of carbonate rocks saturated with [Formula: see text]-rich water. The theory predicts significant decrease in saturated P- and S-wave velocities in the seismic frequency band as a consequence of porosity and permeability enhancement by the process of chemical dissolution of carbonates with the saturating fluid. The study also showed the combined effect of chemical reaction and free [Formula: see text] saturation on the elastic properties of rock. We observed that the velocity dispersion and attenuation increased from complete gas saturation to water saturation. The proposed model can be used to invert geophysical measurements to detect changes in elastic properties of a carbonate reservoir and interpret the extent of [Formula: see text] movement with time. These are the key elements to ensure that sequestration will not damage underground geologic formation and [Formula: see text] storage is secure and environmentally acceptable.

Pore-pressure prediction challenges in chemical compaction regimes: An alternative VP/VS-based approach

2016 ◽  
Vol 4 (4) ◽  
pp. T443-T454 ◽  
Author(s):  
Ajesh John
Keyword(s):  
High Temperature ◽  
Pore Pressure ◽  
Effective Stress ◽  
Text Analysis ◽  
Correction Coefficient ◽  
S Wave ◽  
Wave Velocities ◽  
Temperature Regimes ◽  
Pore Pressure Prediction ◽  
High Degree

Understanding pressure mechanisms and their role in porosity-effective stress relationship is crucial in pore-pressure prediction estimation, particularly in complex geologic and high-temperature regimes. Overpressures are commonly associated with undercompaction and/or unloading mechanisms; those associated with undercompaction generally possess a direct relationship between effective stress and porosity, whereas those associated with unloading do not provide such direct indications from porosity trends. The type of associated unloading mechanism can be correlated when the effective stress and velocity become distorted with the onset of unloading. In the Ravva field, the pore-pressure distribution and overpressure mechanism in the Miocene and below it is a classic example of the unloading mechanism related to chemical compaction, thereby making it difficult to resolve the magnitude and trend of pore pressures. Here, the ratio of P- and S-wave velocities ([Formula: see text]) is analyzed from the drilled locations to understand the effects of lithology, pressure, and fluids on formation velocities and indicates a distinct decreasing trend across the overpressure formations, which I have corresponded to excess pressure resulting from chemical compaction. Across the high-pressured zones, [Formula: see text] ratios show low values compared with normally pressured zones possibly due to the presence of hydrocarbon and/or overpressures. A velocity correction coefficient ranging 0.83–0.71 is resolved for overpressure zones by normalizing the [Formula: see text] values across the normally pressured formations, and thereby assuring that a pore-pressure estimation using corrected velocity from [Formula: see text] analysis shows a high degree of accuracy on prediction trends. Pore-pressure predictions based on [Formula: see text] are a more effective and valid approach in high-temperature settings, in which numerous factors can contribute to pressure generation and a direct effective stress-porosity relationship deviates from the trend.

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