Coarse-scale resistivity for saturation estimation in heterogeneous reservoirs based on Archie’s formula

Geophysics ◽  
2011 ◽  
Vol 76 (2) ◽  
pp. E35-E43 ◽  
Author(s):  
Per Atle Olsen
Keyword(s):  
Water Saturation ◽  
Small Scale ◽  
Coarse Scale ◽  
Derived Relations ◽  
Analytical Expression ◽  
Resistivity Measurements ◽  
Heterogeneous Reservoirs ◽  
Geometric Average ◽  
Harmonic Average

Relations between porosity, saturation, and resistivity are essential when estimating in-place hydrocarbon volumes. The most common relation is the Archie formula. During the last decade, several new coarse-scale electromagnetic techniques for resistivity measurements have been developed. Applications of coarse-scale resistivity must consider the underlying geologic variability of porosity and saturation to be used in such relations. I have investigated the effect of small-scale (logging-scale) variability in porosity and water saturation on coarse-scale resistivity for Archie relations. An analytical expression for coarse-scale resistivity is derived based on the assumption of lognormal distributed porosity and saturation. Similarly, coarse-scale water saturation is derived assuming lognormal distributed porosity and resistivity. The results suggest that the coarse-scale equivalent Archie resistivity is normally less than the geometric average and larger than the harmonic average of the heterogeneous resistivity distribution. An important aspect of the analytical derived relations is the quantification of the effect of the variability (variance and covariance) on the coarse-scale results. Another coarse-scale average resistivity based on macroscopic anisotropy could be a practical approximation of the coarse-scale equivalent Archie resistivity in many cases.

Differences in the Upscaling Procedure for Compositional Reservoir Simulations of Immiscible and Miscible Gas Flooding

2021 ◽  
Author(s):  
Victor de Souza Rios ◽  
Arne Skauge ◽  
Ken Sorbie ◽  
Gang Wang ◽  
Denis José Schiozer ◽  
...  
Keyword(s):  
Computational Cost ◽  
Specific Treatment ◽  
Dynamic Responses ◽  
Scale Model ◽  
Small Scale ◽  
Coarse Scale ◽  
Reservoir Models ◽  
Permeability Upscaling ◽  
Gas Flooding ◽  
Grid Block

Abstract Compositional reservoir simulation is essential to represent the complex interactions associated with gas flooding processes. Generally, an improved description of such small-scale phenomena requires the use of very detailed reservoir models, which impact the computational cost. We provide a practical and general upscaling procedure to guide a robust selection of the upscaling approaches considering the nature and limitations of each reservoir model, exploring the differences between the upscaling of immiscible and miscible gas injection problems. We highlight the different challenges to achieve improved upscaled models for immiscible and miscible gas displacement conditions with a stepwise workflow. We first identify the need for a special permeability upscaling technique to improve the representation of the main reservoir heterogeneities and sub-grid features, smoothed during the upscaling process. Then, we verify if the use of pseudo-functions is necessary to correct the multiphase flow dynamic behavior. At this stage, different pseudoization approaches are recommended according to the miscibility conditions of the problem. This study evaluates highly heterogeneous reservoir models submitted to immiscible and miscible gas flooding. The fine models represent a small part of a reservoir with a highly refined set of grid-block cells, with 5 × 5 cm2 area. The upscaled coarse models present grid-block cells of 8 × 10 m2 area, which is compatible with a refined geological model in reservoir engineering studies. This process results in a challenging upscaling ratio of 32 000. We show a consistent procedure to achieve reliable results with the coarse-scale model under the different miscibility conditions. For immiscible displacement situations, accurate results can be obtained with the coarse models after a proper permeability upscaling procedure and the use of pseudo-relative permeability curves to improve the dynamic responses. Miscible displacements, however, requires a specific treatment of the fluid modeling process to overcome the limitations arising from the thermodynamic equilibrium assumption. For all the situations, the workflow can lead to a robust choice of techniques to satisfactorily improve the coarse-scale simulation results. Our approach works on two fronts. (1) We apply a dual-porosity/dual-permeability upscaling process, developed by Rios et al. (2020a), to enable the representation of sub-grid heterogeneities in the coarse-scale model, providing consistent improvements on the upscaling results. (2) We generate specific pseudo-functions according to the miscibility conditions of the gas flooding process. We developed a stepwise procedure to deal with the upscaling problems consistently and to enable a better understanding of the coarsening process.

ENHANCED ASSESSMENT OF FLUID SATURATION IN THE WOLFCAMP FORMATION OF THE PERMIAN BASIN

2021 ◽  
Author(s):  
Sabyasachi Dash ◽  
◽  
Zoya Heidari ◽  
Keyword(s):  
Water Saturation ◽  
Geometric Model ◽  
Rock Physics ◽  
Model Parameters ◽  
Permian Basin ◽  
Resistivity Measurements ◽  
Clay Concentration ◽  
Resistivity Model ◽  
Shaly Sand ◽  
Hydrocarbon Reserves

Conventional resistivity models often overestimate water saturation in organic-rich mudrocks and require extensive calibration efforts. Conventional resistivity-porosity-saturation models assume brine in the formation as the only conductive component contributing to resistivity measurements. Enhanced resistivity models for shaly-sand analysis include clay concentration and clay-bound water as contributors to electrical conductivity. These shaly-sand models, however, consider the existing clay in the rock as dispersed, laminated, or structural, which does not reliably describe the distribution of clay network in organic-rich mudrocks. They also do not incorporate other conductive minerals and organic matter, which can significantly impact the resistivity measurements and lead to uncertainty in water saturation assessment. We recently introduced a method that quantitatively assimilates the type and spatial distribution of all conductive components to improve reserves evaluation in organic-rich mudrocks using electrical resistivity measurements. This paper aims to verify the reliability of the introduced method for the assessment of water/hydrocarbon saturation in the Wolfcamp formation of the Permian Basin. Our recently introduced resistivity model uses pore combination modeling to incorporate conductive (clay, pyrite, kerogen, brine) and non-conductive (grains, hydrocarbon) components in estimating effective resistivity. The inputs to the model are volumetric concentrations of minerals, the conductivity of rock components, and porosity obtained from laboratory measurements or interpretation of well logs. Geometric model parameters are also critical inputs to the model. To simultaneously estimate the geometric model parameters and water saturation, we develop two inversion algorithms (a) to estimate the geometric model parameters as inputs to the new resistivity model and (b) to estimate the water saturation. Rock type, pore structure, and spatial distribution of rock components affect geometric model parameters. Therefore, dividing the formation into reliable petrophysical zones is an essential step in this method. The geometric model parameters are determined for each rock type by minimizing the difference between the measured resistivity and the resistivity, estimated from Pore Combination Modeling. We applied the new rock physics model to two wells drilled in the Permian Basin. The depth interval of interest was located in the Wolfcamp formation. The rock-class-based inversion showed variation in geometric model parameters, which improved the assessment of water saturation. Results demonstrated that the new method improved water saturation estimates by 32.1% and 36.2% compared to Waxman-Smits and Archie's models, respectively, in the Wolfcamp formation. The most considerable improvement was observed in the Middle and Lower Wolfcamp formation, where the average clay concentration was relatively higher than the other zones. Results demonstrated that the proposed method was shown to improve the estimates of hydrocarbon reserves in the Permian Basin by 33%. The hydrocarbon reserves were underestimated by an average of 70000 bbl/acre when water saturation was quantified using Archie's model in the Permian Basin. It should be highlighted that the new method did not require any calibration effort to obtain model parameters for estimating water saturation. This method minimizes the need for extensive calibration efforts for the assessment of hydrocarbon/water saturation in organic-rich mudrocks. By minimizing the need for extensive calibration work, we can reduce the number of core samples acquired. This is the unique contribution of this rock-physics-based workflow.

Assessment of NPV Uncertainty on Heterogeneous Reservoirs during Polymer Flood

2013 ◽  
Vol 448-453 ◽  
pp. 4033-4037 ◽  
Author(s):  
Kyung Wan Yu ◽  
Byung In Choi ◽  
Kun Sang Lee
Keyword(s):  
Net Present Value ◽  
Water Saturation ◽  
Polymer Flooding ◽  
Water Flooding ◽  
Low Permeability ◽  
Oil Viscosity ◽  
Permeability Model ◽  
Heterogeneous Reservoirs ◽  
Polymer Flood ◽  
Porosity And Permeability

This study shows net present value (NPV) distribution by considering uncertainties in porosity, oil viscosity, water saturation, and permeability for polymer flood with Monte Carlo simulation. For high and low average permeability conditions, differences of NPV between polymer flooding and water flooding have been investigated. According to results both average NPV and range of NPV distribution tend to increase with porosity and permeability in all cases. Although water saturation and oil viscosity affect NPV, they are not important parameters that conclude uncertainty of NPV under the conditions considered in this study. For high permeability model which has Dykstra-Parsons coefficient (DP) as 0.72 and porosity as 0.3088, Monte Carol simulations for polymer flood show that 50th percentile (P50) of NPV is 352.81 M$. If porosity is decreased from 0.3088 to 0.1912, the P50 is also decreased 63.8 %. The reduction of NPV during polymer flooding in low permeability reservoirs are almost 40 % higher than that of water flood. These differences come from polymer adsorption and permeability reduction that easily occurs in low permeability zone. The procedure has proven to be useful tool to generate probability distribution of NPV when polymer flood is selected as a tertiary flood process.

Foam Diversion in Heterogeneous Reservoirs: Effect of Permeability and Injection Method

SPE Journal ◽  
2017 ◽  
Vol 22 (05) ◽  
pp. 1402-1415 ◽  
Author(s):  
A. H. Al Ayesh ◽  
R.. Salazar ◽  
R.. Farajzadeh ◽  
S.. Vincent-Bonnieu ◽  
W. R. Rossen
Keyword(s):  
Oil Recovery ◽  
Water Saturation ◽  
Gas Injection ◽  
Surfactant Solution ◽  
Model Parameters ◽  
High Permeability ◽  
Fractional Flow ◽  
Injection Method ◽  
Heterogeneous Reservoirs ◽  
Irreducible Water Saturation

Summary Foam can divert flow from higher- to lower-permeability layers and thereby improve the injection profile in gas-injection enhanced oil recovery (EOR). This paper compares two methods of foam injection, surfactant-alternating-gas (SAG) and coinjection of gas and surfactant solution, in their abilities to improve injection profiles in heterogeneous reservoirs. We examine the effects of these two injection methods on diversion by use of fractional-flow modeling. The foam-model parameters for four sandstone formations ranging in permeability from 6 to 1,900 md presented by Kapetas et al. (2015) are used to represent a hypothetical reservoir containing four noncommunicating layers. Permeability affects both the mobility reduction of wet foam in the low-quality-foam regime and the limiting capillary pressure at which foam collapses. The effectiveness of diversion varies greatly with the injection method. In a SAG process, diversion of the first slug of gas depends on foam behavior at very-high foam quality. Mobility in the foam bank during gas injection depends on the nature of a shock front that bypasses most foam qualities usually studied in the laboratory. The foam with the lowest mobility at fixed foam quality does not necessarily give the lowest mobility in a SAG process. In particular, diversion in SAG depends on how and whether foam collapses at low water saturation; this property varies greatly among the foams reported by Kapetas et al. (2015). Moreover, diversion depends on the size of the surfactant slug received by each layer before gas injection. This favors diversion away from high-permeability layers that receive a large surfactant slug. However, there is an optimum surfactant-slug size: Too little surfactant and diversion from high-permeability layers is not effective, whereas with too much, mobility is reduced in low-permeability layers. For a SAG process, injectivity and diversion depend critically on whether foam collapses completely at irreducible water saturation. In addition, we show the diversion expected in a foam-injection process as a function of foam quality. The faster propagation of surfactant and foam in the higher-permeability layers aids in diversion, as expected. This depends on foam quality and non-Newtonian foam mobility and varies with injection time. Injectivity is extremely poor with foam injection for these extremely strong foams, but for some SAG foam processes with effective diversion it is better than injectivity in a waterflood.

Quantitative comparison of processes of oil- and water-based mud-filtrate invasion and corresponding effects on borehole resistivity measurements

Geophysics ◽  
2009 ◽  
Vol 74 (1) ◽  
pp. E57-E73 ◽  
Author(s):  
Jesús M. Salazar ◽  
Carlos Torres-Verdín
Keyword(s):  
Electrical Resistivity ◽  
Flow Rate ◽  
Water Saturation ◽  
Base Case ◽  
Petrophysical Properties ◽  
Resistivity Measurements ◽  
Fluid Saturation ◽  
Mud Cake ◽  
Water Based ◽  
Mud Filtrate

Some laboratory and qualitative studies have documented the influence of water-based mud(WBM)-filtrate invasion on borehole resistivity measurements. Negligible work, however, has been devoted to studying the effects of oil-based mud(OBM)-filtrate invasion on well logs and the corresponding impact on the estimation of petrophysical properties. We quantitatively compare the effects of WBM- and OBM-filtrate invasion on borehole resistivity measurements. We simulate the process of mud-filtrate invasion into a porous and permeable rock formation assuming 1D radial distributions of fluid saturation and fluid properties while other petrophysical properties remain constant. To simulate the process of mud-filtrate invasion, we calculate a time-dependent flow rate of OBM-filtrate invasion by adapting the available formulation of the physics of WBM-filtrate invasion. This approach includes the dynamically coupled effects of mud-cake growth and multiphase filtrate invasion. Simulations are performed with a commercial adaptive-implicit compositional formulation that enables the quantification of effects caused by additional components of mud-filtrate and native fluids. The formation under analysis is 100% water saturated (base case) andis invaded with a single-component OBM. Subsequently, we perform simulations of WBM filtrate invading the same formation assuming that it is hydrocarbon bearing, and compare the results to those obtained in the presence of OBM. At the end of this process, we invoke Archie’s equation to calculate the radial distribution of electrical resistivity from the simulated radial distributions of water saturation and salt concentration and compare the effects of invasion on borehole resistivity measurements acquired in the presence of OBM and WBM. Simulations confirm that the flow rate of OBM-filtrate invasion remains controlled by the initial mud-cake permeability and formation petrophysical properties, specifically capillary pressure and relative permeability. Moreover, WBM causes radial lengths of invasion 15%–40% larger than those associated with OBM as observed on the radial distributions of electrical resistivity. It is found also that, in general, flow rates of WBM-filtrate invasion are higher than those of OBM-filtrate invasion caused by viscosity contrasts between OBM filtrate and native fluids, which slow down the process of invasion. Such a conclusion is validated by the marginal variability of array-induction resistivity measurements observed in simulations of OBM invasion compared with those of WBM invasion.

Gridded Operational Consensus Forecasts of 2-m Temperature over Australia

2012 ◽  
Vol 27 (2) ◽  
pp. 301-322 ◽  
Author(s):  
Chermelle Engel ◽  
Elizabeth E. Ebert
Keyword(s):  
Bias Correction ◽  
Statistical Approach ◽  
Weather Prediction ◽  
Weighted Average ◽  
Numerical Weather Prediction Model ◽  
Small Scale ◽  
Coarse Scale ◽  
Consensus Forecasts ◽  
Average Consensus ◽  
Almost All

Abstract This paper describes an extension of an operational consensus forecasting (OCF) scheme from site forecasts to gridded forecasts. OCF is a multimodel consensus scheme including bias correction and weighting. Bias correction and weighting are done on a scale common to almost all multimodel inputs (1.25°), which are then downscaled using a statistical approach to an approximately 5-km-resolution grid. Local and international numerical weather prediction model inputs are found to have coarse scale biases that respond to simple bias correction, with the weighted average consensus at 1.25° outperforming all models at that scale. Statistical downscaling is found to remove the systematic representativeness error when downscaling from 1.25° to 5 km, though it cannot resolve scale differences associated with transient small-scale weather.

scholarly journals Effcts of smooth divergence-free flows on tracer gradients and spectra: Eulerian prognosis description

2021 ◽  
Author(s):  
Valentin Resseguier ◽  
Bertrand Chapron ◽  
Etienne Mémin
Keyword(s):  
Growth Rate ◽  
Finite Time ◽  
Eddy Diffusivity ◽  
Spectral Energy ◽  
Optimal Time ◽  
Small Scale ◽  
Coarse Scale ◽  
Mixing Processes ◽  
Finite Time Lyapunov Exponents ◽  
Flow Gradients

AbstractOcean eddies play an important role in the transport of heat, salt, nutrients or pollutants. During a finite-time advection, the gradients of these tracers can increase or decrease, depending on a growth rate and the angle between flow gradients and initial tracer gradients. The growth rate is directly related to finite-time Lyapunov exponents. Numerous studies on mixing and/or tracer downscaling methods rely on satellite altimeter-derived ocean velocities. Filtering most oceanic small-scale eddies, the resulting smooth Eulerian velocities are often stationary during the characteristic time of tracer gradient growth. While smooth, these velocity fields are still locally misaligned, and thus uncorrelated, to many coarse-scale tracers observations amendable to downscaling (e.g. SST, SSS). Using finite-time advections, the averaged squared norm of tracer gradients can then only increase, with local growth rate independent of the initial coarse-scale tracer distribution. The key mixing processes are then only governed by locally uniform shears and foldings around stationary convective cells. To predict the tracer deformations and the evolution of their 2nd-order statistics, an effcient proxy is proposed. Applied to a single velocity snapshot, this proxy extends the Okubo-Weiss criterion. For the Lagrangian-advection-based downscaling methods, it further successfully predicts the evolution of tracer spectral energy density after a finite time, and the optimal time to stop the downscaling operation. A practical estimation can then be proposed to define an effective parameterization of the horizontal eddy diffusivity.

Scale-up of agitated crystallizers; Cooling batch crystallization of potassium aluminium sulphate

1982 ◽  
Vol 47 (4) ◽  
pp. 1189-1194 ◽  
Author(s):  
Jaroslav Nývlt ◽  
Piotr Karpiński ◽  
Stanislav Žáček ◽  
Miloslav Karel ◽  
Jerzy Budz ◽  
...  
Keyword(s):  
Experimental Error ◽  
Scale Up ◽  
Laboratory Scale ◽  
Small Scale ◽  
Sieve Analysis ◽  
Aluminium Sulphate ◽  
Derived Relations ◽  
Batch Crystallization ◽  
Mean Size ◽  
The Mean

The crystallization of potassium aluminium sulphate was conducted by cooling a solution saturated at 70°C to a temperature of 25°C at three various cooling rates. The measurements were performed on a small scale (160 cm3) and a large laboratory scale (0.021 m3). The mean size of product crystals was determined by sieve analysis, and the system constant, BN, was calculated using previously derived relations. The BN value is the same, within experimental error, for all the experiments and scales, indicating that agitated-vessel cooling crystallizers can be modelled successfully even on a very small laboratory scale.

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