History Matching Heterogeneous Coreflood of CO2/Brine by Use of Compositional Reservoir Simulator and Geostatistical Approach

Summary Numerical modeling and simulation are essential tools for developing a better understanding of the geologic characteristics of aquifers and providing technical support for future carbon dioxide (CO2) storage projects. Modeling CO2 sequestration in underground aquifers requires the implementation of models of multiphase flow and CO2 and brine phase behavior. Capillary pressure and relative permeability need to be consistent with permeability/porosity variations of the rock. It is, therefore, crucial to gain confidence in the numerical models by validating the models and results by use of laboratory and field pilot results. A published CO2/brine laboratory coreflood was selected for our simulation study. The experimental results include subcore porosity and CO2-saturation distributions by means of a computed tomography (CT) scanner along with a CO2-saturation histogram. Data used in this paper are all based on those provided by Krause et al. (2011), with the exception of the CT porosity data. We generated a heterogeneous distribution for the porosity but honoring the mean value provided by Krause et al. (2011). We also generated the permeability distribution with the mean value for the whole core given by Krause et al. (2011). All the other data, such as the core dimensions, injection rate, outlet pressure, temperature, relative permeability, and capillary pressure, are the same as those in Krause et al. (2011). High-resolution coreflood simulations of brine displacement with supercritical CO2 are presented with the compositional reservoir simulator IPARS (Wheeler and Wheeler 1990). A 3D synthetic core model was constructed with permeability and porosity distributions generated by use of the geostatistical software FFTSIM [Jennings et al. (2000)], with cell sizes of 1.27×1.27×6.35 mm. The core was initially saturated with brine. Fluid properties were calibrated with the equation-of-state (EOS) compositional model to match the measured data provided by Krause et al. (2011). We used their measured capillary pressure and relative permeability curves. However, we scaled capillary pressure on the basis of the Leverett J-function (Leverett 1941) for permeability, porosity, and interfacial tension (IFT) in every simulation grid cell. Saturation images provide insight into the role of heterogeneity of CO2 distribution in which a slight variation in porosity gives rise to large variations in CO2-saturation distribution in the core. High-resolution numerical results indicated that accurate representation of capillary pressure at small scales was critical. Residual brine saturation and the subsequent shift in the relative permeability curves showed a significant impact on final CO2 distribution in the core.

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Use of a Reservoir Simulator To Interpret Laboratory Waterflood Data

Society of Petroleum Engineers Journal ◽

10.2118/3551-pa ◽

1973 ◽

Vol 13 (06) ◽

pp. 343-347 ◽

Cited By ~ 33

Author(s):

John S. Archer ◽

S.W. Wong

Keyword(s):

Relative Permeability ◽

Core Sample ◽

Reservoir Rock ◽

Relative Permeabilities ◽

Rock System ◽

The Core ◽

Water Breakthrough ◽

Predicting Performance ◽

Relative Permeability Curves ◽

Reservoir Simulator

Abstract Relative permeability curves calculated from laboratory waterflood history by the method of Johnson, Bossler and Naumann (JBN) are often poorly defined or anomalous at low and intermediate poorly defined or anomalous at low and intermediate water saturations. Poor definition can be encountered with strongly water-wet homogeneous cores when the displacement is piston-like. Anomalous curve shapes are associated with laboratory-observed water breakthrough ahead of the main flood front and are common in cores that have contrasting permeability streaks. The JBN technique, although permeability streaks. The JBN technique, although valid for the conditions assumed in its development, is unsatisfactory for the conditions specified above. A reservoir simulator has been used to model laboratory tests and thereby provide an alternative interpretation procedure. The simulation uses core properties and trial-and-error relative permeabilities. properties and trial-and-error relative permeabilities. The shapes of the relative permeability curves are adjusted until calculated oil recovery and relative injectivity curves match those obtained from the laboratory displacement tests. The technique has been used successfully to obtain meaningful relative permeability curves for piston-like displacement, mixed wettability systems, piston-like displacement, mixed wettability systems, and heterogeneous carbonates. The technique has also been used in evaluating empirical equations for calculating relative permeability. Introduction Numerical reservoir simulators are finding increasing application in production history matching and performance predictions. Because of the degree of sophistication reached with these models, it is mandatory that the fluid flow properties be of the highest possible quality. Of all the rock and fluid properties required in predicting performance, it is properties required in predicting performance, it is often the relative permeability characteristics that are the most critically important. These data are usually obtained from laboratory waterflood tests using reservoir core samples. The laboratory waterflood test is an attempt to represent the linear displacement behavior of the oil/water/reservoir-rock system. The wettability properties of the rock system should be preserved properties of the rock system should be preserved in the laboratory core sample if reliable results are to be obtained. Furthermore, the viscosity ratio and surface tension of the oil/water system in the laboratory test should ideally be made the same as those in the reservoir. In interpreting laboratory waterflood tests the unsteady-state equations are usually solved by methods of Buckley-Leverett, Welge and Johnson, Bossler and Neumann (JBN). These interpretations are sometimes inadequate for defining relative permeability curves for heterogeneous reservoir permeability curves for heterogeneous reservoir rock systems or for water displacing a very light oil in a homogeneous sandstone. For example, a number of writers have observed anomalous changes in the relative permeability to water during the flooding of heterogeneous carbonate core samples. The relative permeability to water does not increase smoothly with increasing water saturation, but increases stepwise or even humps. Such behavior appears to reflect small-scale local heterogeneity in the core sample and is likely to be insignificant on a field scale. The heterogeneity is often indicated in the laboratory by an observed water breakthrough at the core-sample production face ahead of the main flood front. The time of water breakthrough is an important measurement used in the calculation of relative permeability by the JBN method. If the breakthrough permeability by the JBN method. If the breakthrough time observed is not that of the main flood front but is a little early, then the relative permeabilities calculated will not represent the properties of the bulk of the core sample. It is under these conditions that anomalous relative permeability curves usually occur. We suggest in this paper that, in many cases, the small changes in pressure and in oil and water production rate that accompany anomalous relative production rate that accompany anomalous relative permeability curves can be smoothed to reflect permeability curves can be smoothed to reflect properties more consistent with the bulk behavior properties more consistent with the bulk behavior of the core sample. In essence, we are saying that together the smoothed oil and water production history and the pressure history of the laboratory core sample represent a unique property of that sample. SPEJ P. 343

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Reliability of Relative Permeability Measurements for Heterogeneous Rocks Using Horizontal Core Flood Experiments

Sustainability ◽

10.3390/su13052744 ◽

2021 ◽

Vol 13 (5) ◽

pp. 2744

Author(s):

Chia-Wei Kuo ◽

Sally M. Benson

Keyword(s):

Capillary Pressure ◽

Relative Permeability ◽

Synthetic Data ◽

Critical Value ◽

Core Flooding ◽

Fractional Flow ◽

The Core ◽

Heterogeneous Rocks ◽

Core Flood ◽

Relative Permeability Curves

New guidelines and suggestions for taking reliable effective relative permeability measurements in heterogeneous rocks are presented. The results are based on a combination of high resolution of 3D core-flooding simulations and semi-analytical solutions for the heterogeneous cores. Synthetic “data sets” are generated using TOUGH2 and are subsequently used to calculate effective relative permeability curves. A comparison between the input relative permeability curves and “calculated” relative permeability is used to assess the accuracy of the “measured” values. The results show that, for a capillary number (Ncv = kLpc × A/H2μCO2qt) smaller than a critical value, flows are viscous dominated. Under these conditions, saturation depends only on the fractional flow as well as capillary heterogeneity, and is independent of flow rate, gravity, permeability, core length, and interfacial tension. Accurate whole-core effective relative permeability measurements can be obtained regardless of the orientation of the core and for a high degree of heterogeneity under a range of relevant and practical conditions. Importantly, the transition from the viscous to gravity/capillary dominated flow regimes occurs at much higher flow rates for heterogeneous rocks. For the capillary numbers larger than the critical value, saturation gradients develop along the length of the core and accurate relative permeability measurements are not obtained using traditional steady-state methods. However, if capillary pressure measurements at the end of the core are available or can be estimated from independently measured capillary pressure curves and the measured saturation at the inlet and outlet of the core, accurate effective relative permeability measurements can be obtained even when there is a small saturation gradient across the core.

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A Machine Learning Methodology for Rock-Typing Using Relative Permeability Curves

10.2118/205989-ms ◽

2021 ◽

Author(s):

Carlos Esteban Alfonso ◽

Frédérique Fournier ◽

Victor Alcobia

Keyword(s):

Machine Learning ◽

Capillary Pressure ◽

Relative Permeability ◽

Fractional Flow ◽

Flow Curves ◽

Rock Types ◽

Rock Typing ◽

Relative Permeability Curves ◽

Permeability Data

Abstract The determination of the petrophysical rock-types often lacks the inclusion of measured multiphase flow properties as the relative permeability curves. This is either the consequence of a limited number of SCAL relative permeability experiments, or due to the difficulty of linking the relative permeability characteristics to standard rock-types stemming from porosity, permeability and capillary pressure. However, as soon as the number of relative permeability curves is significant, they can be processed under the machine learning methodology stated by this paper. The process leads to an automatic definition of relative permeability based rock-types, from a precise and objective characterization of the curve shapes, which would not be achieved with a manual process. It improves the characterization of petrophysical rock-types, prior to their use in static and dynamic modeling. The machine learning approach analyzes the shapes of curves for their automatic classification. It develops a pattern recognition process combining the use of principal component analysis with a non-supervised clustering scheme. Before this, the set of relative permeability curves are pre-processed (normalization with the integration of irreducible water and residual oil saturations for the SCAL relative permeability samples from an imbibition experiment) and integrated under fractional flow curves. Fractional flow curves proved to be an effective way to unify the relative permeability of the two fluid phases, in a unique curve that characterizes the specific poral efficiency displacement of this rock sample. The methodology has been tested in a real data set from a carbonate reservoir having a significant number of relative permeability curves available for the study, in addition to capillary pressure, porosity and permeability data. The results evidenced the successful grouping of the relative permeability samples, according to their fractional flow curves, which allowed the classification of the rocks from poor to best displacement efficiency. This demonstrates the feasibility of the machine learning process for defining automatically rock-types from relative permeability data. The fractional flow rock-types were compared to rock-types obtained from capillary pressure analysis. The results indicated a lack of correspondence between the two series of rock-types, which testifies the additional information brought by the relative permeability data in a rock-typing study. Our results also expose the importance of having good quality SCAL experiments, with an accurate characterization of the saturation end-points, which are used for the normalization of the curves, and a consistent sampling for both capillary pressure and relative permeability measurements.

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Formation Characterization and Production Forecast of Tight Sandstone Formations in Daqing Oilfield Through Digital Rock Technology

10.2118/206055-ms ◽

2021 ◽

Author(s):

Danhua Leslie Zhang ◽

Xiaodong Shi ◽

Chunyan Qi ◽

Jianfei Zhan ◽

Xue Han ◽

...

Keyword(s):

High Resolution ◽

Capillary Pressure ◽

Relative Permeability ◽

Surfactant Solution ◽

Fluid Models ◽

Pore Scale ◽

Field Development ◽

Digital Rock ◽

Small Pore ◽

Sem Imaging

Abstract With the decline of conventional resources, the tight oil reserves in the Daqing oilfield are becoming increasingly important, but measuring relative permeability and determining production forecasts through laboratory core flow tests for tight formations are both difficult and time consuming. Results of laboratory testing are questionable due to the very small pore volume and low permeability of the reservoir rock, and there are challenges in controlling critical parameters during the special core analysis (SCAL) tests. In this paper, the protocol and workflow of a digital rock study for tight sandstones of the Daqing oilfield are discussed. The workflow includes 1) using a combination of various imaging methods to build rock models that are representative of reservoir rocks, 2) constructing digital fluid models of reservoir fluids and injectants, 3) applying laboratory measured wettability index data to define rock-fluid interaction in digital rock models, 4) performing pore-scale modelling to accelerate reservoir characterization and reduce the uncertainty, and 5) performing digital enhanced oil recovery (EOR) tests to analyze potential benefits of different scenarios. The target formations are tight (0.01 to 5 md range) sandstones that have a combination of large grain sizes juxtaposed against small pore openings which makes it challenging to select an appropriate set of imaging tools. To overcome the wide range of pore and grain scales, the imaging tools selected for the study included high resolution microCT imaging on core plugs and mini-plugs sampled from original plugs, overview scanning electron microscopy (SEM) imaging, mineralogical mapping, and high-resolution SEM imaging on the mini-plugs. High resolution digital rock models were constructed and subsequently upscaled to the plug level to differentiate bedding and other features could be differentiated. Permeability and porosity of digital rock models were benchmarked against laboratory measurements to confirm representativeness. The laboratory measured Amott-Harvey wettability index of restored core plugs was honored and applied to the digital rock models. Digital fluid models were built using the fluid PVT data. A Direct HydroDynamic (DHD) pore-scale flow simulator based on density functional hydrodynamics was used to model multiphase flow in the digital experiments. Capillary pressure, water-oil, surfactant solution-oil, and CO2-oil relative permeability were computed, as well as primary depletion followed with three-cycle CO2 huff-n-puff, and primary depletion followed with three-cycle surfactant solution huff-n-puff processes. Recovery factors were obtained for each method and resulting values were compared to establish most effective field development scenarios. The workflow developed in this paper provides fast and reliable means of obtaining critical data for field development design. Capillary pressure and relative permeability data obtained through digital experiments provide key input parameters for reservoir simulation; production scenario forecasts help evaluate various EOR methods. Digital simulations allow the different scenarios to be run on identical rock samples numerous times, which is not possible in the laboratory.

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Uncertainty span for relative permeability and capillary pressure by varying wettability and spatial flow directions utilizing pore scale modelling

E3S Web of Conferences ◽

10.1051/e3sconf/202014601002 ◽

2020 ◽

Vol 146 ◽

pp. 01002

Author(s):

Thomas Ramstad ◽

Anders Kristoffersen ◽

Einar Ebeltoft

Keyword(s):

Continental Shelf ◽

Pore Structure ◽

Capillary Pressure ◽

Relative Permeability ◽

Phase Flow ◽

Pore Scale ◽

Full Field ◽

Scale Modelling ◽

Relative Permeability Curves ◽

Norwegian Continental Shelf

Relative permeability and capillary pressure are key properties within special core analysis and provide crucial information for full field simulation models. These properties are traditionally obtained by multi-phase flow experiments, however pore scale modelling has during the last decade shown to add significant information as well as being less time-consuming to obtain. Pore scale modelling has been performed by using the lattice-Boltzmann method directly on the digital rock models obtained by high resolution micro-CT images on end-trims available when plugs are prepared for traditional SCAL-experiments. These digital rock models map the pore-structure and are used for direct simulations of two-phase flow to relative permeability curves. Various types of wettability conditions are introduced by a wettability map that opens for local variations of wettability on the pore space at the pore level. Focus have been to distribute realistic wettabilities representative for the Norwegian Continental Shelf which is experiencing weakly-wetting conditions and no strong preference neither to water nor oil. Spanning a realistic wettability-map and enabling flow in three directions, a large amount of relative permeability curves is obtained. The resulting relative permeabilities hence estimate the uncertainty of the obtained flow properties on a spatial but specific pore structure with varying, but realistic wettabilities. The obtained relative permeability curves are compared with results obtained by traditional SCAL-analysis on similar core material from the Norwegian Continental Shelf. The results are also compared with the SCAL-model provided for full field simulations for the same field. The results from the pore scale simulations are within the uncertainty span of the SCAL models, mimic the traditional SCAL-experiments and shows that pore scale modelling can provide a time- and cost-effective tool to provide SCAL-models with uncertainties.

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Branching exponent heterogeneity and wall shear stress distribution in vascular trees

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.2001.280.3.h1256 ◽

2001 ◽

Vol 280 (3) ◽

pp. H1256-H1263 ◽

Cited By ~ 23

Author(s):

Kelly L. Karau ◽

Gary S. Krenz ◽

Christopher A. Dawson

Keyword(s):

Shear Stress ◽

Wall Shear Stress ◽

Coefficient Of Variation ◽

Vessel Diameter ◽

Mean Value ◽

Heterogeneous Distribution ◽

Uniform Shear ◽

The Mean ◽

Wall Shear ◽

Stress Dependent

A bifurcating arterial system with Poiseuille flow can function at minimum cost and with uniform wall shear stress if the branching exponent ( z) = 3 [where z is defined by ( D 1) z = ( D 2) z + ( D 3) z ; D 1 is the parent vessel diameter and D 2 and D 3 are the two daughter vessel diameters at a bifurcation]. Because wall shear stress is a physiologically transducible force, shear stress-dependent control over vessel diameter would appear to provide a means for preserving this optimal structure through maintenance of uniform shear stress. A mean z of 3 has been considered confirmation of such a control mechanism. The objective of the present study was to evaluate the consequences of a heterogeneous distribution of z values about the mean with regard to this uniform shear stress hypothesis. Simulations were carried out on model structures otherwise conforming to the criteria consistent with uniform shear stress when z = 3 but with varying distributions of z. The result was that when there was significant heterogeneity in z approaching that found in a real arterial tree, the coefficient of variation in shear stress was comparable to the coefficient of variation in z and nearly independent of the mean value of z. A systematic increase in mean shear stress with decreasing vessel diameter was one component of the variation in shear stress even when the mean z = 3. The conclusion is that the influence of shear stress in determining vessel diameters is not, per se, manifested in a mean value of z. In a vascular tree having a heterogeneous distribution in zvalues, a particular mean value of z (e.g., z = 3) apparently has little bearing on the uniform shear stress hypothesis.

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Coupling and Coordination Degrees of the Core Water–Energy–Food Nexus in China

International Journal of Environmental Research and Public Health ◽

10.3390/ijerph16091648 ◽

2019 ◽

Vol 16 (9) ◽

pp. 1648 ◽

Cited By ~ 7

Author(s):

Shasha Xu ◽

Weijun He ◽

Juqin Shen ◽

Dagmawi Mulugeta Degefu ◽

Liang Yuan ◽

...

Keyword(s):

Complex System ◽

Sustainable Development ◽

Mean Value ◽

Key Factors ◽

The Core ◽

The Mean ◽

Development Levels ◽

High Level ◽

Coordination Development ◽

Coordination Degree

Achieving sustainable development in the water–energy–food (WEF) nexus is gaining global attention. The coupling and coordination degrees are a way to measure sustainable development levels of a complex system. This study assessed the coupling and coordination degrees of the core WEF nexus and identified key factors that affect sustainable development. First, an index system for assessing coupling and coordination degrees of the core WEF nexus was built. Second, the development levels of three subsystems as well as the coupling and coordination degrees of the core WEF nexus in China were calculated. The results showed that from 2007 to 2016, the mean value of the coupling degree was 0.746 (range (0.01, 1)), which was a high level. This proved that the three resources were interdependent. Hence, it was necessary to study their relationship. However, the mean value of the coordination degree was 0.395 (range (0, 1)), which was a low level. This showed that the coordination development of the core WEF nexus in China was low. It is necessary to take some measures to improve the situation. According to the key factors that affect the development levels of water, energy, and food subsystems, the authors put forward some suggestions to improve the coordination development of the WEF system in China.

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Neighborhood Verification: A Strategy for Rewarding Close Forecasts

Weather and Forecasting ◽

10.1175/2009waf2222251.1 ◽

2009 ◽

Vol 24 (6) ◽

pp. 1498-1510 ◽

Cited By ~ 91

Author(s):

Elizabeth E. Ebert

Keyword(s):

High Resolution ◽

Rainfall Intensity ◽

Mean Value ◽

Forecast Performance ◽

Fractional Coverage ◽

Optimal Scale ◽

Verification Methods ◽

Intercomparison Project ◽

The Mean ◽

Spatial Verification

Abstract High-resolution forecasts may be quite useful even when they do not match the observations exactly. Neighborhood verification is a strategy for evaluating the “closeness” of the forecast to the observations within space–time neighborhoods rather than at the grid scale. Various properties of the forecast within a neighborhood can be assessed for similarity to the observations, including the mean value, fractional coverage, occurrence of a forecast event sufficiently near an observed event, and so on. By varying the sizes of the neighborhoods, it is possible to determine the scales for which the forecast has sufficient skill for a particular application. Several neighborhood verification methods have been proposed in the literature in the last decade. This paper examines four such methods in detail for idealized and real high-resolution precipitation forecasts, highlighting what can be learned from each of the methods. When applied to idealized and real precipitation forecasts from the Spatial Verification Methods Intercomparison Project, all four methods showed improved forecast performance for neighborhood sizes larger than grid scale, with the optimal scale for each method varying as a function of rainfall intensity.

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Neutral Saturated Lapse Rate: An Experimental Check from CALJET-1998 and PACJET-2001

Monthly Weather Review ◽

10.1175/2009mwr3009.1 ◽

2009 ◽

Vol 137 (12) ◽

pp. 4382-4385 ◽

Cited By ~ 1

Author(s):

Renzo Richiardone ◽

Massimiliano Manfrin

Keyword(s):

High Resolution ◽

Normal Distribution ◽

Mean Value ◽

Lapse Rate ◽

Temperature Profiles ◽

Experimental Check ◽

Rate Distribution ◽

The Mean ◽

Lapse Rates ◽

Good Agreement

Abstract The lapse rates of high-resolution temperature profiles during nearly neutral, saturated conditions are compared with the saturated adiabatic lapse rate and with that proposed by Richiardone and Giusti. A good agreement between the latter and the mean value of the observed lapse rate is found, whereas the saturated adiabatic lapse rate differs significantly, confirming experimentally that it is not completely correct to assess the moist neutrality from a comparison with the saturated adiabatic lapse rate. The lapse-rate distribution supports the hypothesis that the lapse-rate statistics is a local collection of saturated adiabatic lapse rates in a background normal distribution centered around the neutrality.

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Axisymmetric convection at large Rayleigh and infinite Prandtl number

Journal of Fluid Mechanics ◽

10.1017/s0022112089002909 ◽

1989 ◽

Vol 208 ◽

pp. 459-478 ◽

Cited By ~ 10

Author(s):

Akira Umemura ◽

F. H. Busse

Keyword(s):

Mean Value ◽

Convection Cell ◽

Special Role ◽

Free Boundaries ◽

Core Flow ◽

The Core ◽

The Mean ◽

Convection Rolls ◽

The Relationship ◽

Matched Asymptotic Analysis

A matched-asymptotic analysis has been carried out for an axisymmetric convection cell in the case of stress-free boundaries. This problem differs from that of two-dimensional convection rolls mainly through the special role played by the central plume. The radius, of order ε, of the latter depends on the Rayleigh number R through the relationship $\epsilon^4(-\ln \epsilon) = R^{\frac{2}{3}}$. The plume velocity is independent of height at lowest order and its magnitude exceeds by a factor (− ln ε)½ the strength, of order $R^{\frac{2}{3}}$, of the core flow. As a result of these properties the central plume is governed by advection, in contrast to the perimeter plume which is affected by conduction as well. This asymmetry is reflected in the different thickness of the horizontal thermal boundary layers and gives rise to the deviation of the core temperature from the mean value of the top and bottom temperatures. This deviation is positive (negative) for the case of a falling (rising) central plume. While the core flow is driven mainly by the perimeter plume the fraction of the heat flux carried by the central plume is always above three-quarters and increases as the radius-to-height-ratio λ decreases.

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