Relative Permeability Functions Research Articles

Impact of gas type on microfluidic drainage experiments and pore network modeling relevant for underground hydrogen storage

Underground hydrogen storage (UHS) in geological reservoirs is proposed as a technically feasible solution to balance mismatch between supply and demand in emerging markets. However, unique hydrogen properties and coupled flow mechanisms require new investigations to fully understand transport and storage of hydrogen in porous media across scales. Here we use microfluidics to investigate the effect of gas type and injection rate on flow patterns, saturation and connectivity of the gas phase. We visually observe that gas flow is characterized by capillary fingering, further confirmed by fractal dimension analysis. At lower injection rates, the gas saturation after drainage appears to increase with gas viscosity, with lower hydrogen saturation compared to methane and nitrogen. The maximum gas saturations (39–46 %) were achieved at higher injection rates, showing no clear correlation to gas type. However, the high-rate injections lead to undesired outcomes in terms of formation of disconnected gas ganglia, mostly pronounced for nitrogen. We identify an optimal injection rate to achieve maximum gas saturation with the least amount of disconnected gas. The experimental results are supported with pore network modeling to derive relative permeability and capillary pressure functions.

The method of calculation of relative phase permeability functions based on the empirical interfacial interaction function

The article describes the results of research about the creation of an empirical method for calculation relative phase permeability functions (RPP). The method based on calculation of interfacial interaction function (IIF) from the experimental SCAL data and searching multi-parameter dependences for the parameters of the approximation dependence of IIF. It is proposed to use a function defined on two segments of the domain of definition, for approximation of IIF. The research had been carried out on laboratory data for group of terrigenous and carbonate samples. It had been established that the pressure losses due to interfacial interaction of oil and water during the joint flow of the water-oil mixture are at the maximum for the considered core samples from 60 to 90% of the total pressure losses. Multi-parameter dependences for IIF parameters were found for both groups of data. It was defined that using of multi-parameter dependences for IIF parameters provides the quality of RPP forecast with deviation by 30% for terrigenous samples and by 22% for carbonate samples. There was conducted the study of the influence of data set amount for multi-parameter dependences (training set) on the quality of RPP forecast (test set). It had been established that increasing of data set amount for multi-parameter dependences of IIF parameters has a positive effect on the quality of RPP functions forecast. At the same time, the increasing of data set amount in 2 times leads to decreasing of the average relative error of RPP calculation from 25.5 to 20.9% for terrigenous samples and from 70.3 to 23.6% for carbonate samples.

Effective permeability of an immiscible fluid in porous media determined from its geometric state

Based on Darcy's law, two-fluid flow is dependent on a relative permeability function of saturation only that is process/path dependent with an underlying dependency on pore structure and wettability. We develop an Artificial Neural Network (ANN) that relies on fundamental geometrical measures to determine relative permeability. The developed ANN is based on a prescribed set of state variables based on physical insights that predicts the relative permeability of 4,500 unseen pore-scale geometrical states with ${R}^{2}$ = 0.98.

Numerical studies of hydrogen buoyant flow in storage aquifers

Understanding buoyancy-driven flow is essential for ensuring the safety, reliability, and efficiency of underground hydrogen storage in saline aquifers. In this study, we develop a three-dimensional (3D) numerical model of an aquifer for hydrogen storage, with an isothermal system at 323.15 K, to investigate the behavior of hydrogen buoyant flow. We perform a series of sensitivity simulations to examine the influence of storage formation heterogeneity, including Dykstra-Parsons coefficient, autocorrelation length, and permeability anisotropy, as well as fluid-rock interaction parameters, such as capillary pressure and relative permeability, on storage efficiency. We evaluate the efficiency of geologic storage containment by quantifying a defined metric “escape ratio,” which is the mass fraction of hydrogen in a presumed escape region over the total mass of hydrogen. Our results indicate that hydrogen escape ratios and migration characteristics are primarily influenced by formation heterogeneities. The escape ratio decreases as Dykstra-Parsons coefficient increases and permeability anisotropy ratio decreases. The specific hydrogen escape path is controlled by spatial structures (i.e., autocorrelation length). Inclusion of capillary heterogeneity results in a decrease in the escape ratio, and the escape region exhibits a smoother appearance in the absence of capillary heterogeneity trapping as compared to when it is modeled. As for fluid-rock interactions, the hydrogen escape ratio is highly susceptible to the exponent of Brooks-Corey relative permeability function. Nevertheless, the magnitude of the escape ratio variation is predominantly determined by formation heterogeneity.

Localized RBF methods for modeling infiltration using the Kirchhoff-transformed Richards equation

We develop a new approach to solve the nonlinear Richards equation based on the Kirchhoff transformation and localized radial basis function (LRBF) techniques. Our aim is to reduce the nonlinearity of the governing equation and apply LRBF methods for modeling unsaturated flow through heterogeneous soils. In our methodology, we propose special techniques which deal with the heterogeneity of the medium in order to apply the Kirchhoff transformation where we used the Brooks and Corey model for the capillary pressure function and a power-law relation in saturation for the relative permeability function. The new approach allows us to avoid the technical issues encountered in the Kirchhoff transformation due to soil heterogeneity in order to reduce the nonlinearity of the model equation. The resulting Kirchhoff-transformed Richards equation is solved using LRBF methods which have advantages in terms of computational cost since they do not require mesh generation. Furthermore, LRBF techniques lead to a system with a sparse matrix which allows us to avoid ill-conditioned issues. To validate the developed approach for predicting the dynamics of unsaturated flow in porous media, numerical experiments are performed in one, two, and three-dimensional soils. The numerical results demonstrate the efficiency and accuracy of the proposed techniques for modeling infiltration through heterogeneous soils.

Calculation and analysis of the unbalanced magnetic thrust for the linear motor drive motion system

AbstractThe unbalanced magnetic thrust caused by the mover eccentricity for the linear motor drive motion system is analytically represented. Firstly, the relative complex magnetic permeability function is introduced to represent the effects of the mechanical installation errors and vibrations on the mover eccentricity. Then, the distortion of the magnetic field caused by the mover eccentricity is represented based on the Maxwell equation. The spectrum characteristics of the unbalanced magnetic thrust force is analytically calculated taking into account the harmonics in the drive circuit. Finally, the validity of the theoretically analysis is verified by the experiments. The results show that the static eccentricity caused by the mechanical installation error will produce the unbalanced magnetic thrust, affecting the thrust characteristics of the linear motor. In particular, the dynamic mover eccentricity caused by the mechanical vibration will produce paired unbalanced magnetic thrust harmonics on both sides of the original thrust harmonics, deteriorating the dynamic precision and efficiency of the direct drive motion system.

Impact of parameter updates on soil moisture assimilation in a 3D heterogeneous hillslope model

Abstract. Variably saturated subsurface flow models require knowledge of the soil hydraulic parameters. However, the determination of these parameters in heterogeneous soils is not easily feasible and subject to large uncertainties. As the modeled soil moisture is very sensitive to these parameters, especially the saturated hydraulic conductivity, porosity, and the parameters describing the retention and relative permeability functions, it is likewise highly uncertain. Data assimilation can be used to handle and reduce both the state and parameter uncertainty. In this work, we apply the ensemble Kalman filter (EnKF) to a three-dimensional heterogeneous hillslope model and investigate the influence of updating the different soil hydraulic parameters on the accuracy of the estimated soil moisture. We further examine the usage of a simplified layered soil structure instead of the fully resolved heterogeneous soil structure in the ensemble. It is shown that the best estimates are obtained when performing a joint update of porosity and the van Genuchten parameters and (optionally) the saturated hydraulic conductivity. The usage of a simplified soil structure gave decent estimates of spatially averaged soil moisture in combination with parameter updates but led to a failure of the EnKF and very poor soil moisture estimates at non-observed locations.

Dynamic Relative Permeabilities for Partially Saturated Porous Media Accounting for Viscous Coupling Effects: An Analytical Solution

We present an analytical model to compute frequency-dependent relative permeability functions for partially saturated porous media accounting for viscous coupling effects. For this, we consider the oscillatory motion of two immiscible fluid phases and solve the Navier–Stokes equations at the pore scale using suitable interface conditions between fluids. These calculations are combined with the generalized two-phase flow Darcy equations to obtain the corresponding upscaled macroscopic fluxes. By means of an analog pore model consisting of a bundle of cylindrical capillaries in which pore fluids are distributed in a concentric manner, we find closed analytical expressions for the complex-valued and frequency- and saturation-dependent relative permeability functions. These expressions allow for a direct assessment of viscous coupling effects on oscillatory flow for all frequencies and saturations. Our results show that viscous coupling effects significantly affect flow characteristics in the viscous and inertial regimes. Dynamic relative permeabilities are affected by the pore fluid densities and viscosities. Moreover, viscous coupling effects may induce two critical frequencies in the dynamic relative permeability curves, a characteristic that cannot be addressed by extending the classic dynamic permeability definition to partially saturated scenarios using effective fluids. The theoretical derivations and results presented in this work have implications for the estimation and interpretation of seismic and seismoelectric responses of partially saturated porous media.

Water Retention Curve–Based Design Method for the Artificial Ground Freezing: The Isarco River Underpass Tunnels within the Brenner Base Tunnel Project

The paper presents an interpretation of the temperature monitored during the application of artificial ground freezing in the Isarco River Underpass tunnel, within the Brenner Base Tunnel project. The observations gathered in the in situ monitoring provided an opportunity to (1) examine the response of a heterogeneous glacial and river deposit composed of gravelly loose sand and boulders subject to seepage, upon freezing; and (2) set up a coupled (thermohydraulic) theoretical formulation, which accounts for the water retention curve and relative permeability function, able to properly simulate the artificial ground freezing process on a heterogeneous coarse subsoil under seepage. The simulation was able to provide a satisfactory representation of the development of the in situ monitoring data and it revealed the dependence between the freezing process, the retention properties of the subsoil, and the seepage velocity. A sensitivity analysis was also carried out to examine the potential effect of water retention parameters on the frozen wall formation in terms of thickness and closing time. The critical examination of in situ observations and the results of the numerical analyses allowed the definition of a new criteria to define the freezing temperature of the soil based on the water retention curve features and the residual degree of saturation, with the aim to optimize the design of the artificial ground freezing process by maintaining the safety level against waterproofing of the excavation area.

A semi-analytical rate-transient analysis model for light oil reservoirs exhibiting reservoir heterogeneity and multiphase flow

Rate-transient analysis (RTA) has been widely applied to extract estimates of reservoir/hydraulic fracture properties. However, the majority of RTA techniques can lead to misdiagnosis of reservoir/fracture information when the reservoir exhibits reservoir heterogeneity and multiphase flow simultaneously. This work proposes a practical-yet-rigorous method to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, and improve the evaluation of reservoir/fracture properties. A new, general, semi-analytical model is proposed that explicitly accounts for multiphase flow, fractal-based reservoir heterogeneity, anomalous diffusion, and pressure-dependent fluid properties. This is achieved by introducing a new Boltzmann-type transformation, the exponent of which includes reservoir heterogeneity and anomalous diffusion. In order to decouple the effects of reservoir heterogeneity and multiphase flow during TLF, the modified Boltzmann variable allows the conversion of three partial differential equations (PDE's) (i.e., oil, gas and water diffusion equations) into ordinary differential equations (ODE's) that are easily solved using the Runge-Kutta (RK) method. A modified time-power-law plot is also proposed to estimate the reservoir and fracture properties, recognizing that the classical square-root-of-time-plot is no longer valid when various reservoir complexities are exhibited simultaneously. Using the slope of the straight line on the modified time-power-law plot, the linear flow parameter can be estimated with more confidence. Moreover, because of the new Boltzmann-type transformation, reservoir and fracture properties can be derived more efficiently without the need for defining complex pseudo-variable transformations. Using the new semi-analytical model, the effects of multiphase flow, reservoir heterogeneity and anomalous diffusion on rate-decline behavior are evaluated. For the case of approximately constant flowing pressure, multiphase flow impacts initial oil rate, which is a function of oil relative permeability and well flowing pressure. However, multiphase flow has a minor effect on the oil production decline exponent. Reservoir heterogeneity/anomalous diffusion affect both the initial oil production rate and production decline exponent. The production decline exponent constant is a function of reservoir heterogeneity/anomalous diffusion only. The practical significance of this work is the advancement of RTA techniques to allow for more complex reservoir scenarios, leading to more accurate production forecasting and better-informed capital planning.

Forced imbibition and uncertainty modeling using the morphological method

The morphological approach is a computationally attractive method for calculating relative permeability and capillary pressure saturation functions. In the corresponding workflow, morphological operations are used to calculate the fluid phase distribution in the pore space of a digital twin. Once the pore space is occupied, the conductivity of the individual fluid phases and thus the relative permeability can be calculated by direct flow simulations. It therefore combines computationally favorable geometric operations with direct flow simulations. In contrast to pore network modeling, all calculations are directly performed on the digital twin without abstraction of the pore space. While the morphological operations conceptually correctly describe primary drainage processes and delivers good results, the method so far failed to describe imbibition processes and the influence of wettability. In this work, we implement contact angle distributions in a deterministic and stochastic way. In this manner, we extend the simulated saturation range from purely spontaneous to forced imbibition, resulting in a full-range imbibition relative permeability. Furthermore, by introducing stochastic contact angle distributions, different fluid phase distributions are obtained, which now allow for an uncertainty analysis. To verify the simulation results, we check (a) whether the simulation results agree with SCAL measurements and (b) compare morphologically and experimentally derived results on the pore scale. With the newly introduced concepts, the imbibition process behaves as physically expected, and shows a good agreement with experimentally derived relative permeability curves and microscopic fluid-phase distributions.

Impact of experimentally measured relative permeability hysteresis on reservoir-scale performance of underground hydrogen storage (UHS)

Underground Hydrogen Storage (UHS) is an emerging large-scale energy storage technology. Researchers are investigating its feasibility and performance, including its injectivity, productivity, and storage capacity through numerical simulations. However, several ad-hoc relative permeability and capillary pressure functions have been used in the literature, with no direct link to the underlying physics of the hydrogen storage and production process. Recent relative permeability measurements for the hydrogen-brine system show very low hydrogen relative permeability and strong liquid phase hysteresis, very different to what has been observed for other fluid systems for the same rock type. This raises the concern as to what extend the existing studies in the literature are able to reliably quantify the feasibility of the potential storage projects. In this study, we investigate how experimentally measured hydrogen-brine relative permeability hysteresis affects the performance of UHS projects through numerical reservoir simulations. Relative permeability data measured during a hydrogen-water core-flooding experiment within ADMIRE project is used to design a relative permeability hysteresis model. Next, numerical simulation for a UHS project in a generic braided-fluvial water-gas reservoir is performed using this hysteresis model. A performance assessment is carried out for several UHS scenarios with different drainage relative permeability curves, hysteresis model coefficients, and injection/production rates. Our results show that both gas and liquid relative permeability hysteresis play an important role in UHS irrespective of injection/production rate. Ignoring gas hysteresis may cause up to 338% of uncertainty on cumulative hydrogen production, as it has negative effects on injectivity and productivity due to the resulting limited variation range of gas saturation and pressure during cyclic operations. In contrast, hysteresis in the liquid phase relative permeability resolves this issue to some extent by improving the displacement of the liquid phase. Finally, implementing relative permeability curves from other fluid systems during UHS performance assessment will cause uncertainty in terms of gas saturation and up to 141% underestimation on cumulative hydrogen production. These observations illustrate the importance of using relative permeability curves characteristic of hydrogen-brine system for assessing the UHS performances.

Simultaneous interpretation of SCAL data with different degrees of freedom and uncertainty analysis

Multiphase flow in porous media is relevant in many areas of geoenergy engineering and is governed by relative permeability and capillary pressure saturation functions. These functions are key uncertainties in reservoir engineering and their measurement is demanding and resource intensive. Despite the experimental effort, it is not yet common practice to numerically interpret the data, nor is it common practice to investigate their uncertainty. Furthermore, data interpretation is limited to power-law functions, which is insufficient for describing complex rock types such as microscopically heterogeneous carbonates.We developed a MATLAB-MRST-based simulator for simultaneous interpretation of data sets from different experimental techniques. We discuss the implementation of the common parametrized relative permeability representations and their deficiency to describe data from complex rocks. To overcome this limitation, a point-by-point approach is developed and applied to an extensive carbonate data set. For uncertainty analysis, a Markov Chain Monte Carlo sampling-based workflow is implemented and applied. The uncertainty is discussed in the frame of the individual data set, simultaneously analyzed data sets, and the sample-to-sample variation. The developed method makes the interpretation of relative permeability and capillary pressure saturation functions conclusive, especially in cases of complex line shapes, and is an essential step toward uncertainty-driven stochastic reservoir modeling.

A dual-continuum model (TOUGH2) for characterizing flow and discharge in a mechanically disrupted sandstone overburden

Underground hard coal mining usually disrupts the mechanical equilibrium of rock sequences, creating fractures within minor permeable rocks. The present study employs a dual-continuum model to assess how both fractured and porous sandstone media influence the percolation process in postmining setups. To test the approach, the software TOUGH2 was employed to simulate laminar fluid flow in the unsaturated zone of the Ibbenbüren Westfield mining area. Compared to other coal mining districts in Germany, this area is delineated by the topography and local geology, leading to a well-defined hydrogeological framework. Results reveal good agreement between the calculated and measured mine water discharge for the years 2008 and 2017. The constructed model was capable of reproducing the bimodal flow behavior of the adit by coupling a permeable fractured continuum with a low-conductivity rock matrix. While flow from the fractured continuum results in intense discharge events during winter months, the rock matrix determines a smooth discharge limb in summer. The study also evaluates the influence of individual and combined model parameters affecting the simulated curve. A detailed sensitivity analysis displayed the absolute and relative permeability function parameters of both continua among the most susceptible variables. However, a strong a priori knowledge of the value ranges for the matrix continuum helps to reduce the model ambiguity. This allowed for calibration of some of the fractured medium parameters for which sparse or variable data were available. However, the inclusion of the transport component and acquisition of more site-specific data is recommended to reduce their uncertainty.

The Role of Immiscible Fingering on the Mechanism of Secondary and Tertiary Polymer Flooding of Viscous Oil

Immiscible viscous fingering in porous media occurs when a low viscosity fluid displaces a significantly more viscous, immiscible resident fluid; for example, the displacement of a higher viscosity oil with water (where μo > > μw). Classically, this is a significant issue during oil recovery processes, where water is injected into the reservoir to provide pressure support and to drive the oil production. In moderate/heavy oil, this leads to the formation of strong water fingers, bypassed oil and high/early water production. Polymer flooding, where the injected water is viscosified through addition of high molecular weight polymers, has often been applied to reduce the viscosity contrast between the two immiscible fluids. In recent years, there has been significant development in the understanding of both the mechanism by which polymer flooding improves viscous oil recovery, as well as in the methodologies available to directly simulate such processes. One key advance in modelling the correct mechanism of polymer oil recovery in viscous oils has been the development of a method to accurately model the “simple” two-phase immiscible fingering (Sorbie in Transp Porous Media 135:331–359, 2020). This was achieved by first choosing the correct fractional flow and then deriving the maximum mobility relative permeability functions from this. It has been proposed that central to the polymer oil recovery is a fingering/viscous crossflow mechanism, and a summary of this is given in this paper. This work seeks to validate the proposed immiscible fingering/viscous crossflow mechanism experimentally for a moderately viscous oil (μo = 84 mPa.s at 31 °C; μw = 0.81 mPa.s; thus, (μo/μw) ~ 104) by performing a series of carefully monitored core floods. The results from these experiments are simulated directly to establish the potential of our modified simulation approach to capture the process (Sorbie, et al., 2020). Both secondary and tertiary polymer flooding experiments are presented and compared with the waterflood baselines, which have been established for each core system. The oil production, water cut and differential pressure are then matched directly using a commercial numerical reservoir simulator, but using our new “fractional flow” derived relative permeabilities. The use of polymer flooding, even when applied at a high water cut (80% after 0.5 PV of water injection), showed a significant impact on recovery; bringing the recovery significantly forward in time for both tertiary and secondary polymer injection modes—a further 13–16% OOIP. Each flood was then directly matched in the simulator with excellent agreement in all experimental cases. The simulations allowed a quantitative visualisation of the immiscible finger propagation from both water injection and the banking of connate water during polymer flooding. Evidence of a strong oil bank forming in front of the tertiary polymer slug was also observed, in line with the proposed viscous crossflow mechanism. This work provides validation of both polymer flooding’s viscous crossflow mechanism and the direct simulation methodology proposed by Sorbie et al. (Transp Porous Media 135:331–359, 2020). The experimental results show the significant potential for both secondary and tertiary polymer flooding in moderate/heavy oil reservoirs.

Parameter estimation from spontaneous imbibition into volcanic tuff

AbstractTwo‐phase fluid flow properties underlie quantitative prediction of water and gas movement, but constraining these properties typically requires multiple time‐consuming laboratory methods. The estimation of two‐phase flow properties (van Genuchten parameters, porosity, and intrinsic permeability) is illustrated in cores of vitric nonwelded volcanic tuff using Bayesian parameter estimation that fits numerical models to observations from spontaneous imbibition experiments. The uniqueness and correlation of the estimated parameters is explored using different modeling assumptions and subsets of the observed data. The resulting estimation process is sensitive to both moisture retention and relative permeability functions, thereby offering a comprehensive method for constraining both functions. The data collected during this relatively simple laboratory experiment, used in conjunction with a numerical model and a global optimizer, result in a viable approach for augmenting more traditional capillary pressure data obtained from hanging water column, membrane plate extractor, or mercury intrusion methods. This method may be useful when imbibition rather than drainage parameters are sought, when larger samples (e.g., including heterogeneity or fractures) need to be tested that cannot be accommodated in more traditional methods, or when in educational laboratory settings.

Role of critical gas saturation in the interpretation of a field scale CO2 injection experiment

Residual trapping of CO2, typically quantified by residual gas saturation (Sgr), is one of the main trapping mechanisms in geological CO2 storage (GCS). An important additional characteristic parameter is critical gas saturation (Sgc). Sgc determines at what saturation the trapped gas remobilizes again if gas saturation increases due to exsolution from the aqueous phase, rather than from further gas injection. In the present study, a pilot-scale CO2 injection experiment carried out at Heletz, Israel, in 2017, is interpreted by taking critical saturation into account. With regards to this experiment, the delayed second arrival peak of the partitioning tracer could not be captured by means of physical models. In this work, the hysteretic relative permeability functions were modified to account for Sgc. The results showed that accounting for the effect of Sgc during the secondary drainage indeed captured the observed delayed peak. The difference between the values of Sgr and Sgc, influenced both the time and peak height of the tracer arrival. To our knowledge this is first time that critical gas saturation has been considered in field scale analyses related to GCS. Accounting for Sgc is relevant where gas saturation during secondary drainage increases due to gas phase expansion or exsolution from the aqueous phase. This will happen in situations where pressure depletion occurs, e.g. due to gas leakage from fracture zones or wells or possibly because of pressure management activities. The findings also have implications for other applications such as underground gas storage as well as for geothermal reservoir management.

Machine learning assisted relative permeability upscaling for uncertainty quantification

Traditional two-phase relative permeability upscaling entails the computation of upscaled relative permeability functions for each coarse block (or interface). The procedure can be extremely time-consuming especially for cases with multiple (hundreds of) geological realizations as commonly used in subsurface uncertainty quantification or optimization. In this paper, we develop a machine learning assisted relative permeability upscaling method, in which the flow-based two-phase upscaling is performed for only a small portion of the coarse blocks (or interfaces), while the upscaled relative permeability functions for the rest of the coarse blocks (or interfaces) are quickly computed by machine learning algorithms. The upscaling procedure was tested for generic (left to right) flow problems using 2D models for scenarios involving multiple realizations. Both Gaussian and channelized models with standard boundary conditions and effective flux boundary conditions (EFBCs) are considered. Numerical results have shown that the coarse-scale simulation results using the newly developed machine learning assisted upscaling are of similar accuracy to the coarse results using full numerical upscaling at both ensemble and realization-by-realization levels. Because the full flow-based upscaling is only performed for a small fraction of the models, significant speedups are achieved.

Sensitivity Analysis Strategy to Assess the Salting-Out Problem during CO2 Geological Storage Process

The sensitivity analysis of the salting-out effect on well injectivity is a significant work in the research of geological storage of CO2 in deep saline aquifers, which is helpful in the selection of storage sites and the design of the injection strategy. We conduct a detailed sensitivity analysis about the salting-out process using the local sensitivity method and two global sensitivity methods. Sensitivity coefficients showed that brine salinity (XNaCl) has the highest sensitivity and interaction effect, the CO2 injection rate (QCO2) has a greater influence in the early stage of the salting-out process and a smaller influence in the end stage, and the other three parameters (empirical parameters related to the pore distribution m, the liquid residual saturation in the relative permeability function Splr, and the liquid residual saturation in the capillary pressure function Sclr) have a smaller sensitivity. This paper also analyzes the calculation amount of different sensitivity methods and suitable ways of obtaining the sensitivity coefficient and reveals the following. (1) The sensitivity coefficient changes dynamically with time, if only the sensitivity of the final state is taken into account on a long-time physical process, and some sensitive parameters during the process may be neglected. (2) The selection of the sample size should be based on the convergence of multiple calculations, and the results of the empirical calculation are uncertain. (3) The calculation of Sobol sensitivity is complicated, the results calculated by surrogate model depend on whether the sample is representative enough; on the other hand, it is feasible to use Sti-Si approximation to characterize the second-order sensitivity to reduce the computation. The research results not only reveal the sensitivity of the parameters related to the injection well salting-out problem during CO2 storage in deep saline aquifers but also guide the calculation of global sensitivity analysis with a similar physical process.

THE CERTAINTY IN UNCERTAINTY: Quantifying coreflood data errors

Multiphase flow in porous media systems is a critical element of many processes in the energy industry. The characteristics of the simultaneous flow of the immiscible phases can be quantified using relative permeability relations. In geoscience applications, these relations are determined in coreflooding studies that often comprise coreflood tests of oil–water mixtures performed on centimetre-scale rock samples. The outcomes of these are subject to uncertainty, which ultimately influences how accurately the parameters from small-scale tests translate to the upscaled estimations. To assess this uncertainty, Shell researchers have developed an inverse modelling workflow for the uncertainty analysis of relative permeability functions derived from coreflood tests. The results suggest that, even at a small scale, the uncertainty can be significant.