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ECMOR XIV - 14th European Conference on the Mathematics of Oil Recovery
- Conference date: September 8-11, 2014
- Location: Catania, Sicily, Italy
- Published: 08 September 2014
21 - 40 of 136 results
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Bias Aware Data Assimilation in Reservoir Characterization
Authors M. Glegola, R.G. Hanea and G. KaletaSummaryIn reservoir characterization, modern reservoir modeling and Assisted History Matching aim at delivering integrated models with quantified uncertainty, constrained on all relevant data.
Traditionally, the reservoir model is updated using only the dynamic production data from the wells. Recently, more and more efforts are made to use Geophysical Reservoir Monitoring (GRM) data in history matching, as these types of data can provide valuable information about the reservoir characteristics and geological formations over the whole field.
Time-lapse (4D) gravimetry is a direct measure of a subsurface mass flow and can provide valuable information in this context. It offers an attractive aerial monitoring technique for reservoirs containing fluids with high density contrasts, e.g., gas and water or oil and steam. The method is especially promising for shallow reservoirs as the 4D signal will be stronger for large and shallow reservoirs, compared to smaller and deeper reservoirs.
In reservoir history matching, often an assumption is made that the forward model predictions and the observations are unbiased, i.e., there are no systematic errors. In this study we investigate the added value of gravimetric observations for gas field monitoring and aquifer support estimation, under the assumption that both model and observations are biased.
We perform a numerical study with a realistic 3D gas field model which contains a large and complex aquifer system. The aquifer support along with other reservoir parameters, such as porosities, permeabilities, reservoir top and bottom horizons etc., are jointly estimated using the Ensemble Smoother (ES).
We show that the influence of the observation bias and/or the model bias on assimilation results can be severe and may lead to large errors in the estimations of the states/parameters. By using bias-aware data assimilation methodology, the bias can be estimated separately from the state, and we show that the deteriorating bias influence on the assimilation results to a large extent can be mitigated.
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On an Alternative Implementation of the Iterative Ensemble Smoother and its Application to Reservoir Facies Estimation
Authors X. Luo, Y. Chen, R. Valestrand, A. Stordal, R. Lorentzen and G. NævdalSummaryFor data assimilation problems there are different ways in using available observations. While certain data assimilation algorithms, for instance, the ensemble Kalman filter (EnKF, see, for example, Aanonsen et al., 2009 ) assimilate the observations sequentially in time, other data assimilation algorithms may instead collect the observations at different time instants and assimilate them simultaneously. In general such algorithms can be classified as smoothers. In this aspect, the ensemble smoother (ES, see, for example, Evensen and van Leeuwen, 2000 ) can be considered as an smoother counterpart of the EnKF.
The EnKF has been widely used for reservoir data assimilation problems since its introduction to the community of petroleum engineering ( Nævdal et al., 2002 ). The applications of the ES to reservoir data assimilation problems are also investigated recently. Compared to the EnKF, the ES has certain technical advantages, including, for instance, avoiding the restarts associated with each update step in the EnKF and also having fewer variables to update, which may result in a significant reduction in simulation time, while providing similar assimilation results to those obtained by the EnKF ( Skjervheim and Evensen, 2011 ).
To further improve the performance of the ES, some iterative ensemble smoothers are suggested in the literature, in which the iterations are carried out in the forms of certain iterative optimization algorithms, e. g., the Gaussian-Newton ( Chen and Oliver, 2012 ) or the Levenberg-Marquardt method ( Chen and Oliver, 2013 ; Emerick and Reynolds, 2012 ), or in the context of adaptive Gaussian mixture (AGM, see Stordal and Lorentzen, 2013).
In this contribution we show that the iteration formulae used in Chen and Oliver (2013) ; Emerick and Reynolds (2012) can also be derived from the regularized Levenberg-Marquardt (RLM) algorithm in inverse problems theory ( Engl et al., 2000 ), with certain linearization approximations introduced to the RLM. This does not only lead to an alternative theoretical tool in understanding and analyzing the behaviour of the aforementioned iterative ES, but also provide insights and guidelines for further developments of the iterative ES algorithm. As an example, we show that an alternative implementation of the iterative ES can be derived based on the RLM algorithm. For illustration, we apply this alternative algorithm to a facies estimation problem previously investigated in Lorentzen et al. (2012) , and compare its performance to that of the (approximate) iterative ES used in Chen and Oliver (2013) .
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Complex Geology Estimation Using the Iterative Adaptive Gaussian Mixture (IAGM)
Authors B. Sebacher, A. Stordal and R.G. HaneaSummaryIn the past years the multi-point geostatistical (MPS) simulation geo-models have been used successfully, creating realistic geological instances(facies
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Evaluation of Ordered Sequential Assimilation for Improved EnKF Sampling
Authors K. Fossum and T. MannsethSummaryEnsemble based data assimilation (DA) methods, such as the (sequential) ensemble Kalman filter (EnKF) and the (non-sequential) ensemble smoother (ES), can both be utilized for solving the inverse problem of estimating poorly known parameters from data consisting of noisy observations of some dynamical system. For cases where we have non-linear data, i.e., when there is a non-linear relationship between the parameters and the dynamical model, both DA methods give inexact results. Moreover, several studies have revealed that for non-linear cases the EnKF and ES give different approximation errors.
We recently conducted a thorough investigation of sequential and non-sequential assimilation schemes. The investigation showed that, for a series of weakly non-linear data, sequential assimilation is favorable to non-sequential assimilation. In addition, analytical, and numerical, evidence showed that by ordering data after ascending non-linearity, one reduces the approximation error for the sequential scheme.
Ordering of data will, however, not reduce the approximation error for all cases. It is clear that for a sequence of highly non-linear data the approximate methods, independent of how the data are ordered, will fail. Likewise, if the data has little variation in non-linearity, nothing is gain by ordered sequential assimilation. In this work, we investigate, by simple toy models, for which range of data non-linearity there is a potential advantage of ordered sequential assimilation.
Furthermore, considering a 2D reservoir case, we evaluate the non-linearity for a collection of production data and production strategies. For each numerical setup, we assess the benefit from ordered sequential assimilation of the data, and we compare the results with results obtained by the toy models.
The assimilation schemes are assessed by comparing their history matching capabilities, and by measuring the stochastic distances between their posterior distributions and the posterior distribution obtained by Markov chain Monte Carlo algorithm. Throughout, the non-linearity is evaluated by a stochastic non-linearity measure.
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Percolation Modeling of Relative Permeability Hysteresis Including Surface and Rheological Effects
Authors V. Kadet and A. GalechyanSummaryThe phenomenon of relative permeability hysteresis is observed during the process of developing the oil field by methods where the flow direction changes. In this case the displacement of oil by water changes into the displacement of water by oil and vice versa. This work is devoted to modeling of relative permeability hysteresis for drainage and imbibition based on percolation theory.
The phenomenon of active oil components adsorption on the rockforming minerals is considered as the first mechanism of hysteresis origin. In the process of drainage this causes surface hydrophobization of initially hydrophilic rock which leads to each phase relative permeability change. To describe this phenomenon percolation model for media with microheterogeneous wettability is used. The second mechanism is fluid rheological properties change, caused by the fluids mixing during drainage. It is described by percolation model for fluids with different rheological properties.
Obtained numerical solution is represented as relative permeability curves and is qualitatively confirmed by the experimental data. The behavior of relative permeability hysteresis is analyzed for various differential radius distribution curves, capillary network coordination numbers, saturation models, hydrophobization degree and fluid rheological properties. It allows to establish general tendencies of relative permeability hysteresis behavior. Introduced methodology can be put into practice for relative permeability calculation in any porous media to reduce the time spent. Also this approach can be embedded in hydrodynamic modeling programs to consider the relative permeability hysteresis effect.
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Four-component Gas/Oil Displacement with Constant Pressure Boundaries
Authors H. Nekouie, L.A. James and T.E. JohansenSummaryThis paper presents the analytical solution of four-component gas/oil displacements under constant pressure boundary conditions. All the previous studies in gas/oil displacement problems have been accomplished under the assumption of constant flux boundaries. In practice however, gas flooding projects are often conducted with constant injection pressure and constant producing well pressure. In this work, a novel generation of Buckley-Leverett’s classic fractional flow theory is applied to solve the problem of four-component gas/oil displacements under constant pressure boundaries.
Conservation of mass in a one-dimensional, dispersion-free medium, for a four-component gas/oil displacement system leads to a set of partial differential equations. The solution of the corresponding initial value problem under constant flux boundary conditions consists of rarefaction waves, shock waves and constant states connecting the injection state to the production state. In incompressible systems with constant pressure boundaries, the total volumetric flux is a function of time and hence, the classical Buckley-Leverett theory is not valid. However, the saturation wave structure obtained from the constant flux boundary condition problem can be used in the solution of the associated problem with constant pressure boundaries by determining the flux analytically as a function of time.
The solution for a four-component gas/oil displacement case study is presented. The determination of time dependent volumetric flux from the solution of the constant flux problem is demonstrated. Results are also obtained using a numerical approach and are compared to the analytical results. This indicates that the analytical solution is indistinguishable from the numerical solution as the number of grid blocks in the numerical method approaches infinity. However, a very fine grid is needed for an acceptable solution.
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Modeling of Black Oil PVT-data
Authors K. Potsch, P. Toplack and T. GumpenbergerSummaryReservoir engineers are in need of information about fluid properties of reservoir fluid before calculating reserves or production scenarios. Mature fields may require reviews of older data sets that are sometimes scarce. The so-called PVT properties (black oil or compositional) are generated in either an in-house or an external lab. Prior to their use, these data sets need to be checked for their correctness and consistency. Modelling with correlations for estimating some of the properties or equations of state (EOS) provides only limited insight. First, they are not applicable for each reservoir fluid. Due to the variety of chemical composition every fluid is unique. Secondly, the correlations are purely numerical, lack non-dimensionality and consider physics only to a limited extent. Black oils separate below saturation pressure into a vapour and a liquid phase. The gas phase, consisting predominantly of the lighter compo-nents, increases with decreasing pressure. In other words, the higher the pressure the more gas is in solution. It influences other quantities, like formation volume factor Bo, oil com-pressibility Cpo and oil viscosity µo. This paper analyzes how the components of the gas phase contribute to the PVT-properties mentioned. It is assumed that the light components assume a certain volume in the liquid phase which is dependent on temperature and pressure. Additionally, the shape of the heavier components plays a role. As the light and heavy molecules in the mixture try to assume a minimal volume, the conversion factor from the va-pour to the liquid volume of the light components varies to some degree. The parameters (conversion factors) necessary to model Bo, Cpo and µo are extracted from experimental data. Mathematically, it is a minimization problem where the variables need to be positive. The solution is sought with a simplex algorithm. Once the parameters are determined, an estimate of Bo, Cpo and µo can be calculated, and plausibility and consistency of lab PVT-data can be carried out. This approach provides a valuable tool for the reservoir engineer in assessing the quality of PVT-data.
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Pore-scale Modelling of Shale Gas Permeability Considering Shale Gas Adsorption
Authors X. Zhao, J. Ma and G. CouplesSummaryShale gas permeability needs to be estimated in order to predict the quality of shale gas reservoirs and to develop shale gas production strategies. With advances in high-resolution imaging technology, one can characterise the pore space of a gas shale sample, which typically contains pores ranging from micrometers to nanometers, and to construct a pore-space model to simulate the gas flow numerically and to calculate the permeability. Gas flow has long been known to behave differently in such a confined space, and the smaller the pores the larger discrepancy is generally expected between gas and liquid (e.g. water) permeability. Since shale gas molecules stored mainly in nano-metre pores in kerogens by gas adsorption, adsorbed gas molecules, of half-nanometres in diameter, could reduce the pore size for free gas flow substantially and so alter the gas permeability significantly.
In this work, we extended a model for modelling shale gas flow to account for the gas adsorption effect. We adopted the Langmuir single-layer adsorption model to the multiple layers. We analysed the gas adsorption impact on the permeability on a cylindrical pore analytically, and on a shale sample whose pore space are represented as a node-and-bond pore network, using our network flow model ( Ma et al., 2014 ). The results revealed that the adsorption effect depends strongly on the gas pressure and the radii of pores. Given that low gas pressure increases gas slippage at pore surfaces and decreases the thickness of the adsorption layers then, consequently, enhances the permeability, undesirable operation conditions could lead to an earlier decline of gas production.
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Finite Volume Method for Modelling Gas Flow in Shale
Authors P. Lorinczi, A.D. Burns, D. Lesnic, Q.J. Fisher, A.J. Crook, C. Grattoni and K. RybalcenkoSummaryGas flow in shale is a complex phenomenon and is currently being investigated using a variety of modelling and experimental approaches. A range of flow mechanisms need to be taken into account when describing gas flow in shale including continuum, slip, transitional flow and Knudsen diffusion. A finite volume method (FVM) is presented to mathematically model these flow mechanisms. The approach incorporates the Knudsen number as well as the gas adsorption isotherm, allowing different flow mechanisms to be taken into account as well as methane sorption on organic matter. The approach is applicable to non-linear diffusion problems, in which the permeability and fluid density both depend on the scalar variable, the pressure. The FVM is fully conservative, as it obeys exact conservation laws in a discrete sense integrated over finite volumes. The method is validated first on unsteady-state problems for which analytical or numerical solutions are available. The approach is then applied for solving pressure-pulse decay tests and a comparison with an alternative finite element numerical solution is made. Results for practical laboratory pressure-pulse decay tests of samples with very low permeability are also presented.
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A Mathematical Model for Flow in Multi-stage Hydraulic Fracture Systems Using Fractal Theory
Authors W. Wang, Y. Su and M. ShahvaliSummaryMulti-stage hydraulic fracturing has received considerable attention for production from unconventional resources. One of the key technologies that made development of unconventional shale formations possible is the creation of complex fracture network systems via interaction of hydraulic fractures, natural and induced fractures. Currently, most modeling approaches for multi-stage hydraulically fractured wells are based on diffusivity flow in several distinct scales (matrix/fracture), in which the network of fractures is assumed to be connected and equivalent to a homogeneous medium of Euclidean geometry. In this paper we incorporate a more detailed description of complex fracture networks to improve the pressure transient analysis of hydraulically fractured shale formations. Specifically, we employ a Fractal Diffusivity approach in which characteristics of flow in a dual-continuum porous medium is taken into consideration using fractal theory. In our dual-mechanism Fractal Diffusivity approach, we represent the average porosity and permeability of the fracture network using the fractal porosity-permeability relations. We use a trilinear flow mathematical model to represent the flow in hydraulic fractures, in the formation between the fractures, and in the formation away from the hydraulic fractures. To solve the equations at different regions, we prescribe proper boundary conditions and use Laplace transformation and numerical inversion from Laplace domain to time domain. Using numerical simulation, we validate the new semi-analytical solutions (Fractal Fracture Diffusivity solution) for flow in finite-conductivity multi-staged fractured reservoirs. We perform sensitivity analysis and show that the solution mostly depends on the value of the fractal parameters chosen. Moreover, we generate type curves for well bore pressure and pressure derivatives for multiple transverse fractures for a variety of external boundary conditions and show that the proposed mathematical model is more general than the dual porosity trilinear flow models. We also show applications of the proposed model in flow regime diagnostics.
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A Study of Hydraulic Fracturing Clean-up Efficiency in Unconventional Gas Reservoirs Using Statistical Approaches
Authors H.R. Nasriani, M. Jamiolahmady, E. Alajmi and P. GhahriSummaryHydraulic fracturing is widely used to improve well productivity especially in unconventional reservoirs. This costly operation, however, sometimes underperforms. One of the main reasons for this poor performance is poor clean-up efficiency of injected fracturing fluid (FF).
In this work, a parametric study of FF clean-up efficiency of hydraulic fractured vertical wells was performed with 49152 simulations (in 12 sets) consisting of injection, soaking and production periods.
Due to the large number of required simulations, that were conducted using a commercial reservoir simulator, a developed computer code was used to automatically read input data, run simulations and creates output data. In each set (consisting of 4096 runs), simultaneous impacts of 12 parameters (fracture permeability, matrix permeability and capillary pressure, end points and exponents of Corey gas and FF relative permeability curve in both matrix and fracture)were studied. To sample the variables domain and analyse results, two-level full factorial experimental design and linear surface model describing dependency of gas production loss (GPL), compared to 100% clean-up, to pertinent parameters at three production periods (10, 30 and 365 days) were considered and supported by the tornado charts of fitted equations, frequency of simulations with given GPL and FF saturation maps.
Results indicate that generally parameters controlling FF mobility within fracture had greatest impact on GPL reduction. However in sets with very low matrix permeability especially when applied pressure drop during production is low, the effect of fluid mobility in the matrix on GPL is more pronounced, in other words, it is important how gas and FF flow within matrix rather than how fast fracture is cleaned. In tighter gas formations, generally more GPL and slower clean-up was observed. The effect of matrix capillary pressure on GPL reduction was more pronounced when drawdown was very low and/or soaking time was extended. This observation was more profound in tighter formations, i.e. for these formations, the effect of a change in drawdown and/or soaking time on matrix capillary pressure and GPL was more pronounced.
These findings can be used to make better decisions on the performance and optimised design of hydraulic fracturing, which is a costly but widely used stimulation technique for unconventional low permeability gas reservoirs.
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Ion Exchange and Osmotic Mechanisms of Low Salinity Water Flooding and Modeling of Oil Displacement in Clay Reservoirs
Authors V.V. Kadet and P.S. ChagirovSummaryMost reservoir sands contain clay minerals. It is the well known fact that fresh water injected into the clay reservoirs causes swelling of clays. The swelling clays partly block the capillary openings in the sand and therefore reduce the rate of flow to the well bore. In addition clay minerals are susceptible to destruction of its molecular structure by exposure to waters [1]. Clay particles emerged from swelling process can block capillary openings as well. However, a great number of laboratory tests [ 1 ] showed that enhanced oil recovery can be obtained when performing a low salinity waterflooding (LSW). Despite increasing interest in LSW, none of the proposed mechanisms have so far been accepted as the “true”, none of the mathematical models of LSW have been created.
Mathematical modeling is based on analysis of electrokinetic and physicochemical effects at micro-level.
This process includes description of electro-osmotic flow in a capillary, ion-exchange process in diffusion layer of a capillary and also osmotic swelling of clays. Porous medium is generally modeled by the parallel conducting chains [ 2 ] bound up with interconnecting capillaries so that current could flow into the other chain. The main characteristic of this capillary system is described by the probability density function f(r). After the all micro- processes having been described, we go on with modeling at macro-level by measuring reservoir and two-phase flow characteristics (porosity, permeability, relative permeabilities, capillary pressure curves) depending on clay factor and mineralization of injected water.
Rapoport-Leas model has been chosen to estimate efficiency of oil displacement. This model allows us to take into account capillary pressure taking place during low salinity waterflooding. Salt transport in porous medium is described by convective diffusion equation which includes ion-exchange reaction rate, diffusivity and hydrodynamic dispersion.
The results of the calculations show the growth of oil production rate, water cut decrease and as a consequence an increase in recovery factor when performing LSW. The results fit well with experimental data.
- Tang, G., Morrow, N. R. Influence of brine composition and fines migration on crude oil/brine/rock interactions and oil recovery. Journal of Petroleum Science and Engineering, 1999, 99–111.
- VI. Selyakov and VV Kadet, Percolation Models for Transport in Porous Media With Applications to Reservoir Engineering. Kluwer Academic Publishers. Dordrecht/Boston/London, 1996, 241 p.
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High-order Simulation of Foam Enhanced Oil Recovery
Authors J.M. van der Meer, D.E.A. van Odyck, P. Wirnsberger and J.D. JansenSummaryIf secondary hydrocarbon recovery methods fail because of the occurrence of gravity override or viscous fingering one can turn to an enhanced oil recovery method like the injection of foam. The generation of foam can be described by a set of partial differential equations with strongly nonlinear functions, which impose challenges for the numerical modeling.
To analyze the effect of foam on viscous fingering, we study the dynamics of a simple foam model based on the Buckley-Leverett equation. Whereas the Buckley-Leverett flux is a smooth function of water saturation, the foam will cause a rapid increase of the flux function over a very small saturation scale. Consequently its derivatives can become extremely large and impose a severe constraint on the time step due to the CFL condition.
Until now, the methods applied to foam EOR processes are only first-order accurate and do not incorporate stabilization near the foam front as far as we know. In order to improve the accuracy near the foam front we make use of total variation diminishing schemes that preserve the numerical stability of the solution. Two dimensional simulations, including gravity, will shed light on the conditions under which foam might exhibit viscous fingering behavior.
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Investigation of Saturation Dependency of Oil Relative Permeability during WAG Process through Linear and Non-linear PCA
Authors E. Ranaee, G. Porta, M. Riva and A. GuadagniniSummaryWe characterize three-phase relative permeability data sets available in the literature in terms of basic descriptive statistics, bivariate correlation, as well as linear (PCA), nonlinear (NLPCA) and hierarchical principal component analyses (h-NLPCA). These studies are viewed in the context of the assessment of three-phase oil relative permeabilities for water alternating gas injection (WAG) protocols, where a proper (qualitative and quantitative) analysis of the dependence of observed three-phase oil relative permeability data on fluid saturations is of critical relevance for practical applications. Here, we focus on the characterization of the dependence of three-phase oil relative permeability on an identifiable set of Principal Components. We analyze the relationship between observed core scale three-phase oil relative permeability and input variables which are typically employed in the application of existing effective (pseudo-empirical) models. Input variables include saturations of fluids, saturations ending points, as well as two-phase relative permeabilities obtained from oil-water and oil-gas environments. The use of available prior information about saturation ending points is also discussed in the framework of Constrained Principal Component Analysis (CPCA). Our results show that: (i) the degree of nonlinearity displayed by the relationship between the input variables and three-phase oil relative permeability is in contrast with the fundamental assumptions underlying existing empirical models; (ii) a sigmoid-based empirical model can effectively characterize three-phase oil relative permeability as a function of fluid saturations, saturation ending points and oil relative permeability data collected under two-phase conditions.
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Barodiffusive Extension of Three-phase Flow Model for NegSat Method and Regularization of Three-phase Instability
Authors M. Panfilov, I. Panfilova and A. NaimanovaSummaryTwo fundamental problems of three-phase compositional flow in underground reservoirs have been solved by introducing the similar technique of barodiffusive extension of the classical three-phase model. It consists of introducing of the pseudo barodiffusion terms that are proportional to the weighted sum of the gradients of phase pressures, due to which one can change the direction of the fluxes of individual chemical components.
First of all, this technique enabled us to complete the method of negative saturations for three-phase flow, which was developed to describe the situations when various zones of reservoir contain different number of phases. The method consists of replacing the true fluid by a fictitious three-phase fluid having specific properties that satisfy the equivalence principle. Two fundamental problems, non resolved in preceding publications, concern (a) the replacement of a two-phase fluid by three phases, and (b) the extension to the case when overcritical zones appear. We have shown that the main difficulty in establishing the equivalence between two-phase and three-phase fluids consists of the non-colinear fluxes of chemical components in a two-phase flow. To reach the vectorial equivalence between fluxes, we have introduced the pseudo barodiffusion in the fictitious three-phase fluid. The barodiffusion coefficients and the directions of the fluxes result from the equivalence conditions in a unique way. The same technique provides the solution for the case when the flow contains the zones occupied by overcritical fluid.
In the case of ideal mixing within the phases without capillarity, the flow equations can be converted to the system of conservation laws with respect to the saturations or total concentrations. However the uniform flow equations are non-classical due to the terms of pseudo barodiffusion. The analysis has revealed that the barodiffusion terms ensure the hyperbolic character of the system. Consequently, the well known physical instability that arises in three-phase flow due the loss of hyperbolicity, does not appear in our extended barodiffusive model. Thus, the introduction of the small barodiffusion is the way to suppress the appearance of three-phase instability.
To ensure the numerical stability, we applied the monotone upwind high-order scheme for conservation laws with predictor-corrector. We have calculated several cases of miscible gas injection into the reservoir containing initially oil and water, and proved the good convergence of the result obtained compared to the simulations performed by Eclipse compositional and other techniques.
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Steady State Upscaling of Polymer Flooding
Authors S.T. Hilden, K.A. Lie and X. RaynaudSummaryUpscaling of parameters involved in single and two-phase flow has been researched quite extensively, and several methods for performing upscaling are known and understood. Less work has been done related to upscaling of enhanced oil recovery simulations. This is what we investigate, and in particular, we consider upscaling of parameters related to polymer flooding, which is the process in which large polymer molecules are added to the injected water to enhance its ability to push hydrocarbons through the reservoir. Herein, the polymer flooding process is described as a two-phase, immiscible system that in addition to a Todd-Longstaff mixing model includes permeability reduction, polymer adsorption, and dead pore space.
Effective parameters are computed by running simulations until a steady-state is reached and then performing upscaling based on the fluxes. This method is used by a major oil company as part of an established work flow for single and two-phase upscaling, and it is therefore natural to try to extend the method to polymer flooding. The upscaling is performed on the meter scale, where the steady-state assumption best can be justified. The procedure involves first performing single-phase upscaling of the absolute permeability, then two-phase upscaling of relative permeabilities, and finally, upscaling of the parameters involved in polymer flooding. The new upscaling method is verified against an analytical solution and validated on two synthetic models that include real data.
Results show that the permeability reduction factor, which only depends on polymer concentration in the fine-scale model, will generally also depend on water saturation in the upscaled model. This introduces addition computational costs in the simulation, since the property evaluations now require extensive use of lookup-tables and interpolation. We therefore suggest making simplifications in order to reduce the complexity.
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Image Based Pore-scale Models of Flow through Porous Media - Oil Recovery Applications
Authors I.I. Bogdanov, J. Kpahou and I. BondinoSummaryThe importance of pore-scale flow models for practical applications is widely recognized. Due to recent advances in computed microtomography (μCT) the reconstructed samples are now used for direct numerical simulations (DNS) of the flow. This technique gives a unique opportunity for non-destructive characterization; nevertheless a typical study encounters several challenges. The discussion of the most difficult steps of modeling methodology is our first objective.
The description of dynamic phase distribution and behavior of the fluid interface is a problem of primary importance. A regularization technique may affect the results in non-trivial ways; instead the diffuse-interface method offers a thermodynamic description of phase “mixing” zone and handles the morphological changes of interface and related physical effects. A series of model tests including the juxtaposition to analytical solutions for capillary channel flow, estimation of spurious velocity around a droplet and others, are presented. The quantitative demonstration of the method is our second objective.
Among numerous oil recovery applications one can mention the transport properties determination for different physical environment, the study of fluids entrapment/mobilization, the flow patterns at different capillary numbers and viscosity ratios, the emulsion and foamy oil flow, etc. Here we address the analysis of viscous fingering dynamics (oil-water systems, 2D synthetic medium) and the 3D stationary configurations of single and two-phase flow in real porous samples at different Reynolds, Cahn and capillary numbers. In particular, the computations based on μCT image reconstruction aims at the examination of fluid irreducible saturations. This constitutes our third objective. A discussion on the possibilities and limits of the model in quantitative characterization of porous materials is offered. Contribution of the pore-scale DNS to reservoir characterization becomes an increasingly important factor for numerous practical oil recovery applications.
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The Significance of a Detailed Phase Description in Simulations of Surfactant Flooding
Authors A.M. Al Sofi and A.M. Al KhatibSummaryTwo simulation approaches for modelling surfactant floods exist in the literature. The main difference between the two is the description of the surfactant phase behavior. The first (detailed) approach includes a thorough representation of the surfactant ternary phase behaviour while the second (simplified) approach ignores the formation of a middle phase microemulsion. Several reasons support the use of a simplified two-phase approach including the commercial availability of this option, the ease of incorporating such option in existing waterflood simulators, and the relative ease of generating input data.
Therefore, the objective of this study is to investigate whether the two approaches differ in terms of their predictions. In other words, we ultimately want to know whether a simplified two-phase simulation approach is suitable for the evaluation and design of a given surfactant formulation in any reservoir and/or operational settings or whether we must account for the ternary phase behaviour. For this purpose, we use the University of Texas Chemical Flooding Simulator (UTCHEM) for evaluating both the simplified and detailed modelling options. Simplified models are also built in UTCHEM by diminishing the salinity window. This option was chosen in order to use the same simulator suite for the evaluation of both the detailed and simplified assumptions.
In this work, we first use a detailed surfactant three-phase simulation model that was previously generated in UTCHEM using laboratory data and calibrated against coreflood experiments to generate three simplified surfactant two-phase pseudo models that are equivalent in 1D. Their equivalency in 1D is demonstrated using analysis of variance (ANOVA). We later design two simulation-based experiments to evaluate the suitability of the simplified models for field-scale predictions. Essentially, we divide the problem into two slightly simpler parts. The first experiment looks at the evaluation of a surfactant flood under uncertainty and the second looks at the optimisation of the surfactant injection scheme under a single deterministic realisation. For each of those two simulation-based experiments, we use a 4 × 4 Graeco-Latin square design requiring 16 simulation runs. Beside the surfactant simulation model, three factors are investigated in each of those experiments. For the robust evaluation experiment, the additional factors are permeability, adsorption, and initiation. For the optimisation experiment, the additional factors are surfactant slug size, surfactant concentration, and the injection rate.
ANOVA results of both experiments suggest the surfactant models do not differ significantly. This conclusion is supported by Tukey comparisons and the main effects plots. Therefore, the results suggest that a surfactant two-phase model can reasonably approximate the actual ternary phase behaviour of surfactants. Consequently, such simplified two-phase models can be used to obtain reliable predictions for field scale simulations.
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Recovery of Light Oil by Air Injection
Authors N. Khoshnevis Gargar, A.A. Mailybaev, D. Marchesin and J. BruiningSummaryIn this paper we review the results of analytical, numerical and experimental studies related to air injection into porous medium containing initially light oil, water and gas at medium pressure conditions. The new combustion mechanism is described, where the process of the medium temperature oxidation interacts with the oil vaporization/condensation, resulting in a resonant combustion wave structure. We discuss bifurcations of combustion regimes with a change of reservoir parameters, and analyze the effectiveness of the proposed technique for recovery in light oil reservoirs.
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Analysis of Heat Loss Effects on Thermal Pressure Falloff Tests
Authors A. Jahanbani Ghahfarokhi and J. KleppeSummaryAnalysis of pressure falloff tests gives initial estimates of swept volume, essential for the evaluation of a thermal recovery process. The analysis is based on a two-zone composite reservoir model with highly contrasting fluid mobilities, where the swept zone is assumed to behave as a closed reservoir for a short period exhibiting pseudo steady state behavior.
The upward buckling of the pressure derivative curves at late times in some cases could not be explained using the conventional composite models. This issue and some of the errors associated with the estimation of swept volume may possibly be related to heat loss which could have significant effects on the pressure behavior and dominate the pseudo steady state flow.
A model for the analysis of falloff tests with significant heat loss was suggested by Stanislav et al. (1989) . However, there are limitations in the application of this approach to practical steam falloff tests. Moreover, permeability should be known in advance for further analysis.
In this paper, a modified method of analysis considering heat loss is discussed which makes the flow regime identification easier and removes some of the practical limitations. Results of the analysis show improvement over the estimates obtained by other methods.
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