Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content

    Rudolf Held

    Summary Condensate blockage is a major risk in gas-condensate field development. In the investigated field, the initial reservoir pressure is close to the dew point, leading to condensate dropout and banking from the very beginning. The... more
    Summary Condensate blockage is a major risk in gas-condensate field development. In the investigated field, the initial reservoir pressure is close to the dew point, leading to condensate dropout and banking from the very beginning. The uncertainty in condensate blockage in the absence of reliable SCAL measurements is considered one of the main challenges. In this work, two approaches were presented to approximate gas-condensate relative permeabilities including high-velocity flow effects. Furthermore, condensate blockage mitigation methods are evaluated. The first investigated method is that of Whitson, based on the relation krg=f(krg/kro) in which PVT data and analog coreflood experimental data were used to generate relative permeabilities, also including a model for the capillary number effect. In the second method, a digital rocks SCAL analysis, based on Lattice Boltzmann two-phase flow simulation on a microscale 3D scan of remnants of sidewall core plugs, was used to simulate the relative permeabilities at low to high capillary numbers. For implementation of the curves in the dynamic simulation, the model by Henderson was used. The estimated relative permeability curves for different rock types were used directly in reservoir simulation to evaluate the risk of condensate blockage. In both methods, the effects of high velocity and non-Darcy flow were considered. The simulation results show that the designed gas plateau production rate cannot be maintained even for a few months. However, in an artificial single-phase gas flow case in which the presence of condensate is not influencing the gas flow, the gas plateau production could be sustained up to four years. As a result, the field needs to be produced three to four years longer to reach the same recovery factor, and thus significantly less return on investment is expected. Comparing both generated relative permeability curves, it is remarkable that the immiscible relative permeability curves (at lower capillary numbers) do not differ significantly from each other, despite the fact that neither of them is based on conventional SCAL experiments. Furthermore, a gas cycling scenario, well placement optimization, and a near wellbore treatment with wettability altering surfactants were analyzed in numerical simulations with promising preliminary results to mitigate condensate banking. The risk of condensate blockage for a real case scenario in the absence of reliable SCAL measurements, by adapting and comparing two approaches to approximate relative permeability curves including high-velocity flow effects, was evaluated and numerically analyzed in the present work.
    ABSTRACT
    The propagation of dense nonaqueous phase liquids (DNAPLs) in water‐saturated, homogeneous porous media was investigated. The static distribution of DNAPL after gravity‐driven displacement was studied using a number of three‐dimensional... more
    The propagation of dense nonaqueous phase liquids (DNAPLs) in water‐saturated, homogeneous porous media was investigated. The static distribution of DNAPL after gravity‐driven displacement was studied using a number of three‐dimensional spill experiments. Fingering intrinsic to the displacement systems was observed in all experiments. The effects of physical and chemical parameters on flow instability were examined for a range of sand grain sizes (fine, medium, and very coarse) and for different DNAPLs (trichloroethylene, trichloroethane, and dibutyl phthalate). Gravitational, viscous, and capillary forces were observed to have a varied influence on the flow behavior in these experiments. Our observations show that the development of finger patterns is sensitive to the porous media grain size, properties of the DNAPL, and spill conditions. By controlling experimental parameters, results are reproducible and yield insight into finger formation and preferential DNAPL flow in homogeneous aquifer materials. This paper discusses the experimental results qualitatively; a companion paper discusses their quantification with fractal concepts.
    A workflow incorporating pore space modelling, small scale heterogeneity and uncertainty modelling has been established and successfully employed in a North Sea oil reservoir. The study was performed on a heterogeneous interval of the... more
    A workflow incorporating pore space modelling, small scale heterogeneity and uncertainty modelling has been established and successfully employed in a North Sea oil reservoir. The study was performed on a heterogeneous interval of the reservoir, with water flooding as the basic recovery strategy. The geology was characterized identifying relevant scales of heterogeneity. The interval consists of hummocky cross-stratified deposits, with varying contrast and lamination. Consequently, small scale models were built capturing the laminations seen in cores at a scale interpreted to be at a representative elementary volume. Pore space reconstruction and property estimation by pore scale modelling were used to obtain realistic relative permeability and capillary pressure data for each lamination. At each stage of the workflow, a set of models was handled to account for uncertain parameters. Uncertain parameters included porosity, permeability, pore space and lithofacies geometry, and rock/fluid wettability. These parameter uncertainties propagated into uncertainty in the multiphase properties, i.e., relative permeability and capillary pressures. Steady-state multiphase upscaling was used to obtain multiphase properties representative for the geo-cellular model scale. The multiphase flow properties generated from pore scale modelling and upscaling were incorporated in an interwell-scale model with a geo-cellular grid resolution, and simulations compared with a base case model with traditional multi-phase flow properties. The updated model demonstrated altered flow behaviour and sweep, which were consistent with field observation. More precisely it showed a water override with by-passed oil in the lower parts of the model, a behaviour which was not adequately captured in the base case model. Moreover, the modified flow physics were relatively easy to implement and could be run with little additional computational cost in the full field simulation model. As the results constitute key information for reservoir monitoring and for improving oil recovery, the operational full field model was updated to include these findings.
    In this paper, the salt balance of the Okavango Delta in Botswana is assessed. Large-scale arguments are presented that show the crucial role of the wetland/dryland interface for balancing the salt budget. On the other hand, modelling and... more
    In this paper, the salt balance of the Okavango Delta in Botswana is assessed. Large-scale arguments are presented that show the crucial role of the wetland/dryland interface for balancing the salt budget. On the other hand, modelling and field studies on selected islands are presented. Modelling results indicate a potentially unstable vertical concentration distribution below the islands. Results from TEM soundings and groundwater surveys clearly show strong conductivity anomalies for the islands. However, the data are still insufficient to prove the occurrence of density driven flow in the Okavango Delta.
    ABSTRACT
    Research Interests:
    A stochastic geometrical modeling method for reconstructing three dimensional pore scale microstructures of multiscale porous media is presented. In this method the porous medium is represented by a random but spatially correlated... more
    A stochastic geometrical modeling method for reconstructing three dimensional pore scale microstructures of multiscale porous media is presented. In this method the porous medium is represented by a random but spatially correlated structure of objects placed in the continuum. The model exhibits correlations with the sedimentary textures, scale dependent intergranular porosity over many decades, vuggy or dissolution porosity, a percolating pore space, a fully connected matrix space, strong resolution dependence and wide variability in the permeabilities and other properties. The continuum representation allows discretization at arbitrary resolutions providing synthetic micro-computertomographic images for resolution dependent fluid flow simulation. Model implementations for two different carbonate rocks are presented. The method can be used to generate pore scale models of a wide class of multiscale porous media.
    Specific internal surface areas and other morphological descriptors of complex disordered systems can be estimated from threedimensional tomographics images using methods of stochastic geometry [1]. Often such data are unavailable for... more
    Specific internal surface areas and other morphological descriptors of complex disordered systems can be estimated from threedimensional tomographics images using methods of stochastic geometry [1]. Often such data are unavailable for realistic media because these exhibit structural features on multiple length scales. A method to reconstruct stochastic morphologies for multiscale media was developed in [2]. The method is particularly suited for modeling sedimentary rocks that exhibit porosity and grain structure covering several decades in length scales. It combines crystallite information from two-dimensional high-resolution images with sedimentary correlations from a three-dimensional low-resolution micro-CT image [3]. The mathematical model reproduces correlations with primordial depositional textures, scale dependent intergranular porosity over many decades, vuggy porosity, a percolating pore space, a percolating matrix space, and resolution dependence of both physical and morph...
    The acquisition of digitized representations of rock microstructures has been established in the workflow for investigation of petrophysical, material, and transport properties. The availability of these data open the way for the... more
    The acquisition of digitized representations of rock microstructures has been established in the workflow for investigation of petrophysical, material, and transport properties. The availability of these data open the way for the development of methods that directly predict effective properties based on digitized topological information. The increasing number of effective properties that may be numerically calculated includes elastic moduli, electrical resistivities, fluid permeabilities, or constitutive relationships for multiphase flow. This work investigates different sandstone lithofacies in a North Sea field with these analyses. We compare samples acquired by X-ray Microtomography with digitized samples of reconstructed lithofacies. The latter are based on back-scattered electron images of standard 2D petrographic thin sections. The study largely shows an excellent agreement of the effective properties for the microCT and reconstructed samples for these heterogeneous rock types...
    Pressure-release experiments of CO2 with impurity contents of 10, 20 and 30 mol% nitrogen have been executed. The experimental investigations were performed in a 140 m long horizontal tube with an inner diameter of 10 mm. The initial... more
    Pressure-release experiments of CO2 with impurity contents of 10, 20 and 30 mol% nitrogen have been executed. The experimental investigations were performed in a 140 m long horizontal tube with an inner diameter of 10 mm. The initial conditions of the CO2-N2 mixtures were in the supercritical region at approximately 120 bar and 20 °C. The results, which showed a good repeatability, were then compared with numerical data from a homogeneous equilibrium model. The investigations have concentrated on the pressure wave at the start as well as the pressure and temperature development during the pressure release. The model, which has a certain complexity, but still contains several simplifications, gave relatively good results for all three gas mixtures. Although the absolute values for the temperature development showed to be consistently higher in the experimental results compared to the numerical results, the liquid dry-out points were predicted with good accuracy at all measurement poi...
    Gas condensate field development is a challenging task involving many technical disciplines, from sedimentology and petrophysics to reservoir and facility engineering. For evaluation of development options in a Nile Delta onshore field... more
    Gas condensate field development is a challenging task involving many technical disciplines, from sedimentology and petrophysics to reservoir and facility engineering. For evaluation of development options in a Nile Delta onshore field with original reservoir pressure close to dew point, reservoir simulation must account for potential condensate blockage near wellbore. Uncertainties related to blockage can severely risk the estimation of gas and condensate reserves and production, and significantly impact project development or even put the investment decision on hold. The method of Whitson8 for determining velocity-dependent gas-condensate relative permeabilities is sufficiently robust and reliable to model well deliverability in moderately homogenous reservoirs. However, with increasing heterogeneity, gas condensate flow in contrasting facies or thin laminated zones requires deeper investigation. Thin low permeability layers can act as bounding surfaces with condensate dropout bel...
    We use a stagnant-layer diffusion concept for mass transfer across individual fluid-fluid interfaces at the pore scale, coupled to a capillary displacement model in a pore network. Mass fluxes are computed across each interface, then... more
    We use a stagnant-layer diffusion concept for mass transfer across individual fluid-fluid interfaces at the pore scale, coupled to a capillary displacement model in a pore network. Mass fluxes are computed across each interface, then transport equations are solved in the pore network to determine concentrations in the aqueous-phase. The model is used to predict dissolution fronts developed by flushing water through a porous medium initially at residual NAPL saturation.
    Microtomographic rock and fluid imaging under in-situ conditions is applied for reservoir wettability characterization. The investigation entails careful sample preparation and cleaning of mini-plugs, operation with reservoir fluids,... more
    Microtomographic rock and fluid imaging under in-situ conditions is applied for reservoir wettability characterization. The investigation entails careful sample preparation and cleaning of mini-plugs, operation with reservoir fluids, wettability restoration, centrifuge wettability testing cycles, repeated sample scanning and image analysis, parametrization of wettability and digital rocks simulation for input into reservoir modeling. The results are compared to conventional Amott testing performed in core laboratories. Determination of saturations from image analysis, instead of centrifuge production, allows the use of stock tank crude, rather than exchanged mineral oil. Doping of the synthetic formation water (here with 1 M sodium iodide) was applied for enhancement of the X-ray contrast. The digital imaging workflow offers insight on the liquid distributions from the plug scale down to the pore-scale, linked to applied pressure gradients and resulting pore fluid occupancies in the...
    ABSTRACT Abstract Every CO2 capture and storage chain will contain injection wells. The most important common operations for wells are shut-ins and depressurizations for reservoir characterization, maintenance stops and testing of valves.... more
    ABSTRACT Abstract Every CO2 capture and storage chain will contain injection wells. The most important common operations for wells are shut-ins and depressurizations for reservoir characterization, maintenance stops and testing of valves. The aim of this work is firstly to demonstrate the need for experiments on these operations. Secondly, a new experimental set-up is proposed for such experiments. The main conclusion from this paper is that the physical phenomena during shut-ins and depressurizations of CO2 injection wells can be described with models, but that that there are still some uncertainties left. The largest uncertainties occur when the transient flow is rapid and/or CO2 is mixed with water. The proposed experimental set-up consists of a well with casing to be drilled vertically 200-250 meter at the Statoil laboratory in Trondheim, Norway. A U-tube with two legs with different diameter will be suspended in the well. Moreover, water or brine can be added for observing the effects of the H2O-CO2 interaction. The U-tube is to be linked to the existing CO2 transport test facility, which has the necessary vessels, compressor and pump. This rig will hopefully contribute in making CO2 injection wells even safer and more cost efficient.
    We use a stagnant-layer diffusion concept for mass transfer across individual fluid-fluid interfaces at the pore scale, coupled to a capillary displacement model in a pore network. Mass fluxes are computed across each interface, then... more
    We use a stagnant-layer diffusion concept for mass transfer across individual fluid-fluid interfaces at the pore scale, coupled to a capillary displacement model in a pore network. Mass fluxes are computed across each interface, then transport equations are solved in the pore network to determine concentrations in the aqueous-phase. The model is used to predict dissolution fronts developed by flushing water through a porous medium initially at residual NAPL saturation.
    Research Interests:
    This work investigates two complex, heterogeneous sandstone lithofacies in a North Sea petroleum reservoir field. We compare samples acquired by X-ray microtomography with numerically reconstructed lithofacies, obtained from a geological... more
    This work investigates two complex, heterogeneous sandstone lithofacies in a North Sea petroleum reservoir field. We compare samples acquired by X-ray microtomography with numerically reconstructed lithofacies, obtained from a geological process based reconstruction technique. Effective material and transport properties of these digitized rocks, such as electrical resistivity, elastic moduli, fluid permeability, and magnetic resonance (NMR), are computed. The comparison largely reveals an excellent agreement of calculated effective properties between the actual and reconstructed pore structures. A dependence of the effective properties on the specific mineralogy could be investigated in case of the reconstructed rocks. Our results allow for an interpretation of trends in effective medium properties and facilitate the construction of cross-property relations for the investigated lithofacies. The present study demonstrates the potential and feasibility of combining computer generated rocks with numerical calculations to derive material and transport properties for reservoir rocks.
    Computational pore-scale network models describe two-phase porous media flow systems by resolving individual interfaces at the pore scale, and tracking these interfaces through the pore network. Coupled with volume averaging techniques,... more
    Computational pore-scale network models describe two-phase porous media flow systems by resolving individual interfaces at the pore scale, and tracking these interfaces through the pore network. Coupled with volume averaging techniques, these models can reproduce relationships between measured variables like capillary pressure, saturation, and relative permeability. In addition, these models allow nontraditional porous media variables to be quantified, such as interfacial areas and common line lengths. They also allow explorations of possible relationships between these variables, as well as testing of new theoretical conjectures. Herein we compute relationships between capillary pressure, saturation, interfacial areas, and common line lengths using a pore-scale network model. We then consider a conjecture that definition of an extended constitutive relationship between capillary pressure, saturation, and interfacial area eliminates hysteresis between drainage and imbibition; such hysteresis is commonly seen in the traditional relationship between capillary pressure and saturation. For the sample pore network under consideration, we find that hysteresis can essentially be eliminated using a specific choice of displacement rules; these rules are within the range of experimental observations for interface displacements and therefore are considered to be physically plausible. We find that macroscopic measures of common line lengths behave similarly to fluid–fluid interfacial areas, although the functional dependencies on capillary pressure and saturation differ to some extent.
    This study uses a numerical model to investigate the groundwater flow and salt transport mechanisms below islands in the Okavango Delta. Continuous evapotranspiration on the islands results in accumulation of solutes and the formation of... more
    This study uses a numerical model to investigate the groundwater flow and salt transport mechanisms below islands in the Okavango Delta. Continuous evapotranspiration on the islands results in accumulation of solutes and the formation of a saline boundary layer, which may eventually become unstable. A novel Lagrangian method is employed in this study and compared to other numerical methods. The numerical results support the geophysical observations of density fingering on Thata Island. However, the process is slow and it takes some hundreds of years until density fingering is triggered. The results are sensitive to changes of the hydraulic gradient and the evapotranspiration rate. Small changes may lead to different plume developments. Results further demonstrate that density effects may be entirely overridden by lateral flow on islands embedded in a sufficiently high regional hydraulic gradient.
    Numerical groundwater modelling is used as the base for sound aquifer system analysis and water resources assessment. In many cases, particularly in semi-arid and arid regions, groundwater flow is intricately linked to salinity transport.... more
    Numerical groundwater modelling is used as the base for sound aquifer system analysis and water resources assessment. In many cases, particularly in semi-arid and arid regions, groundwater flow is intricately linked to salinity transport. A case in point is the Shashe River Valley in ...
    Abstract[1] General upscaling of density-dependent flow is investigated for the classical two-dimensional Henry problem of saltwater intrusion in coastal aquifers. Combined theoretical and numerical results are here presented. Effective... more
    Abstract[1] General upscaling of density-dependent flow is investigated for the classical two-dimensional Henry problem of saltwater intrusion in coastal aquifers. Combined theoretical and numerical results are here presented. Effective flow and transport parameters for saline intrusions could be derived for statistically isotropic and anisotropic heterogeneous permeability fields by use of homogenization theory, applying also to the preasymptotic regime. Our numerical results indicate that heterogeneities in permeability affect foremost the transient evolution of saltwater intrusion, whereas the steady state saltwater distribution is less sensitive to spatially varying permeabilities and longitudinal dispersion. For the isotropic media the effective permeability is found to correspond to the geometric mean, as under conditions without fluid density contrast. The extension of results to anisotropic media requires nontrivial corrections for the effective permeability, which include the variance of log(k) and the directional correlation lengths. The appropriate dispersion coefficients for the problem correspond to the local dispersion coefficients, rather than macrodispersion coefficients. These results are discussed in light of the specific flow configuration posed in the Henry problem.
    We consider saltwater–freshwater fingering instabilities in a saturated porous medium. In the first part, we present three-dimensional results obtained from a laboratory experiment using non-invasive imaging. In the second part, we define... more
    We consider saltwater–freshwater fingering instabilities in a saturated porous medium. In the first part, we present three-dimensional results obtained from a laboratory experiment using non-invasive imaging. In the second part, we define a set of model problems in which the ...