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Reservoir simulation is commonly performed on upscaled models of complex geological models. The upscaling process introduces a principal challenge in accurately simulating two-phase fluid dynamics in porous media. To tackle this challenge, it is important to upscale relative permeability accurately. In this paper, a numerical method, which is based on the mimetic finite difference method (MFD) and digital rock analysis (DRA), is proposed for relative permeability upscaling. The validation of MFD is tested by two different cases with exact pressure solution. Then, the relative permeability of the digital rock (small element) is calculated based on the pore network modeling. The small elements are combined together to make up a larger model with different sizes (4×4×4, 6×6×6, 8×8×8, 10×10×10 elements). Finally, the accuracy of the proposed method is verified by comparing simulated results of the different sizes with that of the original one. The results show that MFD can solve the multi-phase flow scenarios with high accuracy and the L₂ error follows the opposite trend to that of mesh size, which means that more refinement level gives less L₂ error. For the upscaling of absolute permeability, the relative error can be decreased to 2.27%, which confirms that the proposed method is capable of calculating the absolute permeability with higher refinement levels. The fitting degree of the simulated water phase relative permeability to the original one is better than that of oil phase. The average relative error of water pahse relative permeability upscaling can decrease to less than 5.0%. It is found that the results will get worse when the model includes less elements. Especially at low water saturation, there exists some fluctuations for relative permeability curves and it may be due to the unstable state of the waterflood front with less elements involved.

This paper address the numerical simulation of the chemically enhanced gas injection technology (ChEGas-EOR) at core and reservoir scales. In this technique, a liquid chemical solution, having engineered properties, is sprayed along with the gas stream. The mist travels through the wellbore and further introduced in the reservoir. Previous lab tests, pilot studies in light & intermediate oil reservoirs indicate that the application of CheGas-EOR allows for a reduction in operational costs, increases the chemical penetration radii and decreases the retention rate in the rock. However, the associated uncertainty is still too high to develop this process on a productive scale. In this work we use a developed phenomenological model to build a tool that assist in design and evaluation of Chemical Gas EOR operations aiming to reduce the uncertainties and optimize oil recovery.

We developed a mathematical model, based on the most important transport and surface phenomena. Non-equilibrium mass transfer between phases during the interception of the chemical solution droplets with the liquid phases. Active chemical concentration in miscible liquid phases is much lower than liquid-based chemical injection opperations. As a consequence, dissolution and adsorption rate of active chemicals with reservoir rocks are slow. The model is base on the extended black-oil model formulation coupled to local mass balance equations of active chemicals. Non-equilibrium mass transfer processes are represented with interception, dissolution and a first order kinetic sorption models.

The model was adjusted and then validated using experimental data from core-.floodint tests. Good agreement of the simulations results with experimental observations were obtained. The model can predict the relevant behavior of the disperse chemical injection in the gas phase in porous media. Also, well injections simulations at reservoir scale using the matched parameters from laboratory, reproduced pilot field results. Simulation experiments predict that the CheGasEOR process can increased substantially the oil recovery factor.

For the first time, a model for disperse chemical injection for EOR applications is developed and validated at core and reservoir scale. The simulation model allows the evaluation of this technology at different scales. Therefore, it is possible to use it to optimize operating conditions and perform sensitivity analysis for field applications.

A numerical simulation model was designed to evaluate the technical viability of in-situ upgrading using dispersed nanocatalysts in heavy oil reservoirs. Aquathermolysis reactions are represented by a practical kinetic model based on SARA analysis, being consistent with the thermodynamic characterization. With this simplified model, the API gravity enhancement in core-flooding tests was reproduced. The mathematical formulation couples mass and energy transport equations along with a rigorous three-phase equilibrium equation of state. Also, a nanoparticle transport equation was coupled to account for reversible and irreversible non-equilibrium retention, and water-oil partitioning. PVT data were matched successfully, including API gravities and oil viscosities. Reaction rates were adjusted by means of batch-reactor information, while nanoparticle retention was validated using reported single-phase core-flooding tests. Different core-flooding experiments from the literature were reproduced to calibrate the phases transport parameters, and further up-scaled to reservoir conditions. Validation of the model with experimental data suggests that the lumping scheme based on SARA analysis and the modeling of nanoparticle transport and retention, capture the most important phenomena occurring during in-situ upgrading processes. Field-scale simulations, of a sector model from an oil reservoir in the Magdalena Medio Valley basin in Colombia, showed that the in-situ upgrading with nanoparticles can increase the recovery factor up to 5% compared with typical steam injection. However, the oil upgrading achieved in the continuous injection was lower than the one obtained in the core-flooding tests. The numerical model presented in this work, which includes a dynamic nanoparticle retention model, changes on relative permeability alteration due to nanoparticle surface deposition, and a suited kinetic-thermodynamic representation, is able to describe correctly the most relevant phenomena observed during nanocatalysts in-situ upgrading process.

Most commercially available simulators use the trivial two-point flux approximation (TPFA) method for flux computation. However, the TPFA only gives consistent solutions when used for K-orthogonal grids. In general, multi-point flux approximation (MPFA) methods perform better under both heterogeneous and anisotropic conditions. The mimetic finite difference (MFD) method is designed to preserve properties on unstructured polyhedral grids, and its development for simulating full tensor permeabilities is also crucial step. This paper compares the performance, accuracy, and efficiency of these schemes for simulating complex synthetic and realistic hydrocarbon reservoirs.

This paper shows how greater scientific rigor in discussions of modelling 3D saturations in the Middle East can lead to better understanding of the reservoirs. It demonstrates with examples how vocabulary limits ability to solve problems related to saturations, compartmentalization, and permeability. It raises the bar on technical discussions of saturation.

"Saturation-height modelling", "transition zones", and "Thomeer hyperbolas" are examples of terms that repeatedly confuse discussions of modelling 3D saturations in the Middle East. Vocabulary exposes a lack of scientific rigor, impedes progress, and leads to notable failures. Saturation is not merely a function of height. At the very least, it also depends on porosity, permeability, fluid densities, interfacial tension, and contact angle. Limiting it to height requires adding in all of these other functionalities as afterthoughts rather than incorporating them naturally through dimensional analysis. Most glaringly, it obscures the very useful role that saturations have in constraining permeability modelling and identifying reservoir compartments.

"Transition zones" focus on saturation and take emphasis away from relative permeability and fractional flow. Bimodal pore systems (abundant in the Middle East) can have such low relative permeability to water at high saturations that even 70% water saturation can produce dry oil. In such cases, talk of a transition zone is counterproductive as it implies high water production.

"Thomeer hyperbolas" reveal biases in how to fit capillary pressure curves. Force-fitting all data with a single model is inadequate. It takes emphasis away from understanding pore systems of rocks in favor of promoting a single-minded view. These examples and their implications are discussed in detail.

The existing literature is replete with incomplete explanations and misunderstandings that lead to notable failures in modelling Middle Eastern fields. Understandings predicated on simplified descriptions of homogeneous reservoirs are no longer sustainable. A more scientifically rigorous methodology is presented.

In order to improve the oil recovery factor, many oil companies employ surfactant in injected water. On one hand, the injection of surfactant influences the interfacial tension and to a lesser extent, the mobility reduction factor. On the other hand, the efficiency of the surfactant depends strongly on the salinity and temperature conditions. In order to optimize the surfactant injection procedure, the salinity and temperature effects are commonly studied through series of laboratory experiments. However, these types of experiments are often long and expensive. Therefore, engineers use numerical simulations. The present study addresses a numerical model, which allows to take into account the modifications of the interfacial tension (IFT) and the mobility reduction factor due to the salinity and temperature variations during the surfactant injection.

In this work, we propose a coupled numerical model based on five equations: i) two transport equations of water and oil phases modelized by the Darcy's law, ii) two transport equations for the surfactant and the salinity (the surfactant and the salinity are transported only in the water phase) iii) one energy conservation equation to take into account the thermal effect on surfactant flooding. The system of equations includes the salinity and the temperature impacts on the surfactant adsorption and thermal degradation, as well as the interfacial tension. Thus, this model allows improving the analysis of thermal corefloods or reservoir operations resulting from the surfactant injection.

The coupled model is used to reproduce laboratory experiments based on corefloods. We analyze the interaction phenomena between the surfactant, salinity and temperature. Then, we demonstrate a competition between two phenomena: the thermal effect on the viscosity of water on one hand, and the effect of surfactant on the mobility of water on the other hand. This study highlights the efficiency of numerical simulations for the analysis and choice of the surfactant applied to the given reservoir and well conditions.

Obviously, the knowledge of IFT and its dependence on surfactant concentration, salinity and temperature is not sufficient to understand all the physical mechanisms involved in a coreflood study. The phenomena are in fact extremely coupled, and the reservoir simulator coupling all these effects is found to be very helpful for engineers in order to take a good decision about the surfactant species to be used.

In carbonate reservoirs, permeability prediction is often difficult due to the influence of various geological variables that control fluid flow. Many attempts have been made to calculate permeability from porosity by using theoretical and empirical equations. The suggested permeability models have been questionable in carbonates due to inherent heterogeneity and complex pore systems. The main objective of this paper is to resolve the porosity-permeability relationships and evaluate existing models for predicting permeability in different carbonate rock types.

Over 1000 core plugs were studied from 7 different carbonate reservoirs across the Middle East region; mainly cretaceous reservoirs. The plugs were carefully selected to represent main property variations in the cored intervals. The data set available included laboratory-measured helium porosity, gas permeability, thin-section photomicrographs and high-pressure mercury injection. Plug-scale X-ray CT imaging was acquired to ensure the samples were free of induced fractures and other anomalies that can affect the permeability measurement. Rock textures were analyzed in the thin-section photomicrographs and were classified based on their content as grainy, muddy and mixed. Special attention was given to the diagenesis effects mainly compaction, cementation and dissolution.

The texture information was plotted in the porosity-permeability domain, and was found to produce three distinct porosity-permeability relationships. Each texture gave unique poro-perm trend, where the extent of the trend was controlled by diagenesis. Rock types were defined on each trend by detailed texture analysis and capillary pressure. Three different permeability equations (Kozney, Winland, Lucia) were evaluated to study their effectiveness in complex carbonate reservoirs. A new permeability equation was proposed to enhance the prediction results of the experimental data.

Rock types were successfully classified based on porosity, permeability, capillarity and textural facies. Conclusive porosity-permeability relationships were obtained from textural rock properties and diagenesis, which were linked to rock types using capillary pressure. The texture-diagenesis based rock types provided more insight into the effects of geology on fluid flow and saturation. Available models may not fully describe permeability in heterogeneous rocks but they can improve our understanding of fluid flow characteristics and predict permeability in un-cored wells.

To originate a discussion, you may submit a comment to any paper that has been published in a current SPE peer-reviewed journal. Comments should be based on fact, not opinion. Comments are not peer reviewed. Authors are only allowed to submit a single discussion on a paper. Authors may not submit a comment to their own paper.

Money has a time value. This means a dollar received today has more value to us than a dollar received far in the future. Other than a desire for instant gratification, there is a very rational reason for this phenomenon. If we have a dollar today, we can put it to work by making an investment and have more than a dollar at some future date. This concept of putting the money to work has important implications later in this section when discount rates are discussed.

In the last quarter-century, financial options such as "calls" and "puts" on publicly traded stocks have become an integral part of managing stock portfolios. The seminal work on financial options was done by Black and Scholes,[1] published in 1973, and Merton,[2] also published in 1973. Merton and Scholes shared the 1997 Nobel Prize in economics for their work. Black, Scholes, and Merton all worked on attempting to determine the value of an option. In recent years, the concepts of valuing options have been expanded from financial options to what are called "real" options in project evaluation.