The nonlinear differential equation describing flow of a constant compressibility liquid in a porous medium is examined in terms of the Kirchhoff and Cole-Hopf transformations. A quantitative measure of the applicability of representing flow by a slightly compressible liquid – which leads to a linear differential equation, the Theis equation – is identified. The classical Theis problem and the finite-well-radius problem in a system that is infinite in its areal extent are used as prototypes to address concepts discussed. This choice is dictated by the ubiquity of solutions that depend on these archetypal examples for examining transient diffusion. Notwithstanding that the Kirchhoff and Cole-Hopf transformations arrive at a linear differential equation, for the specific purposes of this work – the estimation of the hydraulic properties of rocks, the Kirchhoff transformation is much more advantageous in a number of ways; these are documented. Insights into the structure of the nonlinear solution are provided. The results of this work should prove useful in many contexts of mathematical physics though developed in the framework of applications pertaining to the earth sciences.
Liquid unloading is a very common and important issue in horizontal gas wells, and the presence of curve sections increases the complexity of the phenomenon and its study. Liquid loading in a gas well will sharply reduce production, therefore, the liquid-unloading onset of different curved pipes is essential to gas production. In this work, liquid-unloading onset experiments were conducted in curved pipes with different curvatures. Then, the critical gas velocity VsgCR can be determined according to the measured pressure gradients, liquid holdup, and liquid film reversal. This work analyzes the factors which will lead to the liquid unloading and explores the trend of the pipe curvature’s influence on the liquid unloading under laboratory conditions. The experimental results show that the critical gas velocity rises with the increase of pipe curvature, the increase is mainly due to the centrifugal force. The present work also compares the predicted results of the OLGA model and Beggs–Brill model with experimental data. The comparison results indicate that both models fit relatively well to the experimental data at the low superficial gas velocity, and both models have poor performance at high superficial gas velocity. The OLGA model fits the experimental data better than the Beggs–Brill model at high superficial gas velocity. The error analysis shows that most of the predicted data is not in good agreement with experimental data. Some errors between experimental data and calculation results are out of the range of 50%.
Capillarity refers to the phenomenon of fluids imbibing into fine pores or porous rocks and materials due to surface energy, through the action of capillary pressure.The capillary pressure causes the deformable interfaces formed between two phase fluids in contact with each other, such as a liquid and a vapor.Capillarity and its importance have been widely recognized in various fields, including civil engineering, soil science, hydrology, carbon storage, and petroleum engineering.More than a century ago, the classical Young-Laplace equation and Lucas-Washburn equation laid the foundation for the description of the capillary-driven flow of fluids in porous structures.With the rapid development of computational and experimental techniques, the research on capillarity is advancing at an unprecedented level and provides insight and opportunities for further effort in what is already a flourishing field of research.Four papers on capillarity in porous media are collected in this special issue and are summarized in the following paragraphs:In the paper "Shale adhesion force measurements via atomic force microscopy" [1], Mitiurev et al. used the AFM (Atomic Force Microscopy) technique to measure the adhesion force between cantilever and sample surface at nanoscale for shale.They used topographical analysis, SEM (Scanning Electron Microscopy) and EDS (Energy Dispersive Spectroscopy) to accurately locate the measurement points on a sample surface and obtained consistent adhesion force measurements for quartz grain inclusions.The adhesion forces were determined to equal the waterair capillary pressure under the test conditions.These measurements and results have potential to create a path towards much higher accuracy-wettability measurements and consequently better reservoir-scale predictions and improved underground operations.In the paper "A modified cell-to-cell simulation model to determine the minimum miscibility pressure in tight/shale
Waterflooding is widely implemented to enhance oil recovery. The displacement efficiency of this method depends on multiple factors, including makeup water properties, native oil, and formation rock. The incompatibility of the injected fluid with the pore fluid can result in a chemical non-equilibrium state within porous media that may result in different chemical reactions that depend on the type and number of the existing components within the system. The present research aims to develop a mathematical model capable of handling multiple geochemical reactions to predict pH and ions concentration during an acid injection while considering alterations of rock and fluid properties. The dependency of fluid properties (viscosity and density) is considered based on the system ionic concentration, which can be more crucial in high saline media. The validity of the developed model was evaluated using the experimental literature data. The results reveal that in addition to the effect of injected fluid pH, the process efficiency can be influenced by the composition of the injected fluid. In other words, fluid properties dependency on salinity and the injected fluid composition is significant during geochemical simulations. Comparing homogenous and heterogenous mineral distribution shows an insignificant sensitivity to the amount heterogeneity while the total mineral contents remain constant in both cases.
First, second, third, and fourth-generation biofuels are continuously evolving as a promising substitute to petrodiesel catalyzed by energy depletion, economic and environmental considerations. Bio-diesel can be synthesized from various biomass sources, which are commonly divided into FAME and renewable biodiesel. FAME biodiesel is generally produced by the transesterification of vegetable oils and fats while renewable diesel is produced by hydro-deoxygenation of vegetable and waste oils and fats. The different generation, processing technologies and standards for FAME and renewable biodiesel are reviewed. Finally, the life cycle analysis and production cost of conventional and renewable biodiesel are described.
Hydrodynamic dispersion is a crucial mechanism for modelling contaminant transport in subsurface engineering and water resources management whose determination remains challenging. We use Digital Rock Physics (DRP) to evaluate the longitudinal dispersion of a sandpack. From a three-dimensional image of a porous sample obtained with X-ray microtomography, we use the method of volume averaging to assess the longitudinal dispersion. Our numerical implementation is open-source and relies on a modern scientific platform that allows for large computational domains and High-Performance Computing. We verify the robustness of our model using cases for which reference solutions exist and we show that the longitudinal dispersion of a sandpack scales as a power law of the Péclet number. The assessment methodology is generic and applies to any kind of rock samples.
The Nitrogen Oxides (NOx) from engines aggravate natural environment and human health. Institutional regulations have attempted to protect the human body from them, while car manufacturers have tried to make NOx free vehicles. The formation of NOx emissions is highly dependent on the engine operating conditions and being able to predict NOx emissions would significantly help in enabling their reduction. This study investigates advanced method of predicting vehicle NOx emissions in pursuit of the sensorless engine. Sensors inside the engine are required to measure the operating condition. However, they can be removed or reduced if the sensing object such as the engine NOx emissions can be accurately predicted with a virtual model. This would result in cost reductions and overcome the sensor durability problem. To achieve such a goal, researchers have studied numerical analysis for the relationship between emissions and engine operating conditions. Also, a Deep Neural Network (DNN) is applied recently as a solution. However, the prediction accuracies were often not satisfactory where hyperparameter optimization was either overlooked or conducted manually. Therefore, this study proposes a virtual NOx sensor model based on the hyperparameter optimization. A Genetic Algorithm (GA) was adopted to establish a global optimum with DNN. Epoch size and learning rate are employed as the design variables, and R -squared based user defined function is adopted as the object function of GA. As a result, a more accurate and reliable virtual NOx sensor with the possibility of a sensorless engine could be developed and verified.
Constructing an accurate geological model of the reservoir is a preliminary to make any reliable prediction of a reservoir’s performance. Afterward, one needs to simulate the flow to predict the reservoir’s dynamic behaviour. This process usually is associated with high computational costs. Therefore, alternative methods such as the percolation approach for rapid estimation of reservoir efficiency are quite desirable. This study tries to address the Well Testing (WT) interpretation of heterogeneous reservoirs, constructed from two extreme permeabilities, 0 and K . In particular, we simulated a drawdown test on typical site percolation mediums, occupied to fraction “ p ” at a constant rate Q / h , to compute the well-known pressure derivative (d P /dlnt). This derivative provides us with “apparent” permeability values, a significant property to move forward with flow prediction. It is good to mention that the hypothetical wellbore locates in the middle of the reservoir with assumed conditions. Commercial software utilized to perform flow simulations and well test analysis. Next, the pressure recorded against time at different realizations and values of p . With that information provided, the permeability of the medium is obtained. Finally, the permeability change of this reservoir is compared to the permeability alteration of a homogeneous one and following that, its dependency on the model parameters has been analysed. The result shows a power-law relation between average permeability (considering all realizations) and the occupancy probability “ p ”. This conclusion helps to improve the analysis of well testing for heterogeneous reservoirs with percolation structures.
One of the promising applications of clathrate/gas hydrates is the transport and storage of natural gas. Semi-clathrate hydrates have received more attention due to milder pressure/temperature stability conditions compared to ordinary clathrate hydrates. The most commonly reported semi-clathrate hydrates are formed from a combination of gas + water + quaternary ammonium salts. In this work, a total of 53 equilibrium data for semi-clathrate hydrates of methane + TetraButylAmmonium Bromide (TBAB)/TetraButylAmmonium Acetate (TBAA) aqueous solutions were experimentally measured. For TBAB, three concentrations including 0.0350, 0.0490, and 0.1500 mass fractions were used. For TBAA, a solution with a 0.0990 mass fraction was used. Additionally, the modified Chen–Guo model was applied to calculate the hydrate phase equilibrium conditions of methane + TBAB/TBAA aqueous solutions. The model can accurately calculate the aforementioned semi-clathrate hydrate phase equilibrium conditions with the Average Absolute Deviations ((AAD) T and (AAD) P ) of 0.1 K and 0.08 MPa, respectively. The temperature increments for 0.0350, 0.0490, and 0.1500 mass fractions of TBAB are 7.7, 9.4, and 13.5 K, respectively. This value for 0.0990 mass fraction of TBAA is 6.2 K. Therefore, it is concluded that TBAB is a stronger hydrate promoter compared to TBAA.
Blending a fraction of hydrogen into the natural gas pipeline or urban pipe network is an efficient approach for hydrogen delivery. In this paper, the mathematical model of Hydrogen-Blended Natural Gas (HBNG) transportation is established, and the influences of hydrogen blending on hydraulic and thermal characteristics of natural gas pipeline and pipe network are numerically investigated. The impact of hydrogen blending ratio on the performance of centrifugal compressor and the operating point for joint operation of pipeline and compressor is discussed. Results illustrate that compared with natural gas without hydrogen, the hydrogen blending can reduce the pipeline friction resistance and increase the volume flow rate. However, due to the lower volumetric calorific value of HBNG, the energy flow rate actually decreases under the same transportation condition. Meanwhile, the temperature drop along the pipeline slows down due to the blended hydrogen. The performance degradation of centrifugal compressor occurs with the increasing hydrogen blending ratio, and the operating point for joint operation of pipeline and centrifugal compressor moves to the direction of higher volume flow rate and lower pressure. This study is expected to shed a light on the hydrogen delivery by natural gas pipelines and pipe networks.
Tarim Basin newly discovered the fault-karst carbonate reservoirs, which are formed by the large-scale tectonic fault activities and multiple-stage karstification. Four kinds of mediums coexist in the reservoirs, including the large cave, vug, tectonic fracture and matrix. The tectonic fractures interconnect with large caves in series to form the vertical beads-on-string structure, which is the most common connection pattern in reservoirs. To provide a well test method for evaluating this type of structure, this work firstly presents a multi-fracture-region multi-cave-region series connection physical model by simplifying vertical beads-on-string structure. We consider four kinds of mediums in the proposed physical model, including large caves, small vugs, high-angle tectonic fracture and rock matrix. The fracture regions mainly contain fracture, vug and matrix mediums. The cave regions contain cave medium. The corresponding mathematical model is also developed, in which the flow in fracture regions obeys the Darcy’s law, while the flow in cave regions is assumed to obey free flow. Furthermore, the gravity is taken into account because the flow is along the vertical direction. Then the typical flow regimes are analyzed and sensitivity analysis is conducted on crucial parameters. Results indicate that (a) the typical feature of vertical beads-on-string structure on type curves is that the cave storage regimes and linear flow regimes alternately appear; (b) the type curves will exhibit the cave storage regimes with unit-slope pressure derivative for the existence of large caves, which is different from the inter-porosity flow regimes for the existence of the vugs (slope ≠ 1); (c) the gravity effect could lead to unit-slope pressure and pressure derivative curves, which can be regarded as closed boundary in a peculiar sense; (d) gravity effect is difficult to be observed from well test curves with about 2-weeks test duration in real application. Finally, two cases from Shunbei Oilfield are interpreted to illustrate the practicability and feasibility of proposed method.
The development of natural gas pipeline network towards larger scale and throughput has urged better reliability of the pipeline network to satisfy transportation requirement. Previously, studies of optimizing natural gas pipeline network have been mainly focused on reducing operating cost, with little concern on the reliability of pipeline network. For a natural gas pipeline network with a variety of components and complicated topology, a multi-objective optimization model of both reliability and operating cost is proposed in this study. Failure of each component and the state of pipeline network under failure conditions are taken into account, and minimum cut set method is employed to calculate the reliability of the pipeline network. The variables to be determined for the optimization objectives are the rotating speed of compressors and the opening of valves. Then the solving procedure of the proposed model is presented based on Decoupled Implicit Method for Efficient Network Simulation (DIMENS) method and NS-saDE algorithm. The validity of the optimization model is ascertained by its application on a complicated pipeline network. The results illustrate that the optimization model can depict the relative relationship between reliability and operating cost for different throughput, by which the operation scheme with both satisfying reliability and operating cost can be obtained. In addition, the customer reliability and the impact of the failure of each pipeline on the whole network can be evaluated quantitatively to identify the consumers and pipelines of maintenance priority. The pipeline network reliability can be improved through proper monitoring and maintenance of these consumers and pipelines.
The cyclic methane hydrate production method was proposed with CO2 and N2 mixture stimulation. The cyclic production model was established based on actual hydrate reservoir parameters, accordingly, the production characteristics were analyzed, and a sensitivity analysis was conducted. The results show the following: (1) The depressurization mechanism is dominant in the cyclic production. CH4 production and CH4 hydrate dissociation can be greatly enhanced because the cyclic process can effectively reduce the partial pressure of CH4 (gas phase). However, there is a limited effect for CO2 storage. (2) Heat supply is essential for continuous hydrate dissociation. The CH4 hydrate dissociation degree is the highest in the near-wellbore area; in addition, the fluid porosity and effective permeability are significantly improved, and the reservoir temperature is obviously decreased. (3) The initial CH4 hydrate saturation, absolute permeability, intrinsic CO2 hydrate formation kinetic constant, injection time and production time can significantly influence the production performance of the natural gas hydrate reservoir.
Low Salinity Water (LSW) incorporates in surfactant Enhanced Oil Recovery (EOR) as a pre-flush is a common practice aiming to reduce the formation salinity, which affects surfactant adsorption. However, in a field implementation, the adsorption of surfactant is unavoidable, so creating a scheme that detaches the trapped surfactant is equally essential. In this study, LSW was a candidate to enhance the desorption of surfactant. LSW solely formulated from NaCl (1 wt.%), Sodium Dodecylbenzene Sulfonate (SDBS) was chosen as the primary surfactant at its critical micelle concentration (CMC, 0.1 wt.%). It found that injecting LSW as post-flush achieved up to 71.7% of SDBS desorption that lower interfacial tension against oil (31.06° API) to 1.3 mN/m hence bring the total Recovery Factor (RF) to 56.1%. It was 4.9% higher than when LSW injecting as pre-flush and 5.2% greater than conventional surfactant flooding (without LSW). Chemical analysis unveiled salinity reduction induces Na+ ion adsorption substitution onto pore surface resulting in an increment in surfactant desorption. The study was further conducted in a numerical simulation upon history matched with core-flood data reported previously. By introducing LSW in post-flush after SDBS injection, up to 5.6% RF increased in comparison to other schemes. The proposed scheme resolved the problems of adsorbed surfactant after EOR, and further improve the economic viability of surfactant EOR.
For insuring the safe operation of LNG heat exchanger in the Emergency Stop Operation Process (ESOP), a numerical method is proposed to investigate the stress of Plate-Fin Structures (PFS) in that. The relationship between stress of PFS and ESOP is analyzed in LNG heat exchanger. The results will be obtained that the maximum equivalent stress of PFS is greater at the initial stage of ESOP than that at the last stage when the HMR pressure is more than 5 MPa. The maximum equivalent stress increases with the equilibrium temperature when is greater than 180 K and reaches peak value at the last stage of ESOP. The maximum equivalent stress is larger at the last stage of ESOP than the other stage and increases with the equilibrium pressure. When the temperature difference is more than 5 K in the ESOP, the influence of that is obvious for the stress of PFS. In the ESOP, the equilibrium temperature and temperature difference should be controlled within 240 K and 5 K, respectively.
Nonlocal diffusion to a line source well is addressed by space-time fractional diffusion to model transients governed by both long-range connectivity and distorted flow paths that result in interruptions in the geological medium as a consequence of intercalations, dead ends, etc. The former, superdiffusion, results in long-distance runs and the latter, subdiffusion, in pauses. Both phenomena are quantified through fractional constitutive laws, and two exponents α and β are used to model subdiffusion and superdiffusion, respectively. Consequently, we employ both time and space fractional derivatives. The spatiotemporal evolution of transients in 2D is evaluated numerically and insights on the structure of solutions described through asymptotic solutions are confirmed numerically. Pressure distributions may be classified through two situations (i) wherein 2α = β + 1 in which case solutions may be grouped on the basis of the classical Theis solution, and (ii) wherein 2α ≠ β + 1 in which case conventional expectations do not hold; regardless, at long enough times for the combined case, power-law responses are similar to those for pure subdiffusive flows. Pure superdiffusion on the other hand, although we consider a system that is infinite in its areal extent, interestingly, results in behaviors similar to steady-state flow. To our knowledge, documented behaviors are yet to be reported.
Pilot-scale enhanced oil recovery in hydrocarbon field development is often implemented to reduce investment risk due to geological uncertainties. Selection of the pilot area is important, since the result will be extended to the full field. The main challenge in choosing a pilot region is the absence of a systematic and quantitative method. In this paper, we present a novel quantitative and systematic method composed of reservoir-geology and operational-economic criteria where a cluster analysis is utilized as an unsupervised machine learning method. A field of study will be subdivided into pilot candidate areas, and the optimized pilot size is calculated using the economic objective function. Subsequently, the corresponding Covariance (COV) matrix is computed for the simulated 3-D reservoir quality maps in the areas. The areas are optimally clustered to select the dominant cluster. The operational-economic criteria could be applied for decision making as well as the proximity of each area to the center of dominant cluster as a geological-reservoir criterion. Ultimately, the Shannon entropy weighting and the reference ideal method are applied to compute the pilot opportunity index in each area. The proposed method was employed for a pilot study on an oil field in south west Iran.
Gas injection into a naturally fractured oil reservoir keeps the reservoir pressure and increments the initial recovery from the reservoir. The main aim of this work was to develop a numerical model to calculate the mass transfer (molecular diffusion and convection) between a gas injected in the fracture and residual fluid (gas and oil) in a matrix block. The dual continuum model is applied to describe flow behaviour and fluid recovery in porous media. Finally, the model is validated by comparing the outcomes with the results of two experimental works available in the literature. The mathematical model results are in agreement with the laboratory data including recovery of each component, saturation profile, and the pressure gradient between matrix and fracture. Modeling results show that after 25 days of N 2 injection, the lighter and heavier components (C1 and C5) are recovered about 51% and 39%, respectively. These amounts for CO 2 injection are 49% and 27%. It is found that the convection mechanism has a great effect on preventing the pressure drop of the reservoir during injection operations. In the nitrogen injection, without considering the convection, after 30 days, the matrix pressure reaches 1320 Psi from 1479 Psi but after 30 days, considering the convection, the pressure reaches 1473 Psi from 1479 Psi.
Wettability of sedimentary rock surface is an essential parameter that defines oil recovery and production rates of a reservoir. The discovery of wettability alteration in reservoirs, as well as complications that occur in analysis of heterogeneous sample, such as shale, for instance, have prompted scientists to look for the methods of wettability assessment at nanoscale. At the same time, bulk techniques, which are commonly applied, such as USBM (United States Bureau of Mines) or Amott tests, are not sensitive enough in cases with mixed wettability of rocks as they provide average wettability values of a core plug. Atomic Force Microscopy (AFM) has been identified as one of the methods that allow for measurement of adhesion forces between cantilever and sample surface in an exact location at nanoscale. These adhesion forces can be used to estimate wettability locally. Current research, however, shows that the correlation is not trivial. Moreover, adhesion force measurement via AFM has not been used extensively in studies with geological samples yet. In this study, the adhesion force values of the cantilever tip interaction with quartz inclusion on the shale sample surface, have been measured using the AFM technique. The adhesion force measured in this particular case was equal to the capillary force of water meniscus, formed between the sample surface and the cantilever tip. Experiments were conducted with a SiconG cantilever with (tip radius of 5 nm). The adhesion forces between quartz grain and cantilever tip were equal to 56.5 ± 5 nN. Assuming the surface of interaction to be half spherical, the adhesion force per area was 0.36 ± 0.03 nN/nm2. These measurements and results acquired at nano-scale will thus create a path towards much higher accuracy-wettability measurements and consequently better reservoir-scale predictions and improved underground operations.
In this work, unstable displacements were conducted using special equipment designed to run in-situ CT-scanner experiments. All the displacements were conducted on a homogeneous Bentheimer sandstone plug, of 10 cm in diameter and 40 cm in length. Digitations (or fingering) have been observed under varying conditions of injection flowrate, displaced fluid viscosity, and core wettability. They have been characterized at both the core scale, using the core average oil saturation and the water breakthrough; and at the local scale, using the local saturations and had-hoc image processing analysis. It was found that the effect of the different flowing conditions on the front digitations could not be interpreted independently. The oil recovery at brine breakthrough showed a good correlation with the viscous fingering number for the water-wet case. However, a different scaling was observed for the oil-wet case. The interplay of the different flowing conditions mitigates the possibility of constructing a unique scaling number to account for all experimental condition. The local saturation monitoring has provided a new insight to characterize the finger shapes and analyze the production mechanisms. It allowed to distinguish two independent contributions to early breakthrough: viscous dominated digitations and capillary dominated digitations. A two-phases diagram has been constructed to plot and compare these contributions for all flowing conditions. Their evolutions show the main production mechanisms during the flooding. We observed that the viscous digitations were not causing phase trapping at core scale: the core is completely swept after breakthrough. For the water-wet case, we found that the local oil recovery of swept zone remained constant before and after breakthrough while for the oil-wet case it is improving during all the water flooding process.
