Changes In Relative Permeability Research Articles

Effects of microscopic pore-throat structure on gas–liquid relative permeability: Porous media construction and pore-scale simulation

The porous media structure of the oil/gas reservoir changes greatly after long-term development, which subsequently influences the macroscopic relative permeability. To clarify the effects of microscopic pore-throat structure on macroscopic relative permeability, we first proposed a method to generate two-dimensional porous media images with adjustable structure parameters. The method is based on Delaunay triangulation and is similar to the pore-network generation process, which can provide binary images for direct numerical simulation of flow through porous media. Then, we established the single component multiphase Shan–Chen lattice Boltzmann method coupling the real gas equation of state. Finally, we discussed the effect of pore radius, coordination number, pore-throat ratio, pore shape, and wettability on the gas–liquid relative permeability curve using the lattice Boltzmann simulation. This study provides an effective method to generate porous media and explain the mechanism of relative permeability change at the pore scale.

Effect of Confining Pressure on CO2-Brine Relative Permeability Characteristics of Sandstone in Ordos Basin

CO2-brine relative permeability significantly impacts CO2 injection and is a key parameter for carbon dioxide storage simulation in saline aquifers. In the study of relative permeability, factors such as temperature, pressure, and reservoir rock physical properties play a crucial role. To better understand the impact of confining pressure on the CO2-brine relative permeability characteristics of sandstone in the Ordos Basin, five sets of CO2-brine relative permeability data were obtained through unsteady-state displacement tests conducted at various confining pressures ranging from 12 to 20 MPa. The research findings indicate that with an increase in confining pressure there is a slight decrease in irreducible brine saturation. Furthermore, the CO2 relative permeability in the irreducible brine state decreased by 57% as the pressure increased from 12 MPa to 20 MPa. The study demonstrates notable differences in the CO2-brine relative permeability curves under varying confining pressure conditions. As the confining pressure increases, the CO2 relative permeability curve decreases, while the brine relative permeability increases. The change in brine relative permeability is not as pronounced as that of CO2. These experimental results offer essential support for subsequent numerical calculations and practical applications in engineering. Experimental research holds significant importance in the assessment of storage potential and the prediction of the evolutionary patterns of CO2 migration.

Modeling two-phase flow behaviour in a shale gas reservoir with complex fracture networks and flow dynamics

In this work, a robust and pragmatic method has been developed, validated, and applied to describe two-phase flow behaviour of a multifractured horizontal well (MFHW) in a shale gas formation. As for a fracture subsystem, its permeability modulus, non-Darcy flow coefficient, and slippage factor have been defined and embedded into the governing equation, while an iterative method is applied to update the gas/water saturation in each fracture segment within discrete fracture networks. Different from the traditional treatment that a water-source/sink in the matrix is simplified by assuming it as a constant term, a skin factor on a fracture face is defined and introduced to represent the change in relative permeability in the matrix domain at each timestep, while the adsorption/desorption term is incorporated into the diffusivity equation to accurately calculate the shale gas production by taking the adsorbed gas in nanoscale porous media into account. Then, the theoretical model can be applied to accurately capture the two-phase flow behaviour in different subdomains. The accuracy of this newly developed model has been confirmed by the numerical simulation and then it is extended to field applications with excellent performance. The stress-sensitivity, non-Darcy flow, and slippage effect in a hydraulic fracture (HF) are found to be obvious during the production, while the initial gas saturation in a matrix and HFs imposes an evident influence on the production profile. As for an HF with a high gas saturation, the dewatering stage is missing and water from the matrix can be neglected during a short production time. For the matrix subsystem, a high-water saturation in the matrix near an HF can affect gas production during the entire stage since gas relative permeability in the HF remains low. In addition, the adsorption/desorption in the matrix subsystem can increase gas production but decrease water production. Compared to the observed gas/water production rates for field applications, the solutions obtained from the method in this work are found to be well matched, confirming its reliability and robustness.

Hybrid Machine Learning for Modeling the Relative Permeability Changes in Carbonate Reservoirs under Engineered Water Injection

Advanced production methods utilize complex fluid iteration mechanisms to provide benefits in their implementation. However, modeling these effects with efficiency or accuracy is always a challenge. Machine Learning (ML) applications, which are fundamentally data-driven, can play a crucial role in this context. Therefore, in this study, we applied a Hybrid Machine Learning (HML) solution to predict petrophysical behaviors during Engineered Water Injection (EWI). This hybrid approach utilizes K-Means and Artificial Neural Network algorithms to predict petrophysical behaviors during EWI. In addition, we applied an optimization process to maximize the Net Present Value (NPV) of a case study, and the results demonstrate that the HML approach outperforms conventional methods by increasing oil production (7.3%) while decreasing the amount of water injected and produced (by 28% and 40%, respectively). Even when the injection price is higher, this method remains profitable. Therefore, our study highlights the potential benefits of utilizing HML solutions for predicting petrophysical behaviors during EWI. This approach can significantly improve the accuracy and efficiency of modeling advanced production methods, which may help the profitability of new and mature oil fields.

Pore Structure and Permeability Variations during Gas Displacement in Unconsolidated Sandstone Reservoirs through CT Reconstruction Analysis

The continuous gas displacement in unconsolidated sandstone gas reservoirs will necessarily result in the pore structure and rock permeability variations, which cannot be neglected in the gas development process. However, the variations have not been comprehensively addressed yet, especially for the rock structure in pore scale. This work presented the quantitative results of pore structure in microscale and permeability variations during gas displacement in unconsolidated sandstone reservoirs through computed tomography (CT) reconstruction analysis. The results indicated that a more than 3% increase in porosity after gas displacement resulted from the enlargement of the pore and throat with a diameter of more than 20 μm and 3 μm, respectively, owing to the release and migration of clay and fine particles, in spite of the distribution frequency decline of both pore and throat with a small diameter. The pore connectivity would be enhanced by the increase of the connected pores as well as the enlargement of the pore and throat sizes. However, the pore-throat coordination number could only change with slight improvement. In terms of permeability and relative permeability changes with pore structure, the improvement of permeability after gas displacement was higher than that of porosity, and the continuous gas displacement would broaden gas-water flow region and lower irreducible water saturation and residual gas saturation, and then, the equal phase relative permeability point would shift to the right. These investigations will contribute to more accurate reserve evaluation and productivity prediction.

Electromagnetic Modeling and Investigation for Bearingless Switched Reluctance Motor Considering Magnetic Saturation

For 12/4 bearingless switched reluctance motors (BSRMs), the levitation forces are generated in the maximum-inductance flat region of each phase. The magnetic saturation can be reached with the increase in ampere turns. In this paper, the mathematical model considering magnetic saturation is proposed to overcome the problem associated with the nonlinear characteristic. Three regions are divided in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$B$</tex-math></inline-formula> - <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H$</tex-math></inline-formula> loop according to the change of relative permeability with magnetic field intensity. In addition, the single-valued expression between the flux density and the magnetic flux density is defined. The different parameters, i.e., air gaps, lamination, and rotor angle, influencing the performance of BSRM are analyzed. In the control process, the lookup tables (LUTs) of the electromagnetic forces based on the mathematical model are obtained. Finally, the experimental results for the 12/4 BSRM verify the feasibility of the proposed model.

CO2 sequestration in sandstone reservoirs: How does reactive flow alter trapping mechanisms?

Numerous studies have attempted to assess the possible changes in the petrophysical parameters of sandstone reservoirs for the geological storage of CO2. However, the results have been highly variable and hardly conclusive, highlighting mineral alteration, precipitation, dissolution, and fine migration as the main drivers of changes in porosity, permeability, and surface wettability. In this paper, a series of systematic experimental studies were carried out on the Berea sandstone samples to carefully analyse the changes in porosity, relative permeability, capillary pressure, and surface wettability after CO2 treatment. The results obtained indicated that porosity increased in the samples due to dissolution of minerals (calcite and clay) and there was no sign of pore throat closure due to mineral precipitation. It was found that the surface wettability can be shifted towards a CO2 wet system, probably because of calcite precipitation and clay dissolution or reduction in the hydrophilicity of quartz, leading to a decrease in capillary entry pressure. It appears that the mineral and capillary trapping in sandstone make it a suitable storage site for CO2, but that require further research to fully understand the changes posed by mineral dissolution in the long term.

Low salinity water flooding: Evaluating the effect of salinity on oil and water relative permeability curves using coupling of DLVO and geochemical reactions

Enhancing the oil recovery of carbonate reservoirs with acidic oil depends on injected brine composition and salinity throughout the low salinity water flooding. The typical description of this phenomenon on oil and water relative permeability curves is being put forward by the process-dependent interpolation function, which barely addresses the underlying fundamentals governing the direct impact of wettability alteration and geochemical reactions on flow saturation functions. The main objective of this work is to perform an integrated investigation of the effect of salinity on oil and water relative permeability curves by dynamic coupling of the Derjaguin, Landau, Verwey, and Overbeek (DVLO) theory and geochemical reactions. We studied both the single and two-phase systems using the basis of the geochemical reactions to track the variations of the wetting and non-wetting phase relative permeability curves. In the single-phase scenario, the results show the superiority of the reactive flow modeling technique with kinetic-controlled reactions, in the range between [2–4] of the Damkohler number, to yield a better result for the experimental effluent ions' concentrations than the equilibrium approach. In addition, the single-phase results under dynamic conditions propose Civan correlation as the best predictor of residual resistance factor (RRF) by numerically adjusting the correlation of coefficients based on the physical variables - salinity, dimensionless consumed ion concentration, and Peclet number. Accordingly, the results indicate a novel linkage between the single-phase and two-phase results in the sense that RRF under single-phase mode can be used to estimate the change in the wetting phase relative permeability under the two-phase mode. The single-phase methodology provides the capability for an improvement – up to 15% - in the prediction of the pressure drop curve. For two-phase cases, our procedure involved coupling the characterized geochemical reactions and the DLVO theory to consider the effect of injected water composition on contact angle as the static two-phase parameter. The phase-field method is coupled with DLVO theory to calculate the relative permeability curves for the non-wetting phase, which corresponds to the contact angle at each simulation time step. The two-phase results indicate an improvement – up to 30% - in the prediction of the recovery factor curve, on a history-matching basis, using the DLVO theory with contact angle-dependent correlation of non-wetting phase relative permeability curve. The main novelties of this study are using the single-phase dynamic permeability impairment results in calculating the variation of the wetting-phase relative permeability curve. Moreover, dynamic coupling of DLVO and non-linear contact angle-dependent correlation is used to calculate the non-wetting phase relative permeability curve. According to these novelties, more accurate prediction of the laboratory production profiles can be obtained.

Numerical effects on the simulation of surfactant flooding for enhanced oil recovery

Numerical simulation of surfactant flooding using conventional reservoir simulation models can lead to unreliable forecasts and bad decisions due to the appearance of numerical effects. The simulations give approximate solutions to systems of nonlinear partial differential equations describing the physical behavior of surfactant flooding by combining multiphase flow in porous media with surfactant transport. The approximations are made by discretization of time and space which can lead to spurious pulses or deviations in the model outcome. In this work, the black oil model was simulated using the decoupled implicit method for various conditions of reservoir scale models to investigate behavior in comparison with the analytical solution obtained from fractional flow theory. We investigated changes to cell size and time step as well as the properties of the surfactant and how it affects miscibility and flow. The main aim of this study was to understand pulse like behavior in the water bank, which we report for the first time, Our aim was to identify their cause and associated conditions. The pulses are induced by a sharp change in relative permeability as the interfacial tension changes. Pulses are diminished when adsorption is modeled, and ranged from 0.0002 kg/kg to 0.0005 kg/kg. The pulses are absent for high-resolution model of 5000 cells in x direction with a typical cell size as used in well-scale models. The growth or dampening of these pulses may vary from case to case but in this instance was a result of the combined impact of relative mobility, numerical dispersion, interfacial tension and miscibility. Oil recovery under the numerical problems reduced the performance of the flood, due to large amounts of pulses produced. Thus, it is important to improve existing models and use appropriate guidelines to stop oscillations and remove errors.

Ionic liquids as completion fluids to mitigate formation damage

Formation damage can occur in any phase of oil and gas operation from drilling, completion, or stimulation. Fluids used to drill, complete, and fracture the formation may invade and damage the formation. These fluids may interact with clays present in the formation and adversely affect the flow performance. The change in flow performance could occur due to flow restriction or decrease in permeability, change in relative permeability, or unintended flow restriction during the specific operation. In this work, ionic liquids are proposed as clay swelling additives in completion fluid to overcome the formation damage problem. Imidazolium-based ionic liquids and three different salts are tested with 0.5 wt % and 3 wt % concentration, respectively, on tight sandstone formation containing high clay contents. Completion fluids prepared using ionic liquids resulted in complete stabilization of clays and therefore nearly maintain the in-situ permeability of tight sandstone. The completion fluids are prepared in deionized water for experimental consistency. Coreflooding experiments were performed on Scioto sandstone core samples containing an average porosity and permeability of 16.9% and 0.72 mD., respectively. Cores were saturated with completion fluids based on salts such as calcium chloride (CaCl2), magnesium chloride (MgCl2), and ammonium chloride (NH4Cl) and with Imidazolium-based ionic liquids before the coreflooding experiments. These coreflood experiments involve a preflush with the prepared completion fluid and post-flood with deionized water. Moreover, Nuclear Magnetic Resonance (NMR) tests were performed on all samples before and after coreflood to estimate the change in porosity and pore size distributions of the rock samples. Results showed that the porosity and permeability loss were significantly large in cores flooded with CaCl2 and NH4Cl salts solution when flooded with water. MgCl2 salt solution showed exceptionally stable porosity and permeability compared to other completion fluids. Furthermore, the results of ionic liquid-based completion fluids showed no significant loss in porosity and permeability when flooded with water. Therefore, the proposed ionic liquid-based completion fluids can be used for well-completion operation without any formation damage.

Stimulating relative permeability changes by low-frequency elastic waves: Theory and lab experiments

A model is presented to describe how low-frequency vibrations can induce changes to relative permeabilities in dual-porosity dual-permeability rocks. We show that a combination of two physical processes may cause this effect: 1) the wave-induced two-phase fluid flow between soft pores (fractures or cracks) and stiff pores (matrix); and 2) the contact angle hysteresis effect. These two effects lead to redistribution of fluid saturation between fractures and matrix, which may explain alteration of relative permeabilities by small transient strains (∼10−6) in rocks where the fluid flow occurs primarily through the fracture network, and fluid storage occurs predominantly in the porous matrix. We assume that the frequency is low enough that viscous and inertial effects are negligible and that any stress-induced increments of pore pressure are uniform within wetting and nonwetting fluid phases. We demonstrate that pulse-like vibrations are much more efficient in changing relative permeabilities than sinusoidal-shaped vibrations. Furthermore, we show that two waveforms with the same amplitude and frequency but with different polarities could have opposite effects on the alteration of relative permeabilities. Specifically, extensional pulses increase oil relative permeability and decrease water relative permeability in the water-wet rock. Contrary, compressional pulses decrease oil relative permeability and increase water relative permeability in the water-wet rock. To validate theoretical results, we developed a unique low-frequency laboratory setup and experimental methods. We performed drainage and imbibition cycles on a sandstone sample using oil and water as pore fluids. During flooding, the sample was excited by small-strain seismic pulses of a specific shape, with varying polarization direction, frequency, and amplitude. The preliminary laboratory results validate the theoretical model qualitatively. The proposed model may contribute to environmentally friendly and low-cost methods for stimulating hydrocarbon production in conventional reservoirs without invasive chemicals or fracking. In unconventional reservoirs, however, this technology can be envisioned as supplementary to standard EOR/IOR techniques. Normally, the seismic wave energy is too low to increase absolute permeability or decrease oil viscosity; only relative permeabilities can be affected.

Numerical Study and Force Chain Network Analysis of Sand Production Process Using Coupled LBM-DEM

Sand production has caused many serious problems in weakly consolidated reservoirs. Therefore, it is very urgent to find out the mechanism for this process. This paper employs a coupled lattice Boltzmann method and discrete element method (LBM-DEM) to study the sand production process of the porous media. Simulation of the sand production process is conducted and the force chain network evolvement is analyzed. Absolute and relative permeability changes before and after the sand production process are studied. The effect of injection flow rate, cementation strength, and confining pressure are investigated. During the simulation, strong force chain rupture and force chain reorganization can be identified. The mean shortest-path distance of the porous media reduces gradually after an initial sharp decrease while the mean degree and clustering coefficient increase in the same way. Furthermore, the degree of preferential wettability for water increases after the sand production process. Moreover, a critical flow rate below which porous media can reach a steady state exists. Results also show that porous media under higher confining pressure will be more stable due to the higher friction resistance between particles to prevent sand production.

Calculation Model of Relative Permeability in Tight Sandstone Gas Reservoir with Stress Sensitivity

During the development of tight gas reservoir, the irreducible water saturation, rock permeability, and relative permeability change with formation pressure, which has a significant impact on well production. Based on capillary bundle model and fractal theory, the irreducible water saturation model, permeability model, and relative permeability model are constructed considering the influence of water film and stress sensitivity at the same time. The accuracy of this model is verified by results of nuclear magnetic experiment and comparison with previous models. The effects of some factors on irreducible water saturation, permeability, and relative permeability curves are discussed. The results show that the stress sensitivity will obviously reduce the formation permeability and increase the irreducible water saturation, and the existence of water film will reduce the permeability of gas phase. The increase of elastic modulus weakens the stress sensitivity of reservoir. The irreducible water saturation increases, and the relative permeability curve changes little with the increase of effective stress. When the minimum pore radius is constant, the ratio of maximum pore radius to minimum pore radius increases, the permeability increases, the irreducible water saturation decreases obviously, and the two-phase flow interval of relative permeability curve increases. When the displacement pressure increases, the irreducible water saturation decreases, and the interval of two-phase flow increases. These models can calculate the irreducible water saturation, permeability and relative permeability curves under any pressure in the development of tight gas reservoir. The findings of this study can help for better understanding of the productivity evaluation and performance prediction of tight sandstone gas reservoirs.

Upscaled modeling of complex DNAPL dissolution

A straightforward, upscaled DNAPL mass dissolution model is developed using relatively simple input consisting of characteristic dimensions and saturations of a DNAPL accumulation. Multiple accumulations are aggregated into a single source zone volume. Physically, the dissolution process is a combination of flow through the mass (advective component) and flow around the mass (dispersive component). The contribution of each component is based on initial characteristic length scales and the average initial saturation. Changes over time with the depletion of mass are captured with a changing relative permeability and a power law relationship for the fraction of initial mass remaining. The utility of the upscaled process model is demonstrated with data from three studies: numerical simulation of multiple pools, two-dimensional test cell experiments with mixed architecture and with heterogeneous soil, and a controlled field study of multicomponent DNAPL release and depletion. Use of the model successfully reproduced the observed multistage mass discharge in each study and illuminated the governing processes. The power law exponent was relatively constant for the various conditions and relative permeability changes were integral to the success. The numerical and experimental studies were run to complete mass depletion which the upscaled model matched. The input parameters are minimal and are found in typical DNAPL source zone characterization data.

Productivity Influence Factors of Tight Sandstone Gas Reservoir with Water Produced

Finding ways to accelerate the effective development of tight sandstone gas reservoirs holds great strategic importance in regard to the improvement of consumption pattern of world energy. The pores and throats of the tight sandstone gas reservoir are small with abundant interstitial materials. Moreover, the mechanism of gas flow is highly complex. This paper is based on the research of a typical tight sandstone gas reservoir in Changqing Oilfield. A strong stress sensitivity in tight sandstone gas reservoir is indicated by the results, and it would be strengthened with the water production; at the same time, a rise to start-up pressure gradient would be given by the water producing process. With the increase in driving pressure gradient, the relative permeability of water also increases gradually, while that of gas decreases instead. Following these results, a model of gas-water two-phase flow has been built, keeping stress sensitivity, start-up pressure gradient, and the change of relative permeability in consideration. It is illustrated by the results of calculations that there is a reduction in the duration of plateau production period and the gas recovery factor during this period if the stress sensitivity and start-up pressure gradient are considered. In contrast to the start-up pressure gradient, stress sensitivity holds a greater influence on gas well productivity.

Relative Permeability Hysteresis and Capillary Trapping during CO2 EOR and Sequestration

Residual or capillary trapping is an important mechanism of CO2 trapping in underground porous media. Recent experimental investigation has shown that relative permeability and capillary pressure are function of saturation changing direction or hysteresis phenomenon in addition to the saturation and hysteresis leads to irreversible change in relative permeability and capillary pressure curve. In this paper, an extended review was performed on the relative permeability hysteresis models. Moreover, an experimental investigation was conducted during CO2 injection as the non–wetting phase in carbonate rocks at pressure and temperature of 10.3 MPa and 60 ℃. In this study, the effects of absolute permeability of carbonate rock samples and CO2 injection strategy on hysteresis phenomenon in the CO2 residual trapping process were investigated. During first part of experiments, CO2 relative permeability was examined during CO2 injection and brine injection at constant rate of 0.2 cc/min as drainage and imbibition process for different absolute permeability of rock samples. During second part of experiments, CO2 trapping saturation was calculated during the continuous CO2 injection and CO2 Water Alternative Gas (WAG) injection. Results of first part of experiments showed that increasing of the absolute permeability leads to increasing initial and residual CO2 saturation at the end of drainage and imbibition process, respectively. Moreover, it was concluded that increasing rock permeability results in increasing of the hysteresis effect on the CO2 relative permeability. In the second part of experiments, results revealed that CO2 WAG injection strategy has higher CO2 residual saturation in compared to CO2 continuous injection at equal pore volume of injected CO2. The findings of this paper can be applied for investigating of CO2 sequestration projects in aquifers for improvements of CO2 residual trapping and studying the performance of capillary trapping as one of the main mechanisms of CO2 trapping.

Hash Unit Cell Shape Used To Enhancement Gain and Bandwidth of Metasurface Antenna

In this paper, Low-profile, high gain and wideband antenna loaded with a single layer metasurface are proposed. The process of adding the metasurface layer depends on the Fabry Pérot technology, which required existing an air gap among the slot antenna and the metasurface layer. The metasurface layer consists of an array of 4 × 4 unit elements placed on a Roger Ro4003C substrate layer with a thickness of 2.5mm. Hash shape is used as a radiating element. The metasurface MS is acting as left-hand material in which both permittivity and permeability are negative, leading to negative refractive indexing. The emitted waves from the slot antenna are affected by a set of unit cells on the metasurface MS above the slot antenna because of the structure’s equivalent relative permeability and permittivity changes, and the slot antenna performance changes accordingly. The antenna works at a frequency of 6.75 GHz as a resonant frequency with an improvement in the bandwidth value for the metasurface antenna to get a value of 2.2 GHz instead of 390 MHz for the slot antenna. The proposed antenna has a 37 % bandwidth impedance starting at 4.7 GHz and ending at 6.9 GHz with a 7.43 dB gain value. The suggested antenna is useful for use with Wi-Fi applications.

Novel MNZ-type microwave sensor for testing magnetodielectric materials

A novel microwave sensor with the mu-near-zero (MNZ) property is proposed for testing magnetodielectric material at 4.5 GHz. The sensor has a double-layer design consisting of a microstrip line and a metal strip with vias on layers 1 and 2, respectively. The proposed sensor can detect a unit change in relative permittivity and relative permeability with a difference in the operating frequency of 45 MHz and 78 MHz, respectively. The MNZ sensor is fabricated and assembled on two layers of Taconic RF-35 substrate, with thicknesses of 0.51 mm and 1.52 mm, respectively, for the measurement of the sample under test using a vector network analyzer. The dielectric and magnetic properties of two standard dielectric materials (Taconic CER-10 and Rogers TMM13i) and of yttrium–gadolinium iron garnet are measured at microwave frequencies. The results are found to be in good agreement with the values available in the literature, which shows the applicability of the prototype for sensing of magnetodielectric materials.

Water, Water Everywhere Using ML and Game Theory To Win at Produced-Water Forecasting

In the Bakken-Three Forks play of the Williston Basin, many oil wells that once produced some water have become water wells that produce some oil, as average oil production has flatlined while water production continues to increase. A complex interplay of stepping out beyond the core to where water saturations are higher, upsizing completions, tighter spacing, and dealing with greater parent-child effects and potential changes in relative permeability is significantly increasing volumes of produced water. Similar situations have been occurring in other basins. This is a serious threat for the US unconventional oil and gas industry, for which produced water has become a $34-billion industry and exposes operators to numerous operational, environmental, and economic risks. Software developers are beginning to adapt advanced machine-learning (ML) methods that have proved successful in forecasting oil production and upgrading them with aspects of game theory to make quick and accurate work of understanding and predicting water production in unconventional plays. Novi Labs (Novi), an Austin-based software company focusing on unconventional shale, has developed a solution that is being applied successfully in the Williston Basin to help disentangle the complex interactions of larger completion designs, changing geology, and tighter spacing that contribute to increased water production. According to the firm’s model, fluid per foot ranks as the most important input variable for increasing water production, ranking above proppant per foot and geologic parameters. Ted Cross, technical advisor at Novi and former senior geologist with Conoco Phillips, presented a paper that discussed the produced water challenge at the 2020 Unconventional Resources Technology Conference (URTeC). “How often does an engineer dash off a simple water forecast, doing something like applying a flat water-to-oil ratio to their water prediction?” Cross asked rhetorically. In unconventional oil fields, water forecasting and pre-drill water predictions have not received attention commensurate with their economic importance. “Quick is still common,” he said. Operators, regulators, and water-disposal companies often rely on simplistic water-cut ratios or basin-level extrapolations that ignore the complex interplay of geology, completions, and spacing decisions on water production. “They are starting to realize and incorporate the fact that water-to-oil ratios will evolve over a well’s life, usually increasing. But the critical thing is that the time they spend on water prediction is a tiny fraction of what they spend on oil, and the methods are less sophisticated and developed,” Cross said. Part of the reason, he explained, is that in the early development of the Eagle Ford, Permian, and some core parts of the Williston, either the original wells didn’t produce large volumes of water or the existing infrastructure around conventional plays was sufficient to handle it. But with field evolution and changing completion designs, water has become a critical issue.

Influence of crucial reservoir properties and microbial kinetic parameters on enhanced oil recovery by microbial flooding under nonisothermal conditions: Mathematical modelling and numerical simulation

In the present study, improved mathematical and numerical models are developed in order to simulate the influence of important reservoir (effective porosity and longitudinal dispersivity), fluid and microbial kinetic (Monod half-saturation constant, substrate to biomass yield coefficient and substrate inhibition) parameters on dynamics of in-Situ microbial enhanced oil recovery (MEOR) processes using Bacillus sp. in a typical sandstone reservoir. This numerical model is a novel attempt to consider the coupled effects of heat transport and substrate-inhibition kinetics on reactive-transport of microbes, substrates and biosurfactants as against the conventional models, thus making the prediction of MEOR processes more realistic and may assist in developing suitable strategies to enhance oil recovery at field scale. In addition, the present model also investigates the changes in relative permeabilities of reservoir fluids (oil and water) and fractional flow of water under the influence of nonisothermal condition, substrate inhibition, along with variations in pore-size distribution index, oil to water viscosity ratio and crude oil API gravity within reservoir during microbial flooding for estimating residual oil recovery. The present model results match significantly well, when verified, with the existing analytical and experimental results, thus proving the model's reliability. The results suggest that under nonisothermal conditions, biosurfactant production is maximum (77.8 mg ml−1) at effective reservoir porosity 23.4%, with low substrate half-saturation constant and high substrate-to-biomass yield coefficient values of 0.018 mg ml−1 and 0.8, respectively. Though biosurfactant production is reduced by more than 80% due to substrate inhibition, which is maximum at inhibition constant value 0.1 mg ml−1, residual oil-saturation is decreased by more than 90% at the end of MEOR process, thus enhancing oil displacement, mobility and hence, improved crude oil recovery. The reactive-transport of substrates, microbes and biosurfactants at injection mean fluid velocity of 1.68 m day−1, are also found to be highly sensitive to reservoir longitudinal dispersivity (αL) and maximum biosurfactants are produced (9.74 mg ml−1) at threshold αL value, 0.37 m, which corresponds to reservoir length of 50 m. Besides, a strategy is suggested to improve the oil recovery efficiency of the present in Situ MEOR approach by characterizing the reservoir for its pore size distribution index, and formation fluids (oil and water) for their viscosity ratios and crude oil API gravities, under nonisothermal and substrate inhibition conditions.