Water Saturation Distribution Research Articles

From Streamline to Pathline: Visualizing Particle Trajectories Under Changing Velocity Fields

Summary Monitoring of subsurface fluid motion is critical for optimizing hydrocarbon production and CO2 sequestration. Streamlines are frequently used to visualize fluid flow; however, they provide only an instantaneous snapshot of the velocity field and do not offer an exact representation of fluid movement under varying field conditions. In contrast, pathlines are constructed by tracking individual particles within the fluid, enabling us to trace the movement of these particles as they traverse through changing velocity fields. Pathline is the trajectory that an individual fluid particle follows in the reservoir. It can be thought of as “recording” the path of a fluid element in the flow field for a given time interval. Pathlines are distinct from streamlines which represent a snapshot of the velocity field at a given instant. The direction the path takes is determined by the streamlines at a specific instant. To start with, streamlines are traced based on the grid face fluxes of finite-difference simulation. Streamline tracing continues till the time of flight equals the current time. The endpoints of the current streamlines become the starting points for the next tracing period. Thus, our formulation incorporates changing flow fields, and the process is repeated for each time interval until the end. The proposed injection monitoring method is tested using a 3D field-scale model with complex geologic features to demonstrate its power and utility. The pathlines were compared with streamlines, as well as the water saturation distribution. Three scenarios are tested: a constant well schedule, a changing well schedule with partial shut-in, and a changing well schedule with a whole field cessation. Results indicate that the pathline provides a more accurate swept volume, consistent with saturation distribution. The robustness of our algorithm and implementation is demonstrated with a complex embedded discrete fracture model (EDFM) to visualize flow patterns in discrete facture network. Pathlines display the fluid flow across fractures and are subsequently used to explore the sweep efficiency and the well connectivity.

Spatial Distribution and Diffusion Characterisation of Water in Coal Samples: An Experimental Study

Comprehending the water absorption process inherent to coal, including the associated spatial distribution patterns of water, proves indispensable in the design and evaluation of coal pillar dams in underground water reservoirs. To better understand this process, a series of NMR (nuclear magnetic resonance) tests were carried out on cylindrically shaped coal samples immersed in water for varying durations, with the upper and lower surfaces of the samples sealed. A method involving image digital processing and finite element simulation was used to quantitatively characterise the water absorption process, as well as the spatial distribution of water in the samples. The results showed that NMR imaging colour brightness differences were positively correlated with water content and that the wetted ring gradually increased in width as the water immersion time increased. The expectation and sum of squared deviations of the pixel greyscale values of the NMR images, which were used to characterise the water saturation and spatial distribution of the coal samples, represented positive and negative exponential functions of the water immersion time, respectively. This indicated that the water saturation gradually increased and became more uniformly distributed. Furthermore, based on the set threshold value of the target variable rate of change, the limiting expectation of the pixel greyscale values was obtained, and the limiting water absorption time of the coal sample was predicted. The water diffusion equation was then used to characterise the water absorption process of the coal samples, and a water diffusion model was developed to accurately obtain the wet ring boundary data. A reasonable value of the diffusion coefficient was determined by comparing and correcting the results of the numerical simulation and physical experiments with full consideration of the non-homogeneity of the numerical model. This water diffusion model can better characterise the water transport phenomena in the macroscopic barrier zone of coal pillar dams. Finally, the application prospects in terms of practical engineering were investigated.

FEATURES OF DECOMPOSITION OF GAS HYDRATE IN NONEQUILIBRIUM MODE IN A POROUS MEDIUM

The paper presents a mathematical model of the nonequilibrium decomposition of a gas hydrate contained in a porous reservoir of finite extent. The system of basic equations, which includes the law of conservation of mass, the heat inflow equation and Darcy’s law, also contains an equation describing the kinetics of nonequilibrium hydrate decomposition, which is determined by pressure, temperature and surface area of particles. On the basis of the numerical solution of the problem, dependences are obtained that allow us to identify the regularities of the process of nonequilibrium decomposition of gas hydrate in a natural reservoir when warm gas is injected into a porous reservoir. It is shown that at the initial moments of time after the start of injection, the extent of the region saturated with gas, hydrate and water is very small compared to the extent of the formation, which corresponds to the mode of hydrate decomposition on the frontal surface. At long injection times, the nonequilibrium hydrate decomposition process is characterized by the formation of three characteristic zones: the near one, where the pores are saturated with gas and water, the far one, saturated with methane and its gas hydrate, and the intermediate one, where gas, hydrate and water are located. It is established that the pressure and temperature in the extended region are connected by the condition of phase equilibrium. The influence of the main parameters of the system on the distributions of pressure, temperature, water saturation and hydrate saturation, as well as on the dynamics of their changes over time, is analyzed. It is shown that injection pressure, as well as reservoir permeability and porosity have a significant effect on the decomposition rate of gas hydrate. An increase in the values of these parameters contributes to an increase in the rate of nonequilibrium hydrate decomposition. An increase in the injection temperature leads only to an increase in the extent of the area containing methane and water.

Impacts of geomechanical damage on waterflood-induced fracture propagation in deeply deposited tight oil reservoirs

Waterflood-induced fractures can enhance the production of deep tight oil reservoirs. However, if waterflood-induced fractures propagate fast, they connect injection wells to production wells earlier, inhibiting the production of tight oil reservoirs. In the present research, the fast propagation mechanism of waterflood-induced fractures was mainly investigated. The changes in sandstone mechanical properties by water were investigated by laboratory experiments, and the relationship of the geomechanical damage of sandstones with water saturation was quantified. Flow-geomechanics-coupled numerical simulations were performed to analyze the impacts of water flooding on stress distribution in a deeply deposited tight oil reservoir. Based on the fracture mechanics theory, the propagation length of the waterflood-induced fracture was calculated and the characteristics of waterflood-induced fracture propagation were analyzed. Experimental results revealed that water changed the mineral composition and microscopic structure of sandstones. This phenomenon decreased the Young’s modulus and tensile strength of sandstones and increased the Poisson’s ratio. The changing magnitude of these properties increased with the rise of water saturation, and the maximum changing magnitude reached 70%. The water saturation distribution became heterogeneous after waterflooding, causing a heterogeneous distribution of mechanical properties. The stress around the fracture tip and the fracture propagation length were significantly affected by these property changes. After the geomechanical damage, the fracture propagation pressure decreased by about 20%. Moreover, the initial fracture length enhanced the propagation length of the waterflood-induced fracture. These results suggest that the propagation of waterflood-induced fractures becomes more significant during waterflooding; thus, the injection pressure should be reduced to avoid fast fracture propagation.

Randomness effect of platinum loading distribution in a proton exchange membrane fuel cell: A numerical simulation

The platinum loading is randomly distributed within catalyst layers because of the fabrication way, whereas the platinum loading is considered to follow the homogeneous distribution in the traditional catalyst layer model. The cell performance and heat and species transport laws of the fuel cell with platinum loading random distribution within catalyst layers are not yet clear. Therefore, in this work, a two-dimensional, non-isothermal proton exchange membrane fuel cell model considering the two-phase flow and agglomerate structure of catalyst layers is established to simulate the fuel cell having the catalyst layer where platinum loading is random distribution in a way that is closer to the actual structure. The effect of random distribution of platinum loading on the electrical property, species transfer and temperature distribution is analyzed. Results suggest that the randomness influence needs to be considered when the local distributions of parameters are studied and the research accuracy of parameters is relatively high. In contrast with the homogeneous distribution of platinum loading, the cell performance for the normal random distribution and uniform random distribution cases is reduced. The effects of catalyst loading random patterns on cell performance, species and temperature distributions are different, and the decrease of cell performance for the uniform random distribution case is more obvious. Furthermore, the influence degree of randomness on each parameter is different. The distributions of electrochemical reaction rate, oxygen concentration and temperature display random characteristics, while the liquid water saturation distribution is less influenced by randomness and does not show an obvious random change. These findings can provide a reference for the randomness verification in random simulations and deepen the understanding of species and heat transfer laws in the catalyst layer which is closer to the reality to improve the accuracy of fuel cell simulations.

Advanced Geostatistical Techniques for Building 3D Geological Modeling: A Case Study from Cretaceous Reservoir in Bai Hassan Oil Field

A 3D Geological model was generated using an advanced geostatistical method for the Cretaceous reservoir in the Bai Hassan oil field. In this study, a 3D geological model was built based on data from four wells for the petrophysical property distribution of permeability, porosity, water saturation, and NTG by using Petrel 2021 software. The geological model was divided into a structural model and a property model. The geological structures of the cretaceous reservoir in the Bai Hassan oil field represent elongated anticline folds with two faults, which had been clarified in the 3D Structural model. Thirteen formations represent the Cretaceous reservoir which includes (Shiranish, Mashurah, U.kometan, Kometan Shale, L. Kometan, Gulneni, Dokan, Mauddud, Jawan/Mud, Batiwah, Shuaiba, Garagu, L.Sarmord). According to the property model, the model for each petrophysical property was constructed based on core data and CPI. By using the geostatistical method, the property model was constructed. The Mauddud Formation is considered one of the most promising hydrocarbon reservoirs in the Bai Hassan oil field based on the results of the property model, where the ratio of water saturation is around 30%, the porosity value is reaching up to 31%, and the net to gross ratio is averaging at 70%.

Water saturation distribution in a PEMFC at the cathode side using OpenFOAM

Water management is a critical issue for achieving the optimum performance of proton exchange membrane fuel cells (PEMFC) since water flooding limits the flow of reactants to catalyst zones and produces electrode regions with higher electric resistance. We used a 3D non-isothermal multiphase model of a single PEMFC to investigate the liquid water saturation distribution at the cathode side. We used an open-source toolbox to solve finite volume method calculations and implement an effective diffusion model based on fiber layers. A parametric study of the condensation rate and saturation at 0.4, 0.2, and 0.1 V illustrates the distribution of liquid water saturation and the flooding zones across the electrode components. The comparison shows that the flooding zones are located at the land ribs. Also, increased water saturation and higher oxygen consumption produce a reactant restriction in the porous media and impact the global performance of the fuel cell.

Control of Liquid Water Transport in Cathode of PEFC Using Wettability-Patterned Electrodes

During the operation of polymer electrolyte fuel cells (PEFCs), the product water that accumulates in the cathode electrode blocks the oxygen transport to the reaction sites and causes severe performance degradation. This phenomenon, known as “flooding,” is one of the critical issues to be solved for achieving high efficiency and high power density. To alleviate water flooding, it’s necessary to design an electrode/channel structure that could actively remove liquid water from the porous electrode. Zhang et al. [1] reported that the wettability patterning of a gas diffusion layer (GDL) enables it to provide the liquid water pathway in the cathode electrode. Furthermore, Nishida et al. [2] demonstrated that the hydrophilization of cathode channel walls promotes water removal from the GDL to the flow channel. This study fabricated a wettability-patterned GDL impregnated with a hydrophilic silica-based solvent and newly proposed an electrode/channel structure combining the patterned electrode and hydrophilized flow channel. The effect of its structure on the liquid water distribution within the cathode GDL of an operating PEFC was also investigated using X-ray imaging.The authors fabricated the experimental fuel cell with an effective electrode area of 1.8 x 1.6 cm2. The membrane electrode assembly (MEA) was sandwiched between two carbon separators with a single-serpentine flow field (number of channels: 7, channel width: 1.0 mm, depth: 1.0 mm, total length: 88.5 mm). Fig. 1 shows the regions measured by X-ray imaging in the cross-sectional view of the cathode. Since the cathode GDL is irradiated with an X-ray beam in the in-plane direction, the through-plane distributions of water can be observed in the GDL. The measurement regions were set under the 4th channel and under the land between the 3rd and 4th channel. The GDL in the cathode was impregnated with the silica-based solvent in the range of 0.3 mm width x 10 mm length x 0.1 mm depth. The hydrophilized region was positioned along the right sidewall of the 4th channel. The channel walls of the cathode were also coated with the same hydrophilic solvent. Fig. 2 represents the distribution of water saturation in the (a) uncustomized and (b) wettability-patterned GDL. The current density was increased stepwise from 0.14 to 1.02 A/cm2 for 8 min at room temperature and non-humidified condition. All images were captured at t=6 min after starting the operation. Dry hydrogen (stoichiometry: 1.5@2.0A/cm2) and oxygen (stoichiometry: 3.0@2.0A/cm2) were supplied to the anode and cathode, respectively, in a counter-flow arrangement. As shown in Fig. 2(b), it was noted that the water saturation around the hydrophilized region was effectively reduced due to the in-plane water suction. The patterned GDL partially impregnated with the highly hydrophilic solvent enables to induce the product water from the hydrophobic to hydrophilic region, resulting in the reduction of flooding. To further accelerate the through-plane water transport from the hydrophilized region in the GDL to the channel sidewall, it’s essential to introduce a difference in their wettability and optimize their combinations.

Implementing pore size distribution into saturation height function modelling of reservoir rock types: A case study on a carbonate gas reservoir

The accurate determination of saturation-height functions for modeling multiphase fluid flow in porous media is critical for applications, such as hydrocarbon recovery and subsurface CO2/H2 storage. The challenges associated with water saturation distribution in carbonate reservoirs arise from their inherent heterogeneity and complex pore systems. Addressing such challenges, this study aims to introduce a robust saturation-height function model that considers a non-linear relationship between capillary pressure and saturation, leading to more reliable estimates of fluid saturations. To achieve this, modifications were performed on a saturation height model based on the relationship between porosity, permeability, and pore size distribution (PSD). First of all, the capillary pressure model implemented in the previously introduced PSD-based approach was replaced by a model suitable for heterogeneous reservoirs, fitting the available mercury injection capillary pressure (MICP) data with higher accuracy. Additionally, the derivation of the relations between the optimum pore throat radius and matching parameters of the capillary pressure model was conducted by finding the best correlation among all the available data in the previous approach. For the first time in this study, considering the resemblance in rock properties like capillary pressure and PSD within each rock type, individual correlations among these parameters were established for each reservoir rock type. The predicted saturation height model was cross-checked against the log and core-derived saturation heights, demonstrating a high level of consistency, particularly along the gas-saturated regions. The obtained results were also compared with the conventional saturation height models, including the Leverett J-Function, Johnson's method, and Cuddy's approach. The significance of the modifications was underscored through a comparison of results with those achieved by the previous approach in which the rock typing was ignored. Although the PSD method, which ignored rock types, exhibited high consistency with log data, our modifications yielded far better predictions by improving the coefficient of determination from 0.68 to 0.84.

Assessment of Depth of Mud-Filtrate Invasion and Water Saturation Using Formation-Tester Measurements: Application to Deeply Invaded Tight-Gas Sandstones

Formation pressure/fluid measurements are impacted by mud-filtrate invasion, which may require long fluid pumpout durations to acquire hydrocarbon samples with minimal mud-filtrate contamination. However, unlike other well-logging instruments, formation testers do not have a fixed depth of investigation that limits their ability to pump out mud filtrate until acquiring original formation fluids (i.e., sensing the uninvaded zone). We use an in-house petrophysical and fluid-flow simulator to perform numerical simulations of mud-filtrate invasion, well logs, and formation-tester measurements to estimate the radial distance of invasion and the corresponding radial profile of water saturation. Numerical simulations are initialized with the construction of a multilayer petrophysical model. Initial guesses of volumetric concentration of shale, porosity, water saturation, irreducible water saturation, and residual hydrocarbon saturation are obtained from conventional petrophysical interpretation. Fluid-flow-dependent petrophysical properties (permeability, capillary pressure, and relative permeability), mud properties, rock mineral composition, and in-situ fluid properties are obtained from laboratory measurements. The process of mud-filtrate invasion and the corresponding resistivity and nuclear logs are numerically simulated to iteratively match the available well logs and estimate layer-by-layer formation water saturation. Next, using our multiphase formation testing simulator, we numerically simulate actual fluid sampling operations performed with a dual-packer formation tester. Finally, we estimate irreducible water saturation by minimizing the difference between the hydrocarbon breakthrough time numerically simulated and measured with formation-tester measurements. The examined sandstone reservoir is characterized by low porosity (up to 0.14), low-to-medium permeability (up to 40 md), and high residual gas saturation (between 0.4 and 0.5). The deep mud-filtrate invasion resulted from extended overbalanced exposure to high-salinity water-based mud (17 days of invasion and 1,800 psi overbalance pressure) coupled with the low mud-filtrate storage capacity of tight sandstones. Therefore, the uninvaded formation is located far beyond the depth of investigation of resistivity tools, whereby deep-sensing resistivities are lower than those of uninvaded formation resistivity. Through the numerical simulation of mud-filtrate invasion, well logs, and formation-tester measurements, we estimated radial and vertical distributions of water saturation around the borehole. Likewise, we quantified the hydrocarbon breakthrough time, which matched field measurements of 6.5 hours. The estimated radius of invasion was approximately 2.5 m, while the difference between estimated water saturation in the uninvaded zone and water saturation estimated from the deep-sensing resistivity log was approximately 0.13, therefore improving the estimation of the original gas in place.

Effect of microporous layer structural parameters on heat and mass transfer in proton exchange membrane fuel cells

Proton exchange membrane fuel cells offer promising clean energy solutions for various applications. However, their performance relies heavily on the properties of the microporous layer, which plays a crucial role in transporting and distributing the components in the fuel cell. To date, the potential for optimising the microporous layer material structural parameters to enhance the fuel cell performance remains largely unexplored. This study aims to fill this research gap by conducting a comprehensive investigation of the effects of different microporous layer material structural parameters on the heat and mass transfer in the membrane electrode assembly. MATLAB was used for optimising the performance of the fuel cell components. The results show that increasing the microporous layer thickness from 5 to 50 μm significantly affects the species transport, leading to a substantial reduction in the molar fraction of H2 and O2 at the electrochemical reaction sites. Furthermore, the distribution of the liquid water saturation inside the fuel cell is influenced by the porosity and permeability of the microporous layer. By increasing the porosity from 0.3 to 0.6, the liquid water saturation at the interface of the catalyst layer and microporous layer decreases by 0.52 % and 1.12 % at output voltages of 0.5 V and 0.7 V, respectively. This reduction enhances the efficiency of internal water transport. Moreover, reducing the permeability of the microporous layer from 2 × 10-12 to 1 × 10-13 at 0.5 V and 0.7 V leads to an increase in liquid water saturation at the interface of the proton exchange membrane and the catalyst layer by 1.49 % and 0.74 %, respectively, causing hindrance to the transport of internal liquid water. This study provides valuable insights into the interplay between the properties of the microporous layer material properties and heat and mass transfer characteristics in proton exchange membrane fuel cell.

Pressure transient characteristics of non-uniform conductivity fractured wells in viscoelasticity polymer flooding based on oil–water two-phase flow

Polymer flooding in fractured wells has been extensively applied in oilfields to enhance oil recovery. In contrast to water, polymer solution exhibits non-Newtonian and nonlinear behavior such as effects of shear thinning and shear thickening, polymer convection, diffusion, adsorption retention, inaccessible pore volume and reduced effective permeability. Meanwhile, the flux density and fracture conductivity along the hydraulic fracture are generally non-uniform due to the effects of pressure distribution, formation damage, and proppant breakage. In this paper, we present an oil–water two-phase flow model that captures these complex non-Newtonian and nonlinear behavior, and non-uniform fracture characteristics in fractured polymer flooding. The hydraulic fracture is firstly divided into two parts: high-conductivity fracture near the wellbore and low-conductivity fracture in the far-wellbore section. A hybrid grid system, including perpendicular bisection (PEBI) and Cartesian grid, is applied to discrete the partial differential flow equations, and the local grid refinement method is applied in the near-wellbore region to accurately calculate the pressure distribution and shear rate of polymer solution. The combination of polymer behavior characterizations and numerical flow simulations are applied, resulting in the calculation for the distribution of water saturation, polymer concentration and reservoir pressure. Compared with the polymer flooding well with uniform fracture conductivity, this non-uniform fracture conductivity model exhibits the larger pressure difference, and the shorter bilinear flow period due to the decrease of fracture flow ability in the far-wellbore section. The field case of the fall-off test demonstrates that the proposed method characterizes fracture characteristics more accurately, and yields fracture half-lengths that better match engineering reality, enabling a quantitative segmented characterization of the near-wellbore section with high fracture conductivity and the far-wellbore section with low fracture conductivity. The novelty of this paper is the analysis of pressure performances caused by the fracture dynamics and polymer rheology, as well as an analysis method that derives formation and fracture parameters based on the pressure and its derivative curves.

Analysis of seepage and temperature fields and their influence on collapse pressure while drilling in shale oil reservoirs

Shale wellbore instability poses a considerable challenge in terms of drilling efficiency. However, previous studies typically assumed single-phase flow in the seepage field, neglecting the influences of water saturation and temperature on rock mechanical properties. Furthermore, there has been a lack of quantitative analysis on the degree of correlation between various factors and collapse pressure. To address these gaps, this research introduces an oil–water two-phase seepage model to describe the water saturation distribution surrounding the wellbore,and also constructed a wellbore temperature field model that accounts for mechanical and hydraulic heat sources and validated its accuracy. Furthermore, this paper examines the effects of temperature and seepage on shale mechanical parameters. By incorporating a rock failure criterion that accounts for water saturation, a shale collapse model in thermal-seepage coupling is established, which has also been validated. Finally, this paper utilises the grey relational analysis to quantitatively assess the correlation between different variables and collapse pressure. The results indicate that the temperature field and collapse models are consistent with field data. As drilling time increases, water saturation and invasion distance grow, while the seepage radius hardly increases anymore. When porosity exceeds 0.05, its influence on water saturation weakens. Under unbalanced conditions, capillary force drives drilling fluid into the formation. The maximum wellbore temperature is found near the drill bit and exceeds the formation temperature. The bottom-hole temperature difference increases with the increase in well depth and drilling time, sometimes exceeding 20 °C. Among drilling engineering parameters, pump rate has greater influence on bottomhole temperature than WOB, RPM and ROP. Regarding drilling fluid property parameters, density, flow index and consistency coefficient considerably influence bottom-hole temperature. The influence of seepage on collapse pressure is greater than that of the temperature field. Grey relational analysis reveals that pump rate and water saturation have the highest correlation with collapse pressure. As drilling time increases, the correlation degree of pressure difference, horizontal section length and weight on bit gradually increase, while that of the mud behaviour index, consistency coefficient, rock thermal conductivity and mud yield stress slightly decreases.

Life cycle integrated flow simulation for hydraulic fracturing horizontal wells in shale gas reservoirs

The distribution of matrix pressure and water saturation during the fracturing and shut-in period significantly impacts shale gas production. However, traditional numerical simulations primarily focus on the production period, often overlooking the impact of fracturing and shut-in on the seepage field and production rates. This study uses the dual-porosity/dual-permeability-embedded discrete fracture model (DPDK-EDFM) to characterize matrix mixed wettability and the natural/hydraulic fracture geometry. A multiscale numerical simulation model is constructed to encompass the whole life cycle of shale fracturing, shut-in, and production. The model provides a comprehensive understanding for considering the changes in rock properties and the diverse migration mechanisms. Subsequently, the life cycle model is used for sensitivity analysis on capillary pressure, shut-in time, and fracturing fluid volume. The findings demonstrate that (1) capillary pressure strongly impacts flowback rate. As surface tension increases from 0 to 72 mN/m, the flowback rate decreases from 113.00% to 68.25%. (2) The shut-in time strongly affects the uniformity of pressure distribution. (3) The fracturing fluid volume is directly proportional to the rise in formation pressure. This innovative model provides a robust framework for simulating and analyzing the seepage field behavior of shale gas reservoirs throughout the life cycle. Furthermore, through a comprehensive investigation of the main controlling factors, this study provides valuable insights into the efficient development of shale gas reservoirs, carrying both theoretical and practical significance.

Liquid Water Characteristics in the Compressed Gradient Porosity Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells Using the Lattice Boltzmann Method

The mitigation of water flooding in the gas diffusion layer (GDL) at relatively high current densities is indispensable for enhancing the performance of proton exchange membrane fuel cells (PEMFCs). In this paper, a 2D multicomponent LBM model is developed to investigate the effects of porosity distribution and compression on the liquid water dynamic behaviors and distribution. The results suggest that adopting the gradient GDL structure with increasing porosity along the thickness direction significantly reduces the breakthrough time and steady–state total water saturation inside the GDL. Moreover, the positive gradient structure reaches the highest breakthrough time and water saturation at 10% compression ratio (CR) when the GDL is compressed, and the corresponding values decrease with further increase of the CR. Considering the breakthrough time, total water saturation and water distribution at the entrance of the GDL at the same time, the gradient structure with continuously increasing porosity can perform better water management capacity at 30% CR. This paper is useful for understanding the two–phase process in a gradient GDL structure and provides guidance for future design and manufacturing.

Water contact mapping and saturation estimation using simultaneous inversion of time-lapse seismic data constrained by fluid substitution and Leverett J-function analysis

The integration of a Leverett J-function analysis with the Gassmann and mass-balance equations allows the time-lapse change of seismic reflectivity to be expressed explicitly in terms of the change of the free water-contact (WC) level, reservoir porosity, and initial water saturation. Given the initial 3D distribution of water saturation and porosity and a well-log derived height-saturation-porosity function as a hard inversion constraint, synthetic modeling suggests that time-lapse seismic data can potentially be directly inverted for the change in free-water level, and time-lapse changes in the spatial variation of water saturation can thus be predicted. This integrated inversion approach is applied to a real time-lapse seismic difference volume from the Maui-B field in the Taranaki Basin, New Zealand, where the change of WC level from a baseline model is the only free parameter to be inverted and is obtained by searching for the global error minimum between tmodeled and real time-lapse seismic differences as the modeled WC level is varied. The method correctly predicts the gas depletion and a measurable rise of the water contact on the southern flank of the field.

Modeling bimodal capillary bundle two-phase flow in the shale matrix for predicting water saturation distribution

In gas field development, the distribution of water saturation is one of the most effective estimated two-phase flow law methods for the shale matrix. Water saturation has been widely studied; however, few studies exist to show that water saturation distribution is related to pore diameter distribution of shale matrix. Furthermore, based on experimental observations, imbibition and gas-driven water flow nuclear magnetic resonance experiments also show the phenomenon. Therefore, the objective of this work is to build a bimodal capillary bundle two-phase flow model to investigate the relation of water saturation with pore diameter distribution of shale matrix. Firstly, this work combines the bimodal pore size distribution with the truncated Gaussian distribution theory to present the shale matrix pore. Moreover, we develope a shale core imbibition model and a gas-driven water flow model to predict the distribution of the water saturation distribution during the two-phase flow, by using the gas-water two-phase seepage theory. Shale imbibition and gas-driven water flow experiments are carried out on shale samples from the underground Longmaxi Formation. The relative error of distribution curve of water saturation predicted by model and experiments has been calculated. At the initial stage of imbibition the shale matrix core is not completely dried model values do not match the measured values, but, the relative error is stable at 1–2% at the late stage of imbibition. The average relative error is 2.13% in gas-driven water flow process. As a result, the shale imbibition model and the displacement model can accurately characterize the two-phase (gas-water) flow process, providing a theoretical support to study the two-phase flow in the shale matrix.

An improved method for fitting relative permeability curve using nuclear magnetic resonance imaging

Nuclear magnetic resonance (NMR) technology can be used for online monitoring of the fluid flow in cores. Especially, NMR imaging can visualize the injected fluid distribution and the residual oil location, as well as show the displacement effects of different injected fluid. This provides a new perspective for understanding displacement mechanisms. This paper proposes an improved method for fitting relative permeability curve based on NMR imaging. We established formulas to quantitatively calculate the water saturation profiles at different displacement times. Using the water saturation profiles, the water front position, residual oil saturation, and capillary end effect were analyzed to visualize the fluid flow inside the core. Base on the water saturation distribution, we analyzed the waterflooding characteristics more accurately. Using the oil-water relative permeability equation proposed by Honaropur, the relationship between the water cut and water saturation at the outlet section of the core was fitted to obtain the oil-water relative permeability. Compared with the commonly used Johnson-Bossler-Naumann method for calculating relative permeability, the method proposed in this paper has fewer fitting parameters, is highly precise, and is easy to operate. Additionally, it also broadens the application of NMR technology in the field of oil exploration and development.

Application of particle filter to assess uncertainty for reservoir state and parameter estimation

A bimodal water saturation distribution can be found around the waterfront during water flooding in an oil reservoir, leading to subsequent non-Gaussian distribution of water saturation. Therefore, application of the Gaussian based methods may result in poor history matching and corresponding parameter estimation. For the reliability of the oil reservoir model, it is very important to ensure the realistic update of water saturation during history matching at any phase of production from oil reservoirs. This work employs particle filter (PF) for water flooding reservoir data assimilation, considering the effect of “non-Gaussianity” in water saturation distribution around the shock front during updating model state vector. This paper investigates the performance of the PF in updating state variables, particularly water saturation and efficiency to approximation of posterior probability distribution. In addition, particle perturbation is implemented by applying “ensemble covariance” in resampling stage in order to diverse particles and thereby avoid particle collapse. The methodology is presented stepwise considering a one-dimensional (1D) case first and then two-dimensional (2D) five-spot water flood problem. In both cases, state variables are updated with the application of PF and ensemble kalman filter (EnKF). With respect to history and water saturation matching, and approximation of posterior probability distribution, the performance of EnKF is comparable with PF where the non-Gaussianity is weak. However, in the presence of strong non-Gaussianity, EnKF shows four times higher error compared to PF. Furthermore, between “ensemble covariance” and typical “randomization” cases, “ensemble covariance” case shows a higher number of particles participating in resampling stage in particle perturbation. Therefore, “ensemble covariance” case leads to 5.3% and 7.5% more accurate results in estimating reservoir permeability and porosity, respectively.

NUMERICAL INVESTIGATION ON THE IMPACT OF INITIAL WATER SATURATION DISTRIBUTION ON HOT WATER FLOODING PERFORMANCE UNDER NON-ISOTHERMAL CONDITIONS

The heterogeneity in the spatial distribution of initial water saturation influences the performance of hot water flooding. The prospect of a reduction in oil recovery arises from the development of viscous instability. In the present study, a numerical simulation model has been developed by coupling heat transport, and multiphase flow in porous media integrated with the non-isothermal flow, and the numerical model has been verified with the existing analytical solution by Buckley and Leverett. The formation of a wavy temperature profile at the condensation front was found with a decreased depth of temperature penetration. The average rise of temperature is drastically affected by the spatial distribution of initial water saturation. The formation of viscous fingering was highly dominating in the reservoir, with initial water saturation randomly distributed and causing the front to move in an irregular pattern from the initial stage of the flooding. The heterogeneous reservoir with initial water distribution showed the earlier formation of viscous fingering than the homogeneous reservoir. The heterogeneity in the spatial distribution of initial water saturation had caused viscous instability, lower viscosity reduction, lower displacement sweeps efficiency, and higher residual oil saturation. The present study is limited to spatial distribution in initial water saturation to a certain degree of heterogeneity. The heterogeneity in the spatial distribution of initial water saturation highly impacted the production performance of hot water flooding. The present study provides an idea for the implementation and future development of hot water flooding in a randomly initial water saturation distributed environment.