An experimental investigation of long-distance gas–water two-phase flow behavior in unconsolidated sandstone gas reservoirs

The flow dynamics of low-yield horizontal wells demonstrate considerable complexity and unpredictability, chiefly attributable to the structural attributes of the wellbore and the interplay of gas–water two-phase flow. In horizontal wellbores, precisely predicting flow patterns using conventional approaches is often problematic. Consequently, accurate monitoring and analysis of water holdup in gas–water two-phase flows are essential. This study performs a gas–water two-phase flow simulation experiment under diverse total flow and water cut conditions, utilizing air and tap water to represent downhole gas and formation water, respectively. The experiment relies on the measurement principles of an array fiber holdup meter (GAT) and the response characteristics of the sensors. In the experiment, GAT was utilized for real-time water holdup measurement, and the acquired sensor data were analyzed using three interpolation algorithms: simple linear interpolation, inverse distance weighted interpolation, and Gaussian radial basis function interpolation. The results were subsequently post-processed and visualized with 2020 version MATLAB software, generating two-dimensional representations of water holdup in the wellbore. The study findings demonstrate that, at total flow of 300 m3/d and 500 m3/d, the simple linear interpolation approach yields superior accuracy in water holdup calculations, with imaging outcomes closely aligning with the actual gas–water flow patterns and the authentic gas–water distribution. As total flow and water cut increase, the gas–water two-phase flow progressively shifts from stratified smooth flow to stratified wavy flow. In this paper, the Gaussian radial basis function and inverse distance weighted interpolation algorithms exhibit superior accuracy in water holdup calculations, effectively representing the fluctuating features of the gas–water interface and yielding imaging outcomes that align more closely with experimentally observed gas–water flow patterns.

Fully mass-conservative IMPES schemes for incompressible two-phase flow in porous media

Understanding gas–water two-phase flow mechanisms in deep tight gas reservoirs is critical for improving production performance and mitigating water invasion. However, the effects of pore-throat-fracture multiscale structures on gas–water flow remain inadequately understood, particularly under high-temperature and high-pressure conditions (HT/HP). In this study, we developed visualizable multiscale throat-pore and throat-pore-fracture physical nanofluidic chip models (feature sizes 500 nm–100 μm) parameterized with Keshen block geological data in the Tarim Basin. We then established an HT/HP nanofluidic platform (rated to 240 °C, 120 MPa; operated at 100 °C, 100 MPa) and, using optical microscopy, directly visualized spontaneous water imbibition and gas–water displacement in the throat-pore and throat-pore-fracture nanofluidic chips and quantified fluid saturation, front velocity, and threshold pressure gradients. The results revealed that the spontaneous imbibition process follows a three-stage evolution controlled by capillarity, gas compression, and pore-scale heterogeneity. Nanoscale throats and microscale pores exhibit good connectivity, facilitating rapid imbibition without significant scale-induced resistance. In contrast, 100 μm fractures create preferential flow paths, leading to enhanced micro-scale water locking and faster gas–water equilibrium. The matrix gas displacement threshold gradient remains below 0.3 MPa/cm, with the cross-scale Jamin effect—rather than capillarity—dominating displacement resistance. At higher pressure gradients (~1 MPa/cm), water is efficiently expelled to low saturations via nanoscale throat networks. This work provides an experimental platform for visualizing gas–water flow in multiscale porous media under ultra-high temperature and pressure conditions and offers mechanistic insights to guide gas injection strategies and water management in deep tight gas reservoirs.

Relative permeability of two-phase flow in three-dimensional porous media using the lattice Boltzmann method

Two-phase incompressible flow in porous media plays an important role in various fields including subsurface flow and oil reservoir engineering. Due to the interaction between two phases flowing through the pores, the fluid–fluid friction force may have a significant effect on each phase velocity. In this paper, we propose an energy stable (thermodynamically consistent) Maxwell–Stefan–Darcy model for two-phase flow in porous media, which accounts for the fluid–fluid friction. Different from the classical models of two-phase flow in porous media, the proposed model uses the free energy to characterize the capillarity effect. This allows us to employ the Maxwell–Stefan model to describe the relationships between the driving forces and the friction forces. The driving forces include the pressure gradient and chemical potential gradients, while both fluid–solid and fluid–fluid friction forces are taken into consideration. Thermodynamical consistency is the other interesting merit of the proposed model; that is, it satisfies an energy dissipation law and also obeys the famous Onsager's reciprocal principle. A linear semi-implicit numerical method is also developed to simulate the model. Numerical simulation results are provided to show that the fluid–fluid friction force can improve the oil recovery substantially during the oil displacement process.

Natural oil and gas deposits in most fields include some fluid contacts, such as oil–water, gas–water, or gas–oil. Monitoring the position of the gas–water contact in underground gas storage (UGS) facilities is crucial for monitoring the safety of the subsurface environment. As UGS facilities are geological features of long-term operation, the condition of these features must be regularly monitored for possible gas leaks due to various reasons, whether geological or technical. Periodic surveys of production wells using geophysical methods make it possible to timely detect the reasons for abnormal technical conditions and higher-than-normal water cuts of reservoirs, and to assess shifts in gas–water contact. The suite of production logging methods for surveying and monitoring underground gas storage facilities includes nuclear logging with the use of steady radiation sources (i.e., gamma ray logging and neutron logging). Analysis and interpretation of these methods make it possible to track the shift over time of the gas–water contact in gas-saturated sandstones with an interparticle porosity of >15%. Data from nuclear logging, temperature logs, and composition-based and flow-based surveying are processed and interpreted with the use of known methods and diagnostic indicators to achieve the following goals: to determine the intervals of inter-reservoir and behind-the-casing fluid movement on the base of the well log, to assess the technical condition of the wellbore, to monitor the position of the gas–water contact in the reservoir, to assess the gas saturation of the reservoir, and to monitor the thickness and integrity of the clay caprocks of UGS facilities [1]. This paper discusses the results of automated processing and interpretation of well data recorded during the survey of an UGS facility to determine the current position of the gas–water contact in the reservoir and the gas–water interface in the well. Quantitative interpretation of the neutron logging data with the use of steady radiation sources was performed, and the current gas saturation factor was estimated. Keywords: gas–water contact (GWC); gas saturation; underground gas storage; processing algorithm; gas–water interface (GWI).

Modeling multiphase flow in porous structures remains a challenge due to the complexity of handling multiple interfaces. This paper presents a one-domain pore-resolved simulation approach for immiscible two-phase flows in porous media, using a monolithic fluid–solid coupling framework to implicitly consider the existence of solid objects, with the fluid–fluid interfaces captured through solving an algebraic volume of fluid equation. Fluid interfacial tension is considered by integrating a continuum surface force, and the wall wettability condition is imposed by modifying the contact angle of the fluid interface at the embedded solid surface. The resulting equations are simple and stable, as there are no empirical models or parameters involved for the interface representation. This approach has been validated through performing a series of test-case simulations, including capillary-dominated flow, capillary rise with gravity, Taylor film formation, and finally two-phase flow in a heterogeneous porous structure. The numerical approach is demonstrated to be well suited for investigating pore-scale two-phase flows in realistic porous media.

Log data shows existence of residual trapped gas below the Free-Water-Level (FWL) in a high-quality (multi-Darcy) Jurassic reservoir. During reservoir depletion, it is possible for palaeo residual gas phase to remobilize. A box model was utilized, with a relatively short simulation run-time, to understand potential impacts of palaeo gas on incremental gas and condensate recovery, additional pressure support and effect on water production. Note that limited literature/field experience is currently available on this topic. This paper outlines a workflow to build a fit-for-purpose box model that represents the dynamic performance of gas, palaeo gas and aquifer zones, that contains similar volumes to the existing full field model. The box model also adopts similar fluid composition, equation of state and capillary pressure/relative permeability in the gas zone. The palaeo trapped gas and aquifer are modelled below the current FWL recognising the key uncertainties such as palaeo FWL depth, residual gas saturation, and gas remobilization saturation threshold. The box model initialization is explained to include relative permeability hysteresis, critical gas saturation and the equilibrium test parameters. The box model is a simplified representation of the full-field reservoir grid in which in-place volumes are matched. A vertical producer drains the reservoir. Homogeneous properties of net-to-gross, porosity and permeability are set using average values from the full field model, representing tank-like behaviour. The box model was first initialised and simulated without palaeo gas, to calibrate its volume to the full-field model. Three saturation regions are assumed; a live gas column, a trapped palaeo gas column and a 100% water column honouring the current and interpreted palaeo FWLs. Initialisation with palaeo gas uses a primary imbibition relative permeability model for all regions and modifies the critical residual gas saturation to match the gas remobilization saturation threshold to create secondary drainage, applicable for the trapped gas region. A residual gas saturation (Sgr) and gas remobilization saturation threshold (Sgrc) were based on analogues and literature reviews. The result shows ~50% total incremental resources and ~10 years longer production (without economic cut-off), and improved pressure support, but with additional water production. The box model was used to explore sensitivity to three critical uncertainty parameters: depth of the palaeo FWL, Sgr and Sgrc. Sensitivity shows that recovery increases with deeper palaeo FWL, higher Sgr and lower Sgrc. Trapped gas remobilization is currently treated as upside potential, rather than as inclusion to the reserves range. However, modelling trapped palaeo gas is important to give insight to how gas remobilization could increase both hydrocarbon and water production as well as pressure support, which could potentially affect fluid handling capacity, commercial negotiations, and development project economics. The ability to produce quick-look models and visualize the impact can influence the development project, especially those with marginal return.

Gas–water two-phase flow in horizontal and inclined wells is significantly influenced by gravitational forces and spatial asymmetry around the wellbore, resulting in complex and variable flow patterns. Accurate measurement of water holdup is essential for analyzing phase distribution and understanding multiphase flow behavior. Water holdup imaging provides a valuable means for visualizing the spatial distribution and proportion of gas and water phases within the wellbore. In this study, air and tap water were used to simulate downhole gas and formation water, respectively. An array capacitance arraay tool (CAT) was employed to measure water holdup under varying total flow rates and water cuts in a horizontal well experimental setup. A total of 228 datasets were collected, and the measurements were processed in MATLAB (2020 version) using three interpolation algorithms: simple linear interpolation, inverse distance interpolation, and Lagrangian nonlinear interpolation. Water holdup across the wellbore cross-section was also calculated using arithmetic averaging and integration methods. The results obtained from the three imaging algorithms were compared with these reference values to evaluate accuracy and visualize imaging performance. The CAT demonstrated reliable measurement capabilities under low- to medium-flow conditions, accurately capturing fluid distribution. For stratified flow regimes, the linear interpolation algorithm provided the clearest depiction of the gas–water interface. Under low- to medium-flow rates with high water content, both inverse distance and Lagrangian methods produced more refined images of phase distribution. In dispersed flow conditions, the Lagrangian nonlinear interpolation algorithm delivered the highest accuracy, effectively capturing subtle variations within the complex flow field.

We present a theoretical framework for immiscible incompressible two-phase flow in homogeneous porous media that connects the distribution of local fluid velocities to the average seepage velocities. By dividing the pore area along a cross-section transversal to the average flow direction up into differential areas associated with the local flow velocities, we construct a distribution function that allows us not only to re-establish existing relationships between the seepage velocities of the immiscible fluids but also to find new relations between their higher moments. We support and demonstrate the formalism through numerical simulations using a dynamic pore-network model for immiscible two-phase flow with two- and three-dimensional pore networks. Our numerical results are in agreement with the theoretical considerations.

Immiscible two-phase flow in porous media, which results from the downward injection of a heavier fluid or upward injection of a lighter fluid, is characterized by two shocks, one at each end of a rarefaction wave. The specific details of the saturation profile, such as the shock speeds and the shock saturations, are determined by the fractional flow function for given values of the mobility ratio and the gravity number. We employ a normal mode, matched asymptotic expansion analysis to obtain analytical expressions governing the stability behavior of such flows. Instability occurs at both ends of the one-dimensional base saturation profile with unique characteristics such that the maximum growth rate decreases both when the mobility ratio is increased at the front end and decreased at the back end. This unusual behavior is explained in terms of vorticity eigenfunctions related to nonmonotonic mobility profiles. Analysis of stability behavior as a function of fractional flow profile shows that although the fundamental mechanisms are qualitatively similar, they are associated with different parameter values in view of particular mobility profiles. Growth rates and wavenumbers predicted by the linear stability analysis are observed at the onset of the nonlinear displacement process, which is followed by the fully developed nonlinear flow with large-scale unstable structures.

Purpose – This paper aims to present a computationally efficient finite element model for the simulation of isothermal immiscible two-phase flow in a rigid porous media with a particular application to CO2 sequestration in underground formations. Focus is placed on developing a numerical procedure, which is effectively mesh-independent and suitable to problems at regional scales. Design/methodology/approach – The averaging theory is utilized to describe the governing equations of the involved unsaturated multiphase flow. The level-set (LS) method and the extended finite element method (XFEM) are utilized to simulate flow of the CO2 plume. The LS is employed to trace the plume front. A streamline upwind Petrov-Galerkin method is adopted to stabilize possible occurrence of spurious oscillations due to advection. The XFEM is utilized to model the high gradient in the saturation field front, where the LS function is used for enhancing the weighting and the shape functions. Findings – The capability of the proposed model and its features are evaluated by numerical examples, demonstrating its accuracy, stability and convergence, as well as its advantages over standard and upwind techniques. The study showed that a good combination between a mathematical model and a numerical model enables the simulation of complicated processes occurring in complicated and large geometry using minimal computational efforts. Originality/value – A new computational model for two-phase flow in porous media is introduced with basic requirements for accuracy, stability, and convergence, which are met using relatively coarse meshes.

We develop a mathematical model for hysteretic two-phase flow (of oil and water) in waterwet porous media. To account for relative permeability hysteresis, an irreversible trapping-coalescence process is described. According to this process, oil ganglia are created (during imbibition) and released (during drainage) at different rates, leading to history-dependent saturations of trapped and connected oil. As a result, the relative permeability to oil, modelled as a unique function of the connected oil saturation, is subject to saturation history. A saturation history is reflected by history parameters, that is by both the saturation state (of connected and trapped oil) at the most recent flow reversal and the most recent water saturation at which the flow was a primary drainage. Disregarding capillary diffusion, the flow is described by a hyperbolic equation with the connected oil saturation as unknown. This equation contains functional relationships which depend on the flow mode (drainage or imbibition) and the history parameters. The solution consists of continuous waves (expansion waves and constant states), shock waves (possibly connecting different modes) and stationary discontinuities (connecting different saturation histories). The entropy condition for travelling waves is generalized to include admissible shock waves which coincide with flow reversals. It turns out that saturation history generally has a strong influence on both the type and the speed of the waves from which the solution is constructed.

Two efficient and scalable numerical solution methods will be compared using exact Jacobians to solve the fully coupled Newton systems arising during fully implicit discretization of the equations for two-phase flow in porous media. These methods use algebraic multigrid (AMG) to solve the linear systems in every Newton step. The algebraic multigrid methods rely on (i) a Schur Complement Reduction (SCR-AMG) and (ii) a Constrained Pressure Residual method (CPR-AMG) to decouple elliptic and hyperbolic contributions. Both methods employ automatic differentiation (AD) to calculate exact Jacobians and are compared with finite difference (FD) approximations of the Jacobian. The superiority of AD is shown by several numerical test cases from the field of CO2 geo-sequestration comprising two- and three-dimensional examples. A weak scaling test on JUQUEEN, a BlueGene/Q supercomputer, demonstrates the efficiency and scalability of both methods. To achieve maximum comparability and reproducibility, the Portable Extensible Toolkit for Scientific Computation (PETSc) is used as framework for the comparison of all solvers.

Models of two‐phase flow and displacement in porous media developed so far typically involve one displacing (invader) and one displaced (defender) fluid. However, in many important applications of these phenomena at field scales, such as two‐phase flow in fractured porous media, as well as in laboratory studies, require at least two invaders which also act as the defenders. The results of extensive Monte Carlo simulations of a novel model of such phenomena are reported. The porous medium is represented as a network of pore throats and pore bodies to which effective sizes are assigned that are selected from a given distribution. Both 2‐D and 3‐D networks are used. The simulation results indicate that the structure of the fluids' clusters is volatile, that is, it changes with the time t and length scale. Moreover, ns (s, t), the number of fluid clusters of size s, 〈s(t)〉, the mean cluster size, and S(t), the saturation of the fluids all vary with t in a manner that resembles an oscillatory behavior. This behavior is caused by the dynamic breakup and recoalescence of the fluids' clusters, which is a result of simultaneous invasion of the two fluids. The flow effect of thin wetting fluid films on the dynamics of the displacement is strong over a broad range of the capillary number. Novel dynamical scaling laws for the cluster‐size distribution are obtained. Some results agree qualitatively with the experimental observations, while others provide rational explanations for some unexplained data.