High Permeability Contrast Research Articles

Physics-informed shape optimization using coordinate projection

The rapid growth of artificial intelligence is revolutionizing classical engineering society, offering novel approaches to material and structural design and analysis. Among various scientific machine learning techniques, physics-informed neural network (PINN) has been one of the most researched subjects, for its ability to incorporate physics prior knowledge into model training. However, the intrinsic continuity requirement of PINN demands the adoption of domain decomposition when multiple materials with distinct properties exist. This greatly complicates the gradient computation of design features, restricting the application of PINN to structural shape optimization. To address this, we present a novel framework that employs neural network coordinate projection for shape optimization within PINN. This technique allows for direct mapping from a standard shape to its optimal counterpart, optimizing the design objective without the need for traditional transition functions or the definition of intermediate material properties. Our method demonstrates a high degree of adaptability, allowing the incorporation of diverse constraints and objectives directly as training penalties. The proposed approach is tested on magnetostatic problems for iron core shape optimization, a scenario typically plagued by the high permeability contrast between materials. Validation with finite-element analysis confirms the accuracy and efficiency of our approach. The results highlight the framework’s capability as a viable tool for shape optimization in complex material design tasks.

Synergistic mechanism of enhanced heavy oil recovery by compound flooding using 3D visualization model

Most of oilfields have entered the development stage of high water-cut and low recovery factors, and stabilizing oil production and controlling water production are the key to enhancing subsequent oil recovery. Adopting the 1/4 five-point injection-production well pattern, the chemical flooding experiments were conducted using a three-dimensional (3D) visualization sand-pack model with liquid drain orifices. A real-time image acquisition and dynamic observation device for detecting droplet textures as fluid flowing was developed with experimental system. In heterogeneous reservoirs with a high permeability contrast, the effects of oil-displacement agents on production dynamics, sweep morphology, and emulsifying characteristics of remaining oil at different locations were investigated to reveal the synergistic mechanism of compound flooding for enhanced oil recovery. The results showed that, in the main streamline region, the mean droplet diameter decreased, the distribution density increased first and then decreased, and the maldistribution decreased first and then increased with an increase in injection volume of the compound system. In the vertical region with the main streamline, the mean diameter and maldistribution reduced, and the distribution density increased owing to the synergistic mechanism. The viscosity reducer can increase sweep efficiency by 8.34% and recovery factor by 5.95% due to the viscous crossflow in the high permeability channel. The compound system can increase sweep efficiency by 15.92% and recovery factor by 12.67% due to the synergistic effect of emulsifying-tapping, emulsion plugging conversion, and profile control. Therefore, chemical compound flooding has great potential of enhancing heavy oil recovery in heterogeneous reservoirs due to the synergistic effect of the compound system.

Thermal Treatment of Trichloroethene by Electrical Resistance Heating: Visualization of Gas Production in Coarse Layers

The effective implementation of in situ thermal treatment (ISTT) technologies requires understanding of gas production and migration in heterogenous media. However, investigations of the effects of high permeability contrast on gas formation, accumulation, and migration, as well as its potential effect on the redistribution of dense non-aqueous phase liquid (DNAPL), are relatively rare. In this study, electrical resistance heating (ERH) experiments were conducted in a thin sand-packed cell to simulate common yet not well-studied scenarios encountered during ISTT applications, such as coarse lenses surrounded by finer material. Two packing configurations were employed: 2 mm glass beads surrounded by 20/30 silica sand and 20/30 silica sand overlaying 40/50 silica sand. Each experiment contained an emplaced pool of trichloroethene (TCE) within the coarse material. If permeable material or pathways were present between the coarse lens and the upper cell boundary, the gas migrated along these pathways, and local DNAPL redistribution was limited to near the top of the pool before it vaporized. In contrast, if the coarse material was surrounded by finer material and contained a sufficient volume of DNAPL, the gas accumulated inside the coarse lens leading to DNAPL displacement from the lens. For five selected DNAPLs, this volume was estimated to be 0.1% to 0.5% of the total pore volume of the coarse material. The conceptual model developed in this study improves our understanding of this common geological scenario, demonstrating the importance of considering both lower- and higher-permeability material and their effects on multiphase flow during co-boiling, as well as the design of gas extraction systems during ISTT applications.

Lithofacies, Deposition, and Clinoforms Characterization Using Detailed Core Data, Nuclear Magnetic Resonance Logs, and Modular Formation Dynamics Tests for Mishrif Formation Intervals in West Qurna/1 Oil Field, Iraq

Summary This study considered the complexity of Mishrif geology and its effect on fluid movement within and across Mishrif reservoir intervals. For this purpose, we analyzed the following items: the multiple interval communication with high permeability contrast, the geological setting of the upper Mishrif (mA) interval, the channel structure in the Lower Mishrif-Part 1 (mB1) interval, the thin layers in the upper part of Lower Mishrif-Part 2 (mB2U) of very high permeability, and the microporous interval of the lower part of Lower Mishrif-Part 2 (mB2L); none of them were well defined before this work. The bottom interval of Mishrif or Rumaila (mC) is predominantly microporous, and the best reservoir is at the top of intermediate quality. Two high-porosity layers are systematically found in the mC unit, which is casually referred to as “rabbit ears.” The mB2L contains grainstones in the far north of the West Qurna/1 oil field (WQ1). In the south of mB2L, some of the toe sets from the clinoforms in a distal depositional setting have developed into rather important vertical pressure baffles and barriers to vertical flow. The mB2U generally consists of grainstones with thin streaks of mudstone high flow layers (HFLs), and the rocks underneath are described generally as grainstone shoals. About 80% of stock tank oil originally in place (STOOIP) in mB2U exists in grainstones. There are no known microporous reservoirs in mB2U. The pressure difference across the boundaries between mB1 and mA can be positive or negative. At the base, mB1 channels are always in pressure communication with the mB2U below. The best flow from the mA comes from HFLs, which are found around faults. Reservoir quality within mA is generally best in the first section of the upper Mishrif (mAa), and the majority of STOOIP in mA exists in microporous rocks, while some 30% of STOOIP is contained in grainstones.

An efficient discontinuous Galerkin - mixed finite element model for variable density flow in fractured porous media

Modeling variable density flow (VDF) in fractured porous media is computationally challenging. The challenges are mainly related to: (i) the high permeability contrast between the matrix and the fractures and, (ii) the nonlinearity induced by density variations. Due to their local mass conservation property, cell-centered methods, such as finite volumes (FV), mixed finite elements (MFE) or Discontinuous Galerkin (DG) methods are well suited for modeling mass transfer in highly heterogeneous domains. When applied for fractured media, these methods require small grid cells next to fractures because of the cross-flow equilibrium assumption (i.e. the pressure and concentration in the fracture and in the adjacent matrix grid-cells are assumed the same). To avoid this constraint, an efficient model is developed in this work using advanced cell-centered numerical methods for VDF in fractured porous media with cross-flow equilibrium assumed only across the fractures. The new model uses the hybrid MFE method for the flow discretization in the matrix and in the fracture continua. Mass transport in the matrix is modeled using a monotonic upwind MFE scheme. Advection-dominated transport in fractures is discretized with the DG method, which is well adapted for hyperbolic equations. The new model ensures continuity of pressure, concentration, fluid mass flux, advective and dispersive contaminant fluxes at matrix-fracture interfaces as well as at the intersection of several fractures. The time discretization is performed using high-order adaptive time integration techniques via the method of lines (MOL). The developed model is first validated by comparison against a 2D-2D model for a test problem dealing with linear flow and transport in a 2D domain involving a “+”-shaped barrier/fracture network. Then, the MFE-DG model is used for the simulation of the Henry saltwater intrusion problem and the results are validated by comparison against the semi-analytical solution in the case of unfractured and fractured aquifers. Finally, the simulation of a transport problem with variable viscosity in a fractured heterogeneous domain points out the superiority of the new model in terms of accuracy and efficiency when compared to a standard finite element model.

Experimental investigation of flow diversion and dynamic retention during polymer flooding in high salinity fractured carbonates using CT imaging

The successful record of polymer flooding in improving oil production from sandstone reservoirs has encouraged the expansion of its application in carbonate reservoirs. However, the existence of natural fractures, high permeability contrast, and harsh conditions of carbonate reservoirs provide significant challenges for achieving an optimized performance of polymer flooding. It is crucial to establish an appropriate polymer that can offer an optimum flow behavior for in-depth mobility control under reservoir conditions. This study presents in-situ saturation monitoring to evaluate the mobility control effect and identify the flow diversion during polymer injection in high salinity fractured and unfractured carbonate rocks. A synthetic polymer, acrylamido tertio-butyl sulfonate (ATBS) was used and prepared in 200,000 ppm brine salinity. The flow behavior of polymer solution was investigated in bulk rheology tests followed by single-phase core flooding experiments. The flooding apparatus was coupled with a CT scanner to produce 3D images for determining the fluid saturation distribution and inaccessible pore volume (IPV) in real time. Accordingly, flow diversion across fracture-matrix system during polymer injection and the dynamic retention after brine post-flush were identified. The flow experiments showed a shear thickening behavior for the injected polymer solution in the fractured core and no degradation was noticed under in-situ conditions. Based on the fluid saturation profiles, the established flow resistance in the fracture region was prominent to induce flow diversion from the fracture into the matrix. Compared to the case in unfractured rock, the IPV in the fractured rock was approximately 2.5 times higher which was at 53% after 1 PV injection. An additional 23% of IPV was subsequently penetrated upon a continuous polymer injection for 5 PV. In post-flush stage, the fractured core retained about 87% of the injected polymer solution at 1 PV which was then minimized to 7% after 10 PV injection. The entrapped polymer in the fractured core was potentially induced by hydrodynamic retention. This work ascertained the potential of polymer flooding to effectively sweep the fractured carbonates at high salinity environment under certain circumstances for a better conformance.

Heterogeneity of pore-throat structures and petrophysical properties of tight sandstone and its influence on seepage: A case study of sandstone in the Yanchang Formation, Ordos Basin, China

Tight sandstone reservoirs are characterized by poor petrophysical properties, strong pore-throat structures, and heterogeneous permeability, which prevent oilfield water flooding. We take the tight sandstone reservoir of the Yanchang Formation in Ordos Basin as an example, select samples from the Chang 6 and Chang 8 members in the HX block for constant-rate mercury injection and single-core and combined-core model water-flooding tests, and discuss the effects of heterogeneous pore-throat structures and petrophysical properties on the seepage of the tight sandstone. Constant-rate mercury injection tests found that the permeability of the tight sandstone was controlled by the throats. Compared with the pore structures, the throat structures were more heterogeneous, and the samples with more heterogeneous throats were more permeable. Therefore, in addition to the morphology of the pore-throat structures, the heterogeneity of the throats also was used to evaluate the seepage. When applying the water-flooding tests with the combined-core model, the water absorption capacity of the high-permeability core with a high permeability contrast (7.5) was greater than that of the high-permeability core with a low permeability contrast (3.6). Moreover, by comparing the results from the water-flooding experiment for the same core between a single-core and the combined-core model, the loss of the oil displacement efficiency (70.7%) of the low-permeability core in the combined-core model with a high permeability contrast (7.5) was much higher than that (29.8%) of the low-permeability core in the combined-core model, which had a low permeability contrast (3.6). The water absorption percentage and the recovery of the low-permeability core in the combined-core model with a high permeability contrast were lower, indicating that after water flooding, the remaining oil in the low-permeability reservoir in the area with a strong permeability heterogeneity was enriched. Such enrichment may increase the exploitation potential of tight reservoirs.

Evaluation of viscoelastic surfactant‐based diverting agent during the chemical treatment of sandstone reservoirs

AbstractThe challenges of diversion during the stimulations of carbonate formations have been widely studied for decades. It has been shown that viscoelastic surfactants (VES) are among the effective diverting solutions which can be used during the stimulation of carbonate formations. These chemicals benefit from the reaction products between the acid and the calcite to increase the viscosity of the acid, therefore reducing, temporarily, the permeability of the first invaded rock layer, which holds the highest permeability. This temporary blockage steers the remaining acid to the layers with lower permeability that need treatment. This is usually called self‐diverting acidizing treatment. However, the same approach may not necessarily be applied for sandstone formations that are not calcite rich. In such cases, combining acid stages with batches of diverting agents is still feasible. For this approach, VES is also a suitable, non‐damaging solution that is often overlooked. In this study, the application of VES as a diverting agent was investigated during the chemical treatment operations in sandstone formations. Several dual core‐flooding experiments were performed at high pressure and high temperature (HPHT) conditions using sandstone core samples with high permeability contrast.

Systematic modelling incorporating temperature, pressure, and salinity effects on in-situ microbial selective plugging for enhanced oil recovery in a multi-layered system

The microbial enhanced oil recovery (MEOR) process has been identified as a promising alternative to conventional enhanced oil recovery methods because it is eco-friendly and economically advantageous. Despite its various advantages, the technique is not widely applied because the reservoir conditions such as temperature, pressure, and salinity are extremely harsh for microbial survival. In this study, an accurate microbiological model incorporating the environmental effects has been developed. The efficiency of the MEOR process based on selective plugging by microbial biopolymer generation has been examined in multi-layered systems with high permeability contrast. The MEOR is applied to multi-layered reservoirs of different environmental conditions. When the MEOR is applied to a high temperature reservoir, there is an optimum injection temperature that can greatly improve the oil production. Oil productivity in a high-pressure reservoir is estimated to decrease by 15% when the pressure effect is considered. We simulated different salinity conditions and showed that oil recovery decreased with increasing salinity and only was affected by injected water salinity. The oil recovery obtained by the developed model included all three environmental effects and provided estimates 21% lower than that of a previous model that did not account for the environmental effects.

An Experimental Investigation of In Situ Combustion in High Permeability Contrast Systems

Abstract A significant portion of world oil reserves reside in naturally fractured reservoirs and a considerable amount of these resources includes heavy oil and bitumen. Thermal enhanced oil recovery methods (EOR) are mostly applied in heavy oil reservoirs to improve oil recovery. In situ combustion (ISC) is one of the thermal EOR methods that could be applicable in a variety of reservoirs. Unlike steam, heat is generated in situ due to the injection of air or oxygen enriched air into a reservoir. Energy is provided by multi-step reactions between oxygen and the fuel at particular temperatures underground. This method upgrades the oil in situ while the heaviest fraction of the oil is burned during the process. The application of ISC in fractured reservoirs is challenging since the injected air would flow through the fracture and a small portion of oil in the/near fracture would react with the injected air. Only a few researchers have studied ISC in fractured or high permeability contrast systems experimentally. For in situ combustion to be applied in fractured systems in an efficient way, the underlying mechanism needs to be understood. In this study, the major focus is permeability variation that is the most prominent feature of fractured systems. The effect of orientation and width of the region with higher permeability on the sustainability of front propagation are studied. The contrast in permeability was experimentally simulated with sand of different particle size. These higher permeability regions are analogous to fractures within a naturally fractured rock. Several ISC tests with sand-pack were carried out to obtain a better understanding of the effect of horizontal, vertical, and combined (both vertical and horizontal) orientation of the high permeability region with respect to air flow to investigate the conditions that are required for a self-sustained front propagation and to understand the fundamental behavior. Within the experimental conditions of the study, the test results showed that combustion front propagated faster in the higher permeability region. In addition, horizontal orientation almost had no effect on the sustainability of the front; however, it affected oxygen consumption, temperature, and velocity of the front. On the contrary, the vertical orientation of the higher permeability region had a profound effect on the sustainability of the combustion front. The combustion behavior was poorer for the tests with vertical orientation, yet the produced oil API gravity was higher. Based on the experimental results, a mechanism has been proposed to explain the behavior of combustion front in systems with high permeability contrast.

Acid pre-flushing evaluation before pH-sensitive microgel treatment in carbonate reservoirs: Experimental and numerical approach

pH-sensitive microgel flooding is a deep conformance control technique in which the microgel viscosity depends on formation pH. Lowering the formation pH by an acid pre-flushing treatment guarantees easy injection of these microgels. The applications of these microgels were mainly dedicated to sandstones in the literature. However, this study provides an integrated laboratory and numerical modeling approach to find a proper pre-flushing acid in carbonates. The performance of various acids (strong and weak) is evaluated via batch experiments (static tests). The dynamic of acid pre-flushing (dynamic test) and pH-sensitive microgel injection are investigated by flooding experiments. A compositional reactive flow model (advection-diffusion-reaction), developed in Python, is also used to analyze the behavior of the flooding experiments. To evaluate the flooding performance, a 3-D field-scale reservoir simulation model with high-permeability contrast is then implemented. The batch and dynamic tests show that acetic acid can maintain a low-pH environment across the medium, which provides a favorable condition for pH-sensitive microgel transports. The geochemical model can accurately predict the measured equilibrium pH and calcium concentration of effluents at different injection rates and salinities. After the establishment of a near-equilibrium condition, the remaining unionized acids in the flooding experiments result in deep conformance control of pH-sensitive microgels. The pH-sensitive microgel flooding at the field-scale reveals an excellent performance in permeability modification of high-conductive zones. Plugging the first 30% of a high-permeable channel can guarantee the recovery factor increase of this deep conformance control technique.

Analytical Approximations for Sub Wavelength Sound Absorption by Porous Layers with Labyrinthine Slit Perforations

Analytical approximations for the acoustical properties of a rigid-porous matrix perforated by labyrinthine slits are developed using classical theories for sound propagation in tortuous slits and for sound absorption by double porosity materials. Predictions of enhanced low-frequency absorption result from a combination of pressure diffusion and labyrinth tortuosity if there is a high permeability contrast between the matrix and the labyrinthine slit. Additional insight into the predicted influence of the properties of the porous matrix is gained by considering the matrix porosity to be provided by inclined micro-slits. Extra tortuosity can be introduced by alternating the width of the labyrinthine slit. An alternating-width vertical-wall labyrinth perforation is predicted to lead to low-frequency absorption peaks in a relatively low-flow-resistivity and low-porosity matrix. Example predictions, even when using underestimates of labyrinth tortuosity, demonstrate the potential of labyrinthine slit perforations for achieving narrowband deep sub wavelength absorption peaks from thin hard-backed porous layers.

An Investigation of CO2-Responsive Preformed Particle Gel for Conformance Control of CO2 Flooding in Reservoirs With Fractures or Fracture-Like Channels

Summary Gel treatment is an important technique to solve early CO2 breakthrough and excess–CO2–production problems, caused by the low viscosity and low density of CO2, as well as the heterogeneity of reservoirs with fractures or fracture–like channels. However, there is no reported work on gel that increases its volume after reacting with CO2 (termed CO2–responsive gel) for the conformance control of CO2 flooding. In this paper, the intrinsic properties of a CO2–responsive preformed particle gel (CR–PPG) were evaluated in a water/supercritical–CO2 (scCO2) environment in high–pressure vessels. Continuous scCO2 injection and CR–PPG treatment were conducted in fractured sandstone cores, to probe their plugging performance to scCO2 flow in a high–permeability–contrast system. The volumetric swelling ratio (VSR) of the CR–PPG increased by approximately two times in the presence of scCO2, compared with a sample under similar conditions in the absence of scCO2. The CR–PPG swelling ratio decreased with increasing NaCl concentration. Under the same conditions, the temperature did not have an apparent effect on the swelling ratio after 31 days of swelling. In coreflooding experiments, the placed CR–PPG resisted a considerable pressure up to 617.0 psi before breakthrough. After a shut–in process, CO2–breakthrough pressure was detected at 437.2 psi. It is observed that the shut–in process improved the plugging performance of CR–PPG to CO2 as revealed by the increase in the residual resistance factor. Controlling the shut–in time was found to be effective in augmenting the increase in the residual resistance factor, by increasing the VSR of placed CR–PPG. Resistance of CR–PPG to some real field challenges, including a high pressure gradient and long–term exposure to CO2, was also reported for field–applicability concerns.

A multiscale theoretical approach for the sound absorption of slit-perforated double porosity materials

A multiscale theoretical approach is proposed to design the sound absorption of slit-perforated double porosity materials by employing the double porosity theory. The materials consist of a microporous matrix with periodically perforated narrow slits, in which the micropores of the matrix and the slits are interconnected and together form a multiscale material with double porosity. Considering the different ratios for the characteristic size of the micropores to that of the slits, two contrast cases including low permeability contrast (LPC) case and high permeability contrast (HPC) case are included in the design analysis. Numerical simulations based on COMSOL Multiphysics are conducted to verify the developed theoretical model, with good agreements being achieved. The comparison between the multiscale material and its two constituent elements manifests the superiority of the multiscale material for sound absorption. The analysis on the surface impedance and propagation constant exposes the fact that the multiscale material design improves the acoustic impedance matching between the material and air and leads to an enhancement of sound absorption. Furthermore, the effects of the multiscale parameters on the sound absorption of the double porosity materials are explored in terms of the distribution of the sound pressure and energy dissipation. This work provides a helpful guidance to improve the sound absorption of the microporous materials by employing the multiscale design approach.

Best Practices for Waterflooding Optimization Improve Oil Recovery in Mature Fields

This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper SPE 186431, “Waterflooding Optimization: A Pragmatic and Cost-Effective Approach To Improve Oil Recovery From Mature Fields,” by X.G. Lu, SPE, and J. Xu, C&C Reservoirs, prepared for the 2017 SPE/IATMI Asia Pacific Oil and Gas Conference and Exhibition, Bali, Indonesia, 17–19 October. The paper has not been peer reviewed. Most mature sandstone reservoirs feature natural aquifer drive, artificial water drive, or a combination of the two. These mature fields generally are characterized by high water cut and high recovery efficiency. This paper presents technologies and best practices to improve oil recovery in mature fields through waterflooding optimization. These technologies have proved practical and cost-effective. Introduction Although chemical enhanced-oil-recovery (EOR) technologies such as polymer flood and alkali/surfactant/polymer (ASP) flood can improve oil recovery by 10 and 20%, for waterflooded sandstone reservoirs, respectively, they are expensive and are not applicable in most mature fields at a low oil price. A major problem for waterflooded fields is that, with increased water/oil ratio (WOR), the cost of processing produced fluid soars to exceed the breakeven mark. As a result, many wells are forced to be shut in; in some instances, the entire field may be suspended. Waterflooding-Optimization Methods The technologies discussed in this section are effective generally for multilayer, heterogeneous sandstone reservoirs with high permeability contrast. Zonal Water Injection. This is the most widely applied water-injection-optimization technology. In a multilayered reservoir, early water encroachment along thief zones often occurs. During the mature stage, when the field produces at high water cut, commingled water injection usually leads to ineffective water cycling from the injectors, flowing preferentially through the high-permeability thief zones and back to the surface from the producers. Using the same injecting wellbore, zonal water injection can enhance water-injection rate arbitrarily in low-permeability, low-production, and low-water-cut production zones while reducing the water-injection rate of medium-high permeability, high-water-cut production zones. Thus, the application of this technology can achieve the goal of expanding sweeping efficiency in order to improve oil recovery. Changing the Direction of Fluid Flow. The basic principle is to change the originally fixed injection/production-fluid-flow direction to sweep the remaining oil in bypassed high-oil-saturation areas. This goal is achieved through converting injectors into producers or vice versa. In practice, some injectors are shut in while others are left inactive or regular conversion between injectors and producers is conducted in order to change fluid-flow direction, achieving expanded sweep efficiency. Water Shutoff To Improve Areal Sweeping Volume. This application addresses the challenge of lateral heterogeneities resulting from the permeability contrast of various facies sands. This technique seeks to change the original areal waterflooding direction to constrain ineffective water injection by shutting in the high-fluid-production, high-water-cut wells. The change in liquid-flow direction will benefit the injected water turning to the poorly swept region or bypassed remaining oil to expand sweep volume, achieving the goal of improved ultimate recovery.

Characterization of buried cables and pipes using electromagnetic induction loop-loop frequency-domain devices

The detection and characterization of buried cables and metal pipes has become a key component of field surveys carried out prior to excavation work on construction sites. The very high conductivity and magnetic permeability contrast between any buried cables/pipes compared with the soil makes electromagnetic induction (EMI) instruments very useful for their detection. We have developed a seminumerical method that can be used to model the responses of this type of target. A straight horizontal conductor is equivalent to a series of magnetic dipoles, the magnitude of which can be determined in the spectral domain and then converted back into the spatial domain through the use of an inverse fast Fourier transform. Simulations and case studies allow to establish rules of thumb for the estimation of (1) the nature of the metal: the in-phase response of magnetic cables is of the opposite sign from the conducting ones, (2) the sensitivity to the target characteristic: the influence of the cable/pipe diameter is greater than that of the metal properties, and (3) the depth of the cables. The simulations also underline the role of the coil configuration: Vertical coplanar and perpendicular responses allow a more precise location of the cable/pipe, whereas the horizontal coplanar response is less dependent on the orientation. As ground truth, a known electric cable buried at a depth of 0.5 and 0.002 m in diameter is determined at 0.56 m. The first field test is related to the detection of a buried military cable from World War I, between 2.5 and 3 m below the original ground level. The second field test is related to the detection of a water pipe 0.35 m deep. The modeling technique can be applied to all EMI prospecting methods, and thus it opens the way to the correction of the disturbances generated by cables and pipes.

Numerical simulation of counter-current spontaneous imbibition in water-wet fractured porous media: Influences of water injection velocity, fracture aperture, and grains geometry

Counter-current spontaneous imbibition (SI), in which water and oil flow through the same face in opposite directions, is known as one of the most significant oil recovery mechanisms in naturally fractured reservoirs; however, this mechanism has not received much attention. Understanding the dynamic of water-oil displacement during counter-current SI is very challenging because of simultaneous impacts of multiple factors including geometry complexity and heterogeneity of naturally fractured reservoir materials, e.g., high permeability contrast between the rock matrix and fracture, wettability, and porosity. This study investigates the effects of water injection velocity, fracture aperture, and grain shape during counter-current SI at pore-scale. A robust finite element solver is used to solve the governing equations of multiphase flow, which are the coupled Navier–Stokes and Cahn–Hilliard phase-field equations. The results showed that the case with the highest injection velocity (uinj = 5 mm/s) recovered more than 15% of the matrix oil at the early times and then reached its ultimate recovery factor. However, in the case of the lowest injection velocity, i.e., uinj = 0.05 mm/s, the lowest imbibition rate was observed at the early times, but ultimately 23% of the matrix oil was recovered. The model with uinj = 5 mm/s was able to capture some pore-level mechanisms such as snap-off, oil film thinning, interface coalescence, and water film bridging. The obtained results revealed that changing the fracture aperture has a slight effect on the imbibition rate at the earlier times and ultimate recoveries would be almost equal. To assess the influences of grain shape on the imbibition process, the simulated domain was reconstructed with cubic grains. It was noticed that because of higher permeability and porosity, relatively larger oil drops were formed and resulted in higher oil recovery compared with the model with spherical grains. The developed model can be used as a basis for phase-field counter-current simulations and would be useful to study the qualitative and quantitative nature of this phenomenon.

A Study of the Effect of Fracture Walls on Tracer Transport

Summary Subsurface permeable systems are heterogeneous at multiple scales and are often fractured. Flow and transport in the subsurface formations are impacted by the presence of fractures, both natural and induced. The effects of permeability heterogeneity and fractures on tracer tests are not well-understood. Echo-tracer (i.e., single-well-injection withdrawal) and transmission-tracer (i.e., dipole) tests can provide information on the flow and transport-system heterogeneity in layered formations. The reversal of flow paths in the echo tests tends to cancel out the non-Gaussian, high-permeability flow behavior in the tracer histories, as observed in laboratory experiments. A question arises whether similar Echo-tracer behavior may be observed in tracer responses for an extreme case of heterogeneity, such as a multiporosity fractured permeable system. A fractured rock consists of high-permeability contrast with high fracture permeability and low matrix permeability, often differing by orders of magnitude. The tracer response from an echo test as well as a transmission test in fractured systems, with high level of heterogeneity, is known to be controlled by the extent of molecular diffusion into the matrix. Dispersion may be dominant in the fracture volume, whereas the molecular diffusion is expected to occur across the fracture/wall interface. We discuss the 1D propagator of diffusion, with convection, and its behavior in the presence of a reflecting and absorbing fracture wall. A wave model is presented to understand the tracer transport in a fracture with differential-diffusion properties. The model predicts that diffusion and adsorption of tracer can produce a retardation of the tracer propagation in the fracture in a transmission-tracer test. The retardation leads to a difference in the arrival times of the tracer, which can then be used to calculate the length of a fracture. The model prediction is compared with published transmission-tracer test experimental data in a fractured till rock. Comparison of the model prediction of tracer-front-arrival times shows good agreement. The arrival time depends on the diffusion coefficient, average time of exposure of the solution to the fractured system, the length of the fracture, and the fracture spacing. Prediction of the echo-tracer test shows that for a fractured system, the retardation of the tracer produces a delayed arrival of the diffusing tracer as opposed to the nondiffusing tracer. The study adapts existing techniques for simple-wave description of tracer transport to a fractured system with absorbing walls. The model for prediction of front movement in the fractured system is novel.

Multiscale simulation of acoustic waves in homogenized heterogeneous porous media with low and high permeability contrasts

Acoustic behavior of fluid saturated, heterogeneous, rigid porous media which consist of two micro-porous materials with high permeability contrast is studied using a two-scale model based on the homogenization theory. At the mesoscopic level, the fluid motion is governed by the generalized Darcy flow model. At the macroscopic scale, effective acoustic properties are described by a model which has recently been derived using the periodic unfolding method (Rohan, 2013).This paper presents a computational procedure for estimating the pressure and the velocity fields at both the mesoscale and the macroscale. The model is validated by comparing the multiscale solutions with those of the model with exact periodic mesostructural geometry. The numerical solutions are computed via the finite element method. The ranges of applicability of homogenized models with “high contrast” and “low contrast” permeabilities are also investigated.

Simulation and analysis of wormhole propagation by VES acid in carbonate acidizing

Abstract Uneven distribution of acid due to strong heterogeneity is the main reason to make the stimulation treatment invalid in carbonate acidizing. Viscoelastic surfactant-based self-diverting (VES) acid has the ability to distribute acid evenly in the entire production interval and its diversion effectiveness has been proved not only by tests but also by field application. However, the wormhole propagation behavior by VES acid under the reservoir condition has not been simulated and analyzed. In this paper, a two-scale continuum model coupling with the viscosifying function and the reservoir model is developed. Based on the model, the diverting process is described, and the effects of heterogeneity and the dual-parallel acidizing are investigated. The results show that the secondary wormhole in VES acidizing is well developed compared to that in conventional acidizing due to the changing balance between the viscosifying effect and the wormholing effect. Since the viscosifying effect diverts a certain proportion of acid to other wormholes, the breakthrough volume for VES acid is larger than that for conventional acid at low injection velocity. Due to the dominance of convection effect, the breakthrough volumes for both acids are similar at high injection velocity. The breakthrough volume decreases with the increase of the initial average porosity, and the number of wormhole is proportional to the domain height and inversely proportional to the domain length, respectively. Compared with the conventional acid, the acid diversion effectiveness is significant except for high permeability contrast.