Wormhole Formation Research Articles

Comprehensive Investigation of Factors Affecting Acid Fracture Propagation with Natural Fracture

Acid fracturing is a crucial stimulation technique to enhance hydrocarbon recovery in carbonate reservoirs. However, the interaction between acid fractures and natural fractures remains complex due to the combined effects of mechanical, chemical, and fluid flow processes. This study extends a previously developed hydro-mechano-reactive flow coupled model to analyze these interactions, focusing on the influence of acid dissolution. The model incorporates reservoir heterogeneity and simulates various scenarios, including different stress differences, approaching angles, injection rates, and acid concentrations. Numerical simulations reveal distinct propagation modes for acid and hydraulic fractures, highlighting the significant influence of acid dissolution on fracture behavior. Results show that hydraulic fractures are more likely to cross natural fractures, whereas acid fractures tend to be arrested due to wormhole formation. Increasing stress differences and approaching angles promote fracture crossing, while lower angles favor diversion into natural fractures. Higher injection rates facilitate fracture crossing by increasing pressure accumulation, but excessive acid concentrations hinder fracture initiation due to enhanced wormhole formation. The study demonstrates the importance of tailoring fracturing treatments to specific reservoir conditions, optimizing parameters to enhance fracture propagation and reservoir stimulation. These findings contribute to a deeper understanding of fracture mechanics in heterogeneous reservoirs and offer practical implications for improving the efficiency of hydraulic fracturing operations in unconventional reservoirs.

Deflection of light by wormholes and its shadow due to dark matter within modified symmetric teleparallel gravity formalism

Abstract We explore the possibility of traversable wormhole formation in the dark matter halos in the context of $f(Q)$ gravity. We obtain the exact wormhole solutions with anisotropic matter source based on the Bose-Einstein condensate, Navarro-Frenk-White, and pseudo-isothermal matter density profiles. Notably, we present a novel wormhole solution supported by these dark matters using the expressions for the density profile and rotational velocity along with the modified field equations to calculate the redshift and shape functions of the wormholes. With a particular set of parameters, we demonstrate that our proposed wormhole solutions fulfill the flare-out condition against an asymptotic background. Additionally, we examine the energy conditions, focusing on the null energy conditions at the wormhole's throat, providing a graphical representation of the feasible and negative regions. Our study also examines the wormhole's shadow in the presence of various dark matter models, revealing that higher central densities result in a shadow closer to the throat, whereas lower values have the opposite effect. Moreover, we explore the deflection of light when it encounters these wormholes, particularly noting that light deflection approaches infinity at the throat, where the gravitational field is extremely strong.

Evolving wormhole formation in dRGT massive gravity

Evolving wormhole formation in dRGT massive gravity

A study of the optimum injection rate of carbonic acid during matrix acidizing of carbonate reservoirs: Implications for reducing CO2 emissions

This study investigates the process of optimizing the injection rates of carbonic acid during matrix acidizing in carbonate formations, highlighting its impact on wormhole formation, dissolution, and the changes in rock petrophysical properties. Indiana limestone core samples, with porosity ranging from 14 % to 16 % and permeability from 7 to 12 mD, were flooded using diffrent injection rates (0.5, 1, 2, and 5 cm³/min) to determine the optimal injection velocity. The carbonic acid is prepared by mixing 70 % fresh water with 30 % sc-CO2 at 1500 psi and room temperature. A micro-CT scan was employed to visualize the wormhole patterns, measure its size, and calculate the optimum Damköhler Number. Moreover, inductively coupled plasma (ICP) was used to measure the calcium concentrations from effluents collected at different intervals. Two models were used to ascertain the optimum injection rate; the first model based on PVBT as a function of injection rate, indicated that 2 cm³/min is the optimum injection rate with 22 pore volumes to breakthrough (PVBT). The second model considered the relationship between PVBT and interstitial velocity (Vi), leading to an optimum injection rate of 1.7 cm³/min, corresponding to an interstitial velocity of 1 cm/min. Calculations of the optimum Damkhöler number reveal a value significantly different from the 0.29 proposed by Fredd and Fogler. This study provides valuable insights into the utilization of CO2 to enhance well productivity as a replacement for conventional acids.

Measurement-induced phase transition in teleportation and wormholes

We demonstrate that some quantum teleportation protocols exhibit measurement induced phase transitions in Sachdev-Ye-Kitaev model. Namely, Kitaev-Yoshida and Gao-Jafferis-Wall protocols have a phase transition if we apply them at a large projection rate or at a large coupling rate respectively. It is well-known that at small rates they allow teleportation to happen only within a small time-window. We show that at large rates, the system goes into a new steady state, where the teleportation can be performed at any moment. In dual Jackiw-Teitelboim gravity these phase transitions correspond to the formation of an eternal traversable wormhole. In the Kitaev-Yoshida case this novel type of wormhole is supported by continuous projections.

Time-reversed information flow through a wormhole in scalar–tensor gravity

This Letter aims to advance unexplored properties of a new class of Closed Timelike Curves recently discovered in scalar–tensor gravity, reported in Nguyen and Lobo (2023) [31] and Nguyen and Azreg-Aïnou (2023) [30]. Therein, it was shown that when the Weak Energy Condition is violated, the topology of spacetime in scalar–tensor gravity is altered and directly enables the formation of two-way traversable wormholes. Furthermore, each of these wormholes acts a gateway between two time-mirrored worlds, where the two asymptotically flat sheets in the Kruskal–Szekeres diagram are glued antipodally along three directions—time t and the polar and azimuth angles (θ,φ) of the 2-sphere—to form a wormhole throat. This contrasts with the standard embedding diagram which typically glues the sheets only along the θ and φ directions. Crucially, due to the ‘gluing’ along the t direction, the wormhole becomes a portal connecting the two spacetime sheets with opposite physical time flows, enabling the emergence of closed timelike loops which straddle the throat. In this Letter, we shall point out that this portal mathematically permits the possibility of backward propagation of information against time. This feature is ubiquitous for wormholes in scalar–tensor theories. In addition, we formulate the Feynman sum for transition amplitudes of microscopic particles in the proximity of a wormhole throat in which we account for timelike paths that experience time reversal.

Wormhole Geometry Modelling on Carbonate Matrix Acidizing: A Literature Review

Matrix acidizing is a critical well-stimulation technique used to enhance the permeability of carbonate reservoirs by creating channels or "wormholes" through the dissolution of the rock matrix. The efficiency of this process is significantly influenced by the geometry of the wormholes formed. This review paper provides a comprehensive analysis of current research on wormhole geometry modeling in carbonate matrix acidizing, synthesizing findings from experimental studies, analytical models, and numerical simulations. Key factors affecting wormhole geometry, such as acid concentration, injection rate, and rock properties, are discussed. The review highlights the contributions of various modeling approaches in predicting wormhole formation and propagation, emphasizing the importance of accurately capturing the coupled effects of fluid flow, chemical reactions, and rock dissolution. The implications for optimizing acidizing treatments and enhancing hydrocarbon recovery are explored, alongside recommendations for future research. These include the need for field validation, advanced modeling techniques, real-time monitoring, interdisciplinary collaboration, and sustainability considerations. This synthesis aims to provide a foundation for improving the design and execution of matrix acidizing operations in carbonate reservoirs.

Flowback Additive for Acidizing Fluid to Stimulate Carbonate Gas Reservoirs

Summary Acidizing of oil- and gas-bearing carbonate reservoirs is generally undertaken by using strong mineral acids such as hydrochloric acid (HCl) to enhance permeability. One of the major challenges associated with HCl injection is tuning the reactivity profile to favor the transport of live acid deep into the reservoir while achieving a minimum rock face dissolution. The mineral acid is therefore emulsified in a hydrocarbon phase (e.g., diesel) to retard its reactivity with the rock matrix. The use of emulsified acid is hindered by several limitations such as low emulsion stability at high temperatures, pumping limitations due to high viscosity, the potential of formation damage, and cumbersome mixing procedures at the field scale. In addition, the brines formed as a result of this reaction can be difficult to produce due to higher density and capillary pressures, unfavorable wettability, and low formation pressure. Here, we report on the development of dual-purpose additives that were specifically designed to enhance the recovery of high-density brines and retard the acid/rock reactivity upon addition to the stimulation treatment. Accordingly, seven new additives with fluid flowback properties were developed for use in a single-phase acidizing fluid consisting of HCl (15 wt% and 28 wt%) with the required additives, such as corrosion inhibitor and intensifier, and H2S scavenger. The flowback enhancers (FBEs) were formulated from a blend of water, ester or terpene solvents, alcohols, and surfactants to form optically clear nano- and microemulsions. Surfactant selection was driven by the need to exhibit demulsification properties with condensate, high chemical and thermal stability, compatibility in strongly acidic media, and high-density brines under harsh reservoir conditions. To assess the FBE performance in acidizing formulations (i.e., to serve as both an FBE and retarder), screening studies consisting of static rock dissolution tests and surface tension measurements were performed to downselect FBEs suitable for this application. This was coupled with brine displacement tests in addition to compatibility and stability studies. FBEs that demonstrated superior performance were then selected for further evaluation under reservoir conditions [i.e., core flow matrix acidizing to measure regained permeability and computed tomography (CT) scan for analyzing the wormhole propagation]. The droplet size of the as-prepared nano- and microemulsions was found to be between 10 nm and 850 nm. The FBEs formulated in this study were found to prevent emulsion formation in the presence of condensate and demonstrated remarkable chemical and thermal stability in concentrated acid at temperatures up to 300°F for a duration of up to 24 hours, as confirmed by the consistent low surface tension values (21–29 mN/m). With regard to fluid displacement, column tests performed under ambient conditions revealed quick brine displacement with recovery exceeding 75 vol% in comparison with 16 vol% in the absence of the FBE. Interestingly, the addition of a select FBE from this study to 28 wt% HCl was found to retard the reaction of carbonate dissolution at room temperature. This led us to assess the performance under reservoir conditions utilizing core flow testing. Accordingly, the addition of FBE-F to 28 wt% HCl led to an improvement in permeability by up to 267% as compared with 15% without FBE added. These results are further supported by the CT scan images of the acidized cores, which revealed the formation of a deeper wormhole in the presence of a select FBE.

Unraveling the mysteries of wormhole formation in Rastall–Rainbow gravity: a comprehensive study using the embedding approach

The present work looks for the possible existence of static and spherically symmetric wormhole geometries in Rastall–Rainbow gravity. Since, the Rastall–Rainbow gravity model has been constructed with the combination of Rastall theory and the gravity’s rainbow formalism. Taking advantage of the Karmarkar condition for embedding class one metrics, we solve the modified field equations analytically that describe wormholes for specific choice of redshift function. For specific parameter ranges, the solution represents a traversable wormhole that exhibits the violation of null energy condition and consequently the weak energy condition also. Furthermore, we focus on the wormhole stability via adiabatic sound velocity analysis. This model establishes a strong connection between two model parameters, namely, the Rastall parameters and the Rainbow functions, and how it affects the wormhole solution.

A study of an embedding class-I traversable wormhole in Galileon Gravity

In this article, we examine the possibility of the creation of a traversable wormhole geometry in Galileon Gravity (GG). In this gravity, the alternation of gravity is determined by an effective scalar field ϕ, treated as the Galileon field. From a mechanism perspective, GG is developed by covariantizing the decoupling Lagrangian of the DGP (Dvali-Gabadadze-Porrati) model. Now, to achieve our aim, gravitational field equations have been constructed corresponding to a line element, which represents a static and spherically symmetric spacetime. Next, we have modified these field equations in the context of a Morris-Thorne traversable wormhole spacetime. In particular, we have used the ‘Karmarkar condition’ to evaluate the wormhole solutions in a general sense. Further, for a better understanding of our obtained wormhole solutions, 2-dimensional and 3-dimensional diagrams have been displayed. Later, we scrutinized the possible creation of a traversable wormhole based on the essential requirements, that is, the infraction of energy conditions in the neighborhood of the throat region, especially the Null Energy Condition (NEC). For this purpose, we have discussed three cases like Case-I: without the necessity of dark energy (DE), Case-II: with support of phantom-like DE and Case-III: with the SFDM profile of a dark matter (DM) halo. Next, we have examined the hydrostatic equilibrium position corresponding to our obtained wormhole system in GG. Furthermore, to examine the small and sufficient quantity of exotic matter, the possible formation of a traversable wormhole has been explored by a volume integral quantifier. Lastly, we have shown the nature of active mass. Finally, we have concluded that traversable wormhole solutions can also be established in the presence of an effective scalar field without any essential support of exotic matter in the neighborhood of the throat region by GG.

The river model of gravitational collapse

We show that the transformation of a time-evolving spherically symmetric metric tensor into a Painlevé–Gullstrand–Lemaître form brings forth a few curious consequences. The time evolution describes a non-singular gravitational collapse, leading to a bounce and dispersal of all the clustered matter, or a wormhole geometry for certain initial conditions. The null convergence condition is violated only at the onset of bounce or the wormhole formation. As an example, the requirements to develop a Simpson–Visser wormhole/regular black-hole geometry is discussed. The solution can be regarded as a new time-evolving twin of sonic dumb holes found in analog gravity.

Chemo-hydro-mechanical effects of CO2 injection into a permeable limestone

CO2 storage in carbonate aquifers is a way to mitigate atmospheric CO2 emissions, but it leads to acid-producing reactions that may induce alterations in the rock pore structure and hydromechanical properties. To gain a better understanding of these changes in rock properties, percolation experiments under constant flow-rate conditions with (i) CO2-saturated water (PCO2 = 100 bar and T = 60 °C) and (ii) HCl solutions (P = 1 bar and T = 60 °C) were performed on centimetric cores of the grain-supported Pont du Gard Limestone (permeability about 10−14–10−13 m2). Effluent chemistry analyses, X-ray imaging, and measurements of the hydromechanical properties of intact and altered specimens were used to quantify acid-induced changes in the two acid-rock systems. Experimental results show that the rock dissolution patterns highly depend on the acid type and pore space heterogeneity. Under the flow conditions of these experiments, complete HCl dissociation (strong acid) and rapid HCl-rock reaction result in a compact dissolution pattern that only affects the hydromechanical properties of the core inlet. Conversely, partial dissociation of H2CO3 (weak acid) produces chemical reactions all along the core. Initial structural heterogeneities localize chemical reactions along preferential flow pathways, causing instabilities in the reaction front and wormhole formation, which markedly enhances permeability. A powerlaw relationship with a very large exponent (as high as 24) accounts for the variation in permeability as a function of porosity. Altered cores render both a significant attenuation in mechanical rock properties and ultrasonic velocities, which is reproduced using a Differential Effective Medium (DEM) homogenization approach. The high-pressure percolation experiments of this study using CO2-saturated water represent an extreme scenario of CO2-brine-rock interactions in carbonate reservoirs, which needs to be considered to improve the prediction and monitoring of the storage performance.

Yukawa–Casimir wormhole model in F(R,T) framework

There is an unavoidable association of traversability of wormholes to the violation of null energy condition which in turn indicates the presence of exotic or non-exotic matter in the wormhole geometry. The exotic matter possesses the negative energy that is required to sustain the wormhole. Recently studies are done to solve this problem so as to avoid the exotic matter. In this work, we attempt to find such solution in the framework of [Formula: see text] gravity where [Formula: see text], here [Formula: see text] and [Formula: see text] are Ricci scalar and trace of energy momentum tensor respectively, using the Yukawa–Casimir shape function. For Yukawa–Casimir wormhole, it is assumed that the exotic energy is sourced from the Casimir energy density. We have examined the energy conditions using Yukawa–Casimir shape function [Formula: see text] where [Formula: see text] is a positive mass scale. We have taken different values of [Formula: see text] to study the role of Yukawa–Casimir energy in formation of traversable wormholes. The equilibrium aspect of the model is also investigated with the help of TOV equation.

Wormhole formation in massive gravity: an analytic description

The present study analyses the wormhole solution both in the dRGT-f(R, T) massive gravity and Einstein massive gravity. In both the models, the anisotropic pressure solution in ultrastatic wormhole geometry gives rise to the shape function that involves massive gravity parameters gamma and Lambda . However, the terms consisting of gamma and Lambda acts in such a way that the spacetime loses asymptotic flatness. Similar to the black hole solution in massive gravity, this inconsistency arises due to the repulsive effect of gravity which can be represented by the photon deflection angle that goes negative after a certain radial distance. It is investigated that the repulsive effect induced in the massive gravitons push the spacetime geometry so strongly that the asymptotic flatness is effected. On the other hand, in this model, one can have a wormhole with ordinary matter at the throat that satisfies all the energy conditions while the negative energy density is sourced by massive gravitons. Finally, using the TOV equation, it is found that the model is stable under the hydrostatic equilibrium condition.

Lorentzian wormholes in an emergent universe

A non-singular emergent universe (EU) scenario within the realm of standard Relativistic physics requires a generalization of the equation of state (EoS) connecting the pressure and energy density. This generalized EoS is capable of describing a composition of exotic matter, dark energy and cosmological dust matter. Since the EU scenario is known to violate the null energy condition (NEC), we investigate the possibility of presence of static, spherically symmetric and traversable Lorentzian wormholes in an EU. The obtained shape function is found to satisfy the criteria for wormhole formation, besides the violation of the NEC at the wormhole throat and ensuring traversability such that tidal forces are within desirable limits. Also, the wormhole is found to be stable through linear stability analysis. Most importantly, the numerical value of the EU parameter B as estimated by our wormhole model is in agreement with and lies within the range of values as constrained by observational data in a cosmological context. Also, the negative sign of the second EU parameter A as obtained from our wormhole model is in agreement with the one required for describing an EU, which further indicates on the existence of such wormholes in an EU without accounting for any additional exotic matter field or any modification to the gravitational sector.

Karst genesis and wormhole formation in carbonate joint networks: A comparison between 3D and 2D modeling

Accurate modeling of karst genesis is an important issue to understand the spatial and temporal evolutions of transport properties in karstified carbonate rocks. The previous modeling about karst genesis in fracture networks is mainly based on the simplified 2D conduit/fracture networks without considering wormhole formation on the scale of individual conduits or fractures. In this study, we simulated the karst genesis and wormhole formation (i.e., the emergence of preferential flow pathways within individual fractures) in carbonate joint networks using a DFN model fully-discretized in 3D and compared its difference with the 2D models. The results show that, compared to the 2D modeling, the breakthrough time (time of the abrupt rise in flow rate) in the 3D models may be much less sensitive to the network connectivity because of the flow focusing during wormhole formation on the scale of individual joints with a relatively low flow rate. Also, the dimensions of dissolving networks as well as the position and the number of developed preferential pathways in the well-connected networks may be altered when switching from 2D to 3D modeling. We further provide detailed insights into the underlying mechanism governing the dynamics of wormhole formation based on two representative networks (a critically-connected network and a well-connected network). We observed that the generated incipient karst patterns are similar between 2D and 3D models if the initial flow rate is sufficiently large (i.e., no flow focusing inside individual joints before breakthrough) or small (i.e., wormhole pathway is extremely localized, but the breakthrough time is much overestimated). If the initial flow rate falls within the transition range, the dissolution dynamics are complicated and dominated by the combined effect of flow migration over the network and flow focusing on the scale of individual joints, the magnitude of which depends on the fracture roughness. This study highlights the importance of incorporating the third dimension in DFN for accurate predictions of karst network evolution.

Three-dimensional simulation of wormhole propagation in fractured-vuggy carbonate rocks during acidization

Acidization is a widely used stimulation technique for carbonate reservoirs aimed at removing formation damage, and if successful, can result in the creation of wormholes of specific lengths and conductivities around the wellbore. The formation of wormholes depends on the injection rate for a particular acid-mineral system and can be predicted through numerical simulations of the reactive phenomenon during acidization. In this paper, the commonly used two-scale continuum model is enhanced to encompass fractured-vuggy porous media. The fractures are characterized by a pseudo-fracture model, while vugs are represented by a cluster of anomalous matrices with high porosity. Moreover, a method for generating random pore-fracture-vuggy models is proposed. The governing equations are discretized by the finite volume method and are solved under three-dimensional linear and radial conditions. Sensitivity analysis of dissolution dynamics with respect to fracture and vug parameters is performed. The simulation results indicate that both fractures and vugs significantly impact wormhole development. Except for fractures perpendicular to the acid flow direction, fractures in other directions play a crucial role in determining the direction of wormhole growth. Cited as: Liu, P., Kong, X., Feng, G., Zhang, K., Sun, S., Yao, J. Three-dimensional simulation of wormhole propagation in fractured-vuggy carbonate rocks during acidization. Advances in Geo-Energy Research, 2023, 7(3): 199-210. https://doi.org/10.46690/ager.2023.03.06

Quantization of a black-hole gravity: geometrodynamics and the quantum

Quantum gravity is effective in domains where both quantum effects and gravity are essential, such as in the vicinity of space-time singularities. This paper will investigate the quantization of a black-hole gravity, particularly the region surrounding the singularity at the origin of the coordinate system. Describing the system with a Hamiltonian formalism, we apply the covariant integral quantization method to find the Wheeler–DeWitt equation of the model. We find that the quantized system has a discrete energy spectrum in the region inside the event horizon. Through the Kantowski–Sachs metric, it is possible to correlate the entropic time, which gives the dynamics for this model, to the cosmic time in a non-trivial way. Different configurations for the phase space of a Schwarzschild black hole are obtained in a semi-classical analysis. For lower-energy states, the quantum corrections result in singularity removal and wormhole formation.

Numerical Simulation of the Wormhole Propagation in Fractured Carbonate Rocks during Acidization Using a Thermal-Hydrologic-Mechanics-Chemical Coupled Model

Acidizing is a widely adopted approach for stimulating carbonate reservoirs. The two-scale continuum (TSC) model is the most widely used model for simulating the reactive process in a carbonate reservoir during acidizing. In realistic cases, there are overburden pressure and pore pressure at present. When the injected acid reacts with the rock, the dissolution of the rock and the consumption of the acid in the pore will break the mechanical balance of the rock. Many experimental studies show that cores after acidizing have lower strength. However, it is still not clear how the deformation of rocks by the change of ground stress influences the acidizing dynamics. For fractured carbonate reservoirs, fractures play a leading role in the flow of injected acid, which preferentially flows into the fractures and dissolves the fracture walls. The effect of the combined action of rock mechanical balance broken and fracture wall dissolution on the formation of wormholes in fractured carbonate reservoirs remains to be studied. To address the above-mentioned issues, a thermal-hydrologic-mechanical-chemical coupled model is presented based on the TSC model for studying the wormhole propagation in fractured carbonate reservoirs under practical conditions. Linear and radial flow cases are simulated to investigate the influences of fracture distribution, reaction temperature, and effective stress on acidizing dynamics. The simulation results show that more wormhole branches are formed by acidizing if the fractures are perpendicular to the flow direction of acid. Temperature is a key parameter affecting the acidification dissolution patterns, so the influence of temperature cannot be ignored during the acidification design. As the effective stress of the formation increases, the diameter of the wormhole gradually decreases, and the branching decreases. More acid is needed for the same stimulation result under higher effective stress.

Evaluation of an empirical model for pore volume to breakthrough and wormhole growth in carbonate acidizing

The number of pore volumes to breakthrough is one of the most critical indicators of wormhole characterization in the matrix acidizing process. This number is often needed for experimental work that is time-consuming and costly. In this article, an empirical model was used to evaluate the acidizing procedure in the carbonate cores, including limestone and dolomite. This empirical model measures the number of wormholes formed in the carbonate cores after acid injection by using the conservation of mass law. This approach maintained the transport relative reaction rates of core and acid within the wormhole structure during the wormhole formation procedure. In addition, this empirical model accounted for changes in acid concentration as an injected fluid flow. Also, the changes in carbonate porosity, the effect of the Damköhler number, and injection rate were included in the model. Compared to other experimental and semi-empirical works, the established model gave an excellent assessment of 95.45% for the average accuracy and 0.9933 for the average coefficient of determination. Therefore, an empirical technique to approximate this number in the carbonate formations with high accuracy using physical core and acid properties is herein proposed.