Wormhole Propagation Research Articles

Non-isothermal simulation of wormhole propagation in fractured carbonate rocks based on 3D-EDFM

The current models of fractured carbonate acidizing are limited to 2D simulation or are solely applicable to the acidizing process in porous media with few fractures, neglecting the acid flow between intersecting fractures. In response to these issues, a coupled 3D thermal-hydro-chemical 3D-EDFM method is developed to simulate the acidizing process in fractured carbonate rock. The fractured carbonate acidizing model is coupled by 3D-EDFM, the two-scale continuum model and the heat transfer model in this paper. Numerical simulations of acidizing under different temperatures are performed, and the simulation results are consistent with previous experimental findings, thus verifying the accuracy of the model. Through simulations, we found that as the flow rate increases, the fracture plane transitions from acting as a “dissolution object of acid” to serving as a “transport channel of acid”. The density and inclination angle of the fracture plane significantly affect the wormholes propagation. The presence of fracture planes accelerates the pressure drop during acidizing and complicates the distribution of the acid-rock reaction heat. Unlike in the 2D model, we observe that when cold acid is injected into high-temperature fractured carbonate rock, the acid cools the rock from the inside out. Although higher rock temperatures lead to an increase in , the difference in the optimum injection rate remains minimal. Compared to porous media without fracture planes, the fracture plane increases the optimum injection rate, and appropriately increasing the injection rate can more effectively utilize the transport characteristics of natural fractures.

Investigation of models for predicting the effectiveness of acid treatments in carbonate deposits

This article presents the results of an analysis of the available literature data on the acid treatment of carbonates based on the solution approach. The analysis of various acid treatment liquids, the choice of additives and modeling procedures was also carried out in order to optimally design the process of acid treatment of carbonates. Although theoretical models are designed to predict the effectiveness of acid treatments, their practical applicability for scaling at the field level remains uncertain. Scaling laboratory data to the optimal rate does not always lead to results corresponding to the usual values of processing at the field. In modern models, it is proposed to use the geometry of the pipe to calculate the dominant penetration of wormholes and take into account the competition between them, introducing the density of wormholes in a porous medium. However, assigning values that are sensitive to the rock structure and injection conditions is a major difficulty. Instead of predicting the length of dominant wormholes, it is preferable to focus on estimating the permeability resulting from acid injection. However, the permeability assessment is not possible without first calculating the dissolution coefficient. The simulation results demonstrate that the existence of various zones of recesses or cracks in the formation has a significant impact on the acidification process, especially on the direction of wormhole propagation. This direction can be partially controlled by adding deflecting or retarding agents.

Numerical simulation of wormhole propagation in fractured carbonate rocks during acidizing using a simplified Stokes–Brinkman model

Most numerical simulations for modeling acid reactive fluid transport and wormhole propagation during matrix acidizing, waterflooding, and CO2 sequestration in carbonate formations are computationally expensive, limiting real-time reservoir management and deep learning training datasets generation for inverse modeling research. Therefore, there is a need for less computationally expensive acid-reactive fluid flow models with adequate accuracy. This study developed and validated a simplified acid reactive-transport model by integrating a simplified Stokes–Brinkman model (as opposed to Darcy’s law), an averaged continuum model, and a pseudo-fracture model. Using FEniCS, the model effectively simulates acid-reactive fluid transport and wormhole propagation in carbonate rocks, achieving a high R-square value of about 0.97 based on a quantitative comparison of the breakthrough volume with other models. The simplified model can also simulate wormhole propagation for the reciprocal of the Damköhler number (1/Da) ranging from 0.001 to 1 with adequate accuracy. Sensitivity studies on the natural fracture parameters such as orientation, length, width, and density showed that higher fracture density, wider fracture aperture, longer fracture length, and orientation aligned with the direction of acid injection contribute to lower pore volume to breakthrough ratio but may not increase long-term acid stimulation efficiency. Also, the presence or absence of fractures in the matrix does not alter the dissolving patterns and optimum injection rate. This simple acid reactive-transport model can generate large training datasets for developing surrogate models in deep learning research. Finally, the FEniCS code in this paper is shared so future researchers can reproduce the results or extend the research work.

In-situ study of CO2-saturated brine reactive transport in carbonates considering the efficiency of wormhole propagation

Deep limestone aquifers are potential CO2 storage sites, but CO2-saturated brine reacts with the carbonate rock, changing its transport and storage properties. This study provided a preliminary investigation of the optimal injection rate of CO2-saturated brine in carbonate rocks. Indiana limestone cores were subjected to CO2-saturated brine injection at varied rates using an HPHT coreflooding setup with X-ray CT monitoring. The samples were characterized pre- and post-treatment in terms of porosity and pore size distribution using a gas porosimeter and NMR T2 measurements. Moreover, the reaction was evaluated by measuring the aqueous effluent calcium ions concentration as a function of throughput using ICP-OES analysis. A high-resolution micro-CT scan was used to capture the dissolution post-treatments and characterize the wormhole's size and patterns. Results showed that the wormholes broke through to the sample exit face after injecting 160, 48, and 36 pore volumes at 0.5, 1, and 2 cm3/min, respectively thereby revealing the importance of injection velocity. The ICP-OES analysis revealed that a larger dissolution rate was achieved at 2 cm3/min, which explained the fast wormhole propagation. An increase in rock porosity and the pore-size distributions was observed after coreflooding on all samples with minimum precipitation, as concluded from the NMR T2 relaxation time. A universal optimum Damköhler number can be obtained that enables calculating the optimum injection rate of CO2-saturated brine at different rock and fluid conditions. We speculated that the optimum Damköhler number could be different from the value of 0.29 proposed by Fredd and Fogler (1998). This study provides a preliminary understanding of the optimal CO2-saturated brine injection velocity that has an application for CO2 storage, water alternating gas (WAG) operations, and acid stimulation of carbonate formations.

A coupled three-dimensional wormhole modeling in heterogenous carbonate lithology in limited-entry and openhole completions

Wormhole propagation in carbonate formation is a well-researched area with several proposed empirical, analytical, and numerical models to predict the process efficiency. The most reliable and up-to-date model is the two-scale continuum (TSC) model, based on numerical simulation of reactive transport in a porous medium. The model has been utilized in two and occasionally in three-dimensional space but has yet to consider the lithology impact in three-dimensional space (3D). This study demonstrated the impact of lithology considering both openhole and limited-entry completion in 3D space. Moreover, the model considered the acid temperature impact on acidizing efficiency. Results showed that limited entry results in a longer wormhole at the expense of its coverage along the wellbore. Similarly, the higher the number of perforations, the lower the wormhole radius but the higher the coverage. Increasing acid temperature results in better dolomite and lower limestone acid stimulation efficiency. In mixed mineralogy, the positive impact of temperature appears at 50 °C and higher. Wormholes propagate in the limestone sections in layered formation with openhole completion, leaving the dolomite under-stimulated, even at high acid temperatures. Limited entry completion in dolomite layers did not prevent the acid from traveling to the limestone layers but provided limited stimulation in the dolomite section. This is the first study to utilize the TSC model to predict the acid stimulation outcomes at field conditions in 3D space.

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.

Influence of fractures and heat transmission on wormhole propagation in fractured carbonate rocks

Carbonate reservoirs exhibit significant heterogeneity and often contain natural fractures. Matrix acidizing is a commonly used technique in fractured carbonate formations. Currently, the influences of natural fractures and the acid-rock molar reaction heat on wormhole propagation are rarely considered in acidizing models. In this paper, the two-scale continuum model, the embedded discrete fracture models (EDFM), and the heat transfer model are combined to develop a computational model of acidic fluid reactive flow in carbonate rocks with a complex fracture network that takes into account temperature variations. The model considers not only the temperature variation caused by the acid-rock molar reaction heat, but also simulates carbonate acidizing with any complex fracture network. Numerical simulations of the model were carried out to obtain the wormhole propagation patterns and the breakthrough curves under different conditions, and the simulation results were in good agreement with those of previous study. In particular, the sensitivity of fracture permeability, acid concentration, acid temperature and matrix porosity heterogeneity during acidizing is studied. The simulation results show that fractures can significantly alter the structure of wormholes and decrease the pore volume of acid required to reach the breakthrough (PVBT). However, fractures have minimal impact on the growth structure of wormholes prior to encountering fractures. During the reaction, the highest temperature was observed at the front end of the wormhole, and it was found that the optimum injection rate increased with the increase of the injected acid temperature. Lowering the temperature of the acid can enhance the efficiency of acidizing in fractured carbonate formations, particularly when applied at an optimal injection rate. When carbonate formations have well-developed fractures, the structure of the wormholes is insensitive to the heterogeneity of the matrix porosity, and they tend to grow along the fractures.

Wormholing behavior in matrix acidizing in vuggy, naturally fractured carbonate reservoirs

In vuggy, naturally fractured carbonate reservoirs, hydrocarbon is mainly stored in vugs and natural fractures (NFs). To enhance oil production in such reservoirs, matrix acidizing is used to generate wormholes to connect the wellbore with NFs and vugs. Due to the simultaneous existence of NFs and vugs, the acid flow and interaction with rock in acidizing is complicated, and the wormhole propagation behavior needs to be clarified. To this end, the pore structure characterization method accounting for the matrix, vugs, and NFs is established based on geostatistics methods, which is then combined with the two-scale wormhole model to simulate wormhole propagation in the vuggy, naturally fractured carbonate reservoirs. The effects of geological factors and engineering factors on wormholing behavior are analyzed through extensive numerical simulations. The research shows that both the dimensionless correlation length and the areal proportion of vugs affect wormhole propagation. There is an optimal combination of the dimensionless correlation length and the areal proportion (evaluated by comprehensive influence coefficient), rendering more vugs being connected with wormholes. NFs have a dominant effect on wormhole propagation. The optimal natural fracture density and dimensionless length of NFs exist for a given formation with the same vug distribution. The distribution of the NFs and the vugs has a dominant effect on wormhole pattern and vugs that can be connected. In engineering practice, retarded acid system with low diffusion coefficient of hydrogen ions (H+) is recommended to obtain longer wormholes so as to increase the possibility of connecting remote vugs with the wellbore. Meanwhile, for vuggy, naturally fractured carbonate reservoirs, increasing the injection rate promotes acid flow in NFs, facilitating wormhole propagation and connecting with more vugs with the same injection volume as long as the pumping pressure is lower than the formation breaking pressure. This research provides theoretical basis for matrix acidizing in vuggy, naturally fractured carbonate reservoirs.

A second‐order time discretizing block‐centered finite difference method for compressible wormhole propagation

AbstractIn this paper, a second‐order time discretizing block‐centered finite difference method is introduced to solve the compressible wormhole propagation. The optimal second‐order error estimates for the porosity, pressure, velocity, concentration and its flux are established carefully in different discrete norms on non‐uniform grids. Then by introducing Lagrange multiplier, a novel bound‐preserving scheme for concentration is constructed. Finally, numerical experiments are carried out to demonstrate the correctness of theoretical analysis and capability for simulations of compressible wormhole propagation.

A high-order time discretizing block-centered finite difference method for compressible wormhole propagation

In this paper, a high-order numerical scheme by using fourth-order implicit Runge–Kutta method and block-centered finite difference method is constructed to solve the compressible wormhole propagation. For the evolution of porosity, high-order interpolation technique and cut-off approach are applied to achieve high-order and bound-preserving. Finally, some numerical experiments are presented to demonstrate the correctness and capability of the given scheme.

Fracture and vug effects on wormhole pattern during acidizing of triple porosity carbonate rocks

Carbonate reservoir acidization is performed to mitigate formation damage and create desirable and highly permeable pathways for the movement of oil and gas. The most significant characteristic of carbonate reservoirs is the presence of fractures and vugs within their structure, which contribute to their triple porosity. The presence of fractures and vugs complicates the flow equations in the medium, which can significantly impact the success or failure of the acidizing. Therefore, understanding their role in the behavior of fractured carbonate reservoirs is a challenging and important issue. Comprehensive studies investigating the simultaneous effect of fractures and vugs on the acidizing in these types of reservoirs have not been reported. Therefore, this study provides a detailed and more precise examination of the acidization process within a triple porosity carbonate media. To simulate the acidizing, a two-scale continuum model was coupled with the pseudo-fracture method in a triple porosity carbonate media. The flow within the matrix and the vug were modeled using Darcy's law, while the flow within the fracture was modeled using the cubic law (free flow). This modeling approach accurately simulated the overall flow of the acidizing fluid. Generally, increasing the length and decreasing the width of a single horizontal fracture improves the acidizing, whereas a vertical one causes a delay at average injection rate. The presence of cross-fractures enhances acidization at all injection rates, and when a horizontal fracture is present at the system's outlet, it also significantly reduces the PVbt. Conversely, the presence of multiple vertical ones within the reservoir delays the acid reaction time, Increasing the number and size of vug improves the acidizing. When fractures and vugs coexist within the rock, it is the type and location of these fractures that control the wormhole propagation pattern and the extent of variations in porosity inside the vug.

Computationally Efficient 3D Fully Coupled Reactive Transport Model for Wormhole Propagation in Carbonate Formation

Computationally Efficient 3D Fully Coupled Reactive Transport Model for Wormhole Propagation in Carbonate Formation

A new wormhole mechanistic model for radial acid flow geometry using novel 3D flow correlations

In carbonate reservoirs, matrix acidizing is used to improve well performance by creating conductive channels called wormholes. Predicting wormhole propagation rate in radial acid flow geometry up to the real wellbore scale is the main problem regarding designing field operations in previous studies which are still challenging. In this study, a new mechanistic approach is presented to predict the radial flow acidizing up to near wellbore scale by considering the vital effects of porous media size and geometrical parameters of wormhole patterns.Accordingly, wormhole tip velocity and wormhole wall fluid loss rate will be introduced as the scale transferring parameters between different porous media sizes which are correlated in terms of rock diameter and wellbore height, wormhole size and density. These novel correlations are extracted from the large databank of flux distribution between rock matrix and wormhole channel obtained in 60 different 3D FEM flow simulations for various patterns of wormhole propagating and different wellbore sizes. In addition, an HPHT radial acid flooding setup is designed and constructed to perform radial acid coreflood on ultra-low permeable rocks (k«1md) for model validation. During the experiments, the breakthrough pore volume, pressure behavior and CT scan of samples are closely monitored. The results showed that due to the tight window of pore size distribution, faster breakthroughs with 1.23 and 1.45 pore volumes occurred in these tight samples compared to those reported already which are confirmed by developed model prediction. Besides, the model results showed that increasing the rock height (open-hole interval) would increase wormhole tip velocity and decrease acid breakthrough time. In addition, the higher temperature shifted the acid response curve to the right, toward higher acid breakthrough volume and higher acid concentration shifted it toward lower breakthrough volumes. The model is validated using radial acid experiments and previous radial acid models for different rock sizes with good agreement (R2 = 0.9547, MSE = 0.02161 and RMSE = 0.14701). The new radial acidizing model is capable to quickly predict wormhole propagation rate up to wellbore scale without requiring excess up-scaling data due to considering wide ranges of porous rock sizes from (25.4–152.4 cm) diameter and (5–25.4 cm) pay zone height (sufficient size for considering repetitive wormhole patterns). This technique can be utilized for tuning parameters of various radial cases to predict the acid tests results leading to reduce the number of required experiments.

Numerical Simulation of Wormhole Propagation with Foamed-Viscoelastic-Surfactant Acid in Carbonate Acidizing

Successful matrix acidizing for extremely thick carbonate reservoirs with long horizontal well sections and strong heterogeneity requires efficient temporary plugging and diverting of acid fluid, ensuring acid fluid distribution to each production layer. Foamed-viscoelastic-surfactant (Foamed-VES) acid combines the benefits of both foam acid and viscoelastic surfactant (VES) acid, integrating foam plugging and viscous plugging. It can achieve uniform acid distribution in highly heterogeneous reservoirs. However, little research has been conducted on the wormhole propagation law of foamed-VES acid. To address this gap, this study established a mathematical model of foamed-VES acid wormhole propagation based on the dual-scale model. The model was coupled with a random porosity distribution generated with geological statistical software. The effects of different factors on foamed-VES acid etching were simulated. Numerical results show that foamed-VES acid can stimulate low-permeability reservoirs with a permeability differential of 20. Its inherent mechanism lies in the synergy of foam plugging and VES viscous plugging. This study enhances our understanding of the acid diversion mechanism of foamed-VES acid, providing a theoretical foundation for on-site acidizing treatment.

Permeability anisotropy impact on wormhole propagation in openhole and limited-entry completions: A 3D numerical study

The permeability in carbonate reservoirs is not the same in all directions (i.e., anisotropic), a property seldom considered in acid stimulation. The study hypothesizes that permeability anisotropy impacts acid treatment efficiency significantly. The investigation included the openhole and limited-entry completions in a vertical and horizontal wellbores configuration. A model based on the two-scale continuum approach was constructed in three-dimensional space (3D), resembling the big block experiment with the wellbore at the center. Permeability anisotropy significantly impacts acid efficiency in terms of the pore volume to breakthrough (PVBT) and optimum injection rate. For instance, simulations of acid placement in an openhole horizontal well with 10 anisotropy ratio resulted in PVBT of 0.15 compared to 0.35 in a vertical well. Limited entry completions result in more extended wormholes where the permeability anisotropy positively impacted wormhole length as compared to isotropic permeability. Nevertheless, the permeability anisotropy negatively impacted wormhole coverage along the wellbore in most scenarios. The simulations showed that a spear-like wormhole propagates from a limited entry horizontal wellbore in anisotropic formation, which previous studies assumed to be spherical or ellipsoidal. This implies that the skin factors models should be revised based on the new findings. This is the first study to assess the permeability antitropy impact on the stimulation of openhole and perforated wells in a 3D space.

A new insight into wormhole propagation prediction in carbonate matrix acidizing based on experimental approaches

Carbonate acidizing is a common practice for production/injection enhancement in damaged oil/gas wells by creating conductive flow tunnels called wormholes. Previous linear acid flood studies are mostly performed on core plugs limited to the Darcy scale with a strong dependency on lab results for upscaling techniques. In this study, a novel scale-free approach of wormhole propagation inside linear porous media for small to very large core diameters is introduced. The model associates the wormhole tip velocity and wall fluid loss to the injection rate using novel flow correlations in terms of core diameter and wormhole geometries (wormhole density, length and diameter). These correlations are constructed based on the results obtained from a large number of 3D-FEM (Finite Element Method) simulations of water flow utilizing the porous rock with predefined dominant cylindrical wormholes. The application of the model is easy and quick without complex or time-consuming calculations even for large rock diameters up to 28 in (71 cm) which simultaneously predicts the acid response curve by matching with the acid coreflood experiments on specific acid/rock systems. Also, the output matching parameters for each acid/rock system can be directly used for larger core diameters without extra-large scale acid flood experiments. In the experimental parts of this study, acid flooding is performed on various rock types of four Iranian carbonate reservoir layers to find their corresponding acid response curves and optimum flow conditions required to design stimulation programs. Besides, the collected data bank could help to enrich the data pool required to validate the developed model practically. The proposed model is validated by literature model results and also experimental data obtained in our laboratory and those presented in the literature and the results showed that good agreement is obtained in regression analysis with R2 = 0.953, MSE = 0.046452, RMSE = 0.215528 and MAPE = 24.11357.

Hybrid mixed discontinuous Galerkin finite element method for incompressible wormhole propagation problem

Hybrid mixed discontinuous Galerkin finite element method for incompressible wormhole propagation problem

4D tomography reveals a complex relationship between wormhole advancement and permeability variation in dissolving rocks

Dissolution of porous media induces positive feedback between fluid transport and chemical reactions at mineral surfaces, leading to the formation of wormhole-like channels within the rock. Wormholes provide highly efficient flow and transport paths within rock, and as such, understanding their formation is critical for controlling contaminant migration or preventing CO2 leakage during geological carbon sequestration. Here, using time-resolved X-ray tomography, we capture the dynamics of wormhole propagation, inaccessible by standard experimental methods. We find a highly non-trivial relationship between wormhole advancement and variations in permeability of the rock, with extensive periods of steady advancement not reflected by significant change in permeability. This is in contrast to most existing conceptual models where wormholes advance in a linear fashion. We show that this is caused by the presence of highly cemented regions which act as barriers to flow, as confirmed by multi-scale analysis of the pore geometry based on tomographic, (ultra) small angle neutron scattering, and optical microscopy measurements. These results demonstrate that time-lapse captured wormhole dynamics can be used to probe the internal structure of the rock.

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

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.