Dual-porosity Behavior Research Articles

A solute transport in deformable dual-porosity media using mixture-coupling theory

Rock, soil and many porous-like materials are often fractured or structured media, which can exhibit dual-porosity behaviour. Studies on solute transport in deformable dual-porosity media remain challenging due to the multi-physics coupled effects and the complex interaction between fractures (or macropores) and the porous matrix. Although several studies exist on constitutive modelling of coupled behaviour in deformable dual-porosity media, the previously developed models are not systematic in thermodynamical frameworks. This paper proposes a mixture coupling theory approach based on non-equilibrium thermodynamics to develop a solute transport model with consideration of hydromechanical coupling in dual-porosity media (referred to as the ST-HM model). This paper derives the constitutive equations of fully hydromechanical coupled behaviour in dual-porosity media and considers the pore and fracture porosity evolution influenced by both hydraulic and mechanical fields. Therefore, the governing equations of ST-HM are capable of predicting non-reactive solute transport with a fully hydromechanical coupled effect in dual-porosity media. Then, the model was verified against existing models and validated by relevant experimental results. Further, a numerical example shows that the presented model significantly improves the accuracy of the prediction of porosity, fluid pressure and solute concentration compared with previous models, which ignore the fully hydromechanical coupled effects on solute transport.

A Simple Analytical Model for Oil Production from Partially Fractured Reservoirs to Estimate Size of Finite Fracture Networks

Summary Most oil reservoirs are partially fractured, characterized by finite fracture networks (FFNs) in a sea of isolated fractures. It is necessary to determine size and shape of each FFN explicitly for reservoir simulation. FFN size is correlated with fracture connectivity, which is a function of fracture density, length, and angular scatter. Oil production from FFNs exhibits a long-term dual-porosity behavior. The initial fast rate (Phase I) represents depletion of matrix within FFN, and the subsequent gradual decline phase represents radial flow from the matrix outside the FFN perimeter. Thus, FFN size can be calculated from the cumulative oil production from Phase I, taking into account the pore volume, oil compressibility, and pressure decline. It is not always possible to identify the dual-porosity behavior by visual inspection. A mathematical model is needed to estimate FFN size. For this purpose, a set of three fundamental equations are derived for production rate, cumulative production, and pressure as a function of time. The model is a modified and simplified version of material balance equations with easy analytical solution. It is designed for fractured reservoirs with layer-bound fractures. Production is single-phase black oil under depletion drive. The analytical model was tested on four vertical wells. The unknown parameters such as FFN size, size of well drainage area, and fracture aperture are adjusted until an optimum fit to actual production data is obtained. FFN elliptical shape is estimated from average fracture strike and strike standard deviation. The results are validated by FFN size, fracture length, and aperture measurements from borehole images. The results are approximate but sufficient for preliminary mapping of FFNs with location and size and other critical attributes including fracture drainage area, matrix block size, fracture aperture, and permeability in partially fractured reservoirs.

A sorption-kinetics coupled dual-porosity poromechanical model for organic-rich shales

The flow of gas in shale formations is influenced by several coupled processes including matrix and fractures deformations, and gas sorption. An increase in effective stress by pore-pressure decline, for example, reduces the formation’s porosity and permeability whereas gas desorption results in shrinkage of the rock matrix, causing an increase in permeability. The sorption-driven characteristics of such coupled systems, however, are dependent on gas sorption kinetics. In this study, we thus utilized the concepts of non-equilibrium thermodynamics and continuum mechanics to develop a fully coupled sorptive-poroelastic constitutive equations to describe the impact of sorption kinetics induced deformation on the dual porosity behaviour of gas-shales. These developed constitutive equations were then solved using the finite element method. After verifying the model performance against existing analytical solutions and experimental data from the literature, numerical sensitivity analyses were performed to specifically investigate the gas sorption kinetics on multi-physical processes. Additional numerical sensitivity analyses were performed to assess the importance of the newly derived coupling thermodynamics coefficients. The results showed that the effect of the coupling coefficient between the chemical potential of the adsorbed gas and the porosity of the bedding planes is important in gas production, especially in the long term. Numerical results also showed that the effect of sorption kinetics on gas production is a strong function of gas diffusivity in the matrix and desorption rate. It is also realized that the effect of sorption kinetics on gas production cannot be ignored when the matrix has high gas diffusivity.

Deriving celerity from monitoring data in carbonate aquifers

Celerity (the speed of a pressure wave) in fracture networks in bedrock can result in large and rapid water level responses in both aquifers and streams, but has been little documented in detail. To examine the role played by preferential flow in fracture networks, groundwater and stream data were analysed in a headwater catchment in a chalk aquifer in the UK. Hourly data show that aquifer water levels and streamflow both respond promptly to rain and have a high correlation. The stream exhibits double peaks in flow during stormflow events. The initial peak hardly lags rainfall, is composed of dilute water, and is attributed to direct flow (i.e. overland flow and/or interflow). The second peak occurs several days after rainfall, has high solute concentrations and a high correlation with aquifer water levels, indicating that the second peak is composed of groundwater. Groundwater inputs provide 89% of quickflow in the stream. Calibration of a numerical model gave a fissure porosity (calculated as an equivalent specific yield) of 0.0015, with the low porosity being associated with high celerities and a fissure residence time of 0.14 years. Conversely, the low matrix permeability results in a residence time of 26 years. A review of a further 13 carbonate aquifers in six countries shows that similar dual-porosity behaviour is common. High celerities in fissure networks provide a potent process for the rapid transfer of groundwater to stormwater hydrographs in streams.

Analytical dual-porosity gas model for reserve evaluation of naturally fractured gas reservoirs using a density-based approach

The development of naturally fractured gas reservoirs often requires the deployment of rigorous techniques for production data analysis incorporating dual-porosity gas behavior. It has been a prominent problem to linearize and analytically solve the governing equations for dual-porosity gas systems. This study applies a pseudo-pressure-based interporosity flow equation to derive a density-based rate-transient analysis method to accurately predict the gas production rate and estimate the amount of original gas in place (Gi) for the systems. The methodology also predicts the gas production rate by transforming the response of its liquid counterpart via a decoupling of the pressure-dependent effects using dimensionless depletion-driven parameters.For the first time, the density-based flowing material balance method is derived for the dual-porosity gas reservoir. More than that, an innovative fracture productivity equation that was missing for the dual-porosity system is derived as well. This study provided detailed derivations for the model and relationship used in past density-based dual-porosity rate-transient analysis. The dual-porosity productivity equation and the relationship between average matrix pseudopressure and average fracture pseudopressure are rigorously derived. The rescaling relationship between the dual-porosity liquid solution and the dual-porosity gas solution is also demonstrated in detail. An appropriate interporosity flow equation for gas is used. Based on that, the results show that the density-based approach is able to successfully capture the dual-porosity behavior of gas for constant bottomhole pressure condition.

Analyzing of Drill Stem Test (DST) Result for Dual Porosity Limestone Reservoir

The aim of this paper is to discuss and evaluate the result of DST which was conducted in a limestone reservoir of an oil field at the depth interval 3764.29-3903.0 meter in well-1 to evaluate the dynamic characteristics of the reservoirs, for instance: skin effect, permeability, wellbore storage, reservoir boundary and average reservoir pressure. Reservoir Pressure profiles has been recorded for both Buildup and draw down intervals. Semi-log and log-log coordinates have been used to plot the pressure signature date of both buildup period and its derivative to improve diagnostic and Horner plot. In addition, a dual porosity reservoir and infinite acting characteristic was discovered as a result of the well test data interpretation. Wellbore storage, skin factor and transient flow effects have been detected in the DST analysis on the dual porosity behavior due to phase re distribution. Using final buildup sections, the flow parameters of dual porosity reservoir were determined as the flow between fissure and matrix was (7.558 x 10-6) while, the storability ratio between fissure and matrix was calculated as 0.3 and permeability is 102 MD for both matrix and the fissure together. However, negative value of skin factor mostly appears in double porosity limestone reservoirs, positive skin factor of the reservoir has been observed in this study. It can be considered that the positive skin factor can be resulted in either the formation was partially penetrated and /or wells were not cleaned up properly.

Pressure-Transient Characteristics of Fractured Horizontal Wells in Unconventional Shale Reservoirs With Construction of Data-Constrained Discrete-Fracture Network

Summary Unconventional shale reservoirs require massive and multistage hydraulically fractured horizontal wells to produce economically. Induced hydraulic fractures interacting with in-situ natural fractures result in complex or discrete fracture networks (DFNs). Even though well-testing characteristics in fractured reservoirs with vertical wells have been investigated extensively, there is a lack of good understanding of well-testing response for hydraulically fractured horizontal wells in complex fracture networks. First, three practical approaches are presented regarding how to generate complex fracture networks in the context of developing unconventional shale reservoirs with hydraulically fractured horizontal wells. Complex fracture networks can be generated (1) from stochastic algorithms that enter fracture density, length, and strike distributions, or (2) from the flowing-producing DFN (FP-DFN) area that is constrained by microseismic information, or (3) from digitization of realistic outcrop maps. Then, new unstructured fracture gridding and discretization techniques specially tailored for complex fracture networks are developed to handle nonuniform fracture aperture, extensive fracture clustering, and nonorthogonal fracture intersections. Finally, the numerical simulation of pressure buildup is performed in complex fracture networks that are generated from three proposed approaches with both synthetic and field examples. Flow regimes are identified and are discussed on the basis of pressure-derivative plots. Complex fracture networks show that the most representative characteristics are formation/fracture bilinear flow and formation linear-flow regimes. The appearance of the bilinear-flow regime during early period might not be clear because of the impact of the wellbore-storage effect as both the wellbore volume and the volume of the larger natural fractures in communication with the wellbore. In addition, the microseismic-based approach reduces the uncertainties of fracture characterization with percentiles of FP-DFN areas. The pressure-buildup response observed clearly indicates that the higher the percentiles of FP-DFN areas (or intense naturally fractured portion of the completion), the lower the pressure difference and derivative curves. Fracture mineralization affects pressure-buildup responses significantly. The decrease in nonuniform fracture apertures causes pressure-diagnostic plots to shift upward. The effect of boundary in the outcrop-based complex fracture network shows an early deviation from the formation linear-flow regime. No classic dual-porosity behavior is observed in all cases to quantify related parameters. Three practical techniques are proposed to generate complex fracture networks. Pressure-transient characteristics are identified and summarized. Further research areas are discussed and highlighted. The combination of techniques such as microseismic, horizontal core, production logging or some method to characterize the fracture network can be used to close the loop between the inferred network and the response that it should exhibit during pressure-transient analysis.

Unconventional multi-fractured analytical solution using dual porosity model

Five-region linear flow system proved to be a useful model to reproduce the flow behavior for multi-fractured horizontal wells in shale reservoirs. In earlier developments, the model was assumed single-porosity throughout all five regions. However, assumption of single porosity system for stimulated region may promote errors in pressure transient analysis. So by adopting the existing mathematical models for naturally fractured reservoirs (dual-porosity system), one can apply the dual-porosity nature of flow in the stimulated reservoir volume (SRV). In this study the analytical solution for single-porosity model is reproduced and compared with numerical solution. Then the five-region model of previous studies is modified by implementing the dual porosity behavior in Laplace domain and compared to single-porosity solution using the same reservoir properties. Furthermore, a series of type-curves is constructed in this study using dimensionless properties, such as matrix-fracture capacity ratio and storativity ratio, hydraulic fracture conductivity, and hydraulic fracture half-length. Theses curves could provide valuable information to characterize the multi-fractured complex systems.

Technical Note: The use of an interrupted-flow centrifugation method to characterise preferential flow in low permeability media

Abstract. We present an interrupted-flow centrifugation technique to characterise preferential flow in low permeability media. The method entails a minimum of three phases: centrifuge-induced flow, no flow and centrifuge-induced flow, which may be repeated several times in order to most effectively characterise multi-rate mass transfer behaviour. In addition, the method enables accurate simulation of relevant in situ total stress conditions during flow by selecting an appropriate centrifugal force. We demonstrate the utility of the technique for characterising the hydraulic properties of smectite-clay-dominated core samples. All core samples exhibited a non-Fickian tracer breakthrough (early tracer arrival), combined with a decrease in tracer concentration immediately after each period of interrupted flow. This is indicative of dual (or multi-)porosity behaviour, with solute migration predominately via advection during induced flow, and via molecular diffusion (between the preferential flow network(s) and the low hydraulic conductivity domain) during interrupted flow. Tracer breakthrough curves were simulated using a bespoke dual porosity model with excellent agreement between the data and model output (Nash–Sutcliffe model efficiency coefficient was > 0.97 for all samples). In combination, interrupted-flow centrifuge experiments and dual porosity transport modelling are shown to be a powerful method to characterise preferential flow in low permeability media.

Simulation of Reactive Diffusion in Clays By a Continuous-Time Markovian Particle-Tracking Scheme

Clay minerals and clay rocks are considered as efficient components of engineered and natural barriers in many high-level radioactive waste disposal programs worldwide because of their low permeabilities and high sorption capabilities. In this paper we present an approach for modeling solute diffusive transport in saturated clay minerals at the structure map scale based on an extension of the Kolmogorov–Dmitriev theory of stochastic branching processes. The proposed modeling framework allows a simple description of (i) the dual-porosity behavior typical of some compacted clay structures, where diffusion occurs both in the interlayers and in the pore space between clay particles, and (ii) the chemical interactions between the dissolved ions and the solid matrix surfaces (both at nonequilibrium and equilibrium conditions). Furthermore, the Markovian nature of the modeling approach lends itself to a continuous-time particle-tracking scheme of resolution of the model equations, which, in general, easily allows us to deal with the complex geometrical structures of the porous media. Finally, in order to account for the uncertainty in the geometrical properties of the clay samples within the proposed modeling framework, the structure map is represented as a stochastic network of interconnected, one-dimensional interlayers with different lengths and orientations. The combined methods are demonstrated on a two-dimensional literature case study of diffusion through a compacted clay sample, and the resulting average diffusion coefficients are in general agreement with those obtained by a different simulation-based technique found in the literature. Then, the methods are applied to model the diffusion of the weakly sorbing cation Na+, providing results in accordance with physical intuition.

Extending Well-Productivity Life in a High-Pressure/ High-Temperature Tight Gas/Condensate Carbonate Reservoir by Acid Refracturing

This article, written by Senior Technology Editor Dennis Denney, contains highlights of paper SPE 142444, ’Extending Well- Productivity Life by Acid Refracturing in a High-Pressure/High-Temperature Tight Gas/Condensate Carbonate Reservoir in a Jurassic Formation of Northern Kuwait,’ by Mir Kabir, SPE, Qasem Dashti, SPE, J.R. Singh, SPE, and San Prasad Pradhan, SPE, KOC, and Ikhsan Nugraha, SPE, Liu Hai, and Hamed Al-Ghadhban, Schlumberger, prepared for the 2011 SPE Middle East Unconventional Gas Conference and Exhibition, Muscat, Oman, 31 January- 2 February. The paper has not been peer reviewed. Productivity of the subject well, which had been on production for 3 years after an initial acid-fracture treatment with almost 90% of its cumulative production occurring during the last year, was declining faster than expected. Review of the well’s performance indicated two possible causes: reservoir-pressure decline and reduced fracture-length/conductivity ratio. Acid refracturing was chosen to restore the well’s productivity by extending the fracture half-length to enhance fracture conductivity. The results showed that the productivity index (PI) increased by a factor of 2.5 during the post-treatment production test. However, after 3 months of production, this declined to 1.2. Introduction Several major fields in north-ern Kuwait, including Sabriyah, Raudathain, Umm Niqqa, Bahra, and Dhabi, produce gas from the Jurassic Middle Marrat formation, an important carbonate reservoir. Typical depth is 14,000 ft, reservoir pressure ranges from 10,000 to 12,000 psi, and the bottomhole static temperature averages 275°F. The Middle Marrat formation is mostly limestone (calcite>90%) with minor dolomitization. Only traces of clay and silt are found. High heterogeneity, both laterally and vertically, has been reported. Core permeability matches log permeability, and the high permeability value obtained from the core could be the result of induced fractures. Pressure-transient analyses of some wells showed dual-porosity behavior with low matrix permeability. Generally, the absolute matrix permeability is less than 1 md. The production mechanism is a combination of matrix and natural-fracture permeability. Acid Refracturing In regions where acid fracturing is common, there are questions that arise. When is the best time to refracture? What is the justification to repeat the treatment? If there is justification, what needs to be done differently in the subsequent treatment? The decision usually relies on the post-treatment production behavior compared with the pretreatment condition.

Gas-phase diffusivity and tortuosity of structured soils

Modeling gas-phase diffusion of volatile contaminants in the unsaturated zone relies on soil-gas diffusivity models often developed for repacked and structureless soil columns. These suffer from the flaw of not reflecting preferential diffusion through voids and fractures in the soil, thus possibly causing an underestimation of vapor migration towards building foundations and vapor intrusion to indoor environments. We measured the ratio of the gas diffusion coefficient in soil and in free air ( D p / D 0) for 42 variously structured, intact, and unsaturated soil cores taken from 6 Danish sites. Whilst the results from structureless fine sand were adequately described using previously proposed models, results that were obtained from glacial clay till and limestone exhibited a dual-porosity behavior. Instead, these data were successfully described using a dual-porosity model for gas-phase diffusivity, considering a presence of drained fractures surrounded by a lower diffusivity matrix. Based on individual model fits, the tortuosity of fractures in till and limestone was found to be highest in samples with a total porosity < 40%, suggesting soil compaction to affect the geometry of the fractures. In summary, this study highlights a potential order of magnitude underestimation associated in the use of classical models for prediction of subsurface gas-phase diffusion coefficients in heterogeneous and fractured soils.

An Integrated Geologic and Engineering Assessment of Fracture-Flow Potential in the Ratawi Reservoir of the Wafra Field, Partitioned Neutral Zone

SummaryThe extent to which fractures affect fluid pathways is a vital component of understanding and modeling fluid flow in any reservoir. We examined the Wafra Ratawi grainstone for which production extending for 50 years, including recent horizontal drilling, has provided some clues about fractures, but their exact locations, intensity, and overall effect have been elusive. In this study, we find that a limited number of total fractures affect production characteristics of the Ratawi reservoir. Although fractures occur throughout the Wafra field, fracture-influenced reservoir behavior is confined to the periphery of the field where the matrix permeability is low. This work suggests that for the largest part of the field, explicit fractures are not necessary in the next-generation Earth and flow-simulation models.The geologic fracture assessment included seismic fault mapping and fracture interpretation of image logs and cores. Fracture trends are in the northeast and southwest quadrants, and fractures are mineralized toward the south and west of the field. Pressure-falloff tests on some peripheral injectors indicate partial barriers, and most of these wells lie on seismic-scale faults in the reservoir, suggesting partial sealing. A few wells show fractured-reservoir production characteristics, and rate-transient analysis on a few producers indicates localized dual-porosity behavior. Producers proximal to dual-porosity wells display single-porosity behavior, however, to attest to the notion of localized fracture response. The spatially restricted fracture-flow characteristics appear to correlate with fracture or vug zones in a low-permeability reservoir.Presence of fracture-flow behavior was tested by constructing the so-called flow-capacity index (FCI), the ratio of khwell (well test-derived value) to khmatrix (core-derived property). Data from 80 wells showed khmatrix to be consistently higher than khwell, a relationship that suggests insignificant fracture production in these wells.

Flow behavior in a dual fracture network

A model that incorporates a pseudo-random process controlled by mechanical rules of fracturing is used to generate 3D orthogonal joint networks in tabular stratified aquifers. The results presented here assume that two sets of fractures, each with different conductivities, coexist. This is the case in many aquifers or petroleum reservoirs that contain sets of fractures with distinct hydraulic properties related to each direction of fracturing. Constant rate pump-tests from partially penetrating wells are simulated in synthetic networks. The transient head response is analyzed using the type curve approach and plots, as a function of time, of pressure propagation in the synthetic network are shown. The hydrodynamic response can result in a pressure transient that is similar to a dual-porosity behavior, even though such an assumption was not made a priori. We show in this paper that this dual porosity like flow behavior is, in fact, related to the major role of the network connectivity, especially around the well, and to the aperture contrast between the different families of fractures that especially affects the earlier hydrodynamic response. Flow characteristics that may be interpreted as a dual porosity flow behavior are thus related to a lateral heterogeneity (large fracture or small fault). Accordingly, when a dual porosity model matches well test data, the resulting reservoir parameters can be erroneous because of the model assumptions basis that are not necessarily verified. Finally, it is shown both on simulated data and well test data that such confusion in the interpretation of the flow behavior can easily occur. Well test data from a single well must therefore be used cautiously to assess the flow properties of fractured reservoirs with lateral heterogeneities such as large fractures or small faults.

Transient Dual-Porosity Behavior for Horizontal Wells

This article is a synopsis of paper SPE 71580, "Transient Dual-Porosity Behavior for Horizontal Wells: Case Histories," by F.M. Verga, SPE, Politecnico di Torino, and E. Beretta, ENI-Agip Div., originally presented at the 2001 SPE Annual Technical Conference and Exhibition, New Orleans, Louisiana, 30 September-3 October.

Converging flow tracer tests in fissured limestone

As part of an investigation into the dual porosity behaviour of fractured limestone aquifers, a sequence of converging flow tracer tests was devised and conducted at an extensively investigated experimental site in a major aquifer in the UK. The tests were designed specifically to produce detailed, high-resolution information about the tails of the breakthrough curves typically observed in this kind of aquifer and test. A set of mutually compatible, low detection limit tracers was identified through laboratory investigations. Two tests were carried out over distances of 20 m and 40 m along each of the two radii towards an abstraction borehole where tracer concentration was monitored. Simple dual porosity models were calibrated using the data from one test on each radius. Blind validations of these models were undertaken by attempting to predict the outcome of the second test on each radius, producing one success and one significant failure.

Poromechanical response of fractured-porous rock masses

An analytical model based on a poromechanical formulation for dual-porosity media is presented. In comparison with traditional conceptualizations such as by Barenblatt et al. (1960), the proposed model contains both additional terms in the governing flow equations to provide a physically more realistic description of the change in storage, and a natural accommodation of body displacements. Solution is developed for radial flow in a reservoir subject to the conditions of both constant bottom hole pressure and constant flow rate using Hankel transforms. The poromechanical effect, resulting from the coupling between fluid flow and solid deformation, is significant in the well vicinity where the modifications of initial pressure and stress state are substantial. Different from the conventional approach in which the impact of fluid properties is generally emphasized, the presented case studies highlight the critical influence of mechanical properties of the fractured rock mass on the change of fluid pressure in a producing reservoir. The study indicates that dual-porosity behavior is most obvious only when the poromechanical properties fall within a certain range.

Dual-porosity behaviour of naturally fractured reservoirs : M. Bai, Q. Ma & J.-C. Roegiers, International Journal for Numerical & Analytical Methods in Geomechanics, 18(6), 1994, pp 359–376

Dual-porosity behaviour of naturally fractured reservoirs : M. Bai, Q. Ma & J.-C. Roegiers, International Journal for Numerical & Analytical Methods in Geomechanics, 18(6), 1994, pp 359–376

Extension of Acid Fracture Penetration by Drastic Fluid-Loss Control

Summary Creation of an optimum etched fracture length in an acid fracture treatment is often a problem because of high acid leakoff through the wormholes. This paper presents a unique acid system, compatible with most carbonate formations, that controls fluid loss in the wormholes. Production and treatment pressure data validating successful fluid-loss control and improved fracture extension also are presented. Introduction Acid fracturing is a well-stimulation process commonly used in carbonate reservoirs. HCI is usually injected into the formation above the fracture pressure to create a fracture or to open existing natural fractures. Unlike proppants, acid etches the fracture faces unevenly, creating on closure a highly conductive channel for the reservoir fluid to flow into the wellbore. The key to the success of hydraulic fracturing is the achievement of fracture penetration, conductivity, or both, depending on the formation permeability. In general, in lower formation permeabilities, penetration is more important than fracture conductivity for optimum production. From experience and mathematical simulations, it is believed that. for similar fluid and petrophysical properties, adequate fracture penetration is more difficult to achieve in acid fracturing than in propped fracturing. This paper presents state-of-the-art technology available to mitigate acid penetration problems and discusses the importance of acid penetration in carbonate formations. Carbonate Formations Carbonate formations normally show secondary porosity and permeability because of the presence of natural fissures. The limestone matrix generally is very tight, with high storativity but very low transmissivity or permeability. Exceptions include dolomites or oolitic limestones where primary or intergranular porosity and permeability often are present. Low-permeability carbonate formations are natural candidates for hydraulic fracturing. These formations have very tight matrices and are naturally fissured. In pressure-transient tests, these reservoirs often exhibit dual-porosity behavior. Such transient behavior presumes that the matrix stores most of the fluid and slowly transmits it to the fracture network, while the fracture network produces the fluids into the wellbore. These natural fractures or fissures often are damaged by scaling or calcification, especially in the presence of flowing water at high temperature. The scaling process intensifies at the natural fracture nodes with large pressure losses, such as at the wellbore or where hairline fractures intersect with major fracture arteries. The resulting blockage of major fracture arteries drastically impedes flow into the wellbore. Matrix acid treatments (i.e., treatments that do not induce fractures) clean up such blockages at or near the wellbore. However, depending on the spatial density of the fracture or fissure network, the wellbore of very restricted dimensions may or may not intersect an adequate number of these fractures or fissures. Consequently, matrix treatments may fail to clean up an adequate number of fissures with sufficient penetration to stimulate the formation effectively. Thus, matrix acidizing in naturally fissured carbonate formations often fails to provide sustained improvement in production.