Effects of different numerical algorithms on simulation of chemical dissolution-front instability in fluid-saturated porous rocks

Many scientific and engineering problems need to use numerical methods and algorithms to obtain computational simulation results because analytical solutions are seldom available for them.The chemical dissolution-front instability problem in fluid-saturated porous rocks is no exception.Since this kind of instability problem has both the conventional(i.e.trivial)and the unconventional(i.e.nontrivial)solutions,it is necessary to examine the effects of different numerical algorithms,which are used to solve chemical dissolution-front instability problems in fluid-saturated porous rocks.Toward this goal,two different numerical algorithms associated with the commonly-used finite element method are considered in this paper.In the first numerical algorithm,the porosity,pore-fluid pressure and acid/solute concentration are selected as basic variables,while in the second numerical algorithm,the porosity,velocity of pore-fluid flow and acid/solute concentration are selected as basic variables.The particular attention is paid to the effects of these two numerical algorithms on the computational simulation results of unstable chemical dissolution-front propagation in fluid-saturated porous rocks.The related computational simulation results have demonstrated that:1)the first numerical algorithm associated with the porosity-pressure-concentration approach can realistically simulate the evolution processes of unstable chemical dissolution-front propagation in chemical dissolution systems.2)The second numerical algorithm associated with the porosity-velocity-concentration approach fails to simulate the evolution processes of unstable chemical dissolution-front propagation.3)The extra differential operation is the main source to result in the failure of the second numerical algorithm.

Finite element modeling of convective pore-fluid flow in fluid-saturated porous rocks within upper crust:An overview

Convective pore-fluid flow (CPFF) plays a critical role in generating mineral deposits and oil reservoirs within the deep Earth. Therefore, theoretical understanding and numerical modeling of the thermodynamic process that triggers and controls the CPFF are extremely important for the exploration of new mineral deposits and underground oil resources. From the viewpoint of science, the CPFF within the upper crust can be treated as a kind of thermodynamic instability problem of pore-fluid in fluid-saturated porous media. The key issue of dealing with this kind of problem is to assess whether a nonlinear thermodynamic system under consideration is supercritical. To overcome limitations of using theoretical analysis and experimental methods in dealing with the CPFF problems within the upper crust, finite element modeling has been broadly employed for solving this kind of problem over the past two decades. The main purpose of this paper is to overview recent developments and applications of finite element modeling associated with solving the CPFF problems in large length-scale geological systems of complicated geometries and complex material distributions. In particular, two kinds of commonly-used finite element modeling approaches, namely the steady-state and transient-state approaches, and their advantages/disadvantages are thoroughly presented and discussed.

Elastic wave propagation and scattering in prestressed porous rocks

Poro-acoustoelastic theory has made a great progress in both theoretical and experimental aspects,but with no publications on the joint research from theoretical analyses,experimental measurements,and numerical validations.Several key issues challenge the joint research with comparisons of experimental and numerical results,such as digital imaging of heterogeneous poroelastic properties,estimation of acoustoelastic constants,numerical dispersion at high frequencies and strong heterogeneities,elastic nonlinearity due to compliant pores,and contamination by boundary reflections.Conventional poroacoustoelastic theory,valid for the linear elastic deformation of rock grains and stiff pores,is modified by incorporating a dualporosity model to account for elastic nonlinearity due to compliant pores subject to high-magnitude loading stresses.A modified finite-element method is employed to simulate the subtle effect of microstructures on wave propagation in prestressed digital cores.We measure the heterogeneity of samples by extracting the autocorrelation length of digital cores for a rough estimation of scattering intensity.We conductexperimental measurements with a fluid-saturated sandstone sample under a constant confining pressure of 65 MPa and increasing pore pressures from 5 to 60 MPa.Numerical simulations for ultrasound propagation in the prestressed fluid-saturated digital core of the sample are followed based on the proposed poro-acoustoelastic model with compliant pores.The results demonstrate a general agreement between experimental and numerical waveforms for different stresses,validating the performance of the presented modeling scheme.The excellent agreement between experimental and numerical coda quality factors demonstrates the applicability for the numerical investigation of the stress-associated scattering attenuation in prestressed porous rocks.

Frost deformation and microstructure evolution of porous rock under uniform and unidirectional freeze-thaw conditions

The frost deterioration and deformation of porous rock are commonly investigated under uniform freeze-thaw(FT)conditions.However,the unidirectional FT condition,which is also prevalent in engineering practice,has received limited attention.Therefore,a comparative study on frost deformation and microstructure evolution of porous rock under both uniform and unidirectional FT conditions was performed.Firstly,frost deformation experiments of rock were conducted under cyclic uniform and unidirectional FT action,respectively.Results illustrate that frost deformation of saturated rock exhibits isotropic characteristics under uniform FT cycles,while it shows anisotropic characteristics under unidirectional FT condition with both the frost heaving strain and residual strain along FT direction much higher than those perpendicular to FT direction.Moreover,the peak value and residual value of cumulative frost strain vary as logarithmic functions with cycle number under both uniform and unidirectional FT conditions.Subsequently,the microstructure evolution of rock suffered cyclic uniform and unidirectional FT action were measured.Under uniform FT cycles,newly generated pores uniformly distribute in rock and pore structure of rock remains isotropic in micro scale,and thus the frost deformation shows isotropic characteristics in macro scale.Under unidirectional FT cycles,micro-cracks or pore belts generate with their orientation nearly perpendicular to the FT direction,and rock structure gradually becomes anisotropic in micro scale,resulting in the anisotropic characteristics of frost deformation in macro scale.

Effects of porosity on seismic velocities, elastic moduli and Poisson's ratios of solid materials and rocks

The generalized mixture rule(GMR) is used to provide a unified framework for describing Young’s(E),shear(G) and bulk(K) moduli, Lame parameter(l), and P- and S-wave velocities(Vpand Vs) as a function of porosity in various isotropic materials such as metals, ceramics and rocks. The characteristic J values of the GMR for E, G, K and l of each material are systematically different and display consistent correlations with the Poisson’s ratio of the nonporous material(v0). For the materials dominated by corner-shaped pores, the fixed point at which the effective Poisson’s ratio(n) remains constant is at v0=0.2, and J(G) > J(E) > J(K) > J(l) and J(G) < J(E) < J(K) < J(l) for materials with v0> 0.2 and v0< 0.2, respectively.J(Vs) > J(Vp) and J(Vs) < J(Vp) for the materials with v0> 0.2 and v0< 0.2, respectively. The effective n increases, decreases and remains unchanged with increasing porosity for the materials with v0< 0.2,v0> 0.2 and v0=0.2, respectively. For natural rocks containing thin-disk-shaped pores parallel to mineral cleavages, grain boundaries and foliation, however, the n fixed point decreases nonlinearly with decreasing pore aspect ratio(a: width/length). With increasing depth or pressure, cracks with smaller a values are progressively closed, making the n fixed point rise and finally reach to the point at v0=0.2.

Effects of porosity heterogeneity on chemical dissolution-front instability in fluid-saturated rocks

Homogeneity and heterogeneity are two totally different concepts in nature.At the particle length scale,rocks exhibit strong heterogeneity in their constituents and porosities.When the heterogeneity of porosity obeys the random uniform distribution,both the mean value and the variance of porosities in the heterogeneous porosity field can be used to reflect the overall heterogeneous characteristics of the porosity field.The main purpose of this work is to investigate the effects of porosity heterogeneity on chemical dissolution front instability in fluid-saturated rocks by the computational simulation method.The related computational simulation results have demonstrated that:1) since the propagation speed of a chemical dissolution front is inversely proportional to the difference between the final porosity and the mean value of porosities in the initial porosity field,an increase in the extent of the porosity heterogeneity can cause an increase in the mean value of porosities in the initial porosity field and an increase in the propagation speed of the chemical dissolution front.2) An increase in the variance of porosities in the initial porosity field can cause an increase in the instability probability of the chemical dissolution front in the fluid-saturated rock.3) The greater the mean value of porosities in the initial porosity field,the quicker the irregular morphology of the chemical dissolution front changes in the supercritical chemical dissolution systems.This means that the irregular morphology of a chemical dissolution front grows quicker in a porosity field of heterogeneity than it does in that of homogeneity when the chemical dissolution system is at a supercritical stage.

Chemical grout diffusion in porous rock based on response of geoelectric feld

Porous rock chemical grouting simulation test was conducted using established large scale physical model.Chemical grout diffusing rule in porous media with different permeability was studied by monitoring the spontaneous potential and exciting current response during grouting.The results show that chemical grout spread evenly in all directions and diffusion areas are approximately concentric circles in the cross section of homogeneous transverse isotropic pore medium,the grout spread flling range can be quantitatively decrypted by the diffusion radius.The average diffusion speed and radius increase approximately as the square root with the permeability coeffcient in different permeability media under the same conditions.Calculation results using Maag cylindrical diffusion equation show that the calculated value of diffusion radius is in good agreement with the test value under different grouting pressures and permeability conditions.

THEORETICAL MODEL OF EFFECTIVE STRESS COEFFICIENT FOR ROCK/SOIL-LIKE POROUS MATERIALS

Physical mechanisms and influencing factors on the effective stress coefficient for rock/soil-like porous materials are investigated, based on which equivalent connectivity index is proposed. The equivalent connectivity index, relying on the meso-scale structure of porous material and the property of liquid, denotes the connectivity of pores in Representative Element Area （REA）. If the conductivity of the porous material is anisotropic, the equivalent connectivity index is a second order tensor. Based on the basic theories of continuous mechanics and tensor analysis, relationship between area porosity and volumetric porosity of porous materials is deduced. Then a generalized expression, describing the relation between effective stress coefficient tensor and equivalent connectivity tensor of pores, is proposed, and the expression can be applied to isotropic media and also to anisotropic materials. Furthermore, evolution of porosity and equivalent connectivity index of the pore are studied in the strain space, and the method to determine the corresponding functions in expressions above is proposed using genetic algorithm and genetic programming. Two applications show that the results obtained by the method in this paper perfectly agree with the test data. This paper provides an important theoretical support to the coupled hydro-mechanical research.

Hysteresis in the ultrasonic parameters of saturated sandstone during freezing and thawing and correlations with unfrozen water content

Determining the mechanical properties of frozen rock is highly important in cold-area engineering.These properties are essentially correlated with the content of liquid water remaining in frozen rock.Therefore,accurate determination of unfrozen water content could allow rapid evaluation of mechanical properties of frozen rock.This paper investigates the hysteresis characteristics of ultrasonic waves applied to sandstone(in terms of the parameters of P-wave velocity,amplitude,dominant frequency and quality factor Q)and their relationships with unfrozen water content during the freeze-thaw process.Their correlations are analysed in terms of their potential for use as indicators of freezing state and unfrozen water content.The results show that:(1)During a freeze-thaw cycle,the ultrasonic parameters and unfrozen water content of sandstone have significant hysteresis with changes in temperature.(2)There are three clear stages of change during freezing:supercooled stage(0℃to-2℃),rapid freezing stage(-2℃to-3℃),and stable freezing stage(-3℃to-20℃).The changes in unfrozen water content and ultrasonic parameters with freezing temperature are inverse.(3)During a single freeze-thaw cycle,the ultrasonic parameters of sandstone are significantly correlated with its unfrozen water content,and this correlation is affected by the pore structure.For sandstones with mesopores greater than 50%,there are inflection points in the curves of ultrasonic parameters vs.unfrozen water content at-3℃during freezing and at-1℃during thawing.It was found that thermal deformation of the mineral-grain skeleton and variations in the phase composition of pore water change the propagation path of ultrasonic waves.The inflection point in the curve of dominant frequency vs.temperature clearly marks the end of the rapid freezing stage of pore water,in which more than 70%of the pore water freezes.Consequently,the dominant frequency can be used as an index to conveniently estimate the unfrozen water content of frozen rock and,hence,its mechanical properties.

The influence of pore characteristics on rock fragmentation mechanism by high-voltage electric pulse

High-voltage electric pulse(HVEP)is an innovative low-energy and high-efficiency technique.However,the underlying physics of the electrical breakdown within the rock,and the coupling mechanism between the various physical fields involved in HVEP still need to be further understood.In this study,we establish a 2D numerical model of multi-physical field coupling of the electrical breakdown of porous rock with randomly distributed pores to investigate the effect of pore characteristics(porosity,pore media composition)on the partial electrical breakdown of rock(i.e.the generation of a plasma channel inside the rock).Our findings indicate that the generation of a plasma channel is directionally selective and extends in the direction of a weak electrical breakdown intensity.As the porosity of the rock increases,so does the intensity of the electric field in the‘electrical damage’region—the greater the porosity,the greater the effectiveness of rock-breaking.As the fraction of pore fluid(S_(water)/S_(air))gradually declines,the generation time of the plasma channel decreases,and the efficacy of rock-breaking by HVEP increases.In addition,in this study,we conducted an indoor experiment utilizing an electric pulse drill to break down the rock in order to recreate the growth mode of the plasma channel in the rock.Moreover,the experimental results are consistent with the simulation results.In addition,the development of this type of partial electrical breakdown is confirmed to be related to electrode polarity and pore characteristics via the experiment of the symmetrical needle-needle electrode arrangement,which further demonstrates the mechanism of partial electrical breakdown.This research is significant for comprehending the process of electric impulse rock-breaking and gives theoretical guidance and technological support for advancing electric impulse drilling technology.

Experimental study on formation mechanism of compaction bands in weathered rocks with high porosity

Since Mollema and Antonellini observed compaction bands in the field in 1996,different patterns of compaction bands have been found in laboratory experiments.There are some discrepancies between the laboratory experiments and the field observations:compared to the field observation,the stress levels required to induce compaction bands in laboratory experiments are usually higher than the inferred in the field,and the grain crushing are more intense in the laboratory experiments.In this paper,compaction bands were observed at the maximal principal stresses below 8 MPa,which is lower than the stress level inferred in the field,and there was no severe comminution inside the compaction bands.Experimental results indicate that the porosity and confining pressure have great impacts on the types of localization bands.Lower porosity and confining pressure can promote the growth of shear bands and high-angle shear bands.Higher porosity and confining pressure can promote the growth of discrete compaction bands.Intermediate porosity and confining pressure are favorable for the growth of hybrid modes involving two of the three,i.e.,discrete compaction band,diffuse compaction band and high-angle shear band.The formation of discrete compaction bands is more unstable compared to diffuse compaction bands.The two types of compaction bands can appear in the same type rocks,and diffuse compaction bands are formed under lower confining pressure compared to discrete compaction bands.The reduction of permeability was within 2 orders of magnitude in this study,and it is 2 3 orders of magnitude lower than those obtained by other researchers.