^{1, 2}

^{1, 2}

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^{1, 2}

^{3}

^{4}

^{1}

^{2}

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Utilizing deep rock salt cavern is not only a widely recognized energy reserve method but also a key development direction for implementing the energy strategic reserve plan. And rock salt cavern adopts solution mining techniques to realize building cavity. In view of this, the paper, based on the dissolving properties of rock salt, being simplified and hypothesized the dynamic dissolving process of rock salt, combined conditions between dissolution effect and seepage effect in establishing dynamic dissolving models of rock salt under different flow quantities. Devices were also designed to test the dynamic dissolving process for rock salt samples under different flow quantities and then utilized the finite-difference method to find the numerical solution of the dynamic dissolving model. The artificial intelligence algorithm, Particle Swarm Optimization algorithm (PSO), was finally introduced to conduct inverse analysis of parameters on the established model, whose calculation results coincide with the experimental data.

Reda and Russo [

Past research has yielded significant results for shape control of rock salt cavities and stability analysis. Dynamic dissolving properties of rock salt, however, require further in-depth analysis and research [

Natural rock salt from the Himalayan Mountains in Pakistan was utilized as the experimental specimen. The rock salt is located at a depth of 2000 to 3000 meters and exhibits coloring of white mixed with light red or glass white. Specimens are manufacturer-processed into test specimens of 50 × 100 mm for experimental purposes. Components of the specimens are comprised of 99.8% soluble substance with average density of 2959 kg/m^{3} as listed in Table

Components of rock salt specimens (%).

Soluble substance | Insoluble substance | |
---|---|---|

NaCl | K_{2}SO_{3} |
Small amount of muddy |

99.4 | 0.4 | 0.2 |

A water-passage pinhole with 6 mm diameter is drilled at the center of the sample’s axial position and processing conducted strictly in line with the experimental regulations. The processed sample size accuracy must be kept within the deviations. Figure

Rock salt samples.

Rock salt dynamic dissolving experimental devices (Figure

Device for dynamic dissolving test for rock salt.

Flexible pipe and joint

Joint

Connect device with (a) and (b)

Fluid flowmeter

Faucet

Connect faucet with the device (c)

Iron pedestal and beaker chain clip

Dynamic dissolving experimental set-up

Test procedures are as follows.

Weigh the bored test sample utilizing the electronic balance and measure length and diameter by vernier calipers.

Seal the test sample utilizing the waterproof coating material “703 glue” and then weigh the sealed samples.

Adjust flow quantity with the water faucet switch to allow the flowmeter to display 20 L/h.

Attach the beaker chain clip to the waterproofed test sample, insert the water passage pipe into the test sample and begin timing.

Remote the water-passage pipe until three minutes run out and place the pipe into another large beaker for continuation of flow quantity. Then detach the test sample and dry the sample with facial tissue and the air blower and weigh with the electronic balance.

Adjust the flowmeter to display the flow quantity numbers of 30 L/h, 40 L/h, and 50 L/h. Repeat experiment procedures in

The rock salt dynamic dissolving curve is not a smooth curve but rather a slightly fluctuating curve as demonstrated in Figures

The curve of test specimen’s mass under different flow quantity.

The curve of test specimen’s dissolving mass every 3 minutes under different flow quantity.

Dissolving rate of rock salt accelerates with a larger value of flow quantity

Data of rock salt specimens.

Serial number of the test sample | Diameter/mm | Length/mm | Mass of the test sample/g | Mass of the sample that has been sealed with waterproof coating materials/g | Density/g·cm^{−3} |
---|---|---|---|---|---|

A1 | 49.32 | 100.78 | 394.25 | 434.01 | 2.0797 |

A2 | 51.84 | 101.08 | 432.54 | 464.3 | 2.0284 |

A3 | 50.92 | 101.96 | 441.22 | 480.62 | 2.156 |

A4 | 52.56 | 101.38 | 446.39 | 482.25 | 2.0572 |

Results of dynamic dissolving test for rock salt (g).

Time/min | Flow quantity | |||
---|---|---|---|---|

20 L/h | 30 L/h | 40 L/h | 50 L/h | |

A1 | A2 | A3 | A4 | |

0 | 434.01 | 464.3 | 480.62 | 482.25 |

3 | 429.79 | 458.07 | 472.94 | 472.61 |

6 | 424.81 | 448.93 | 460.94 | 458.62 |

9 | 419.08 | 437.85 | 449.2 | 443.57 |

12 | 412.41 | 423.76 | 434.81 | 421.86 |

15 | 405.26 | 412.15 | 418.64 | 402.34 |

18 | 396.49 | 400.18 | 401.54 | 377.38 |

21 | 386.28 | 387.63 | 382.57 | 351.8 |

24 | 376.87 | 374.89 | 363.75 | |

27 | 364.95 | 359.72 | ||

30 | 354.28 | 348.66 | ||

33 | 340.33 | 336.11 | ||

36 | 325.35 | |||

39 | 311.13 |

Ideal conditions are assumed for rock salt samples as follows.

The diffusion effect can be described according to the First Diffusion Laws of Fick: the diffusion coefficient is directly proportional to the gradient of concentration, described as follows (^{−2}·s^{−1}), ^{−1}), ^{2}·s^{−1}), and, under normal circumstances, the diffusive coefficient is relevant to the solvent and temperature of solute.

Micro units ^{3}·s^{−1}), ^{−1}),

Sketch for dynamic dissolution of rock salt.

Combining (

The concentration-distribution curve of the rock salt boundary layer, according to research by Jessen [

Derivatives of (^{−1}) and ^{−1}).

Substituting (

The dissolving process of rock salt is also influenced by the fluid’s flow rate

Disregarding changes in the fluid volume inside the pinhole caused by rock salt dissolution, it is discovered, according to the mass balance principle, that the difference between

Presuming the flow loss is not considered, then^{3}·s^{−1}).

Combining (

Partial differential equations are composed of (^{−1}).

Among the rock salt dynamic dissolving models, the partial differential equations (

A difference grid is established as Figure

Sketch for difference grids.

The difference scheme that is built from (

Assuming that

Owing to known initial conditions,

As known from the recursion equation (

Parameters of the experiment are as follows: ^{3}, and ^{3}.

The diffusion coefficient

Particle swarm optimization (PSO), a type of artificial-intelligence algorithm, is introduced in this research to conduce parameters inversion of the rock salt dynamic dissolving model.

Particle swarm optimization is a new Evolutionary Algorithm (EA) developed in recent years. PSO is similar to the Simulated Annealing Algorithm as both originate from random solutions and seek to find optimal solutions through recursion. PSO also evaluates the quality of solutions through fitness value, but is simpler than the Genetic Algorithm rules as it does not have operations such as “Crossover” and “Mutation.” PSO simply searches for the global optimum through the found optimal value and is even known for its simplicity, high precision, and quick convergence while demonstrating advantages in the solving of practical problems.

The inverse programs will be realized in the MATLAB software and include three parts (Figure

Flow chart for program realization.

The second part, according to the M file, solves the dissolving radius through applying the finite-difference method programmed on the basis described in Section

The third part, referred to as “main.m” is the main program written based on the particle swarm optimization. The program’s major steps include

retrieve the cc.Mat file; obtain the random displacement matrix and velocity matrix; implement the Numerical.m file to calculate the dissolving radius

compare the value of each particle’s fitness; retrieve the global optimal solution (or the minimum); and record value and position of the global optimum;

update the velocity matrix and position matrix according to the particle swarm optimization; save the renewed data and create overlay for the part one file cc.Mat;

implement the Numerical.m file again after the renewed particle velocity and position matrix and calculate the dissolving radius

compare the fitness value of each particle after renewed. If the upgraded fitness value is smaller, save and record the corresponding value and position. If the value is larger, do not save;

compare the fitness value of each particle after renewed with the global optimum. If the fitness value of the particle with renewed information is smaller, then save and record the value and position. If the value is larger, do not save;

repeat steps

Ren et al. [

Fitness function can be established as follows:

Parameters of rock salt dynamic dissolving models parameters are inversed under different flow conditions according to the particle swarm optimization in this research effort (see Figures

Particle swarm optimization algorithm inversion results.

Flow quantity |
Parameter |
Fitness value |
Relevance coefficient |
---|---|---|---|

20 | 0.001554 | 0.005234 | 0.9999 |

30 | 0.002043 | 0.05365 | 0.9923 |

40 | 0.002567 | 0.02488 | 0.9986 |

50 | 0.003059 | 0.02211 | 0.9991 |

Comparison of the dissolved radius between test data and calculated results under 20 L/h.

Comparison of the dissolved radius between test data and calculated results under 30 L/h.

Comparison of the dissolved radius between test data and calculated results under 40 L/h.

Comparison of the dissolved radius between test data and calculated results under 50 L/h.

An in-depth and systematic research effort was conducted on the properties of the rock salt dynamic dissolving model and tests under difference flow conditions drawing the following conclusions.

Experimental research on the rock salt dynamic dissolving processes under different flow conditions was conducted by adopting a self-designed rock salt dynamic dissolving experimental set-up. Dynamic dissolving test data of the rock salt was obtained under various flow conditions with varying dissolution time. The dynamic dissolving curve for rock salt was discovered as a fluctuating curve and the dissolving rate of rock salt increased with the increasing of flow quantity

According to the dissolving properties of rock salt, the study reasonably simplifies and hypothesizes the rock salt dynamic dissolving process. The study accounts for combined conditions involving the dissolution effect and seepage effect changes of rock salt to establish the rock salt dynamic dissolving model.

The study introduces the particle swarm optimization (PSO) to inverse parameters on the model established by applying the finite-difference method to calculate the numerical solution for the rock salt dynamic dissolving model. Calculation results were found to relatively coincide with the experimental data, indicating the rock salt dynamic dissolving model established is capable of effectively describing the dynamic dissolving process and dissolving mechanisms for rock salt.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This study is supported by the Fundamental Research Funds for Central Universities of China (Project no. CDJXS12200005), the National Natural Science Foundation of China (Project no. 41202195), and National Key Basic Research Program of China (Project no. 2009CB724606); the authors gratefully acknowledge these supports.