Experimental And Mathematical Modelling Investigations Into Water Condensation In Nanopores Of Calcium Carbonate

Condensed water in the nanopores of rocks is extremely important to better understand many hydrogeological and engineering geological problems.Condensed water in arid areas is an important water resource to maintain local ecological balance,condensed water is one of the key factors to be considered for the protection of stone carvings,and condensed water in shale nanopores exerts an important effect on the gas accumulation and flow in the project of shale gas engineering.Previous investigations by many scholars have indicated the significance of condensed water,and numerous field observations on condensate water have been carried out.However,as the condensed water amount is extremely sensitive to environment and the influencing factors are numerous and complex,study on the condensed water amount and their influencing factors are still staying in the qualitative stage.Therefore,it is necessary to establish a mathematical model to quantitatively calculate the condensed water amount based on the formation mechanism of capillary condensate.After conducting laboratory experiments under controllable conditions to verify the theoretical results of condensation amount at equilibrium calculated by the mathematical model.this model can be used to systematically study investigate the influencing factors.In this study,calcium carbonate powders with different particle sizes were used to manufacture six columnar samples by controlling the strength of tamping,of which four samples had the same particle size and different porosity,and three samples had the same porosity and different particle size.The dried samples were placed in a constant temperature and humidity environment,and water vapor was condensed in the pores of the samples by both adsorption and capillarity.The samples were weighed periodically to determine the condensed water amount until the condensation process reached equilibrium.The packing models were established based on the pore structures of the experimental samples,and the mathematical relationship between the condensed amount per unit volume of rock and temperature,relative humidity,porosity,particle size and hydrophilicity of media was described when condensation reached equilibrium.In this relationship,the amount of water adsorbed on the particles surface was calculated based on the disjoining pressure theory,and the amount of water condensed between particles by capillary condensation was calculated based on Kelvin law and Young-Laplace equation.The total amount of condensed water of the sample was the sum of adsorbed water and capillary water.In this study,the variation of the condensate amount per unit volume of samples with time and the condensation amount at equilibrium of each sample were experimentally measured.Based on the experimental data,the relationship between the condensate rate as well as condensate amount of the sample and time was obtained through the nonlinear multivariate function fitting,and the effect of relative humidity,particle size and porosity on the condensation rate was quantitative analyzed.By comparing the theoretical and experimental condensate amount per unit volume of the samples,the mathematical model of the equilibrium concentration of the samples were verified.the relative error ranges from-6.43% to 20.05%.This indicates that model-predicted results agree well with the experimental data.The effect of relative humidity,particle size and porosity to the condensate amount were quantitatively analyzed.The effect of temperature and medium hydrophilicity to the condensate amount at equilibrium was predicted based on the mathematical model.The results show that relative humidity is the most important factor affecting the condensate amount at equilibrium,followed by rock pore structure,temperature and medium hydrophilicity.