Effect of Water Distribution on Spontaneous Imbibition of Tight Rocks: A Fractal Approach

The original water distribution characteristic plays an important role in the fracturing liquid retention in actual tight reservoirs. In this paper, an analytical model was proposed to characterize the water distribution and its effect on the spontaneous imbibition, based on the capillary tube model and fractal theory. Furthermore, the effect of the water film and the non-piston-like front related to the pore size are included in our model. The proposed model was successfully validated with the experimental results of core imbibition tests. Our work demonstrates that water distribution is influenced by displacement pressure and pore structure. For a small differential pressure, the porous media with richer large pores usually possesses a lower water saturation, and this difference will decrease with the increase of differential pressure. Moreover, compared with previous studies, the proposed imbibition model can not only distinguish the valid pores and invalid pores for imbibition but it can also predict the initial imbibition rate and equilibrium time of tight porous media with different water saturation. The results show that the equilibrium time is controlled by the minimum effective pore radius while the initial imbibition rate is mainly controlled by the large pores. Both of these two parameters will decrease with an increase of water saturation; the former is more sensitive to a low water saturation, while the latter decreases more quickly for a middle-high water saturation.

PREDICTED MODEL OF RELATIVE PERMEABILITY CONSIDERING WATER DISTRIBUTION CHARACTERISTICS IN TIGHT SANDSTONE GAS RESERVOIRS

A novel predictive model for calculating relative permeability was derived based on a capillary tube model with fractal theory. Different forms of immovable water including water film (WF) and microcapillary water were incorporated in the new model. Special immovable water called lost dynamic water (LDW) was introduced in the proposed model. The results of verification show that there is agreement between the calculated results and the published experimental data and analytical model. The results indicated that the effect of LDW, WF, and stress dependence had a significant influence on the relative permeability, which cannot be neglected. A larger LDW coefficient, more dead-end pores, and corners in porous media yielded a more complex pore structure. Therefore, more water was trapped in the pore and became connate water, resulting in higher gas relative permeability and lower water relative permeability at a given water saturation. Due to the microcapillary effect, the relative permeability of the water/gas increased/decreased as the drawdown pressure increased at the same water saturation. Higher effective stress was more likely to cause rock deformation, resulting in higher gas relative permeability and lower water relative permeability at a given water saturation. This study provides a significant reference for reservoir engineers conducting water and gas two-phase flow analysis. The theoretical model is beneficial for research into the interpolation of relative permeability via numerical simulation.

Fractal Analysis of Microscale and Nanoscale Pore Structures in Carbonates Using High-Pressure Mercury Intrusion

This paper investigated fractal characteristics of microscale and nanoscale pore structures in carbonates using High-Pressure Mercury Intrusion (HPMI). Firstly, four different fractal models, i.e., 2D capillary tube model, 3D capillary tube model, geometry model, and thermodynamic model, were used to calculate fractal dimensions of carbonate core samples from HPMI curves. Afterwards, the relationships between the calculated fractal dimensions and carbonate petrophysical properties were analysed. Finally, fractal permeability model was used to predict carbonate permeability and then compared with Winland permeability model. The research results demonstrate that the calculated fractal dimensions strongly depend on the fractal models used. Compared with the other three fractal models, 3D capillary tube model can effectively reflect the fractal characteristics of carbonate microscale and nanoscale pores. Fractal dimensions of microscale pores positively correlate with fractal dimensions of the entire carbonate pores, yet negatively correlate with fractal dimensions of nanoscale pores. Although nanoscale pores widely develop in carbonates, microscale pores have greater impact on the fractal characteristics of the entire pores. Fractal permeability model is applicable in predicting carbonate permeability, and compared with the Winland permeability model, its calculation errors are acceptable.

Using BIB-SEM Imaging for Permeability Prediction in Heterogeneous Shales

Organic-rich shale samples from a lacustrine sedimentary sequence of the Newark Basin (New Jersey, USA) are investigated by combining Broad Ion Beam polishing with Scanning Electron Microscopy (BIB-SEM). We model permeability from this 2D data and compare our results with measured petrophysical properties. Three samples with total organic carbon (TOC) contents ranging from 0.7% to 2.9% and permeabilities ranging from 4 to 160 nD are selected. Pore space is imaged at high resolution (at 20,000x magnification) and segmented from representative BIB-SEM maps. Modeled permeabilities, derived using the capillary tube model (CTM) on segmented pores, range from 2.3 nD to 310 nD and are relatively close to measured intrinsic permeabilities. SEM-visible porosities range from 0.1% to 1.8% increasing with TOC, in agreement with our measurements. The CTM predicts permeability correctly within one order of magnitude. The results of this work demonstrate the potential of 2D BIB-SEM for calculating transport properties of heterogeneous shales.

Adiabatic Capillary Tube Model for a Carbon Dioxide Transcritical Cycle

This paper presents a mathematical model for a capillary tube using CO 2 as fluid in steady flow transcritical cycle. The capillary tube is divided into N volumes controls and the model is based on applying the equations of conservation of energy, mass and momentum in the fluid in each of these volumes controls. The model calculates the mass flow of the CO 2 in the capillary tube as a function of CO 2 pressures at the inlet and outlet of the capillary and the temperature of CO 2 at the input of this device. The capillary tube is considered to be adiabatic, and the limit of operation due to blocked flow condition is also considered in the model. The validation of the model was performed with experimental data and the results showed that the model is capable of predicting the mass flow in the capillary tube with errors less than 10%. The model was also used to determine the minimum diameter of the capillary tube for various conditions of CO 2 transcritical cycle.

Model Investigation on Coupled Throttling Flow Characteristic of Stepped Capillary Tube with R22

In order to calculate the structure size of stepped capillary tube, the experiments of flow characteristic of it were performed. The experience benchmark model of flow characteristics of R22 was set up through experimental method in specific reference conditions based on the impedance calculation method. The variable working condition model suitable for a range of conditions was obtained through fixing the condition based on the reference model. The mass flow rate of refrigerant R22 in two stepped capillary tubes with different size was tested. The experimental results show that the stepped capillary tube model has a high precision and working condition of certain flexibility. The deviation of cooling and heating flow between the calculated values and measured values are less than±10%. The model can meet the need of matching for stepped capillary tube on the heat pump type air conditioner with R22.