Xiao-Gang Li

Numerical model and investigation of simultaneous multiple-fracture propagation within a stage in horizontal well

Abstract Multistage hydraulic fracturing in combination with horizontal drilling has been widely used in tight reservoirs. This technology can enlarge the drainage area of per well while reduce the operational costs. However, production data and fracturing field experiments both indicated that multiple fracture in horizontal well are nonuniform growth, and even some fractures are invalid. Therefore, we simultaneously consider the stress shadowing effect, flow resistance from wellbore friction, perforation friction and fracture friction to establish a simultaneous multiple-fracture propagation numerical model. In our model, the flow rate distributing into different fractures is determined based on Kirchhoff’s second law, and the multiple-fracture expansion velocity is calculated according to their energy release rate. Based on our numerical model, we investigate the influence factors of multiple-fracture even propagation within a stage. The single-fracture propagation results obtained from our numerical model and simplified semi-analytical solution have a good agreement, besides our four cluster fracturing numerical results are consistent with Wheaton et al. (Unconventional resources technology conference, Denver, Colorado, 2014) field experiment results; these two comparisons prove that our model is effective. Numerical results indicate that one or two clusters are more likely to achieve uniform expansion of multiple fractures than three or more clusters. In order to promote multiple-fracture uniform propagation, not only can we adjust the cluster number or cluster spacing, but also we can regulate the perforation friction.

A new model for gas–water two-immiscible-phase transport in fractal-like porous media

A new model for gas–water two-immiscible-phase transport in a fractal-like porous medium is developed based on the assumptions that the porous medium consists of a bundle of non-interconnected tortuous capillaries and that the size distribution of the capillaries follows a power law relationship when both the capillary pressure and the compressibility of gas are considered. The model is a function of the structural parameters of the porous medium and the parameters of the fluid properties. The new model does not contain empirical constants, and every parameter has a clear physical meaning. The relative permeability predicted by the proposed model is compared with experimental data, and the comparison results are in rational agreement. Finally, the parameters influencing the relative permeability are explored.

A new model for gas transport in fractal-like tight porous media

A new gas transport model for fractal-like tight porous media is proposed by simultaneously considering the microstructural complexity of real porous media, the compressibility of gas, and the gas slippage effect. This model clarifies the gas transport mechanisms in porous media: the total gas flow volume is governed by the weighted addition of viscous flow and slippage flow, and the distribution weighting factor depends on the capillary diameter and the mean free path of the gas. Based on the proposed model, a new permeability model was derived for gas transport in fractal-like tight porous media. The new permeability model does not have any empirical constants, and every parameter in the model has clear physical meaning. The predictions from the model were then compared with experimental data to show that the model is valid. Furthermore, the parameters influencing gas permeability were analyzed.

A coupling algorithm for simulating multiple hydraulic fracture propagation based on extended finite element method

Combining fluid mechanics, fracture mechanics, and extended finite element method, a coupling algorithm for simulating multiple hydraulic fracture propagation is established in this research. In comparison with the current existing XFEM models for hydraulic fracturing, this approach neither needs to introduce leak-off coefficient to describe the fluid leak-off phenomenon, nor requires to predetermine fracture propagation orientation. The single-fracture propagation results obtained from our numerical model and semi-analytical (KGD) solution show similar trends. Based on our numerical model, the effect of cluster space on multiple hydraulic fractures propagate in the horizontal well is discussed. Simulation shows that the stress interference among the fractures decreases with the increase in cluster space, and the average width of fractures increases with an increase in cluster space, the fracture width at the fracture inflection point may have a local minima value, which can lead to proppant screen out; therefore, in fracturing design, designer should use the quartz sand with smaller particle size as the slug to grind fracture. Since bottom and top fracture are interfered by the middle fracture, they are both away from the middle fracture, while middle fracture extends in straight line due to the symmetry of stress interference. At the beginning, the pressure at the fracture entrance increases with increase in injection time, and then the pressure decreases rapidly as the injection time increases.

Wellbore temperature and pressure calculation model for coiled tubing drilling with supercritical carbon dioxide

ABSTRACT To better control the state of carbon dioxide during supercritical carbon dioxide drilling, a mathematical model is established to analyze the wellbore carbon dioxide temperature and pressure influencing factors. In this model, the influences of formation temperature change and fluid-friction-generated heat on wellbore temperature distribution are considered. Additionally, the impact of casing, tubing, and cement sheath thermal resistance on heat transfer are considered. The model is validated by comparing the wellbore temperature data calculated from this model with data from previous models. Based on the model, the factors that may affect the wellbore carbon dioxide temperature and pressure are analyzed. The results show that the downhole temperature decreases with the decrease in nozzle diameter and geothermal gradient, and with the increase in injection rate. The injection temperature significantly affects the wellbore temperature near the wellhead, but it does not affect the downhole temperature. Therefore, for low geothermal gradient formation, reducing the injection rate and increasing the nozzle diameter are two effective methods to maintain the CO2 at the downhole in the supercritical state. The pressure inside the coiled tubing increases with the increase in injection rate and decrease in nozzle diameter, but the injection temperature and geothermal gradient has little effect on the pressure inside both the coiled tubing and annulus.

Wellbore temperature and pressure calculation model for supercritical carbon dioxide jet fracturing

ABSTRACT A new numerical calculation model for wellbore temperature and pressure for SC-CO2 jet fracturing was proposed in this research. In our model, the impact of tubing, casing, and cement on heat transfer, and the heat generated by fluid friction losses are all taken into consideration. The CO2 physical properties are calculated by the Span–Wagner and Vesovic models. Based on our calculation model, the factors that may affect the wellbore temperature and pressure are discussed. The results indicated that ignoring the influence of the cement sheath thermal resistance on heat transfer would lead to a wellbore temperature higher than the actual value. The wellbore CO2 pressure is always higher than its critical value, but the CO2 temperature at the jet point in some cases is lower than its critical value. The wellbore CO2 temperature is increased with the increase in injection temperature and cement sheath thermal conductivity and the decrease in annulus injection rate and coiled tubing injection rate. However, the decrease in the coiled tubing injection rate and increase in the cement sheath thermal conductivity are the only effective ways to ensure that the CO2 temperature at the jet point exceeds its critical value.