RESUMEN
In this study, the pressure drop obtained from physical experiments and theoretical approaches of a single horizontal wellbore is reviewed and a comprehensive wellbore pressure-drop model is derived for a multibranch well. We propose a new coupling model for fluid flow in multibranch wells and reservoirs. Based on this coupling model, we introduce a theoretical approach for the calculation of the pressure drop in a multibranch horizontal well with variable mass transfer. To facilitate the understanding of the physical model, the entire coupling model was divided into three parts: (1) the pressure-drop model of the wellbore, (2) the reservoir inflow model, and (3) the coupling model. By incorporating the acceleration, friction, mixing, confluence, and gravity pressure drops, a coupling model with a finite-conductivity multibranch horizontal well was developed. Newton-Raphson iterations and Visual Basic programming were employed to solve the coupling model and to obtain the pressure and the inflow rate of the wellbore. The wellbore pressure-drop model was verified by comparing it with different models for the same case study, which has been previously introduced in a different research work. Furthermore, the forecast and sensitivity analysis were conducted, and then the results are discussed. In the proposed new model, several factors are considered, including the wellbore structure, the wellbore completion method, the wellbore, and the fluids and formation properties. The presented approach can be used as a valuable tool to analyze the influence of the pressure drop on the productivity of complex-structured wells and vice versa, and to quantitatively investigate the various pressure drops in wellbores, including the friction, acceleration, mixing, confluence, and gravity pressure losses.
RESUMEN
Objective: To explore the efficacy of dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) histogram molecular imaging index, apparent diffusion coefficient (ADC) in different types of lung cancer and explore their correlation with Ki-67. Methods: A total of 33 cases of lung cancer patients confirmed by pathology in Shaoxing People's Hospital from March 2017 to March 2018 were collected, 28 males and 5 females aged 50-85 years old, including 15 cases of squamous cell carcinoma, 12 cases of adenocarcinoma, and 6 cases of small cell carcinoma. All patients performed DCE-MRI and DWI imaging within one week before surgery or puncture. ADC values, DCE-MRI quantitative perfusion parameters by histogram metrics analysis (mean value, skewness, kurtosis, uniformity, entropy, energy, quantile) of K(trans), K(ep), V(e), and V(p) were then collected. Ki-67 expression in lung cancer tissue was detected by immunohistochemical method. One-way analysis of variance and least significant difference were used to compare the differences among the parameters of the three groups which were normal distribution and equal variances, while Kruskal-Walls test and Mann-Whitney U test were used to compare the parameters that did not conform to normal distribution or variance. Pearson correlation analysis was used to compare the correlations between quantitative perfusion histogram parameters, ADC values and immunohistochemical scores of Ki-67. Results: The Ki-67 count in small cell lung cancer(458±82, P=0.011) and squamous cell carcinoma(355±277, P=0.034)were significantly higher than that in adenocarcinoma (168±164). The correlation analysis showed that there was a significant negative correlation between ADC values and Ki-67 (P=0.018, r=-0.416). And V(e) (Q5, Q10) was negatively related to Ki-67 (P=0.017, r=-0.420; P=0.040, r=-0.366). In squamous cell carcinoma patients, V(e) (homogeneity) was significantly negatively correlated with the expression of Ki-67 (P=0.033, r=-0.570). K(trans)(homogeneity) and V(e) (homogeneity, Q5, Q10, Q25) were significantly positively correlated with ADC values (P value from 0.001 to 0.035, r value from 0.545 to 0.765). Conclusion: DCE-MRI quantitative perfusion histogram parameters, ADC value can evaluate the lung cancer cell proliferation activity in different pathological types.
