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This work presents a novel computational model for the 3D flow in a rigid stator Progressing Cavity Pump (PCP), using an element based finite volume method, which includes the relative motion between rotor and stator. Usual flow models in PCPs consider a Poiseuille flow along the seal lines, i.e., along the positive clearance between cavities in order to predict the internal slip and then, the volumetric efficiency for different pressures, rotations and fluid viscosities. Furthermore, some attempts for more detailed models including computational solutions for the flow in simplified geometries can be encountered in literature. These approaches include, treating cavities as parallel plates or computing the flow between two static cavities, in all cases considering steady state flow, which is a strong hypothesis in this case. Nevertheless no models considering the solution for the full transient 3D Navier-Stokes equations and the relative motion between rotor and stator were encountered. The main challenge at this point was the imposition of the mesh motion and mesh generation process, mainly, because of the mesh quality control (element distortion) in regions near the seal lines, or in the clearance regions between rotor and stator. The model developed is capable to predict accurately the volumetric efficiency and the viscous looses as well as provide detailed information of pressure and velocity fields inside this device. Furthermore, the present model could be used to predict the hydraulic performance of an elastomeric progressing cavity pump after stator wear or deformation and allow for the development of a computational model for the fluid-structure interaction which permits the analysis of the non-rigid stator case. Introduction Progressing Cavity Pumping is being more and more used in oil production, mainly in heavy oil fields, due to its numerous technical advantages. Simplest models for PCP design, firstly presented by Moineau (1930), are based on calculating the slippage across the pump, considering a Hagen-Poiseuille flow in the sealing region, which is subtracted from the volume displaced, giving the volumetric flow pumped. As differential pressure increases, so does the slippage, and the relation between differential pressure across the pump and net volumetric flow pumped, can be calculated. After Moineau's models, several attempts for more precise fluid dynamic and fluid-structure interaction models have been presented. For oil production applications works due to Robello Samuel & Saveth (1998), Olivet et al. (2002), Gamboa et al. (2002) and Gamboa et al. (2003) constitute the main references in this field of research. Robello Samuel & Saveth (1998) developed optimal relationships between the pitch and the diameter of the stator to achieve a maximum flowrate for multilobe pumps. Olivet et al. (2002) performed an experimental study and obtained characteristic curves and instantaneous pressure profiles along metal to metal pumps for single- and two-phase flow conditions. Gamboa et al. (2002) presented some attempts of flow modeling within a PCP using Computational Fluid Dynamics with the aim of getting a better comprehension of the flow inside the pump. Nevertheless, attempts for developing a three-dimensional model including rotor motion were failed even for rigid stator (this means constant clearance) due to the complexity of the geometry, mesh motion and (may be) the inadequateness or limitations of the numerical approach used to solve the governing equations. In virtue of this, Gamboa et al. (2003) presented simplified models for single phase flow considering the possibility of variable gap due to elastomeric stator deformation. The basic approach does not differ too much from previous works based on metallic stator, but the slippage is calculated cavity by cavity and the possibility of a variation of the clearance as function of differential pressure is considered. In this way they were able to reproduce the characteristic non-linear behavior of volumetric flow versus differential pressure in a PCP with elastomeric stator.

The Generalized Integral Transform Technique (GITT) is utilized in the hybrid numerical-analytical solution of the Reynolds averaged Navier-Stokes equations, for developing turbulent¯ow inside a parallel-plates channel. An algebraic turbulence model is employed in modelling the turbulent diffusivity. The automatic global error control feature inherent to this approach, permits the determination of fully converged reference results for the validation of purely numerical methods. Therefore, numerical results for different values of Reynolds number are obtained, both for illustrating the convergence characteristics of the integral transform approach, and for critical comparisons with previously reported results through different models and numerical schemes.

ObjectivesTo evaluate the clinical outcomes of epithelial ovarian carcinoma patients who underwent cardiophrenic lymph node resection.MethodsWe retrospectively reviewed the records of all surgically treated patients with advanced epithelial ovarian carcinoma (stages IIIC–IV) who underwent cardiophrenic lymph node resection between 2002 and 2018. Only those in whom cardiophrenic lymph node involvement was the only detectable extra-abdominal disease were included. Patients with suspected cardiophrenic lymph node metastasis on staging images underwent a transdiaphragmatic incision to access the para-cardiac space after complete abdominal cytoreduction achievement. Data on disease-free survival, overall survival, and surgical procedures performed concurrently with cardiophrenic lymph node resection were collected.ResultsOf the total 456 patients, 29 underwent cardiophrenic lymph node resection; of these, 24 patients met the inclusion criteria. Twenty-two, one, and one patients had high grade serous epithelial ovarian carcinoma, low grade epithelial ovarian carcinoma, and ovarian carcinosarcoma, respectively. Ten patients had recurrent disease (recurrence group). Fourteen patients underwent cytoreduction during primary treatment (primary debulking group); four underwent cytoreduction after neoadjuvant chemotherapy. Cardiophrenic lymph node resection was performed on the right side in 19 patients, left side in three, and bilaterally in two. The average procedural duration was 28 minutes, with minimal blood loss and no severe complications. Twenty-one patients had cardiophrenic lymph node positivity. The median disease-free intervals were 17 and 12 months in the recurrent and primary debulking surgery groups, respectively. The mediastinum was the first recurrence site in 10 patients. Five patients developed brain metastases. Five patients had an overall survival beyond 50 months.ConclusionsAlthough rare, the cardiophrenic lymph nodes may be a site of metastasis of ovarian cancer. Although their presence might indicate future recurrence, some patients may achieve long-term survival. Resection should be considered in cases of suspicious involvement to confirm extra-abdominal disease and achieve complete cytoreduction.