Limiting Distributions in a Linear Fractional Flow Model

1976 ◽  
Vol 30 (3) ◽  
pp. 402-406 ◽  
Author(s):  
Richard C. Grinold ◽  
Robert E. Stanford
Keyword(s):  
Flow Model ◽  
Fractional Flow ◽  
Limiting Distributions

Limiting Distributions in a Linear Fractional Flow Model

1973 ◽  
Author(s):  
Richard C. Grinold ◽  
Robert E. Stanford
Keyword(s):  
Flow Model ◽  
Fractional Flow ◽  
Limiting Distributions

scholarly journals Numerical simulation of the fractional flow reserve (FFR)

2018 ◽  
Vol 13 (6) ◽  
pp. 57 ◽  
Author(s):  
Keltoum Chahour ◽  
Rajae Aboulaich ◽  
Abderrahmane Habbal ◽  
Cherif Abdelkhirane ◽  
Nejib Zemzemi
Keyword(s):  
Fractional Flow Reserve ◽  
Flow Model ◽  
Rigid Wall ◽  
Fractional Flow ◽  
Wall Model ◽  
Factors Affecting ◽  
Non Invasive ◽  
Flow Reserve ◽  
Weakly Coupled ◽  
Preliminary Study

The fractional flow reserve (FFR) provides an efficient quantitative assessment of the severity of a coronary lesion. Our aim is to address the problem of computing non-invasive virtual fractional flow reserve (VFFR). In this paper, we present a preliminary study of the main features of flow over a stenosed coronary arterial portion, in order to enumerate the different factors affecting the VFFR. We adopt a non-Newtonian flow model and we assume that the two-dimensional (2D) domain is rigid in a first place. In a second place, we consider a simplified weakly coupled FSI model in order to take into account the infinitesimal displacements of the upper wall. A 2D finite element solver was implemented using Freefem++. We computed the VFFR profiles with respect to different lesion parameters and compared the results given by the rigid wall model to those obtained for the elastic wall one.

scholarly journals Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Keltoum Chahour ◽  
Rajae Aboulaich ◽  
Abderrahmane Habbal ◽  
Nejib Zemzemi ◽  
Chérif Abdelkhirane
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Fluid Model ◽  
Invasive Procedure ◽  
Navier Stokes ◽  
Fractional Flow ◽  
Flow Reserve ◽  
Arbitrary Position ◽  
Model Versus ◽  
Good Agreement

Fractional flow reserve (FFR) has proved its efficiency in improving patient diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and use a coupled multidomain method to implement Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the virtual FFR and conduct several numerical experiments. We compare FFR results from the Navier–Stokes model versus generalized flow model and for Windkessel versus traction-free outlet boundary conditions or mixed outlet boundary conditions. We also investigate some sources of uncertainty that the FFR index might encounter during the invasive procedure, in particular, the arbitrary position of the distal sensor. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between the Navier–Stokes model and the non-Newtonian flow model adopted in classifying coronary lesions. Furthermore, we highlight that the lack of standardization while making FFR measurement might be misleading regarding the significance of stenosis.

Prediction of mobile water in a tight gas sandstone reservoir using NMR and fractional flow model

2014 ◽  
Vol 54 (2) ◽  
pp. 1
Author(s):  
Maria Anantawati ◽  
Suryakant Bulgauda
Keyword(s):  
Steady State ◽  
Relative Permeability ◽  
Flow Model ◽  
Bound Water ◽  
Free Water ◽  
Development Project ◽  
Asia Pacific ◽  
Fractional Flow ◽  
Reservoir Properties ◽  
Mobile Water

One of the objectives of petrophysical interpretation is the estimation of the respective volumes of formation fluids. With traditional interpretation using conventional openhole logs it is only possible to determine the total amount of water. The challenge is to determine the volumes of bound water (clay-bound and capillary-bound) and free water. At the moment, NMR is the only measurement that can help distinguish the volumes of each water component (clay-bound, capillary-bound and mobile), using cut-offs on T2 (transverse relaxation time). However NMR interpretation also requires information on reservoir properties. Alternatively, steady-state relative permeability and fractional flow of water can be used to determine the potential of mobile water. The study area, located in the Cooper Basin, South Australia, is the target of a planned gas development project in the Patchawarra formation. It comprises multiple stacked fluvial sands which are heterogeneous, tight and of low deliverability. The sands are completed with multi-stage pin-point fracturing as a key enabling technology for the area. A comprehensive set of data, including conventional logs, cores and NMR logs, were acquired. Routine and special core analysis were performed, including NMR, electrical properties, centrifuge capillary pressure, high-pressure mercury injection, and full curve steady state relative permeability. A fractional flow model was built based on core and NMR data to determine potential mobile water and the results compared with production logs. This paper (SPE 165766) was prepared for presentation at the SPE Asia Pacific Oil & Gas Conference and Exhibition, held in Jakarta, Indonesia, from 22–24 October 2013.

Fractional-Flow Model for High-ph Flooding

1989 ◽  
Vol 4 (01) ◽  
pp. 59-68 ◽  
Author(s):  
T.S. Ramakrishnan ◽  
D.T. Wasan
Keyword(s):  
Flow Model ◽  
Fractional Flow ◽  
High Ph

scholarly journals Ensemble-based method with combined fractional flow model for waterflooding optimization

2021 ◽  
Vol 76 ◽  
pp. 7
Author(s):  
Dilayne Santos Oliveira ◽  
Bernardo Horowitz ◽  
Juan Alberto Rojas Tueros
Keyword(s):  
Optimization Problem ◽  
Flow Model ◽  
Computational Cost ◽  
Fractional Flow ◽  
University Of Texas ◽  
Flow Models ◽  
Proxy Models ◽  
The Difference ◽  
The University ◽  
Low Computational Cost

Proxy models are widely used to estimate parameters such as interwell connectivity in the development and management of petroleum fields due to their low computational cost and not require prior knowledge of reservoir properties. In this work, we propose a proxy model to determine both oil and water production to maximize reservoir profitability. The approach uses production history and the Capacitance and Resistance Model based on Producer wells (CRMP), together with the combination of two fractional flow models, Koval [Cao (2014) Development of a Two-phase Flow Coupled Capacitance Resistance Model. PhD Dissertation, The University of Texas at Austin, USA] and Gentil [(2005) The use of Multilinear Regression Models in patterned waterfloods: physical meaning of the regression coefficient. Master’s Thesis, The University of Texas at Austin, USA]. The proposed combined fractional flow model is called Kogen. The combined fractional flow model can be formulated as a constrained nonlinear function fitting. The objective function to be minimized is a measure of the difference between calculated and observed Water cut (Wcut) values or Net Present Values (NPV). The constraint limits the difference in water cuts of the Koval and Gentil models at the time of transition between the two. The problem can be solved using the Sequential Quadratic Programming (SQP) algorithm. The parameters of the CRMP model are the connectivity between wells, time constant and productivity index. These parameters can be found using a Nonlinear Least Squares (NLS) algorithm. With these parameters, it is possible to predict the liquid rate of the wells. The Koval and Gentil models are used to calculate the Wcut in each producer well over the concession period which in turn allows to determine the accumulated oil and water productions. To verify the quality of Kogen model to forecast oil and water productions, we formulated an optimization problem to maximize the reservoir profitability where the objective function is the NPV. The design variables are the injector and producer well controls (liquid rate or bottom hole pressure). In this work the optimization problem is solved using a gradient-based method, SQP. Gradients are approximated using an ensemble-based method. To validate the proposed workflow, we used two realistic reservoirs models, Brush Canyon Outcrop and Brugge field. The results are shown into three stages. In the first stage, we analyze the ensemble size for the gradient computation. Second, we compare the solutions obtained with the three fractional flow models (Koval, Gentil and Kogen) with results achieved directly from the simulator. Third, we use the solutions calculated with the proxy models as starting points for a new high-fidelity optimization process, using exclusively the simulator to calculate the functions involved. This study shows that the proposed combined model, Kogen, consistently generated more accurate results. Also, CRMP/Kogen proxy model has demonstrated its applicability, especially when the available data for model construction is limited, always producing satisfactory results for production forecasting with low computational cost. In addition, it generates a good warm start for high fidelity optimization processes, decreasing the number of simulations by approximately 65%.

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