Data-Driven Calibration of P3d Hydraulic Fracturing Models

Zio, Souleymane; Rochinha, Fernando A.

doi:10.1615/int.j.uncertaintyquantification.2020033602

Cited by 1 publication

(7 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We consider the present work a follow-up of our previous efforts reported in Ref. [23] to build simplified and fast simulators for HF simulation departing from P3D, the industry workhorse. Here, we employ a nonlinear bi-fidelity formulation differently from our initial approach but still somewhat similar using a data-driven strategy.…”

Section: Final Remarks and Discussionmentioning

confidence: 99%

“…For the sake of space, we do not give a detailed description of ILSA here as, like in, here as in Ref. [23,35] and 21 , the main goal here is to leverage, through a muli-fidelity approach, the predictive capacity of P3D, a model well accepted in the industry, with a limited additional computational cost. Instead, we invite interested readers to find more details in the above-cited references.…”

Section: Hydraulic Fracturing -Mathematical and Computational Modelsmentioning

confidence: 99%

“…We pursue here a different avenue to enhance the predictive ability of the P3D model, employing data-driven approaches. 23 Instead of proposing a new model or a new numerical method, recognizing that P3D is one of the work-horse tools for the industry, particularly within the multi-query scenarios mentioned before, we propose alternative formulations to leverage the accuracy of the P3D model. Specifically, we use multi-fidelity formulations [24][25][26][27] that blend low and high-fidelity models to balance computational budget and accuracy.…”

Section: Introductionmentioning

confidence: 99%

“…[30][31][32][33] In particular, such a framework is explored to build an enhanced P3D model by the present authors in Ref. [23]. Here, motivated by limitations found in some situations that are frequently attributed to the inability of the linear formulation to capture complex correlations between models within the hierarchy chain, we go further and employ a generalization of this previous formulation, 34 in which a nonlinear function maps the lower fidelity model output to the higher fidelity one.…”

Section: Introductionmentioning

confidence: 99%

“…Like in Ref. [23], we propose a bi‐fidelity model combining P3D (low‐fidelity) with a high‐fidelity model 6 that considers more complex geometries for the fracture and encompasses different physical mechanisms of the fracture evolution.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A bi‐fidelity model for hydraulic fracturing

Zio,

Rochinha

2023

Num Anal Meth Geomechanics

Self Cite

View full text Add to dashboard Cite

Hydraulic fracture, whether a natural phenomenon or an engineered process, consists of a highly pressurized flow evolving within a rock and, when necessary, fracturing such a medium. Particularly, in the context of oil and gas exploitation, a mixture of water and proppant is injected through a well to improve the oil extraction conditions by artificially increasing the local permeability. From a modeling standpoint, it is fundamental to acknowledge that this complex flow involves, among other disciplines, fracture mechanics, fluid dynamics, non‐Newtonian flow, solid mechanics, and flow in porous media. Therefore, explicitly or not, a model bears multiple scales and multiple physics, leading to a non‐linear moving boundary mathematical problem that is hard to solve through analytical techniques. Amongst them, the Pseudo‐3D, which computes fracture evolution in reservoirs confined by symmetric stress barriers, is frequently employed in the oil and gas industry domain. The different assumptions made to obtain the P3D model lead to inaccurate predictions, like the overestimation of fracture height for important operating conditions. We propose a model discrepancy term in a multi‐fidelity approach to correct such drawbacks. The main difficulty associated is constructing a mapping between the inputs and outputs that faithfully represents the error between high and low fidelity models. In this paper, we investigated the performance of a nonlinear multi‐fidelity approach relying on Gaussian Processes. We present a careful analysis to assess the good performance of such a proposition and also present results involving Uncertainty Quantification, which is made feasible by using the bi‐fidelity surrogate.

show abstract

Section: Final Remarks and Discussionmentioning

confidence: 99%