Proppant backflow: Mechanical and flow considerations

McLennan, John; Walton, I. C.; Moore, Joseph N.; Brinton, Daniel; Lund, Jeff

doi:10.1016/j.geothermics.2015.06.006

Cited by 33 publications

(17 citation statements)

References 19 publications

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“…A second class of approaches represents explicitly the backflow phenomenon via detailed numerical models (de Borst, 2017;Jia et al, 2019;Medina et al, 2018). Detailed laboratory experiments on proppant backflow were conducted by McLennan et al (2015), demonstrating differences in behavior between the planar and the radial geometry.…”

Section: Introductionmentioning

confidence: 99%

Non‐Newtonian Backflow in an Elastic Fracture

Chiapponi

Ciriello

Longo

et al. 2019

Water Resources Research

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Backflow phenomenon, as a consequence of hydraulic fracturing, is of considerable technical and environmental interest. Here, backflow of a non-Newtonian fluid from a disk-shaped elastic fracture is studied theoretically and experimentally. The fracture is of constant aperture h and the outlet section at constant pressure p e . We consider a shear-thinning power-law fluid with flow behavior index n. Fracture walls are taken to react with a force proportional to h , with a positive elasticity exponent; for = 1 linear elasticity holds. Constant overload f 0 , acting on the fracture, is also embedded in the model. A transient closed-form solution is derived for the (i) fracture aperture, (ii) pressure field, and (iii) outflow rate. The particular case of a Newtonian fluid (n = 1) is explicitly provided. For p e = 0 and f 0 = 0, the residual aperture and outflow rate scale asymptotically with time t as t −n/(n+ +1) and t −(2n+ +1)/(n+ +1) , respectively, thus generalizing literature results for n = 1 and/or = 1. For nonzero exit pressure and/or overload, the fracture aperture tends asymptotically to a constant value depending on , n, p e , f 0 , and other geometrical and physical parameters. The results are provided in dimensionless and dimensional form, including the time to achieve a given percentage of fluid recovery. In addition, an example application (with values of parameters derived from field scale applications) is included to further characterize the influence of fluid rheology. Experimental tests are conducted with Newtonian and shear-thinning fluids and different combinations of parameters to validate the model. Experimental results match well the theoretical predictions, mostly with a slight overestimation.

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Section: Introductionmentioning

confidence: 99%

Non‐Newtonian Backflow in an Elastic Fracture

Chiapponi

Ciriello

Longo

et al. 2019

Water Resources Research

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“…where σ r is the closure stress. Many authors note that this stress affects proppant flowback and consider it as one of the main terms to control the proppant flowback [Milton-Tayler et al 1992;Asgian et al 1995;McLennan et al 2015;Andrews and Kjørholt 1998;Canon et al 2003;Aidagulov et al 2007;Vo et al 2014;Lu et al 2016;Barree and Conway 2001;Larsen and Smith 1985;Ely et al 1990]. The value of the closure stress is significant enough to hold the packed proppant in the fracture even when the outgoing force is big enough.…”

Section: Physicomathematical Modelmentioning

confidence: 99%

“…Some experiments on proppant flowback for proppants of different properties and a very simple mathematical model can also be found in [McLennan et al 2015]. This model offers a phenomenological dependence of pressure in a proppant pack on oil production rate.…”

Section: Introductionmentioning

confidence: 99%

A model of the proppant flowback: setup of the theoretical framework

Frolova

Grigoreva

Lezhnev

et al. 2019

Math. Mech. Compl. Sys.

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Proppant flowback control is one of the main issues in hydraulic fracture modeling since the propping agent maintains the crack in an open state and therefore provides oil inflow to the wellbore. The main objective of this paper is to determine the conditions that can lead to proppant flowback during the direct operation of the well. The main outcome of this paper is an evolution criterion for proppant flowback occurrence, which takes the external pressures affecting the proppant particles, the proppant properties, and the crack opening width into account. We propose a two-component continuum model consisting of the proppant and the oil to find the stress-strain state of the proppant and thereby to obtain the stress components in the evolution criterion. We solve both a stationary problem for estimating the probability of the proppant flowback occurrence under regular conditions as well as a transient problem for taking the possibility of fast changing external conditions into account.Communicated by Francesco dell'Isola. MSC2010: 70E50, 70E55, 74B15, 74F10, 76S05.

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“…If the drag forces are sufficiently high to make the arch fail, proppant production is started. Some experiments on proppant flowback for proppants of different properties and a very simple mathematical model can also be found in [McLennan et al 2015]. This model offers a phenomenological dependence of pressure in a proppant pack on oil production rate.…”

Section: Introductionmentioning

confidence: 99%

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2019

Math. Mech. Compl. Sys.

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This work is focused on polymorphic uncertainties in the framework of constitutive modeling for transversely isotropic materials. To this end, we propose a hybrid fuzzy-stochastic model, where the stochastic part accounting for aleatory uncertainties of material parameters is expanded with the multivariate polynomial chaos expansion. In order to account for epistemic uncertainties, polynomial chaos coefficients are treated as fuzzy variables. The underlying minimum and maximum optimization problem for the fuzzy analysis is approximated by α-level discretization, resulting in a separation of minimum and maximum problems. To become more universal, so-called quantities of interest are employed, which allow a general formulation for the target problem. Numerical examples with fuzzy, fuzzy-stochastic, and hybrid fuzzy-stochastic input demonstrate the versatility of the proposed formulation. Communicated by Paul Steinmann. MSC2010: 60A86. 99 100 EDUARD PENNER, ISMAIL CAYLAK, ALEX DRIDGER AND ROLF MAHNKEN numerically using a stochastic simulation, where the Monte Carlo (MC) method [Caflisch 1998; Hurtado and Barbat 1998] is widely used. Alternatively, spectral stochastic surrogate models, e.g., polynomial chaos expansion (PCE), are used in order to reduce the computational effort. Corresponding research areas are: linear elasticity of solids and mechanics [Ghanem and Spanos 1991], plasticity of solids and mechanics [Anders and Hori 1999; Rosić 2013], large deformations [Acharjee and Zabaras 2006; Acharjee 2006; Caylak et al. 2018], fluid flow [Le Maître et al. 2001; 2002], flow-structure interactions [Xiu and Karniadakis 2002; Xiu et al. 2001], and linear convection problems [Jardak et al. 2002].Contrary to aleatory uncertainties, epistemic uncertainties refer to subjectivity as a consequence of, e.g., incomplete scientific understanding or lack of measurements, which indicate a possible value range rather than a probability function. In addition, epistemic uncertainties are reducible by empirical effort, e.g., investing more in measurements. Methodologies for the modeling of epistemic uncertainties are, e.g., interval analysis and, increasingly applied over the last years, fuzzy analysis, which represents indistinct boundaries [Zadeh 1965]. In order to perform mathematical operations with fuzzy sets, the so-called α-level discretization method is applied. Here, the fuzzy response at each selected α-level is obtained by solving a minimum-maximum problem of a quantity of interest (QoI). In [Mahnken 2017] QoIs are employed within a variational formulation for fuzzy analysis in continuum mechanics.A realistic modeling of uncertainties requires a combination of different uncertainty types. Following [Graf et al. 2015], this is referred to as polymorphic uncertainties. Corresponding models are: Dempster-Shafer evidence theory [Dempster 1967], coherent lower prevision theory [Walley 1991], possibility theory [Dubois and Prade 2012], probability box (P-box) theory [Ferson et al. 2003], and fuzzy probability theory [Gudder 1998...

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Proppant backflow: Mechanical and flow considerations

Cited by 33 publications

References 19 publications

Non‐Newtonian Backflow in an Elastic Fracture

Non‐Newtonian Backflow in an Elastic Fracture

A model of the proppant flowback: setup of the theoretical framework

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