18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS COMPRESSION AND FLOWBACK IN POLYDISPERSE COMPOSITE GRANULAR PACKS M. Kulkarni and O. Ochoa * Mechanical Engineering, Texas A&M University, College Station, USA * Ozden O. Ochoa (oochoa@tamu.edu) Keywords : composite proppants, granular media, discrete simulation, polydispersity 1 Introduction 2 Analysis Granular materials are a collection of individual Herein we present models of the granular media solid particles large enough so that the physics of with a combined finite/discrete element method motion is independent of temperature. Their employing ABAQUS explicit code. General contact application areas range from geophysics, pharmacy, capability is utilized to simulate inter-particle oil & gas, powder metallurgy, polymer technology, interaction [5]. The primary parameters of interest casting technology, agriculture, and construction are stresses developed in the particles and the industry [1]. Analytical characterization of granular corresponding void spaces. packs are carried out with discrete element method The proppant pack is analyzed under confined (DEM) to obtain nonlinear stress-strain response, compression to reflect the state within the pack far failure envelopes, transition from brittle to ductile away from the wellbore. Proppant flowback (out behavior, hysteresis as well as identifying local flow of the particles from a compressed pack) is also failure and shear bands. In general, DEM studied by adding a transverse load on the particles formulation utilizes simplified contact relationships, to simulate pressure gradient and fluid drag forces, neglects rotational stiffness and it is not conducive while the particles continue to be subjected to for large deformations in particles. These limitations compressive forces. can be alleviated with the explicit dynamic finite 2.1 Particle Distributions and Pack Formation element method wherein each particle is represented with its own mesh to simulate multi-particle The random number generation function in interactions accounting for changes in the particle MATLAB is invoked to generate an initial random geometry due to plastic deformation and damage [2]. distribution of particles and sizes in a rectangular domain as shown in Figure 1a. The loose Our objective is to understand the effects of particle material, shape and size in granular packs configuration mesh is created with the preprocessing software Altair Hypermesh [6]. (proppants) enlisted in hydraulic fracturing treatments employed for oil/gas well simulation. The particles are considered as linear elastic and Proppants are delivered to these fractures to ensure allowed to undergo a fall under gravitational loading that the fluid flow paths remain open by resisting the in ABAQUS explicit 6.8.3. Three dimensional rock pressure (closure stresses). The replacement of continuum elements, C3D8R, with eight nodes and sand with a mixture of lightweight ground-nut- reduced integration are used to model the particles shells, ceramic and metal particles has opened new and the rock platens. The spherical particles are research areas aimed at reducing the fracturing fluid represented as cylinders for simplicity. Plane strain viscosity enabling efficient particle placement while conditions are enforced along the cylinder axis. The increasing the resistance to closure stresses [3, 4]. largest particles are composed of 1200 elements The effectiveness of a proppant pack is dependent while the smallest particles are described with 150 on its ability to withstand closure stresses while elements. There are total of 32,265 elements with maintaining a highly permeable pack with large void 71,332 nodes. The configuration at the end of the spaces, which ensure a high fluid flow rate. free fall (Figure 1b) is imported into a new analysis step where the particles are assigned their
appropriate material properties; elastic or elastic- compression load, to avoid spurious proppant plastic. This approach removes the need to monitor production and ii) transverse load with simultaneous the plastic strains developed in particles during free removal of one side enclosure, Fig. 3. The loading fall. is incremental and quasi-static, and the confined compression stage is load controlled. The 2.2 Confined Compression Study concentrated force is applied at the reference node of This model consists of 150 particles placed between the rigid top layer of the rock platen. Note that the the two horizontal rock platens that represent the transverse force representing flowback is dependent fracture width (f w ) as shown in Figure 2. Two both on the pressure gradient and the particle additional rigid platens are introduced as side diameter. In this model the force is equivalent to enclosures. The distance between the two rigid 1.686 MPa/m (75 psi/ft). platens represents the fracture length (f l ). The lower The flowback resistance of a proppant pack is rock platen (B) is constrained against any motion studied by observing the number and distance from and the compressive load is introduced through the the unconstrained end over which particles fall out rigid elements at the upper surface of the rock platen of the pack and the formation of a stable arch. Two (A). The maximum value of the compressive load is different packs are considered; first one has 15% 100 N, equivalent to 77 MPa closure stress. walnut and 85% ceramic particles and the second The particle mixture is identified with weigh percent one consists of 100% ceramic particles. Two models of its composition; walnut (15%) and ceramic with coefficient of friction µ = 0 and 0.3 are (85%). Gaussian distribution for particle radii is as considered to study the influence of inter-particle follows; the walnut diameter range is from 0.8-1.2 friction. The effect of closure stress on the mm while the ceramics vary between 0.35-0.55 mm . flowback is considered by comparing particle The specific gravity of ceramic and walnut is 3.6 response at 50 MPa and 100 MPa pressure for both and 1.25 respectively. Walnut is described with an packs without inter-particle friction. Treating shale elastic-plastic constitutive behavior obtained from rock as linear elastic as well as elastic-plastic single particle compression tests [7]. Ceramic is material address the influence of the rock. represented as a quasi-brittle material where it remains linear-elastic until the tensile stresses reach its bending strength. At this stage micro-cracking is 3 Observations assumed to occur and at subsequent increments, the 3.1 Confined Compression modulus is represented as E = (1-d)E 0 . E 0 is the undamaged elastic modulus and d is the scalar The effects of polydispersity on the pack response reveal the following observations. At the end of the degradation variable, which is defined as a part of free fall, particles are segregated where the larger material strain softening data in the concrete damage plasticity model [5]. The rock platens are assigned particles tend to stay at the top of the pack as shown in Fig. 1b. This is in line with the findings for linear elastic material properties of shale rock. The granular material segregation in the literature [1]. ratio of elastic moduli of ceramic to walnut and shale rock to walnut is 80:1 and 4:1 respectively. Compression response of the granular pack reveals that the harder ceramic particles carry most of the The analysis is quasi-static with incremental load which appears as stress chains in the von Mises compressive load. Mass scaling is employed to stress contour plot in Fig. 4. The softer and larger speed up the analysis. Inertia effects are monitored walnut particles undergo significant plastic during the simulation to ensure that they are deformation but do not carry high loads as can be negligible. seen in Fig. 5. 2.3 Proppant Flowback Study The value of the damage variable for the ceramic This model accommodates 200 particles, each 1mm particles indicating degradation in the element in diameter, in the fracture width of 4.5 mm. The stiffness is presented in Fig. 6. In the current model fracture length is modeled with 50 particles. The a limited degradation approximately 15% of its load is applied over two steps i) confined original value for only a few elements is observed. 2
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