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Hydraulic Fracturing Basic Relations - New Mexico Tech ...

Hydraulic Fracturing Basic Relations Basic Relations Necessary to understand to apply to Fracturing pressure analysis and design parameters Material balance provides Basic design requirements for fluid volumes and proppants Fluid flow in a fracture Interaction of fluid and formation Rock deformation Copyright, 2011. Hydraulic Fracturing Basic Relations Material Balance expressions Flow rate In = Flow Rate Out + Accumulation Qout Qi Qf At the end of pumping, cumulative volume of volume of .. volume created fluid lost Pumping, tp injected fracture to formation Closure, Dt . Vi V fp VLp (1) Lost VLp Stored VLs (Dt) VLs (Dt). Vfp Vf (Dt) Vprop Copyright, 2011. Hydraulic Fracturing Basic Relations Material Balance expressions At any time during shutin, Pumping, tp Closure, Dt volume volume of volume of . Lost of the created fluid lost VLp fracture fracture from t Dt . p Stored VLs (Dt) VLs (Dt).

Title: Hydraulic Fracturing Basic Relations Author: Dr. Engler Created Date: 9/19/2011 9:54:07 AM

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Transcription of Hydraulic Fracturing Basic Relations - New Mexico Tech ...

1 Hydraulic Fracturing Basic Relations Basic Relations Necessary to understand to apply to Fracturing pressure analysis and design parameters Material balance provides Basic design requirements for fluid volumes and proppants Fluid flow in a fracture Interaction of fluid and formation Rock deformation Copyright, 2011. Hydraulic Fracturing Basic Relations Material Balance expressions Flow rate In = Flow Rate Out + Accumulation Qout Qi Qf At the end of pumping, cumulative volume of volume of .. volume created fluid lost Pumping, tp injected fracture to formation Closure, Dt . Vi V fp VLp (1) Lost VLp Stored VLs (Dt) VLs (Dt). Vfp Vf (Dt) Vprop Copyright, 2011. Hydraulic Fracturing Basic Relations Material Balance expressions At any time during shutin, Pumping, tp Closure, Dt volume volume of volume of . Lost of the created fluid lost VLp fracture fracture from t Dt . p Stored VLs (Dt) VLs (Dt).

2 Vfp V f ( Dt ) V fp VLs ( Dt ) (2). Vf (Dt) Vprop At closure, Dt = Dtc volume volume of .. of the proppant . fracture (solids pore space) .. V f (Dtc ) V prop (3). Combining (1) and (3). Vi V prop VLp VLs(Dtc ). (4). Copyright, 2011. Hydraulic Fracturing Basic Relations cumulative volume of volume of .. At the end of pumping, volume created fluid lost . injected fracture to formation .. Vi V fp VLp Lost VLp 2K LC L rp A f t p VLp Vi qi * t p Stored Vfp V fp Af * w qi = injection rate tp = injection time Af = area of one face of fracture w = average created fracture width,in CL = fluid loss coefficient, ft/(min)1/2. rp = fluid loss area to fracture area KL = fluid loss multiplier Copyright, 2011. Hydraulic Fracturing Basic Relations Proppant scheduling Lost Prop Conc, c/cf 1. VLp Define efficiency as: V fp h Stored Vi Vfp=hVi 0. Or 0 fpVi Vi Dtc h time for the fracture to close defines the efficiency tp Amount of pad and proppant scheduling depends on h Pad fraction: 1 h fp.

3 1 h Copyright, 2011. Hydraulic Fracturing Basic Relations Example Copyright, 2011. Hydraulic Fracturing Basic Relations Example pad Pre-pad flush Copyright, 2011. Hydraulic Fracturing Basic Relations Pumping Closure Pressure geometry Pressure CL. Time h Design q i t p A f w 2K L C L rp t p . Model . Volume required Proppant schedule Copyright, 2011. Hydraulic Fracturing Basic Relations Rock deformation Compliance of fracture describes the ease of fracture deformation Principle of crack advance and stresses at the crack tip The strain in the formation created by Hydraulic Fracturing is minor. As a result, formation deformation is linear elastic Based on the linear elastic assumption, the behavior of a fracture can be modeled using Sneddon's classical solutions: 2D crack or radial crack Both are: 2D with one-dimension infinite in extent Elliptic shaped cracks Inversely proportional to E' plain strain modulus E.

4 Proportional to a characteristic dimension and net pressure E . 1 2 .. Copyright, 2011. Hydraulic Fracturing Basic Relations Rock deformation Stress intensity factor, KI, - characterizes the magnitude of the stresses near the crack tip - f (geometry of body, loading parameters). - LEFM states a fracture will advance when KI reaches a critical value. Stress concentration near the tip of the crack. Fracture toughness measure of the resistance of the rock to crack, , propagate. Copyright, 2011. Hydraulic Fracturing Basic Relations Fluid flow in fracture Pressure gradient exists along the fracture DPnet Pfracture Pclosure Pnet Pnet=0. rw xf tip Local pressure gradient is given by the fluid rheology, velocity, and fracture width. n . dp k qi .. 2 n 1. dx w h . f . where k' and n' are consistency and behavior indices, respectively, for a power law model. If k' = m and n' = 1, then this equation reduces to Newtonian fluid.

5 Copyright, 2011. Hydraulic Fracturing Basic Relations Fluid flow in fracture: pressure gradient correction Classical fracture models assume pressure in the fracture is constant. However, the fluid flow relation indicates a gradient from pwf to pc. Thus define, p f pc Dp f . pw pc Dp f where pf is average pressure within the fracture. Consequently, substitute for pf smin in width equations with, p f s min Dp f Dp f Includes the pressure gradient effect from flow and fluid rheology along the fracture Includes wellbore pressure Copyright, 2011. Hydraulic Fracturing Basic Relations Fracture compliance, cf Proportionality between the pressure and width . w c f Dp f c f pw pc . With . hf PKN.. cf 2x f GDK. 2E . 32 / 3 2 R Radial . Copyright, 2011. Hydraulic Fracturing Basic Relations Rock deformation Pc smin ?? Fracture closure pressure is a global parameter which defines the fluid pressure for which the fracture effectively closes.

6 It is the average of formation heterogeneities. The minimum stress is a local parameter which generally varies over the plane of the fracture. Copyright, 2011.


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