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Summary We present a new model of fluid loss with wall building that applies to gelled fracturing and drilling fluids. Our model separates leakoff into two parts: an invasion phase and a wall-building phase. The invasion phase begins with Darcy flow, which carries residue into pore spaces near the rock face. This phase ends when sufficient residue has accumulated to allow the formation of a wall on the rock face. Once the wall has formed, it dominates the fluid-loss mechanism through its extremely low permeability. During the wall-building phase our model predicts a hyperbolic rather than a linear relation between leakoff volume and t. We made laboratory fluid-loss measurements for a variety of fluids and rock materials to test this model. We monitored effluent volume produced by flowing a gel or suspension through a fully saturated core sample. We found that the new model fit these measurements over periods of several hours, whereas the conventional Cw model did not. The Cw method can lead to large errors in fluid-loss estimates for long-term operations, such as massive fracturing and drilling. Our model requires the measurement of three leakoff parameters. We collected enough measurements to determine some general relations between these parameters and fluid and rock properties. These relations are discussed in terms of practical applications. Introduction Fluid loss with wall-building fluids has been investigated many times, both in laboratory and field settings. Most of this work has been associated with hydraulic fracturing applications, but the same technology is applicable to drilling operations with wall-building muds. The commonly used model of fluid loss with wall building was developed early in these investigations. It is based on the simple concept of a linear relation between leakoff volume and the square root of flow time. This is the relation consistently reported from fluid-loss measurements in the laboratory under constant driving pressure. This model requires only two parameters to describe it. The quantities Cw and spurt loss have been used traditionally to account for the slope and intercept associated with the linear dependence of leakoff volume on t. This model has been applied for many years as a standard part of hydraulic fracturing technology. Service companies have faithfully provided Cw and spurt-loss data for all common fracturing fluids. The only innovation in this approach have been related to dynamic fluid-loss effects. Hall and Dollarhide were among the first to recognize the importance of these effects. They showed that fluid flow along the face of the wall affects its buildup and thus influences the leakoff mechanics. A variety of innovative methods have been used to investigate these effects and to develop fluid-loss models to account for them. Williams developed one such model. Additional contributions to the technology of dynamic fluid loss have been made by Refs. 5 through 13. In this paper we neglect dynamic effects and return to the basic problem of static fluid-loss mechanics. We develop a new model based on concepts introduced earlier. This model separates fluid loss into two parts: an invasion phase and a wall-building phase. We assume that the invasion phase begins with Darcy flow and ends when a wall is formed. During the wall-building phase, our model predicts a hyperbolic rather than linear relation between leakoff volume and t. We have made a large number of fluid-loss measurements to test this model. We show that the new model fits the measurements over periods of several hours, whereas the Cw model does not. Our model introduces a new set of three fluid-loss parameters that can be measured easily by service companies. Results are presented for a variety of fluid and rock materials to establish general relations between these parameters and fluid and rock properties. Wall-Building Model The basic elements of a model for fluid loss by wall-building fluids was given earlier. This model (Fig. 1) applies to all gels or suspensions of the type commonly used in fracturing or drilling operations. Leakoff is assumed to occur in accordance with Darcy's law and a piston-like displacement of reservoir fluid by the fluid filtrate. The filtrate is taken to be incompressible and the reservoir fluid compressible. The reservoir fluid is driven at a moving boundary designated a(t). The pressure at the boundary is p1(a). As the gel or suspension leaks off, a wall or filter-cake layer of low-permeability residue is deposited on the fracture face with a pressure drop pw-p0 across it. Experience shows that this wall does not necessarily start building immediately. Generally, an initial flow of volume Vf0 must take place over a period of t0 before the wall is formed. Our model defines two regions beyond the wall: the region occupied by the filtrate of viscosity ยต2 and the region of compressed reservoir fluid with viscosity ยต1. The filtrate region contains long-chain gel molecules or suspension particles trapped by the pore structure. The model is based on the assumption that the pressure drop pw-p0 across the wall is proportional to the product of the leakoff rate and the volume of fluid, Vf, that has passed through the wall. In terms of the fluid displacement, s, this corresponds toEquation 1 and 2 where A is a constant. With Eqs. 1 and 2, it is convenient to divide the fluid-loss process into two periods: t t0 (invasion phase) and t>t0 (wall-building phase). To treat the invasion phase, we assume that fluid loss begins in accordance with Darcy's law. We assume that permeability, k, and ยต2 are constant at first. Thus,Equation 3 where ? is a mobility given byEquation 4 and L is the sample length. Substituting Eq. 3 into Eq. 1 and integrating givesEquation 5 which is a parabola in the (t, s) plane. It is clear that this parabolic relation cannot prevail for long because ? does not remain constant. As fluid loss proceeds, the permeability decreases in the invaded zone because of the buildup of residue in the pore structure. Similarly, at a given distance beyond the face, ยต2 increases with time as the concentration of gel molecules or suspended particles builds up. Under these conditions, s(t) will tend to trail off in time and fall below the initial parabolic trend. This condition will continue until time t0, when a wall or filter cake forms. At this time, invasion ceases because no further polymer or suspended particles are lost through the wall. From this time on, ? is assumed to remain constant.
- Geology > Geological Subdiscipline > Geomechanics (0.55)
- Geology > Rock Type (0.47)
Summary A basic theory of two-dimensional (2D) fracture propagation has been developed with a Lagrangian formulation combined with a virtual work analysis. Fluid leakoff is included by the assumption that an incompressible filtrate produces a piston-like displacement of a compressible reservoir fluid with a moving boundary between the two. Poiseuillc flow is assumed in the fracture. We consider both Newtonian and Poiseuillc flow is assumed in the fracture. We consider both Newtonian and non-Newtonian fluids with and without wall building. For non-Newtonian fluid, we assume the usual power-law relation between shear stress and shear rate. The Lagrangian formulation yields a pair of nonlinear equations in and, the fracture length and half-width. By introducing a virtual work analysis, we obtain a single equation that can be solved numerically. For non-wall-building fluids, it predicts much higher leakoff rates than existing methods. The Lagrangian method also allows nonelastic phenomena, such as plasticity, to be included. A practical computer phenomena, such as plasticity, to be included. A practical computer program developed from this theory has been used for more than 10 years to program developed from this theory has been used for more than 10 years to design fracturing treatments in oil and gas reservoirs in Canada, California, the midcontinent and Rocky Mountain areas, the U.S. gulf coast, the North Sea, and in northern Germany. In most of these applications, it has predicted fracture dimensions that have been in line with production experience. Optimization methods based on this program led to very large fracturing treatments in low-permeability gas sands that were forerunners of massive fracturing treatments in tight gas sands. Specific examples in which this method was used to design fracturing programs in large gas fields in Kansas and Texas are discussed. Introduction We present here a new approach to the 2D problem of fracture propagation based on Lagrangian methods. The Lagrangian formulation has been applied to a variety of problems in physics and chemistry. To the best of our knowledge, however, this is the first application to fracture mechanics. The Lagrangian formulation is based on the classical form of Lagrange's equations. As applied here, it produces a basic equation that expresses the balance between work expended and work done in propagating a 2D crack. Existing theories of crack propagation have all been developed by the application of equations from classical elasticity theory. This approach assumes linear elastic behavior of the reservoir rock and ignores surface energy considerations at the crack tip and plastic deformation effects. Leakoff, if it is included, is treated as an independent process and merged with the crack propagation problem by iterative methods that assume self-consistency. Some well-known examples of this approach have been presented by Zheltov and Khristianovich, Perkins and Kern, Nordgren presented by Zheltov and Khristianovich, Perkins and Kern, Nordgren Geertsma and de Klerk, Daneshy, Le Tirant and Dupuis, and Cleary. Geertsma and Haafkens have compared many of the results of these theories. A more general approach, the Lagrangian method is not restricted to elastic behavior, and leakoff can be included as an integral part of the formulation. We include leakoff by assuming a piston-like displacement of compressive reservoir fluid by an incompressible fracture fluid filtrate with a moving boundary between the two. The Lagrangian formulation yields a pair of nonlinear differential equations in fracture length and fracture half-width, which are reduced to a single equation in by introduction of a virtual work analysis. This equation can be solved numerically and can be used with other relations to obtain fracture dimensions and injection pressure as a function of time at constant injection rate. Experimental laboratory measurements reported previously confirm basic results obtained from such computations. The Lagrangian formulation presented here has been used for many years in our field operations to predict fracture dimensions. It has provided a means to plan and to optimize fracture treatments in a variety of field operations. Some specific field applications will be discussed.
- North America > United States > Texas (1.00)
- North America > United States > California > Kern County (0.28)
- North America > United States > Colorado > Piceance Basin > Williams Fork Formation (0.99)
- North America > United States > California > San Joaquin Basin > South Belridge Field > Tulare Formation (0.99)
- North America > United States > California > San Joaquin Basin > South Belridge Field > Diatomite Formation (0.99)
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