A New General Model of Fluid Loss in Hydraulic Fracturing
- A. Settari (Simtech Consulting Services Ltd.)
- Document ID
- Society of Petroleum Engineers
- Society of Petroleum Engineers Journal
- Publication Date
- August 1985
- Document Type
- Journal Paper
- 491 - 501
- 1985. Society of Petroleum Engineers
- 4.1.2 Separation and Treating, 3.2.3 Hydraulic Fracturing Design, Implementation and Optimisation, 5.2 Reservoir Fluid Dynamics, 3 Production and Well Operations, 1.6.9 Coring, Fishing, 5.3.1 Flow in Porous Media, 2.5.2 Fracturing Materials (Fluids, Proppant), 2.5.1 Fracture design and containment, 5.3.2 Multiphase Flow
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This paper gives a new formulation of fluid loss in hydraulic fracturing that is much more general than the classical theory while retaining its simplicity. The model allows many parameters to vary during filtration and can, therefore, simulate nonlinear effects. The model has been validated against laboratory data for Newtonian fluids and crosslinked gels. The results show that the finite length of the core, viscosity screenout, and shear sensitivity are important parameters that can be represented by the model. The standard analysis gives values of leakoff coefficients that will give incorrect, considerably higher leakoff when applied to field conditions.
The estimate of fluid loss is an important part of a hydraulic fracturing treatment design. Although the control of fluid loss has improved with the use of modern fracturing fluids, the size of the generated fracture areas increases with the size of a job. Consequently, fluid loss can be important even in low-permeability reservoirs for large treatments. For design calculations, fluid loss has been treated in the past by use of the simplified theory proposed by Howard and Fast, which expresses the rate of filtration perpendicular to a fracture wall as a simple function of perpendicular to a fracture wall as a simple function of leakoff coefficients. The advantage of this approach, besides its simplicity, is that it can be directly (if not always correctly) related to experimental data on fluid filtration obtained in a laboratory. Apart from the correction of the derivation of the combined leakoff coefficient, very little has been done to improve the classical theory. With the recent development of a simulation approach to fracturing design, it has been recognized that fluid loss can be computed directly by solving the basic multiphase flow equations in porous media. Such an approach is more general and does not have many of the assumptions that limit the classical theory. However, the computational cost is much higher and the data required to describe the process are difficult to measure. This paper presents a generalization of the classical approach that includes the effect of several parameters that are variable in the field. The mathematical formulation includes the model of filter-cake behavior developed by the author and the results of the work of Blot et al., which improves the calculation of flow in the reservoir. The model is then formulated numerically, which allows us to introduce the effects of variable pressure, fluid viscosity, and different fluids contacting the wall in the filtration process, in accordance with real conditions during the treatment. Comparison with the experimental data of McDaniel et al. shows that the model is capable of exhibiting nonlinear behavior matching the laboratory data, which cannot be explained in terms of the previous simple theory. An important feature of the model is incorporation of the length of the core, which produces nonlinear behavior and can cause large errors in calculating the true value of the leakoff coefficient when the simple formulas are used. The new model retains the simplicity of the classical leakoff theory, although it is more comprehensive and potentially more accurate than the simulation-type potentially more accurate than the simulation-type leakoff calculations, because it is formulated in terms of measurable variables.
Leak-off Models vs. Simulation
The flow of fracturing fluid into the reservoir can be described, at least in principle, by the equations of multiphase flow in porous media. It would thus seem natural that an improved treatment of fluid loss would use numerical simulation of flow in the reservoir with the properties and pressure at the wall (behind the filter properties and pressure at the wall (behind the filter cake) as the boundary conditions. This approach, which we have taken in our current work, is indeed more general. It is not restricted by the assumption of one-dimensional (1D) flow, and it includes the effects of relative permeability and capillary pressure and handles changing conditions at the fracture face. However, the simulation approach also has problems. First, the process of fracture fluid filtration is more complicated than the reservoir multiphase flow. The properties of the invading fluid are greatly different from the properties of the invading fluid are greatly different from the reservoir fluid and are changing with time because of breakers, temperature changes, and mixing. The fluid can be miscible with one of the resident fluids. The proper formulation would require solution of three-phase proper formulation would require solution of three-phase flow (one phase being the fracture fluid) with relative permeability, capillary pressure, and viscosities permeability, capillary pressure, and viscosities changing with time. Even though such a formulation and solution is possible, the multiphase data are almost impossible to obtain because of the nonlinearity and instability of the gets. Consequently, one must make simplifying assumptions (e.g., the filtrate assumes the properties of the reservoir water). On the numerical level, an extremely fine grid would be required owing to usually very small penetration of the fracture fluid.
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