Fracturing Models

Summary - Models for Fractured Injection

Summary

This page is a summary overview of some of the key aspects of monitoring PWRI operations. You can move on to evaluate tools, methods and models in more detail by clicking here.

Contacts

Karim Zaki karim@advantekinternational.com Advantek International

Key Issues

Models for Fracture Propagation

The available models have been described and have been compared in tabular form. The models are reviewed and compared but there is no endorsement of any one particular model. Each has its strengths can weaknesses.

The fracturing models evaluated included:

BPOPE: Planar fractures of arbitrary shape are modeled using a three-dimensional boundary element method. Fracture growth is governed by linear elastic fracture mechanics. Pore pressure and thermal stress changes are coupled in this model using a three-dimensional finite difference reservoir simulation of fluid and heat flow in the region around the well. At each time step during injection, the pressure, saturation and temperature are calculated in the gridblocks of the reservoir model, using the fracture as the fluid source term. At intervals, the stress state in the plane of the fracture is calculated and the fracture size is updated so that it is in equilibrium with the new stress field. The effect of face-plugging due to suspended solids is modeled as a static filtration process. Model constants can be determined from core flooding tests. This model for formation damage due to suspended solids was found reasonable for low solid content injection.
BP Spreadsheet: This two-dimensional model is capable of modeling produced water re-injection into multiple zones such as for multi-lateral wells. Fluid flow in a deviated well is first modeled for both laminar and turbulent flow. Various pressure losses such as frictional loss along the pipe and perforation friction are considered explicitly. Both matrix injection with formation damage and fracturing injection are considered. The fracturing model considers a fracture with a fixed fracture height. Stress changes due to temperature and pore pressure changes are considered. Formation damage due to suspended solids and oil in water is considered. Permeabilities in the vertical and horizontal directions do not need to be the same. The well can be vertical or deviated.
GEOSIM: This model considers many of the differences between conventional hydraulic fracturing and long term, lower rate water injection. One of the major differences is leak-off and thus efficiency. Fluid efficiency for stimulation fracturing is much higher than the fluid efficiency for PWRI. Therefore, the conventional Carter leakoff model was revisited in the model and a two-dimensional leakoff model adopted. This model shows that Carter’s leakoff model may underestimate leak-off by several orders of magnitude, especially for low injection rates. The model presents a mechanism to partially couple the fracturing model with reservoir simulation, where fracture dimensions are determined from the fracturing model and reservoir model is executed with the predetermined fracture. Modelling parameters can be adjusted in order for the two models to give the same injection pressure. The model is capable of considering variations in thermal stress, pore pressure and saturation in the water invaded zone. This model also considers effects of previous injection, and pre-existing propped/acid fractures. These features are important in analyzing step rate tests and fall-off tests after a period of injection.
HydFrac: HydFrac (developed by TFE) is a numerical model based on a three-dimensional, two-phase thermal reservoir simulator. It incorporates fracture mechanics and formation plugging due to injected particles. Special attention is paid to the analysis of fracture closure during injection shut-in and to the description of formation damage. The media are represented as heterogeneous, anisotropic and compressible and there is a thermo-poroelastic stress model. After fracture initiation, propagation is described by a two-dimensional PKN model with a model for fracture plugging by particles. Internal and external filter cakes are considered.
MWFlood: MWFlood (avaialble commercially from Meyers and Associates) is a pseudo-three-dimensional simulator for predicting the pressure and geometry of conventional hydraulic fractures associated with waterflooding. The program was specifically designed for evaluating the effects of injecting large fluid volumes over long periods and for fracture efficiencies approaching zero. MWFlood has options for conventional (diffusion controlled) and steady-state (non-diffusion) fluid loss. "At early times, fluid loss from the fracture is generally diffusion controlled, but at large times the fluid loss is governed by steady-state or pseudosteady-state leakoff. The fluid loss option has a marked effect on fracture geometry with larger leakoff rates at later times as compared to diffusion alone."
Perkins and Gonzalez Model: This is one of the earliest fracturing models that consider thermal stress and pore pressure change during injection. The model considers thermal stress that would result from cooled regions with fixed thickness and elliptical cross section. Thermoelastic stresses for a region with an elliptical cross-section and finite thickness are determined approximately with a numerical procedure. Empirical equations were developed to estimate the average interior thermal stresses in elliptical cooled regions of any height. Stress changes induced by pore pressure changes during fracturing are calculated using the same equations that were derived for thermal stresses. Since for linear elasticity, the form of the equations is the same, this is accomplished by replacing the linear thermal expansion coefficient with the coefficient of pore pressure expansion and temperature change with pore pressure change. The computed thermal stresses and stress changes due to pore pressure changes are coupled with closed-form solutions for a PKN hydraulic fracturing model to determine fracture dimensions – including length and width as functions of injection volume or time. Examples, using typical elastic and thermal properties, showed that injection of cool water can reduce in-situ stresses around injection wells substantially, causing them to fracture at pressures considerably lower than would be expected in the absence of the themoelastic effect. Thermal effects have been proved to be a very important factor in many water injection projects. A mechanism is also presented in the model to study the effect of water quality on injection performance.
Predictif:This model (developed by TFE) first considers the wellbore temperature profile as water flows down the injection string from the surface to bottom-hole. A linear geothermal gradient is assumed in calculating the temperature distribution along the wellbore. Thermal stress and poroelastic effects are considered in the model using the solution given by Perkins and Gonzalez.[2] Two-dimensional hydraulic fracturing model such as KGD is used in predicting fracture length and fracture width. Radial flow is considered before fracturing. Case studies are available to show the importance of thermally induced fracturing in water injection. Based on the model, the entire injection history can be divided into different regimes and the injection history over each regime can be matched with the model.
PWFRAC: PWFRAC was developed for the PEA-23 project and is not in the open literature. All of the information presented here is from the feature article in the October 1999 PWRI Newsletter (Volume 1, No. 3). Coupling of the pore fluid movement, pore pressure change, and stress changes associated with injection operations are incorporated in the model. Both internal formation damage and external cake are considered. When the open gap (the part of the fracture that is open between the filter cake on the fracture walls) does not extend to the tip of the fracture, the pressure-flow relationships along the open fracture gap satisfy the usual equations for viscous hydraulic flow between two surfaces. The pressure within the closed gap (designated as a tip plug) may have different pressure profiles, depending on the filter cake permeability. Opening of the fracture is computed from pressure along the fracture, based on poroelastic theory, resulting from Darcy flow in the formation. The fracture propagation criterion is based on a stress intensity factor. The filter cake buildup is linked to the amount of solid particles that are deposited by PW entering the formation at the fracture face. Erosion of particles, caused by shear stresses on the filter cake surface, and the pressure drop across the filter cake are also considered. The model also provides a detailed description of the near-tip region.
Shell/Maersk Models: This two-dimensional model has been described Ovens and Niko and Ovens et al. The Barenblatt fracture growth criterion is combined with thermal and poroelastic effects and fracture toughness to yield a compact formulation, relating changes in fracture length to changes in fracture pressure. It is assumed that fractures grow with a constant height. Two dimensionless parameters are introduced: one relates the magnitude of in-situ stress changes due to thermal and poroelastic effects and one relates to toughness. Proximal producers are not considered. Coupling with a reservoir simulator is necessary for considering injector/producer interaction. Flux of water exiting the fracture is uniformly distributed along the length of the fracture.
Shell 1: This is another one of Shell's internal PWRI models. The model is an extension of Koning’s model for waterflood-induced fracturing. The fracture is assumed to fully penetrate a permeable layer and is bounding above and below by impermeable material. The fracture is surrounded by four elliptically shaped zones that include an impaired zone where oil and/or solids have penetrated, a cooled (or heated depending on the injected fluid) zone, a zone flooded by injected water that "has warmed up," and, a virgin oil zone. Each zone is characterized by its own temperature, saturant viscosities, and relative permeabilities. The extent of each zone is determined from mass balance as well as heat capacities of the water and the target formation (using the methods outlined in Koning’s thesis). The fracture face is covered with an external filter cake consisting of injected oil and solids that have not penetrated into the formation. Eventually, the fracture may be filled with solids (oil) that have not penetrated into the formation, leading to a finite fracture conductivity. This is a significant departure from Koning’s model.
Shell 2: This is a pseudo-three-dimensional fracture growth model which permits the description of elliptical fractures in a multi-layered reservoir. Symmetrical vertical growth is not a pre-requisite. This model is analytical and it is coupled with a reservoir simulator. It is assumed that fracture growth and development of the pressure field can be decoupled. This permits modelling of the pressure field in the reservoir using a constant fracture length. The transient pressure is approximated by applying the Laplace equation with a moving boundary for the pressure disturbance. Fracture friction (shear) is ignored although pressure drop along the length of the fracture can result due to plugging. It is assumed that when multiple layers are present that there is no crossflow in the reservoir.
TerraFrac^TM: TerraFrac^TM is a PC-based hydraulic fracturing simulator with fully coupled three-dimensional elasticity and two-dimensional fluid flow between fracture surfaces. Fracture growth is governed by fracture mechanics. The fracture is subdivided into discrete triangular elements by an adaptive meshing generator and the governing equations for these elements are solved by an approach similar to finite element method. That is, the modal force and displacement are related by a stiffness matrix. These governing equations consists of elasticity equations that relate the pressure over the fracture to the fracture opening for an arbitrary shaped, planar fracture, fluid flow equations that relate the flow of the slurry between the fracture surfaces to the pressure gradients in the fluid, and, a fracture criterion that relates the intensity of the stress state ahead of the fracture front to the critical stress intensity necessary for tensile fracture of the rock. Thermoelastic and poroelastic effects are considered in the model. Elastic modulus contrast between layers and their effects on fracture growth are modeled. For long-term injection, fractures can cross many different zones and all or parts of the fracture can close during injection. The model can simulate fracture closure on part of the fracture and re-opening if pressure becomes high enough again during injection.
VISAGE^TM: The VISAGE^TM System provides for two software options in approximating hydraulic and thermal fracture propagation during reservoir simulations in both small (around wells) and large scale reservoir simulations. The first option caters for partially coupled simulations, whereby VISAGE^TM when linked to ECLIPSE, VIP, ATHOS and FRONTSIM forms the SIM2VIS System. The second option is to use a fully coupled stress/fluid/thermal multiphase flow module VIRAGE. It also offers a fully coupled stress sensitive multiphase flow Simulator, the VIRAGE module, for approximate fracture propagation studies in a compressible non-linearly deforming porous media.
WID: WID is a PC-based simulator developed at the University of Texas at Austin. It can accommodate layered reservoirs, horizontal wells, and constant injection pressure boundary conditions. The principles are as follows:
- Determines the concentration of deposited particles around the injection well as a function of time and distance from the well. This is done by solving the filtration equations in that region.
- Calculate the altered permeability in the near-well zone due to retained particles.
- Determine how this near-well damage changes the injectivity of the well. This depends on the formation parameters as well as the completion geometry.
- Calculate the transition time, i.e., the time where an external filter cake starts building on the wellbore. Before the transition time, only internal filtration is considered. After the transition time, only external damage is considered. The default porosity for the external cake is 0.25 and permeability is calculated from particle size and the Cozeny equation.

Models for Soft Formations

Some models can approximate behavior in soft formations. Click here for more information on modelling soft formations.

Models for Matrix Injection

Click here for more information on modelling under matrix injection conditions.

An Index of Monitoring Topics

Monitoring: Models and monitoring methods often go hand in hand. If you click here you will go to an index that will let you choose more detailed information on monitoring methods, and on hydraulic fracturing models.

Background on Models: If you would like to go to a Tutorial on models used for simulating fractured PWRI injectors, select from one of the links in the box below.

An Introduction
Differences From Stimulation Models
Types of PWRI Models
Audit of PWRI Models

Top Previous Next Documents