This paper presents fracture simulations of multiple, interacting, non-planar fractures in three dimensions. The paper provides a short description of the mathematical formulation of the model but the primary focus is on fracture propagation examples and illustrations of how multiple hydraulic fractures interact in three dimensions. The examples which are presented are intended to provide insight into how the number of growing fractures affects fracture shapes, how changes in fluid viscosity can cause fractures to grow together or grow apart, and how limited-entry at the perforations affects the propagation of interacting fractures. The fracture simulator discussed in this paper models the simultaneous growth of non-planar hydraulic fractures in a three-dimensional linear elastic media, and it can also incorporate stress shadows from hydraulic fractures created during earlier fracture stages. The program uses a symmetric Galerkin boundary element method to model fracture shapes and fracture growth, while flow in the fractures is modeled as power-law fluid flow in arbitrary curved channels. The program uses an effective mode-I stress intensity factor to determine which portions of each fracture will propagate and employs mixed-mode stress intensity factors, K I and K II , to determine propagation directions.

A new geomechanical reservoir simulator has been developed that combines hydraulic fracture growth, multiphase/multicomponent Darcy/nonDarcy porous flow, heat convection and conduction, solids deposition, and poroelastic/poroplastic deformation in a single application. The equations for the different mechanisms such as fracture-width changes, laminar-channel flow in the fracture, porous flow in the reservoir, heat convection and conduction, and poroelastic/poroplastic deformations are combined to produce an implicit fully coupled formulation. The nonlinear system of equations is solved through use of a full Newton-Raphson expansion of all solution variables, which enhances solution stability and allows second-order convergence rates for the nonlinear iterations.The program contains two separate criteria that one can use to model fracture propagation. Fracture-growth computations can be based on critical stress-intensity factors or can use cohesive elements that exhibit strain-softening behavior. The critical stressintensity factor is based on the asymptotic stress/strain state at the tip of a fracture and is limited to linear poroelastic applications or applications in which the plastic zone is small relative to the fracture length; while cohesive elements are based on energy-release rates and cohesive stresses and can be used for both poroelastic and poroplastic applications. In addition to the fracture-propagation logic, the program allows a dry zone to develop at the fracture tip as a natural part of the solution process. It is shown in sample simulation that a dry zone may develop naturally at the tip of a propagating fracture when there is a large pressure drop down the fracture.The new geomechanical simulator is described and several examples are included to demonstrate the predictive capability of the application. Examples are also included to highlight the differences between the two fracture-propagation models and to illustrate when a dry zone may be expected to develop at the fracture tip. The examples also allow one to compare the program's predictions with analytic solutions validating the fracture propagation algorithms used in the application.

A new geomechanical reservoir simulator (GMRS®) has been developed which combines hydraulic fracture growth, multiphase/ multi-component Darcy/non-Darcy porous flow, heat convection and conduction, solids deposition, and poroelastic/poroplastic deformation in a single application. The equations for the different mechanisms such as fracture width changes, laminar channel flow in the fracture, porous flow in the reservoir, heat convection and conduction, and poroelastic/poroplastic deformations are combined to produce an implicit fully-coupled formulation. The nonlinear system of equations is solved using a full Newton-Raphson expansion of all solution variables which enhances solution stability and allows second order convergence rates for the nonlinear iterations. The program contains two separate criteria that one can use to model fracture propagation. Fracture growth computations can be based on critical stress intensity factors, or can use cohesive elements that exhibit strain-softening behavior. The critical stress intensity factor is based on the asymptotic stress/strain state at the tip of a fracture and is limited to linear poroelastic applications or applications where the plastic zone is small relative to the fracture length, while cohesive elements are based on energy release rates and cohesive stresses and can be used for both poroelastic and poroplastic applications. In addition to the fracture propagation logic, the program allows a dry zone to develop at the fracture tip as a natural part of the solution process. It is shown that a dry zone develops naturally at the tip of a propagating fracture for an example having a largepressure drop down the fracture. The new geomechanical simulator is described and several examples are included to demonstrate the predictive capability of the application. Examples are also included to highlight the differences between the two fracture propagation models and to illustrate when a dry zone may be expected to develop at the fracture tip. The examples also allow one to compare the program's predictions with analytic solutions validating the fracture propagation algorithms used in the application. Introduction There are several different fracture simulators, both finite element (Lam and Cleary 1986; Boone and Ingraffea 1990; Papanastasiou 1997; Lujun and Settari 2007) and boundary element (Clifton and Abou-Sayed 1979; Yew and Liu 1993; Yamamoto et al. 1999; Rungamornrat et al. 2005) that predict hydraulic fracture geometry. Even though there are several fracture simulators, there are very few simulators that model complex reservoir flow, geomechanics, and fracture growth in a single application. The fracture model by Lujun and Settari uses a critical stress criterion for propagation, uses an iteratively coupled technique to combine the different physical aspects of the problem, and combines the flow in the fracture with the reservoir flow to account for fluid flow in and near the fracture. The model presented in this paper is similar in some ways to the model presented by Lujun and Settari, but allows one to use a stress intensity factor or cohesive elements for fracture propagation, uses separate grids for modeling flow in the fracture and reservoir, and fully expands the Jacobian for the full system of equations and solves all equations simultaneously in the linear solver. Modeling the fracture flow separate from the reservoir flow allows one to account for a dry zone at the fracture tip, and using a fully expanded Jacobian from an implicitly coupled system of equations provides more stability for the solution process. Numerical stability may be critical when dealing with fracture growth, cavity generation, or with any simulation that involves very small cells.

Summary This paper reports the first results of stress-oriented and aligned perforating of deviated wells at the Kuparuk River field, Alaska. Preferred perforation alignment and Preferred perforation alignment and spacing are calculated for each well so the fractures from individual perforations link to produce a single perforations link to produce a single "zipper" fracture plane along the deviated wellbore. Results of the first application of this technique are presented from the 26-well development presented from the 26-well development of Drillsite 2K. The results from use of three different oriented casinggun systems and pertinent data from Drillsite 2K fracture stimulation treatments are discussed. Comparisons to drillsites where nonaligned perforating strategies were used show a perforating strategies were used show a significant reduction in perforation friction, enabling the placement of larger, more productive fracture treatments. Application of this technique to deviated and vertical wells and its use at Kuparuk on developments after Drillsite 2K are discussed. Introduction Perforation design for a well that will be Perforation design for a well that will be hydraulically fractured is usually controlled by the requirements to place the stimulation treatment. Key parameters are the number, size, orientation, and phasing of perforations. Typically, the objective is either perforations. Typically, the objective is either to minimize or, in the case of limited entry treatments, to control the amount of perforation friction during the stimulation perforation friction during the stimulation treatmeat. No uniform criteria exist within the industry for defining perforation phasing or shot density. Different operators use different techniques. However, the pumping of a fluid stage to break down the well and to calculate the perforation friction loss is routine to verify that sufficient communication exists between the wellbore and the formation to place the fracture treatment. Often, a ballout treatment is pumped before the main stimulation to force additional perforations to breakdown. Although it is perforations to breakdown. Although it is generally acknowledged that the optimal placemeat of perforations in a vertical well is placemeat of perforations in a vertical well is 180 phasing in the fracture plane, which is perpendicular to the far-field minimum stress, there are, to the best of our knowledge, no reported efforts of routinely practicing such a technique. Laboratory practicing such a technique. Laboratory investigations into fracture initiation from deviated wells showed the importance of perforation placement on the length of perforation placement on the length of wellbore intersecting the fracture. During the past 7 years, more than 600 new development wells have been fracture -stimulated in the Kuparuk River field. The large number of treatments has provided the opportunity for significant advances in the technical and operational aspects of hydraulically fracturing deviated wells that are not aligned colinear to a direction of principal stress. The success of this stimulation principal stress. The success of this stimulation program was documented in Refs. 4 and 5. program was documented in Refs. 4 and 5. Perforation strategy during the initial development consisted primarily of perforating the net pay intervals in the Kuparuk A sand. Depending on the drillsite, this would result in the perforating of two or three separate zones. Before the wellbore tubulars and completion equipment were run, casing guns (4 1/2-in.) were shot with a typical shot density of 4 shots/ft and a phasing of either 90 or 120. We often used largehole shots every fifth hole. Most initial fracture treatments pumped in wells where this strategy was used had relatively high perforation friction drops ranging from 500 to perforation friction drops ranging from 500 to 1,500 psi. Post-treatment temperature and tracer logging often showed fluid entry into a few discreet points along the perforated interval, with the lowest zone of the A sand often showing no evidence of fracture stimulation. The poor communication at the wellbore is thought to have caused many treatment screenouts in the field.

Problems in hydrology frequently have moving fronts and dynamic driving mechanisms such as wells. Since the location of important features changes during a simulation, accurate modeling requires uniformly fine resolution or the ability to change resolution during the simulation. We will describe an algorithm for refinement and unrefinement of tetrahedral/triangular meshes that has been implemented in the adaptive hydrology (ADH) code. The codes including the refinement/unrefinement algorithms are implemented in parallel to accommodate problems with large run time and memory requirements. In this paper, we describe the parallel, adaptive grid algorithm used in ADH and show the resulting grids from some example problems.