bluuebunny/crossref_metadata_2025_split huggingface dataset:
PEBI Grid Selection for Numerical Simulation of Transient Tests
Authors: Escobar Freddy H. , Tiab Djebbar 
Published: December 2007

Abstract
Accuracy and efficiency of reservoir simulators in complex systems depend highly upon a proper grid selection. Grids based on a cartesian coordinate system have been widely used, but have some disadventages: (a) Flexibility in description of faults, pinchouts, hydraulic fractures, horizontal wells and general discontinuities presented in reservoirs, (b) inflexibility in representing well locations; and (c) suffer of grid orientation effects1,6.
Local grid refinement2, nine-point3,4, and thirteen point5 schemes were introduced to enhance the performance of cartesian grids. Research has covered other techniques to reduce grid orientation effects, starting from the development of a uniform hexagonal grid block pattern until the application until the application of Voronoi or PEBI grids. However, the experience on PEBI grids is very limited since their application and development are still in their childhood, as far as the oil industry is concerned. PEBI grids have been applied to the oil industry for about a decade. Besides, last applications are being introduced during the last three years. On the other hand, generation and construction of PEBI grids are not as easy as cartesian grids. The construction of a PEBI grid for a reservoir is feasible only if it is done by a numerical grid generation procedure. A PEBI (PErpendicular BIsection) grid or Voronoi6,7 grid is defined as the region of the space that is closer to its gridpoint than to any other gridpoints. The PEBI is locally orthogonal. It means the block boundaries are normal to lines joining the nodes on the two sides of each boundary. This allows a reasonable accurate computation of interblock transmissibility for heterogeneous but isotropic permeability distribution.
Currently, five types of PEBI grids–namely: hexagonal, elliptical, rectangular, circular and varieable – are being applied, but there is no evidence of their limitations and/or applicability to simulate well transient behavior. Therefore, the point of this paper is to establish and recommend their use for simulation of transient pressure behavior horizontal wells, vertical wells and vertical hydraulic fractured wells. The effectiveness of the PEBI grids was tested by matching numerical to analytical results.
It was found and shown though simualtion experiments that any PEBI grid describes very well the transient behavior of a horizontal well, however, it is not the same for vertical wells. For instance, it is shown that only the elliptical PEBI grid describes transient behavior of hydraulically fractured vertical wells. Circular PEBI grids are good to simulate vertical unfractured wells. Additionally, it is also demonstrated through different simulated experiments the power of PEBI grids to handle non-orthogonal systems8.
A Multi-Level Iterative Method For Solving Finite Element Equations
Authors: Bank Randolph E. , Sherman Andrew H. 
Published: December 2007

Abstract
Subroutine PLTMG is a Fortran program for solving self-adjoint elliptic boundary value problems in general regions of R2. It is based on a piecewise linear-triangle finite element method, an adaptive grid refinement procedure, and a multi-level method to solve the resulting sets of linear equations. In this work we describe the method, and present some numerical results and comparisons.

Introduction
Consider the model elliptic boundary value problem problem(1.1)
where the coefficient a(x,y) (b(x,y)) is positive (nonnegative) in omega. In this work we discuss the performance of a program which solves (1.1) using a performance of a program which solves (1.1) using a Rayleigh-Ritz-Galerkin method based on piecewise-linear triangular finite elements, a multi-level piecewise-linear triangular finite elements, a multi-level iterative scheme for solving the resulting matrix equations, and an adaptive grid refinement procedure. A more detailed discussion of the program appears in [14].
For expositional convenience, we assume g1 + g2 = 0, and that omega is a polygon, although our FORTRAN subroutine PLTMG is designed for the more general equation (1.1).
In the Rayleigh-Ritz-Galerkin procedure, we seek an approximate solution to the weak form of
(1.1)
(1.2)
where
and (,) denotes the usual L2(omega) inner product. We use (omega) (omega) to denote the subspace of the usual Sobolev space (omega) whose elements satisfy essential boundary conditions. Associated with the bilinear form a(,) is the energy norm= a(u,u).
Let denote a triangulation of omega, and let(omega) denote the N-dimensional space of C piecewise-linear polynomials associated with. The piecewise-linear polynomials associated with. The finite element approximation of u in (1.2) is the function epsilon which satisfies
(1.3)
Once a basis for has been selected (the nodal basis is usually chosen), (1.3) can be reformulated as a system of linear equations
(1.4)
where Aij = a(phi j, phi i), and Fi = (f, phi i). Usually N is large and the stiffness matrix A is sparse.
Our multi-level solution procedure involves a sequence of nested triangulations, with nested in, and the corresponding Nj-dimensional subspaces,, of C0 piecewise-linear polynomials. (By nested, we mean that each triangle polynomials. (By nested, we mean that each triangle of intersects the interior of exactly one triangle of. Corresponding to each subspace N is the problem Pj, the analog of (1.3): Find uj epsilon Mj satisfying
(1.5) a(uj,v)=(f,v) for all v epsilon j.
Solving Approximations To The Convection Diffusion Equation
Authors: Eisenstat S.C. , Elman H. , Schultz M.H. , Sherman A.H 
Published: December 2007

Abstract
Several numerical algorithm for solving a discretized version of the convection-diffusion equation are examined. The algorithms considered areiterative methods derived from the conjugate gradient method, with preconditioning by point - SSOR and incomplete LU factorization. The results ofnumerical experiments with the algorithms, for various values of the coefficient of the convection term and various mesh sizes, are reported.
We consider algorithms for solving a finite difference discretization of the convection-diffusion equation(P)â?'(uxx+u yy)+Bux=f
on the unit square with homogeneous Dirichlet boundary conditions. For the discretization of (P), we use the modified upwind scheme described by Axelsson and Gustafsson [1].[2/(1+(1/2)Bh)+2+Bh] u(i,j)â?'[1/(1+(1/2)Bh)]u(i+1,j)â?'u(i,j+1)â?'[1/(1+(1/2)Bh)â?'Bh] u(iâ?'1,j)â?'u(i,jâ?'1)=f(i,j).
which provides order of accuracy 0(h**2), where h is the mesh size. If the coefficient B of the convection term is nonzero, then the above system of linear equations is nonsymmetric.
The conjugate gradient algorithm for solving systems of linear equationsAx=b
requires that the matrix A be symmetric and positive definite. This paper reports the results of some numerical experiments run on a collection of algorithms modeled after the conjugate gradient algorithm for which it issufficient that the symmetric part M of A,M=(1/2) (A+AT),
be positive definite,
Three classes of algorithms are considered:a collection of algorithms modeled after the conjugate residual algorithm(described below);the generalized conjugate gradient algorithm developed by Concus and Golub[3] and Widlund [9] andthe conjugate gradient algorithm applied to the normal equationsATAx=ATb.
The conjugate residual algorithm for the symmetric problem consists of the following iteration:Choose x(0).Compute r(0)=bâ?'Ax(0)Set p(0)=r(0).
For i=0,1,2, . . ., computea(i)=(r(i),Ar(i)/(Ap(i),ap(i)),x(i+1)=x(i)+a(i)p(i),r(i+1)=r(i)â?'a(i)Ap(i),b(i)=(r(i+1),Ar(i+1))/(r(i),Ar(i))p(i+1)=r(i+1)+b(i)p(i)
Ignoring roundoff error, this algorithm produces the solution to the system of equations in at most N iterations, where N is the size of the system (see Chandra, [2]). Each direction vector p(i) is ATA-orthogonal to the previous directions computed. The choice of a(i) minimizes the L 2-norm of the residual r(i+1) considered as a function of a(i). x(i+1) is also the point in the affine spacex(0)+&lt;p(0), . . . , p(i)&gt;
which minimizes the L2-norm of the residual.
Novel High Membrane Efficiency Water-Based Drilling Fluids for Alleviating Problems in Troublesome Shale Formations
Authors: Tan Chee P. , Amanullah Mohammed , Mody Fersheed K. , Tare Uday A. 
Published: December 2007

Abstract
A major collaborative effort was undertaken to develop novel environmentally acceptable water-based drilling fluids with high membrane efficiency to help meet the future requirements of the petroleum industry. This paper describes the development of the drilling fluids and practical guidelines for maintaining shale stability with the drilling fluids. Specialised test equipment, including a membrane efficiency screening equipment, and test procedures were developed for simulation of key drilling fluid-shale interaction mechanisms. More than 300 membrane efficiency screening tests were performed on Pierre II shale samples to screen a wide range of novel compounds for their membrane generation capacity in the shale. Typical examples of the tests conducted with three novel compounds that generated moderately and highly efficient membranes are presented and discussed. The results demonstrate that some of the compounds are capable of generating membrane efficiencies of between 55% and 85%. The new generation of water-based drilling fluids developed performs essentially like oil-based muds in terms of shale stabilisation. Practical mud design guidelines developed can be used to optimise the drilling fluid design, in terms of mud weight, salt type and salt concentration, to manage time-dependent well-bore instability in troublesome shale formations efficiently.
Phenomenological Inventory Analysis of Underground Gas Storage in Salt Caverns
Authors: Steinberger Anita , Civan Faruk , Hughes Richard G. 
Published: December 2007

Abstract
This paper presents a model for effective management of natural gas storage in salt caverns. An interactive and dynamic phenomenological inventory model is developed that considers the effects of hydrocarbon thermodynamics, phase behavior, and heat and mass exchanges along cavern walls during gas loading, storage and unloading. The model predicts cavern behavior and accounts for gas ballooning, losses due to porous characteristics and leaky salt formation fractures, variation of temperature and pressure, vapor and liquid composition changes and cavern volume change due to salt creep. The model consists of a set of coupled nonlinear algebraic and differential equations, for which the solution as a function of time is obtained by numerical means. The capabilities of the proposed model are demonstrated by analyses of several field scenarios. The dynamic response of the cavern-well assemblage to injection and production cycles is simulated.
Making a Case for Rethinking Lost Circulation Treatments in Induced Fractures
Authors: Ivan Catalin D. , Bruton James R. , Thiercelin Marc , Bedel Jean-Philippe 
Published: December 2007

Abstract
The challenges of preventing and controlling fluid losses when drilling formations prone to induced fractures have been well documented. The narrow operating window between pore pressure and fracture gradient often results in massive fluid losses when drilling, running casing, and cementing.
Many products and techniques have been used in attempts to restore circulation while drilling induced fractures. These include fibrous, flaky and granular materials, as well as techniques such as gunk and reverse gunk squeezes, high fluid-loss squeezes and cement squeezes. Even though these techniques sometimes restore partial or full circulation, more often than not they are temporary solutions as losses often reoccurre as drilling proceeds. It was thought that the particulate materials and the high compressive strength lost-circulation pills first were failing to reach the tip of the induced fracture and nevertheless were acting as a proppant, thus not allowing the fractures to heal. The low fracture reopening pressures then allow for continued losses.
More recently, a new generation of chemically activated cross-linked pills has been developed and applied to challenging induced fractures environment to cure and limit losses.
This paper substantiates the observed effectiveness of soft visco-elasto-plastic lost circulation pills in solving lost circulation problems in induced fractures as well as the application of the cross-linked polymer pills. The work presented in this paper first consisted of determining the mechanical properties of these pills under downhole conditions by using a vane rheometer. The theory of hydraulic fracture mechanics was then applied to model the behavior of these visco-elasto-plastic soft pills and demonstrate the superiority of these pills in solving lost circulation problems. Results show that once the soft cross-linked polymer pills have been squeezed into the induced fracture, the fracture gradient has been increased. This behavior, enhanced by the gel elasticity, helps the fractures to heal and the losses to be stopped. In addition to healing fractures, the soft cross-linked polymer pills also provide a mechanism for bridging micro-fractures and thus preventing losses into the formation.
Application of Quantitative Risk Analysis to Pore Pressure and Fracture Gradient Prediction
Authors: Liang Q. J. 
Published: December 2007

Abstract
The present deterministic pore pressure and fracture gradient prediction techniques simplify the input variables from a statistical range of data to a deterministic value, thereby producing over-simplified deterministic pore pressure and fracture gradient results. As a consequence, we lose the ability to quantitatively analyze risks, and we cannot quantify the uncertainties of our pore pressure and fracture gradient prediction.
This paper describes a methodology for quantitative risk analysis (QRA) of pore pressure and fracture gradient prediction and shows that applications of QRA in this area will improve the techniques of pore pressure and fracture gradient calculations. In addition, QRA will open a full range of new applications in risk prediction, risks evaluation, risk management, decision making, real-time kick and loss-return risk monitoring, risk control, and casing design.
Assessing the Value of 3D Seismic Data in Reducing Uncertainty in Reservoir Production Forecasts
Authors: Varela Omar J. , Torres-Verdín Carlos , Lake Larry W. 
Published: December 2007

Abstract
Using three-dimensional (3D) seismic data has become a common way to identify the size and shape of putative flow barriers in hydrocarbon reservoirs. It is less clear to what extent determining the spatial distribution of engineering properties (e.g., porosity, permeability, pressures, and fluid saturations) can improve predictions (i.e., improve accuracy and reduce uncertainty) of hydrocarbon recovery, given the multiple non-linear and often noisy transformations required to make a prediction. Determining the worth of seismic data in predicting dynamic fluid production is one of the goals of the study presented in this paper.
We have approached the problem of assessing uncertainty in production forecasts by constructing a synthetic reservoir model that exhibits much of the geometrical and petrophysical complexity encountered in clastic hydrocarbon reservoirs. This benchmark model was constructed using space-dependent, statistical relationships between petrophysical variables and seismic parameters. We numerically simulated a waterflood in the mo del to reproduce time -varying reservoir conditions. Subsequently, a rock physics/fluid substitution model that accounts for compaction and pressure was used to calculate elastic parameters. Pre-stack and post-stack 3D seismic data (i.e., time -domain amplitude variation of elastic responses) were simulated using local one-dimensional approximations. The seismic data were also contaminated with noise to replicate actual data acquisition and processing errors. We then attempted to estimate the original dis tribution of petrophysical properties and to forecast oil production based on limited and inaccurate spatial knowledge of the reservoir acquired from wells and 3D seismic data.
We compared the multiple realizations of the various predictions against predictions with a reference model. Adding seismic data to the static description affected performance variables in different ways. For example, the seismic data did not uniformly improve the variability of the predictions of water breakthrough time; other quantities, such as cumulative recovery at a later time, did exhibit an uncertainty reduction as did a global measure of recovery. We evaluate how different degrees of spatial correlation strength between seismic and petrophysical parameters may ultimately affect the associated uncertainty in production forecasts.
Most of the predictions exhibited a bias in that there is a significant deviation between the medians of the realizations and that the value from the reference case. This bias is evidently caused by noise in the various transforms (some of which we introduced deliberately) coupled with nonlinearity. The key nonlinearities seem to be in the numerical simulation itself, specifically in the transform from porosity to permeability, in the relative permeability relationships and in conservation equations themselves.
Real-Time 4D Reservoir Characterization Using Passive Seismic Data
Authors: Maxwell S. C. , Urbancic T. I. 
Published: December 2007

Abstract
This paper details the application of passive seismic monitoring to image reservoir fracturing and deformation from the stage of an initial well completion to final field production. Instrumented oilfields with either permanently seismic arrays or temporarily deployed on wireline, offers the possibility of imaging production activities in a real-time sense that compliments other seismic reflection and enpineering measurements. During the well completion stage of development, real time microseismic imaging of well stimulation offers the ability to ensure the execution of the intended fracture design. Fracture images can also be used to optimize the fracture design and the net present value well production, understand fracture complexity and the associated well drainage pattern to target future well placement. During production, time-lapse microseismic imaging can be used to image deformation associated with fracture sealing and reservoir compartmentalization, localization of deformation associated with compaction, fracture reactivation or pressure or stress changes, monitor deformations in the overburden in fields with casing deformation problems, and image fronts associated with secondary recovery. In this paper, case studies are used to illustrate various potential applications along with discussion of the potential limitations. The reservoir conditions necessary for the successful application are presented along with a potential method to quanitify the technical feasibility at a particular site.
Correlating Particle Size Distribution in a Crushed Zone to Perforating Permeability Damage and Modeling Using Fragmentation Fractal Theory
Authors: Karacan C. Ozgen , Halleck Phillip M. 
Published: December 2007

Abstract
Conventional oilfield shaped charges form a jet consisting of hypervelocity metallic particles, whose pressure pulse can exceed 4 × 106 psi. When the metallic jet hits the rock target, the resulting shock forms a path of mechanically deformed rock as a tunnel. The shock wave also alters the rock mass around the tunnel by fragmenting rock and mineral grains. This is phenomena is an important issue in shaped-charge perforating due to its potential effect on decreasing the permeability of the rock surrounding the tunnel and decreasing the efficiency of costly perforating job. Although operating parameters can be set to remove fragmented sand grains (underbalanced perforating), it is practically difficult to remove all of them to regain the decreased permeability.
Determination of permeability and the thickness of crushed zone around perforation tunnel are important for productivity calculations and especially for near-wellbore modeling. Although productivity of a well after perforating is a good indication of the permeability damage due to perforating, it does not give the permeability distribution at the vicinity of the tunnel. Even in the laboratory shots performed under insitu pressure conditions, it is a difficult task to map the permeability distribution around the tunnel.
This paper proposes an easier way to estimate the permeability distribution in the crushed zone by modeling the distribution of grain fragments using fragmentation fractal theory. The resulting Eq. describes the permeability by a fractal model. It calculates pore size distribution from particle size data by setting up a hierarchical scaling concept for fragmentation to calculate the porosity of incompletely fragmented fractal porous medium. Estimated permeabilities were compared against the permeability distribution measured by using pressure transient analysis and computerized tomography (CT) scanning during injection test. It was seen that the values are close to each other.
New Reservoir Dynamic Connectivity Measurement for Efficient Well Placement Strategy Analysis Under Depletion
Authors: Ballin P. R. , Solano R. , Hird K. B. , Volz R. F. 
Published: December 2007

Abstract
A dynamic measurement of reservoir connectivity based on a parameter called resistivity index (RI) is evaluated. The RI parameter takes into account the pressure effects from wells but does not solve pressure equations. This technique is compared with other static connectivity measurements and with streamlines (another dynamic-connectivity technique) for gas reservoirs producing by depletion. Reference flow simulations were used to validate these comparisons.
Two real field models were used in this study. In both cases, the RI analysis reproduced the reference flow simulation results significantly better than the other techniques while requiring orders of magnitude less time than the finite difference flow simulator. The results of an uncertainty study based on the RI supported the approval of the infill-drilling program for the first field model. This technique has been implemented as a special option for a commercial geostatistical software application.
A Combined Geostatistical and Streamline-Based History Matching Procedure
Authors: Le Ravalec-Dupin Mickaële , Fenwick Darryl H. 
Published: December 2007

Abstract
One of the most challenging subjects in reservoir engineering concerns the conditioning of large reservoir models to the available data: dynamic data in the form of production history and a priori (static) geological or geostatistical knowledge. Streamline simulation has been proposed as an ideal tool for rapid conditioning of large, fine-grid geologic models. We develop a novel procedure that combines a streamline-based history matching method and a geostatistical parameterization technique to estimate the distributions of permeability and porosity in heterogeneous petroleum reservoirs.
An efficient two-step procedure was introduced recently for history matching. It consists first in matching the streamline effective permeabilities to production data, then mapping the resulting perturbations to the grid block permeabilities. This procedure requires relatively simple postprocessing of a single, standard streamline simulation and results in an extremely rapid history match to the production data. However, the mapping step often induces an undesired departure from the a priori geostatistical variability model. To circumvent this drawback, we modify the second step. The "optimal" streamline effective permeabilities obtained at the end of the first step are integrated into a new objective function which is minimized using the gradual deformation method. This parameterization technique allows for matching the "optimal" streamline effective permeabilities by changing the grid block permeabilities while at the same time preserving the a priori spatial variability model.