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ECMOR XIII - 13th European Conference on the Mathematics of Oil Recovery
- Conference date: 10 Sep 2012 - 13 Sep 2012
- Location: Biarritz, France
- ISBN: 978-90-73834-30-9
- Published: 10 September 2012
81 - 100 of 114 results
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Multi-core and GPU Parallelization of a General Purpose Reservoir Simulator
Authors Y. Zhou and H. TchelepiWe describe our multi-threading parallelization strategy of a general-purpose reservoir simulator (GPRS) based on a flexible Automatic Differentiation (AD) framework. Parallel Jacobian construction is achieved with a thread-safe extension of our AD library. For linear solution, we use a two-stage CPR (Constrained Pressure Residual) preconditioning strategy, combining the parallel multigrid solver XSAMG and the Block Jacobi technique with Block ILU(0) applied locally. The speedup of the full SPE 10 problem (1.1M cells) is about 5.0X on a dual quad-core Nehalem node. We then discuss the GPU parallelization of Nested Factorization (NF). The Massively Parallel NF (MPNF) algorithm was first introduced by Appleyard et al. (2011), where the 3D structured grid is divided into kernels, and each kernel is assigned a color such that no neighbouring kernels share the same color. Then, parallelism is exploited in the concurrent solution of all kernels with the same color. The most important aspects of our algorithm are: 1) coalesced memory access via special ordering of the matrix elements, and 2) application of the twisted factorization technique that further improves parallelism. With a 512-core Tesla M2090 GPU, the speedup of the full SPE10 problem is about 26X for single precision, and 19X for double precision.
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HPC-Based Optimal Well Placement
Authors A.M. Kuvichko and A.I. ErmolaevThis paper studies the mathematical aspects of well location and related optimization problems. These problems are formulated in terms or integer programming. Optimal solutions found are to formulate initial sets of cases and to improve the efficiency of oil and gas recovery. Described optimization algorithms are presented as high-scalable parallel programs making a vast majority of cases to be considered. Considered integer programming problems are extremely large-scale problems. The matrix structure, the number of feasible solutions, etc. was taken into account. A new fast algorithm for the generalized assignment (transportation) problem has been designed. Programs implementing this algorithm for CPU and GPU were tested and the results presented. A high scalability and good speedup achieved. Performed tests had also shown better timing results comparing to well-known common algorithms. It is reasonable to use the approach studied in the paper to design a set of appropriate initial cases for the small fields or fields with a complex geology. Presented workflow finds optimal well positions for a field or its part. A Brugge field has been taken as a test case. An improvement of production and NPV achieved the comparison between an initial and an optimal case presented.
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A Multilevel Multiscale Finite Volume Method
More LessThe Multiscale Finite Volume (MsFV) method has been developed to efficiently solve reservoir-scale problems while conserving fine-scale details. The method employs two grid levels: a fine grid and a coarse grid. The latter is used to calculate a coarse solution to the original problem, which is interpolated to the fine mesh. The coarse system is constructed from the fine-scale problem using restriction and prolongation operators that are obtained by introducing appropriate localization assumptions. Through a successive reconstruction step, the MsFV method is able to provide an approximate, but fully conservative fine-scale velocity field. For very large problems (e.g. one billion cell model), a two-level algorithm can remain computational expensive. Depending on the upscaling factor, the computational expense comes either from the costs associated with the solution of the coarse problem or from the construction of the local interpolators (basis functions). To ensure numerical efficiency in the former case, the MsFV concept can be reapplied to the coarse problem, leading to a new, coarser level of discretization. One challenge in the use of a multilevel MsFV technique is to find an efficient reconstruction step to obtain a conservative fine-scale velocity field. In this work, we introduce a three-level Multiscale Finite Volume method (MlMsFV) and give a detailed description of the reconstruction step. Complexity analyses of the original MsFV method and the new MlMsFV method are discussed, and their performances in terms of accuracy and efficiency are compared.
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The Gravitational Instability of a Diffusive Boundary Layer; Towards a Theoretical Minimum for Time of Onset of Convecti
More LessIn this paper we extend previous work in on the linearized analysis of gravitational instability of a diffusive boundary layer in a semi-infinite anisotropic homogenous porous medium. We express the time derivative of the square of the standard L^2-norm of a given perturbation as a time dependent quadratic form on an appropriate Hilbert space . Numerical analysis of the spectra of these quadratic forms give rise to results qualitatively similar to previous results in the litterature. We demonstrate that after the time of instability only perturbations having a non-zero projection onto a one-dimensional subspace of are unstable. We also find that the space of neutrally stable perturbations before onset of instability form a large subspace of the space of possible perturbations, where numerical analysis strongly indicate that this subspace is infinite dimensional. Error estimates for a certain part of the numerical analysis are not yet rigorous. In particular, estimating the spectrum of unbounded linear operators using finite matrix approximations still lacks a theoretical basis. However, the largest eigenvalues of larger and larger matrices approximating the operator converge quickly to well defined values, and it is conjectured that the given critical values are the correct ones for the problem at hand.
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Efficiency of Dissolution Trapping in Geological Carbon Storage
Authors M.T. Elenius, J.M. Nordbotten and H. KalischDuring geological storage of carbon dioxide (CO2), several mechanisms contribute to safe storage by immobilizing the CO2 in the injection formation. It has been shown that dissolution into resident brine can be one of the major contributors. The injected supercritical CO2 is buoyant, but dissolved CO2 increases brine density and therefore reduces the tendency for upward CO2 migration. The density increase with dissolved CO2 leads to convective mixing of the brine, thereby enabling more CO2 to dissolve. It is important to quantify the efficiency of CO2 dissolution, and therefore the efficiency of convective mixing. In previous work, we have shown that convective mixing can be considerably enhanced when taking into acccount the interaction between the two-phase region (supercritical CO2 and brine), and the single-phase brine region. Bounds on this impact were obtained for onset times, wavelengths of unstable fingers, and dissolution rates. The maximum increase in the dissolution rate was found to be large, when interaction with the plume was considered. In this paper, we use stability analysis to further study the dissolution in more detail. We make technical contributions to the field of stability analysis and in obtaining more reliable estimates of the efficiency of dissolution trapping.
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Evolution of Seismic Responses due to CO2 Injection in Carbonates Including Chemical Reactions and Rock-Physics Model
Authors L.G. Rodrigues, J.P. Nunes and D.R. GuérillotThe increase in worldwide activities related to CO2 injection in geological formations, for both EOR/CO2 and CCS projects, has pushed oil companies and universities to enhance the modeling of these processes for their better (1) designing and (2) monitoring. The objective of this paper is to describe new improvements for these two aspects through a multi-scale methodology of simulations from laboratory experiments to full-field modeling passing by studies around the wells including new rock-physics model. When injecting CO2 in carbonate rocks, one of the most critical aspects is to understand the complex chemical reactions occurring between the acidic fluid formed by the CO2, the in-situ water (connate and aquifer) and the carbonate matrix depending on its mineralogy. The mathematical formulation of the simultaneous thermodynamic equilibrium and the chemical reactions will be described completely. An original construction of the rock-physic model developed for this multi-phase flow based an effective medium theory will be described. A specific power law equation will be proposed to fit the relation between porosity and permeability obtained in the laboratory for carbonate rocks replacing the classically used Kozeny-Carman equation not valid in our case. To improve the quality of the forecasts at the entire reservoir level, simulations at different scales are performed and used sequentially. Results of sensitivity studies with various rock and mineralogy characteristics showing the impact on (a) the porosity and permeability field on the CO2 segregation, (b) the pH evolution in space and time, (c) the synthetic seismograms, will be described. This paper demonstrates the practicality of the modeling approach and software tools to address the design and monitoring of CO2 injected in a geological formation for CO2/EOR and or CCS processes. In particular, it helps the geophysicists and reservoir engineers based on the geological description of the reservoir to design injection plans for EOR or CCS processes defining plans for well tests and seismic campaigns around the wells and in between them (2D or 3D) whether such changes may be observable as a function of time. Technical contributions: 1. Multi-phase flows on realistic carbonate reservoirs with multi-phase thermodynamic equilibrium and geochemical reaction, 2. New rock-physic model for the evolution of the density and velocities used to construct surface seismic responses, 3. Methodology to improve the quality of the full-field forecast checking the results of the simulations results at the laboratory scale and generating synthetic seismograms to design seismic campaigns for monitoring.
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Classification of Digital Rocks by Machine Learning
Authors J. Ma, Z. Jiang, Q. Tian and G.D. CouplesThe availability of high-resolution 3D digital rocks in ever increasing quantities calls for intelligent Machine Learning (ML) techniques to classify them according to diverse characteristics of their pore structures. If stable classes could be identified, they would aid us to develop better models for rock typing, to gain sounder understanding of the links between the pore structures and the fluid flow behaviours and to develop predictive models of effective flow properties with many potential applications in the petroleum industry and beyond. We reported an approach that the authors developed for classifying digital samples. There, the pore structure is characterised by topological and geometrical attributes obtained from topology-preserved pore networks for each sample. Each attribute is then represented as a 1st-order tensor and normalised so that it is comparable for images sampled at different scales and resolutions. Machine learning techniques are then used to carry out actual classification from a training dataset containing labelled and unlabelled samples. The viability and extendibility of this approach are discussed. We show that this approach can be implemented to classify samples in progressive, recursive and regressive manners, and can be extended to develop correlation between the classes of samples and their fluid flow properties.
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A Flow and Transport Model in Porous Media for Microbial EOR Studies at Core Scale
Authors M. A. Diaz-Viera and J.R. Hernandez-PerezThe oil fields at their initial operation stage produce using basically its natural energy which is known as a primary recovery. As the reservoir loses energy in order to maintain the pressure it requires the injection of gas or water, which is called a secondary recovery. When the secondary recovery process becomes ineffective it is necessary to apply a more sophisticated approach such as steam injection, chemicals, etc. These are known as enhanced oil recovery methods. Some important oil fields in Mexico are entering the third stage. For the optimal design of oil recovery methods it is required to perform a variety of laboratory tests under controlled conditions to model the fundamental recovery mechanisms for a given recovery method in a specific reservoir. However, the laboratory tests commonly have a number of drawbacks, which include among others that they are very sophisticated, time consuming, expensive and always not enough to cover the whole range of field conditions involved. A proper modeling of the laboratory tests would be decisive in the interpretation, analysis and understanding of recovery mechanisms as well as in obtaining the relevant parameters for the subsequent implementation of recovery processes at the well and the reservoir scale. In this work we present a flow and transport model which was implemented using the finite element method to simulate, analyze and interpret MEOR processes at core scale under laboratory conditions. The flow model is biphasic and is based on the oil phase pressure and total velocity formulation given by Chen Z. et al. 2006, in which the capillary pressure, relative permeabilities, the effects of gravity and the dynamic porosity and permeability modification due to the clogging-declogging phenomena (adsorption-desorption of microorganisms) are taken in account. Whereas, the transport model consists of two phases (water-biofilm) and three components (microorganisms, nutrients and bioproducts). The transport model includes physical-chemical-biological phenomena such as advection, diffusion, dispersion, adsorption-desorption, growth and decay of microorganisms. Adsorption of nutrients is implemented through a linear adsorption isotherm. The effects of the bioproducts on the residual oil saturation are also included. From the methodological point of view, each stage of model development (conceptual, mathematical, numerical and computational) is described. Finally, the resulting coupled flow and transport model is numerically validated in a case study of oil displacement by the injection of water follows by the injection of water with microorganisms and nutrients. The oil recovery evaluation considering different scenarios is shown.
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Pore-scale Single and Two-phase Transport in Real Porous Medium
Authors I.I. Bogdanov, J. Kpahou and F. GuertonSince long time it has been recognized that the typical pore size is a fundamental scale in understanding of transport phenomena and determination of global transport properties of porous media. In a similar way like the Navier-Stokes equations may be used at certain limit to derive the Darcy law and define single phase transport properties, the modified Navier-Stokes model might be used to determine medium two-phase flow properties. Instead of using a regularization technique to capture the interface (cf. VOF or level-set functions approach), which may affect the modelling results in a non-trivial way, the diffuse interface method offers a thermodynamic treatment of phase “mixing” zone. As a result, it is a good choice for a numerical technique, handling the morphological changes of the interface which is of great importance for modelling of such a kind. Like zero-order approximation which is at the same time the classical theory assumptions case, the two-phase flow properties (e.g. phase relative permeabilities) are simply two ultimate single phase flow configurations, one per each phase. In both cases only volumes occupied by one fluid are considered so that wetting and capillary properties becomes very important, probably along with the process history as they all are responsible for particular fluid distribution in pore space. Taking advantage of recent advancements in X-ray computed micro-tomography (μCT), the reconstructed real porous medium samples (Bentheimer sandstone) are used for direct numerical simulations (DNS) of single and two-phase transport problems. Main model parameters - capillary, Reynolds, Cahn and Peclet numbers - are defined for each flow case. Emphasis is made on characterization of different steps and features of methodology based on μCT measurements, geometrical reconstruction, grid generation and computational models. The contribution of DNS to understanding of transport phenomena in real media becomes increasingly important factor of porous medium description efforts.
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Multi-scale Simulation of Permeability Fields and History-matching
Authors C. Gardet, M. Le Ravalec and E. GloaguenThe prediction of fluid flows within oil reservoirs or gas storage sites or aquifers requires the characterization of its petro-physical properties, i.e., facies, porosity, permeability, etc. This issue can be addressed through history-matching which calls for the determination of a three-dimensional model representing the studied reservoir. In a nutshell, a model is a grid populated by petrophysical properties. These ones have to be sequentially adjusted until the flow responses simulated for the resulting reservoir model reproduce the available dynamic data: pressures, flow rates, water cuts, 4D-seismic... A difficulty usually disregarded is that these data provide information about petrophysical properties at different scales. Referring to sequential simulation, we propose a method for generating multiscale realizations of both continuous or discrete random fields. These ones are then used to populate reservoir models with the required petrophysical properties. The integration of multiscale simulation within history-matching provides new facilities and makes it possible to incorporate dynamic data at different scales of resolution. When combined with geostatistical parameterization techniques as the gradual deformation method, it gives the essential ability to adjust the reservoir model at various scales. In addition, the overall history-matching process becomes more efficient as targeting the appropriate scale entails an economical parameterization of the model, i.e., the coarser the scale, the smaller the number of unknown parameters. Last, we present a numerical application case to highlight the advantages of the method for conditioning permeability models to dynamic data. For simplicity, we focus on two-scale processes. The coarse scale describes the variations in the mean while the fine scale characterizes local variations around the mean. We investigate the relationships between data resolution and parameterization.
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Upscaling of Vertically Heterogeneous Reservoirs
Authors A. Stovas and Y. RoganovAn accurate description of a reservoir is crucial to the management of production and efficiency of oil recovery. Reservoir modeling is an important step in a reservoir’s future performance, which is in direct proportion to reservoir management, risk analysis and making key economic decisions. Saturation and pressure changes, and porosity and permeability distributions are the most common parameters to estimate in the oil industry. In order to reduce the number of parameters in reservoir description, the different upscaling techniques have been used. At the rock physics level, the Gassmann and Hertz-Mindlin theories are applied in order to incorporate the fluid substitution and pressure changes, respectively. The most popular method at the elastic level is the Backus (1962) averaging. This method is based on the zero frequency limit of seismic wave field in a vertically heterogeneous structure. We extend the Backus averaging for the low-frequency regime by using the Baker-Campbell-Hausdorff series (Serre, 1965). That allows us to compute the frequency dependent effective medium parameters. These parameters can be used in seismic modeling and inversion with band-limited seismic wavelet.
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Homogenization of Relative Permeabilities Curves for Two-phase Flow in Porous Media Using an Optimization Method
Authors F. McKee, C. Preux and C. BerthonGrid coarsening remains essential in practical reservoir studies in order to get acceptable simulation time. This implies being able to upscale two-phase flow in particular the relative permeability. Upscaling can be divided in two stages: homogenization and mesh changing. Optimization gets involved here in the homogenization part. We proceed by identification between fine grid simulation on both representative heterogeneous regions and homogeneous equivalent region. We start with a mesh containing heterogeneous rock type. Each rock type has its own relative permeability curve and these curves are homogenized throughout the mesh with a unique relative permeability curve. In order to do this, the exit oil flow rates from the heterogeneous rock type case are considered as a reference solution. We then simulate the same flow except for the unique effective relative permeability curve. The exit oil flow rates from the two simulations are extracted to build a least squares objective function. The effective relative permeability curve (kr) is the main parameter of the optimization problem : the end points of a Brooks-Corey relative permeabilities model are used to look for a minimum objective function value.
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Mathematical Model of Horizontal Well Acidizing
Authors S.U. Zhuchkov and R.D. KanevskayaHorizontal wells are widely used to increase reservoir development efficiency. The most important factor of successful use of such wells is their capability to preserve reservoir properties in the vicinity of horizontal well. Acid treatment leads to dissolution of rock matrix and rock particles, which can plug flow channels. Therefore it is often used to recover permeability and intensify oil production. Acidizing of horizontal wells requires a special approach. The efficiency of stimulation depends on reagent distribution along the borehole, depth of acid penetration and reaction kinetics. To evaluate these characteristics it is necessary to work with adequate mathematical models giving the possibility to plan the acid treatments. These models should take into account the specific character of fluid flow close to horizontal well, pressure loss along the well, influence of gravity and heterogeneity of reservoir properties. The modeling of rock matrix dissolution should be carried out. Mathematical two-phase multicomponent model describing the flow of acid solution close to horizontal well is presented. The effects related to chemical reactions and fluid flow in well are taken into account. Calculation results for different cases are presented.
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Mixture Models for Sampling Conditional Facies Realizations from Multiple Training Images
Authors B. Jafarpour and M. KhodabakhshiMultiple point statistics (MPS) provides a systematic approach for pattern-based simulation of geologic objects from a conceptual training image (TI). The TI encodes the higher-order spatial statistics of the expected connectivity structures through stationary patterns representing the underlying geologic features. The pattern-imitating nature of MPS simulation implies that the simulated facies inherit the spatial structure of the general features in the TI. This property makes the MPS approach very sensitive to uncertainty in the prior TI. Since TIs are constructed using uncertain data and imperfect assumptions, multiple TIs may be necessary to account for the uncertainty and full range of structural variability in facies descriptions. We present a Bayesian mixture modeling approach for adaptively sampling conditional facies from multiple uncertain TIs using a probability conditioning method (PCM). Using the PCM, we invert the flow data to obtain a facies probability map for drawing conditional facies realizations from each TI. The number of samples drawn from each TI is proportional to the weight assigned to them. The TI weights are assigned based on the predictive performance of its corresponding conditional facies realizations. We demonstrate the suitability of the proposed method using numerical experiments in fluvial formations.
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Optimization of Dynamic 3D Hex-dominant Mesh Adapted for Basins Simulation Using the Smoothing Laplacian 2D
Authors B. Yahiaoui, H. Borouchaki, A. Benali and C. BennisTo improve a dynamic hex-dominant mesh for basins, a particular optimization in shape is proposed in this article. The aim is to return a mesh as regular as possible on $xy$ coordinates and align the $z$ coordinates. This optimization must complete an existing approach generate a hex-dominant mesh to improve these generated elements. To do this optimization for the $xy$ coordinate a Transformation called Smoothing Laplacian is applied. After, an iterative method which transforms some connections between layers in verticals. And it’s possible to conclude that this kind of optimization can be improved to have any shape wanted.
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Quantification of Uncertainty in Reservoir Connectivity for Field Test Evaluation
By H. OkanoProduction forecasts for petroleum reservoirs are essentially uncertain due to the lack of data. The unknown parameters are calibrated so that the simulated profile can match the observed data. A Bayesian framework has been applied to the evaluation of CO2 injection test in a tight oil reservoir. The observed data used for history-matching include the bottom-hole flowing pressure at the injector well and the gas composition at the wellhead of the producer wells. The key is starting with a simple model, because it is much quicker to adjust large-scale heterogeneity in a simple model than in a detailed model. The in-place volumes and connectivity between the wells have been calibrated in the simple models using a stochastic sampling method called the Neighbourhood Approximation algorithm. The aim of our study is to quantify uncertainty of reservoir connectivity. A Bayesian framework along with Markov Chain Monte Carlo and Neighbourhood Approximation in parameter space is used to calculate the posterior probability. We showed the best fit model for the gas breakthrough and the P10-90 envelopes in the forecast of the CO2 mole fraction in the produced gas. Our results contribute to the evaluation of the pilot test for a continuous CO2 injection.
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Development of Iterative Algorithms of Increased Convergence and Accuracy for Multiphase Flow Simulation
Authors D. Yu. Maksimov and M.A. FilatovMost of commercial simulators for multiphase flow in porous media use implicit or adaptively implicit discretization schemes which allow for rather large time steps. It is important that in the iterative process the equations being approximated may change, e.g. in cases of well target change, counterflow. To increase stability of nonlinear iterations convergence, we propose a method relying on the control of residual norm decreasing and taking into account the features of the problem under consideration. Final correction of recurrent solution increment is carried out after direct calculation of the residual with corresponding approximation before and after the point where equations change. Correction of the increment which tries to retain form of equations being approximated (e.g. well mode) makes convergence more stable and additionally allows avoiding convergence to nonphysical solution. In the paper a number of possibilities for safeguard retaining of approximation type from the previous iteration is pointed out for situations (e.g. for low filtration rate) where it has to be changed by algorithm in the strict sense, given constraints being controlled to obtain “physical” solution. Several simulation results are presented, demonstrating the robustness and effectiveness of the proposed method for challenging problems.
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Permeability Change Estimation from Microseismic Event Activity Variations
Authors S.B. Turuntaev, O.Y. Melchaeva, E.V. Zenchenko and E.I. Eremeevaactivated by the pore pressure change. It was found, that the probability distribution of these “potential fractures” can be approximated by a Weibull distribution. It was shown that it is possible to solve the inverse problem of defining local permeability from registered microseismic activity variation in a particular volume of porous medium.
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Modeling the Feasibility of Gas-Water or Gas-Oil Contact Control by Microgravity Monitoring during Enhanced Oil Recovery
By J. MrlinaMonitoring of fluids in reservoirs has become an essential tool for the control of active hydrocarbon fields, including EOR process. Repeated microgravity (time-lapse gravity, 4D gravity) can determine especially gas-water or gas-oil contact displacement in time. The technique can also be used in industrial and construction areas, contrary to 4D seismic and electromagnetics. The efficiency of the technique has been already proven by successful time-lapse gravity surveys, e.g. in Alaska, France, Italy, Oman and Qatar. Based on experience from water penetration to a sandstone formation in Egypt, gravity modelling was performed to simulate gas - water/oil contact movement in reservoirs related to pumping, water-flooding, etc. Various reservoir parameters were changed - depth, thickness, geometry, porosity and density. Gas or steam injecting/pumping was investigated, too. It was found that such processes can be observed by time-lapse microgravity, but the success depends on local geological conditions and reservoir parameters. New complex feasibility parameter cF was developed and established in graphic and tabular forms based on the time- and space-domain 3D and 4D gravity modelling. This parameter should provide fast pre-survey estimation of the effectiveness of microgravity monitoring. This procedure has not been developed before.
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Interactive Sketch-based Estimation of Stimulated Volume in Unconventional Reservoirs Using Microseismic Data
Authors Y. Hajizadeh, R. Amorim, N. Boroumand, E. Vital Brazil, D. Eaton and M. Costa SousaThe development of unconventional reservoirs has received tremendous attention from energy companies in recent years. Due to the low permeability nature of these resources, a hydraulic fracturing is often applied to stimulate the near-well region to enable economic production. The injection pressure, as it propagates, creates fractures that generate microseismic events. The monitoring of such events has become an important tool to better understand hydraulic fracture geometry, to estimate stimulated reservoir volume, to refine fracture treatment, and to optimize long-term field development. In the estimation of Stimulated Reservoir Volume (SRV) from microseismic data, recent literature highlights the importance of using time and uncertainty to achieve a more accurate estimation, as well as the influence of more complex geometries in understanding the microseismic event cloud. However, the current methods do not take any of these factors into consideration. In this work, we propose two different approaches to estimate the SRV that integrate spatial correlation together with time to obtain more accurate volume estimations. The first method is called alpha-shapes which is a generalization of the well-known shrink-wrap algorithm. The second approach is the density-based region reconstruction which considers the density of the microseismic samples in the space to reconstruct the SRV. The density-based approach uses radial basis function with Gaussian kernels to account for uncertainty in microseismic events. In addition to these two methods, we also developed a sketch-based tool to assist the users in filtering microseismic events that are visibly wrong. We molded these two approaches to allow for direct user changes to the final volume through sketch-based tools, and thus giving the expert the ability to guide the SRV estimation and to create "what-if" scenarios for a better understanding of the microseismic data. We also integrated the developed tools in this work with an interactive tabletop multitouch display to create a collaborative work environment for the experts.
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