Calibrate complex fracture model for subsurface flow based on Bayesian formulation
5
Citation
68
Reference
10
Related Paper
Citation Trend
Abstract:
In practical development of unconventional reservoirs, fracture networks are a highly conductive transport media for subsurface fluid flow. Therefore, it is crucial to clearly determine the fracture properties used in production forecast. However, it is different to calibrate the properties of fracture networks because it is an inverse problem with multi-patterns and high-complexity of fracture distribution and inherent defect of multiplicity of solution. In this paper, in order to solve the problem, the complex fracture model is divided into two sub-systems, namely "Pattern A" and "Pattern B." In addition, the generation method is grouped into two categories. Firstly, we construct each sub-system based on the probability density function of the fracture properties. Secondly, we recombine the sub-systems into an integral complex fracture system. Based on the generation mechanism, the estimation of the complex fracture from dynamic performance and observation data can be solved as an inverse problem. In this study, the Bayesian formulation is used to quantify the uncertainty of fracture properties. To minimize observation data misfit immediately as it occurs, we optimize the updated properties by a simultaneous perturbation stochastic algorithm which requires only two measurements of the loss function. In numerical experiments, we firstly visualize that small-scale fractures significantly contribute to the flow simulation. Then, we demonstrate the suitability and effectiveness of the Bayesian formulation for calibrating the complex fracture model in the following simulation.Keywords:
Complex fracture
Summary Recent advances in hydraulic-fracture-mapping technologies have provided a wealth of information on the created fracture length in numerous geologic settings. Before having such measurements, fracture length was estimated using "uncalibrated" fracture-propagation models, but there was significant uncertainty in the results that cascaded into subsequent production analyses. However, we also need to understand how the created fracture length relates to the location of proppant in the fracture and to the producing or effective length to evaluate well performance and improve stimulation designs. Unfortunately, the advanced fracture-mapping technologies that provide accurate measurements of the created fracture length cannot provide any insights (yet) into the propped and effective fracture lengths. Advanced production-data analyses (PDAs), pressure-transient testing, and/or numerical reservoir modeling are required to determine the effective fracture length. This paper begins with a comparison of the strengths, weaknesses, and limitations of fracture modeling, PDA, pressure-transient analysis (PTA), and numerical reservoir modeling to estimate effective fracture length and conductivity. This work also evaluates how the complexities (in the hydraulic fracture) associated with non-Darcy flow, multiphase flow, and complex fracture geometries affect the results from the various techniques. This work documents the significant differences in "effective" fracture length that, in many cases, can result from each technique and how these uncertainties can impact fracture treatment designs and field-development decisions. The paper concludes with several field case histories that illustrate the integration of multiple technologies to determine the created, propped, and effective fracture length. The case histories illustrate the dramatic differences in created and effective fracture length that can occur in some reservoirs, while also showing that in some cases, effective fracture lengths can be very similar to the created length (and quite long). Integrating the results from multiple diagnostic techniques in a consistent and coherent manner can provide significant insights into created, propped, and effective fracture length that are otherwise unattainable from each technique alone.
Complex fracture
Well stimulation
Fracture treatment
Transient (computer programming)
Cite
Citations (12)
A new theorem of inverse formula is introduced for a kind of infinite series. Thus some new results for important inverse problems in physics are presented in this paper. These are the inverse problems for obtaining the phonon density of states, the inverse blackbody radiation problem for remote sensing, and the solution for inverse Ewald summation. Of more importance, it shows the possibility of the application of number theory to physical problems.
Black-body radiation
Cite
Citations (223)
Maximum flow problem
Cite
Citations (1)
The properties of natural fractures (NFs), including fracture size, aperture width, and mechanical properties, etc., cannot be neglected when developing a model of hydraulic fracturing. Without considering the geological characterisation of NF properties, hydraulic fracture simulations will give much less accurate prediction of complex fracture propagation pattern. In this research, a novel two-dimensional finite-discrete element method (FDEM) model has been developed to describe complex fracture propagation in unconventional formations. We developed a natural fracture network builder by considering natural fractures geological observations. Simulations have been conducted to investigate single fracture and complex fracture network propagation in naturally fractured reservoirs. In hydraulic fracturing treatments, opening of natural fractures is determined by geological properties of NFs. For multiple fractures propagation in naturally fractured reservoirs, stress shadowing effect plays a key role in fracture network evolution. This work provides a framework for more realistic prediction of complex fracture geometry in naturally fractured formations. [Received: December 11, 2017; Accepted: July 6, 2018]
Complex fracture
Cite
Citations (0)
Summary In many reservoirs, fracture growth may be complex because of the interaction of the hydraulic fracture with natural fractures, fissures, and other geologic heterogeneities. The decision whether to control or exploit fracture complexity has significant impact on fracture design and well performance. This paper investigates fracture-treatment-design issues as they relate to various degrees and types of fracture complexity (i.e., complex planar fractures and network fracture behavior), focusing on fracture-conductivity requirements for complex fractures. The paper includes general guidelines for treatment design when fracture growth is complex, including criteria for the application of water-fracs, hybrid fracs, and crosslinked fluids. The effect of proppant distribution on gas-well performance is examined for cases when fracture growth is complex, assuming that proppant was either concentrated in a primary planar fracture or evenly distributed in a fracture network. Examples are presented that show that when fracture growth is complex, the average proppant concentration will likely be too low to materially impact well performance if proppant is evenly distributed in the fracture network and unpropped-fracture conductivity will control gas production. Reservoir simulations illustrate that the network-fracture conductivity required to maximize production is proportional to the square root of fracture spacing, indicating that increasing fracture complexity will reduce conductivity requirements. The reservoir simulations show that fracture-conductivity requirements are proportional k1/2 for small networks and k1/4 for large networks, indicating much higher conductivity requirements for low-permeability reservoirs than would be predicted using classical dimensionless conductivity calculations (FCD) where conductivity requirements are proportionate to reservoir permeability (k). The results show that when fracture growth is complex, proppant distribution will have a significant impact on network-conductivity requirement and well performance. If an infinite-conductivity primary fracture can be created, network-fracture-conductivity requirements are reduced by a factor of 10 to 100, depending on the size of the network. The decision to exploit or control fracture complexity depends on reservoir permeability, the degree of fracture complexity, and unpropped-fracture conductivity. It can be beneficial to exploit fracture complexity when the permeability is on the order of 0.0001 md by generating large fracture networks using low-viscosity fluids (water fracs). As reservoir permeability approaches 0.01 md, fluid efficiency decreases, and fracture-conductivity requirements increase, fracture designs can be tailored to generate small networks with improved conductivity using medium-viscosity or multiple fluids (hybrid fracs). Fracture complexity should be controlled using high-viscosity fluids, and fracture conductivity should be optimized for moderate-permeability reservoirs, on the order of 1 md.
Complex fracture
Dimensionless quantity
Fracture treatment
Cite
Citations (193)
Summary The classical optimization design dependent on a single-fracture (SF) assumption is widely applied in performance optimization for hydraulically fractured wells. The objective of this paper is to extend the optimal design to a complex fracture network to achieve the maximum productivity index (PI). In this work, we established a pseudosteady-state (PSS) productivity model of a fractured horizontal well, which has the flexibility of accounting for the complexity of fracture-network dimensions. A semianalytical solution was then presented in the generalized matrix format through coupling reservoir- and fracture-flowing systems. Subsequently, several published studies on the PSS productivity calculation of a SF were used to verify this model, and a 3D transient numerical simulation of an orthogonal fracture network was used to perform further verification. We show that results from our solutions agree very well with those benchmarked results. On the basis of the model, we provide a detailed analysis on the productivity enhancement of the fracture-network/optimization work flow using unified fracture design (UFD). The results show the following: The PI is determined by fracture conductivity and complexity (network size, spacing, and configuration), and it is a function of fracture complexity and conductivity when the influence of proppant volume is not considered. Under the constraint of a given amount of proppant known as UFD, the maximum PI would be achieved when the best balance between network complexity and conductivity was obtained. It is more advantageous to minimize fracture complexity by creating relatively simple-geometry fractures with smaller network size and larger fracture spacing in the condition of small and intermediate proppant numbers. It should be the design goal to generate a complex network by creating relatively complex-geometry fractures with larger network size and smaller fracture spacing in the condition of a large proppant number. Increasing fracture complexity could reduce the optimal requirement of fracture conductivity. The proposed approach can provide guidance for a network-hydraulic-fracturing design for an optimal completion.
Complex fracture
Cite
Citations (6)
The properties of natural fractures (NFs), including fracture size, aperture width, and mechanical properties, etc., cannot be neglected when developing a model of hydraulic fracturing. Without considering the geological characterisation of NF properties, hydraulic fracture simulations will give much less accurate prediction of complex fracture propagation pattern. In this research, a novel two-dimensional finite-discrete element method (FDEM) model has been developed to describe complex fracture propagation in unconventional formations. We developed a natural fracture network builder by considering natural fractures geological observations. Simulations have been conducted to investigate single fracture and complex fracture network propagation in naturally fractured reservoirs. In hydraulic fracturing treatments, opening of natural fractures is determined by geological properties of NFs. For multiple fractures propagation in naturally fractured reservoirs, stress shadowing effect plays a key role in fracture network evolution. This work provides a framework for more realistic prediction of complex fracture geometry in naturally fractured formations. [Received: December 11, 2017; Accepted: July 6, 2018]
Complex fracture
Cite
Citations (1)
Abstract Microseismic mapping (MSM) has shown that the occurrence of complex fracture growth is much more common than initially anticipated and is becoming more prevalent with the increased development of unconventional reservoirs (shale-gas). The nature and degree of fracture complexity must be clearly understood to select the best stimulation design and completion strategy. Although MSM has provided significant insights into hydraulic fracture complexity, in many cases the interpretation of fracture growth has been limited due to the absence of evaluative and predictive hydraulic fracture models. Recent developments in the area of complex hydraulic fracture propagation models now provide a means to better characterize fracture complexity. This paper illustrates the application of two complex fracture modeling techniques in conjunction with microseismic mapping to characterize fracture complexity and evaluate completion performance. The first complex fracture modeling technique is a simple, yet powerful, semi-analytical model that allows very efficient estimates of fracture complexity and distance between orthogonal fractures. The second technique is a gridded numerical model that allows complex geologic descriptions and more rigorous evaluation of complex fracture propagation. With recent advances in complex fracture modeling, we can now evaluate how fracture complexity is impacted by changes in fracture treatment design in each geologic environment. However, quantifying the impact of changes in fracture design using complex fracture models alone is difficult due to the inherent uncertainties in both the Earth Model and "real" fracture growth. The integration of MS mapping and complex fracture modeling enhances the interpretation of the MS measurements, while also calibrating the complex fracture model. Examples are presented that show that the degree of fracture complexity can vary significantly depending on geologic conditions.
Microseism
Complex fracture
Cite
Citations (166)
Abstract There is a very long and continuously expanding list of considerations in the process of designing and optimizing fracture stimulation treatments. As a result, there exists today an equally long and varied list of recommended design and optimization procedures for fracture stimulation. However, for each of these methods, the key parameters that ultimately govern the production response after fracture stimulation remain effective fracture length and effective fracture conductivity. This paper presents a simple and easily applied fracture stimulation design and optimization procedure that centers on these two vital parameters. The analysis includes adjustments to fracture conductivity for closure pressure, temperature, embedment, gel damage, non-Darcy turbulent flow, and non-Darcy multi-phase flow. A methodology is presented that optimizes fracture stimulation design for any reservoir type and can be readily applied by practicing stimulation engineers.
Embedment
Complex fracture
Well stimulation
Cite
Citations (10)
Some examples of inverse problem approach of the phenomena related to materials are introduced. What is the inverse problem?, what could be obtained, identified or estimated by an inverse approach? are discussed based on the inverse processing of elastic waves. Some problems and uncectainities involved in inverse processing are also discussed.
Inverse method
Cite
Citations (0)