PEBI Grids Research Articles

Simulation Optimization on Multi-Well Fracturing Sequence of Chang 7 Formation

In order to study the engineering problems of shale oil horizontal well platform fracturing mode, a three-dimensional geological model and a three-dimensional geomechanical model were constructed according to the characteristics of Chang 7 section in Ordos Basin. The fracture propagation under different well spacing, cluster spacing, and fracturing sequence was simulated. The PEBI grid was used to refine the local grid of the fractures and predict the performance of the multi-well pad. The finite element model was used to analyze the change of induced stress field. The numerical simulation analysis shows that: 1) Comparing the simulation results of sequence fracturing and zipper fracturing under the condition of 300 m well spacing, the induced stress generated by zipper fracturing is more conducive to the formation of complex fractures, improving the effect of transformation and higher production after fracturing. 2) Under the condition of 200 meters or 300 meters well spacing, zipper fracturing is carried out, and the cluster spacing is reduced from 5 meters to 3 meters. The stress shadow between wells and sections leads to adverse effects, and the production will decrease after fracturing. Therefore, 5 meters is recommended as the cluster spacing.

Pressure transient behaviors for horizontal wells with well interferences, complex fractures and two-phase flow

During the production of multi-stage, multi-well pads in shale reservoirs, there are common phenomena of well interferences, complex fracture generation, and multi-phase flow for the multi-well pad. However, there still lacks an understanding on the pressure transient behaviors with those phenomena. To narrow this gap, the pressure transient behaviors of oil-water two-phase flow of fractured horizontal wells with complex fractures and well interferences are studied by a numerical pad-well model, based on PEBI grids and discrete fracture model (DFM).The pressure transient solutions of fractured horizontal wells with complex fractures and well interferences have been demonstrated by model verifications and field applications. The results show that the flow regime of interference effects is stronger when the child well has a larger production rate, a smaller well spacing, more secondary fractures, longer secondary fractures, and higher fracture conductivity. It is also found that the formation pressure loss increases with increasing oil phase viscosity and oil volume factor when the viscosity of water is constant. The oil/water volume factor mainly affect the well testing interpretation of parameters such as wellbore reservoir coefficient. What's more, the field application shows that the well testing data are interpreted and the fracture parameters are evaluated successfully with well interferences, while the single-well testing model without considering well interference cannot match with field data at the late stage and the estimation errors will occur. This work is meaningful to understand the well interference and to evaluate the fracture parameters in multi-stage, multi-well pad with multi-phase flow.

Study on Double Pressure Funnels and Gas-Liquid Two-Way Mass Transfer after Fracturing in Shale Gas Reservoirs

Well shut-in and drainage after shale gas fracturing are important factors affecting the productivity. Due to the imperfect optimization method of shale gas flowback, there has been no clear explanation for the problems such as “formulation of reasonable well shut-in time” and “less fracturing fluid flowback but high-gas production phenomenon” during shale gas drainage. In this paper, the double pressure funnels (one funnel is formed during fracturing by pressure difference from wellbore to formation, and two funnels are formed during flowback by pressure difference from fracture to formation and from fracture to wellbore) and gas-liquid two-way mass transfer (gas transfer by diffusion and liquid transfer by pressure difference) in shale gas drainage are investigated by calculating the pressure distribution after fracturing shale gas wells. The discrete numerical simulation by using unstructured PEBI grid is conducted, and the result is as follows: when shale gas well is shut-in for 20 days and produce for 1 year, the daily gas production corresponding to fracturing fluid flowback rates of 20%, 10%, and 5% are 47700 m3, 5800 m3, and 72700 m3, respectively. The investigation of double pressure funnels and gas-liquid two-way mass transfer explains clearly the phenomenon “less fracturing fluid flowback but high-gas production.” Meanwhile, the two conditions for optimizing the well shut-in time after fracturing are presented. That is, as for the studied case, the moving speed of the pressure boundary line should be less than 0.1 m/d, and the water-gas ratio near the fracture should be less than 1 / d with time. Consequently, the reasonable well shut-in time is optimized to be 20-25 days. The findings in this work are of benefit to enrich the flowback theory of shale gas after fracturing and provide a theoretical basis for the optimization technology of shale gas drainage after fracturing.

Physics-constrained deep learning for solving seepage equation

With the development of deep learning algorithms, neural networks (NNs) have been widely used in physics, computer science, and other fields. Solving partial differential equations (PDEs) based on NNs is one of the research hotspots. The existing methods can be divided into two categories: one is data-driven method, and the other is physics-constrained method. Physical-constrained method is more popular due to the convenience of constructing NNs and excellent generalization ability. However, the physical-constrained method cannot ensure the solution precision when PDEs are more complex, such as seepage equations with source and sink terms. In this paper, an improved physics-constrained PDE solution method is proposed that incorporates potential features of the PDE in the loss functions. A gradient model is proposed to describe the potential feature based on spatial pressure distribution, which can be used as the additional signpost to guide NNs to approximate PDEs. The gradient models are described as special neurons that are added into the hidden layer of the NN. Based on the new ideas, the seepage equation is well solved without using any exact solutions. The effectiveness of the proposed method is verified by numerical simulation results based on PEBI grid. • An improved PDE solution method is proposed based on physics-constrained neural network. • A gradient model is proposed based on spatial distribution features to help signpost neural network (SNN) converge. • SNNs reduces the network parameters required to achieve the local minimum and improves the solution accuracy.

Continuous streamline trajectories on complex grids

Streamlines have been used for reservoir modeling and flow visualization in the petroleum industry and in computational fluid dynamics. When applied to the calculation of volumetric sweep and the identification of by-passed hydrocarbons for improved oil recovery, it is important that the velocity models that are used to trace trajectories across the cells of a grid are flux conservative. As such, the requirements on their tracing may be more stringent than in other disciplines. Flux conservation is also important at faults, at locally refined or coarsened embedded grid boundaries, and within unstructured grids, where the modeling of flow within a cell may not be consistent with the connection fluxes from adjacent cells. In such cases, additional degrees of freedom must be introduced to satisfy flux conservation. In this study, we introduce a flux conservative conforming cell face local boundary layer construction to resolve these inconsistencies. In contrast, solutions that rely upon spatial continuity of streamlines between elements are shown to not be flux conservative when these inconsistencies are present. The use of flux conservative conforming elements also allows the solution to be developed in local isoparametric coordinates, without explicit reference to cell or connection geometry. The solution has been implemented for both 3D corner point and for 2.5D PEBI grids. In all cases we utilize the lowest order Raviart–Thomas zeroth order velocity model, for which the trajectories and transit times may be obtained analytically. The results are demonstrated on a sequence of increasingly complex type, sector and full-field model applications.

An equivalent single-phase flow for oil-water two-phase flow and its potential application in well test

In this work an equivalent single-phase flow model is proposed based on the oil-water two-phase flow equation with saturation-dependent parameters such as equivalent viscosity and equivalent formation volume factor. The equivalent viscosity is calculated from the oil-water relative permeability curves and oil-water viscosity. The equivalent formation volume factor is obtained by the fractional flow of the water phase. In the equivalent single-phase flow model, the equivalent viscosity and phase saturation are interdependent when the relative permeability curves are known. Four numerical experiments based on PEBI grids show that equivalent single-phase flow has a good agreement with the oil-water two-phase flow, which shows that the equivalent single-phase flow model can be used to interpret oil-water two-phase pressure data measured in the wellbore during the buildup period. Because numerical solution of single-phase flow model is several times faster than that of the two-phase flow model, whether the new model interprets the pressure data directly or offers good initial values for the true oil-water two-phase pressure data interpretation, it will obviously improve the efficiency of the interpretation of oil-water pressure data and decrease the burden of engineers.

Pressure transient analysis of low permeability reservoir with pseudo threshold pressure gradient

Threshold pressure gradient (TPG) is an important mechanism for fluid flow through low-permeability reservoirs, which would explain the phenomena that pressure derivative curves exhibit a straight line of slope that is larger than zero after radial flow regime. A mathematical single-phase flow model incorporating pseudo TPG is proposed to describe the flow behavior in low permeability reservoirs. Fully implicit numerical simulation based on PEBI grid is developed to study the transient pressure response. Two field data are used to calibrate and validate the proposed model and the code. Based on one of field data, parametric studies are conducted to investigate the effect of minimum TPG, pseudo TPG and nonlinear exponent on the pressure transient response for a vertical well. We find that pseudo TPG can explain the unique and consistent characteristic of the pressure transient response in low permeability reservoirs. The finding is useful for petroleum engineers to interpret the field data to obtain some basic parameters for low permeability reservoirs.

Three-dimensional hydrocarbon migration and accumulation modeling based on finite volume method

Abstract Aiming at the issue that the application effect of current 3-D hydrocarbon migration and accumulation modeling technique cannot meet the actual requirement because of over-simplified geologic model, a 3-D dynamic geologic model using PEBI grid in bedding and columnar shape was established, which can be used to solve the heterogeneity in reservoirs of various sedimentary facies, and to reduce the effect of mixed lithologies on modeling accuracy. A 3-D numerical modeling technique based on finite volume method was established, including the construction of variable grid flow equation, decomposition and calculation of full-tensor permeability, and calculation of conductivity etc. Some related processing techniques, such as smoothing of key parameter curves, stability processing of upstream and downstream of grid flow, etc. were used to improve the convergence of Newton's iteration. Automatic adjustment of time step and multi-core parallel computation were taken to enhance the running efficiency of the software. In a case study of Nanpu sag in the Bohai Bay Basin, the hydrocarbon migration and accumulation process, oil saturation and hydrocarbon resources abundance in various periods were simulated, the modeled oil saturation, accumulation quantity and hydrocarbon distribution locations coincide with current exploration status. The results also showed that the proved ratio of hydrocarbon resources in target layers is 84.4%, the majority of the resources are distributed in Block B and Block C, and it is predicted that undiscovered resources are mainly near Well NP2-16 in Block C and in the structure north of Well NP5-4 in Block A.

On the Use of PEBI Grids in the Numerical Simulations of Two-Phase Flows in Fractured Horizontal Wells

On the Use of PEBI Grids in the Numerical Simulations of Two-Phase Flows in Fractured Horizontal Wells

Open-source MATLAB implementation of consistent discretisations on complex grids

Accurate geological modelling of features such as faults, fractures or erosion requires grids that are flexible with respect to geometry. Such grids generally contain polyhedral cells and complex grid-cell connectivities. The grid representation for polyhedral grids in turn affects the efficient implementation of numerical methods for subsurface flow simulations. It is well known that conventional two-point flux-approximation methods are only consistent for K-orthogonal grids and will, therefore, not converge in the general case. In recent years, there has been significant research into consistent and convergent methods, including mixed, multipoint and mimetic discretisation methods. Likewise, the so-called multiscale methods based upon hierarchically coarsened grids have received a lot of attention. The paper does not propose novel mathematical methods but instead presents an open-source Matlab® toolkit that can be used as an efficient test platform for (new) discretisation and solution methods in reservoir simulation. The aim of the toolkit is to support reproducible research and simplify the development, verification and validation and testing and comparison of new discretisation and solution methods on general unstructured grids, including in particular corner point and 2.5D PEBI grids. The toolkit consists of a set of data structures and routines for creating, manipulating and visualising petrophysical data, fluid models and (unstructured) grids, including support for industry standard input formats, as well as routines for computing single and multiphase (incompressible) flow. We review key features of the toolkit and discuss a generic mimetic formulation that includes many known discretisation methods, including both the standard two-point method as well as consistent and convergent multipoint and mimetic methods. Apart from the core routines and data structures, the toolkit contains add-on modules that implement more advanced solvers and functionality. Herein, we show examples of multiscale methods and adjoint methods for use in optimisation of rates and placement of wells.

Unstructured Gridding for Full-Field Simulation of a Giant Carbonate Reservoir Developed With Long Horizontal Wells

This article, written by Technology Editor Dennis Denney, contains highlights of paper IPTC 11512, "The Application of Unstructured Gridding Techniques for Full-Field Simulation of a Giant Carbonate Reservoir Developed With Long Horizontal Wells," by H. Vestergaard, SPE, H. Olsen, SPE, and A.S. Sikandar, SPE, Maersk Oil Qatar, and I.A. Al-Emadi and R. Noman, SPE, Qatar Petroleum, prepared for the 2007 International Petroleum Technology Conference, Dubai, 4–6 December. The paper has not been peer reviewed. A case history is presented on reservoir simulation of a giant, complex, low-permeability, carbonate reservoir completed with many long horizontal wells. The multiple radial layouts of 75 very long horizontal wells in the field posed a challenge in modeling individual-well performance with a manageable grid size and acceptable run time for history matching. The gridding dilemma was solved by use of 2.5D perpendicular-bisector (pebi) grids around each individual wellbore. This method provided sufficient resolution between wells and aligned the grid with the well paths, thereby avoiding grid nonorthogonality issues. Introduction The Al Shaheen field is offshore Qatar, covering an area of 800 sq miles. The Kharaib formation is part of the Lower Cretaceous Thamama group. The dome-shaped reservoir has a net oil-column thickness of 23 ft at the crest of the field, thinning toward the flank. The field has relatively low permeability, ranging from 1 to 15 md. Developed wells have no pressure support from the distant flank aquifer or the trapped water in the central part of the field. Oil gravity varies significantly: saturated low-viscosity (<1 cp) oil to highly undersaturated higher-viscosity (35-cp) oil. The field has several local gas caps and a free-water level (FWL) dipping more than 500 ft across the field. At the time of this study, the reservoir was developed with 75 ultralong horizontal wells, up to 30,000 ft long, drilled in alternating producer/injector patterns from five platforms. Production from the field began in 1994, and secondary recovery by water injection commenced in 1997. Continuing evaluation of reservoir performance and assessment of further development potential of the field prompted the need for detailed history matching on a full-field basis. Modeling issues detailed in the full-length paper were part of a history-matching study completed in 2004 that formed the basis to develop the reservoir with an additional 89 wells to infill existing well pat-terns and to develop the thinner oil column toward the flank of the reservoir. Background The Kharaib B formation is a laterally continuous limestone with a relatively constant thickness of approximately 80 ft within the subject area. Oil gravity ranges from 38°API at the crest of the field to 12°API at the northern flank. The saturation pressure varies from saturated near the gas caps to 1,300 psi undersaturated in low-gravity areas. There is not, however, a distinct correlation between saturation pressure and oil gravity. The large variation in saturation pressure indicates different natural-drive mechanisms in different areas of the reservoir.

Recent Advances in Upgridding

Upscaling is the process whereby the properties of a high resolution geologic description are approximated by a lower resolution flow simulation model. Upgridding is the process whereby we determine the spatial resolution (the 3D computational grid) of the simulation model. In our current work we explore different measures of the error introduced by the upscaling approximations. These measures are based upon local flow properties and hence are not dependent upon knowledge of global fluid flow patterns. Based upon these error measures it is possible to design a computational grid that is optimal, i.e., that introduces the minimal upscaling error for a specific number of cells. We explore three different applications of these error measures. In the first, an optimal reservoir simulation layering scheme is derived from the layering scheme of the geologic description by sequentially grouping the layers in such a way to minimize the error. The error associated with this sequence explores the trade-off between upscaling bias and variance, with the optimal scheme being determined by a balance between the two. The second application is in areal upscaling. Here we utilize two different definitions of transmissibility and the cross-terms in the upscaled full permeability tensor, to provide local measures of error. The final application examines other constraints or considerations that we may place upon the reservoir simulation grid design. In terms of reservoir characterization, these constraints are associated with preserving reservoir structure, stratigraphy and layering, or locally, facies continuity. Simulation and process representation will also have an impact on the optimal grid design, i.e., the optimal simulation grid design will differ between a waterflood and a gas displacement process. The resulting simulation grid will be a composite of corner point cells, with many of the computational advantages of an unstructured PEBI grid, without the requirement to revise our modeling technology to utilize such grids.

Overview: Reservoir Simulation and Visualization (April 2005)

The success of reservoir development and reservoir management can be summed up in one statement: The explosion of data available to today’s reservoir engineer mandates the use of advanced simulation and visualization technology. With ongoing technological advances, our capability to measure and acquire more and more data will continue to increase. This increase in data will stretch the limits of our capacity to gather, manage, and use this information effectively. Our appetite for data will increase further, because as we learn to analyze this data efficiently, we realize additional data are needed. That is, the more we know, the more we realize what we do not know. Advances in collaborative visualization, along with efficient asset-team organization, are having a profound effect on our ability to make proper use of this wealth of data. Software tools that facilitate true integrated work processes are emerging, providing asset teams the ability to characterize, model, and simulate reservoirs in a multidisciplinary manner. This ability for all asset-team members to communicate by use of visualization throughout the reservoir-management process provides more fit-for-purpose reservoir models, which in turn leads to better drilling choices; improved reservoir development and performance predictions; and, ultimately, better economic decisions under uncertainty. Additionally, significant advances in reservoir-simulation technology continue. Many of these advances represent approaches to take advantage of the growing mountain of data. More data leads to larger and more-complex reservoir models. Despite ever-increasing computation power, improved methods for scaling up models are needed. Streamline simulation, integrated with dynamic data, has become an effective tool for use in screening, scaling up, and history matching these models. With increased model complexity comes the need to use reservoir-simulation models that maintain that complexity. A new generation of reservoir simulators is emerging that captures the complexity through unstructured gridding, advanced formulations, and integrating surface and reservoir modeling. Going forward, visualization and reservoir-simulation technology will continue to advance in an attempt to keep pace with the ever-increasing volume of data. In the future, look for advances in real-time data acquisition leading to the need for ever-improving visualization and reservoir-simulation techniques to contribute to the optimization of daily reservoir-management operations. Additional Reservoir Simulation and Visualization Technical Papers Available at the SPE eLibrary: www.spe.org SPE 93080 - Development and Field Application of a High-Performance Unstructured Simulator With Parallel Capability SPE 90009 - Dynamic Flow-Based PEBI Grids for Reservoir Simulation SPE 93339 - A New Upscaling Approach for Highly Heterogeneous Reservoirs