Fine Scale Simulation of Fractured Reservoirs: Applications and Comparison

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A Force-Balanced Control Volume Finite Element Method for Multi-Phase Porous Media Flow Modelling

Dr D. Pavlidis would like to acknowledge the support from the following research grants: Innovate UK ‘Octopus’, EPSRC ‘Reactor Core-Structure Re-location Modelling for Severe Nuclear Accidents’) and Horizon 2020 ‘In-Vessel Melt Retention’. Funding for Dr P. Salinas from ExxonMobil is gratefully acknowledged. Dr Z. Xie is supported by EPSRC ‘Multi-Scale Exploration of Multi-phase Physics in Flows’. Part funding for Prof Jackson under the TOTAL Chairs programme at Imperial College is also acknowledged. The authors would also like to acknowledge Mr Y. Debbabi for supplying analytic solutions.Peer reviewedPublisher PD

Modelling of Multiphase Fluid flow in Heterogeneous Reservoirs

Computational modeling of multiphase fluid flow in highly heterogenous problems with complicated geometries is a challenging problem for reservoir engineers, with a rich research in establishing best methods and approaches. The novelty in this work is centered around the implementation and comparison of simulation results from two software - the open source ICFESRT and the commercial software ECLIPSE - for a two-phase multiphase problem (oilwater) in both simple and complex geometries. The work involves: (a) implementation and comparison of simulation results from the two software on three different, hypothetical but typical geometries; (b) consideration of a real field case and the associated data analysis, rock characterization, and geostatistics of a real field representative of a highly heterogeneous reservoir; and (c) implementation of both software on the real field case for predictions of oil production at the site, and comparison of the simulation results from the two software. The initial comparison of simulation results for was carried out using three hypothetical (but common) geometries, these being: (a) a quarter five spot with one geological layer; (b) the same geometry as in (a) but with a vertical heterogeneity i.e. 5 different geological layers; (c) and lastly a full 5 spot with 5 different geological layers was implemented. Three different mesh resolutions were applied in both software and comparisons were carried out for mesh-independency. The results showed that in all these three scenarios, good agreement was observed between IC-FERST (coarse mesh) and ECLIPSE (fine mesh) with an average percentage difference at the production well ranging between 2.5% and 10.5% for the oil production and 12% and 26% for the water production. Both the ICFERST and ECLIPSE were subsequently implemented on a real, heterogeneous field – which consisted of 25 producing wells and 8 injections wells. Prior to the software implementation, a data analysis and rock characterization was carried out –Using data from the 33 wells. The logging and core data (a total of 30,000 log readings and 1150 core samples) were utilized and a novel rock characterization technique -Balaha Rock Characterization Code- was implemented to allow for the optimal clustering of rock types within the reservoir, The rock characterization resulted in identifying 7 rock types with their unique porosity-hydraulic permeability relationships. Subsequently, geostatistical methods were implemented – which enabled populating the computational cells of the two software with the corresponding reservoir properties (porosity, hydraulic permeability). To achieve the property population into the unstructured computational domain of the ICFERST software, a newly-developed script was written in Matlab and Python. The rock properties data populated on IC-FERST consist of porosity, permeability, relative permeability, capillary pressure and connate water saturation. A further comparison between the IC-FERST simulation results with the corresponding ECLIPSE simulations was carried out – were all simulations were carried out for a period of 40 years. The percentage differences between the two software simulations were estimated for : (i) ten individual production wells and (ii) the total of all production wells. The results showed that a good agreement exists between the IC-FERST and ECLIPSE simulations, with an average percentage difference for the total oil production of 10.5%, the total water production of 26% and the total water injection of 14%. The results for the ten individual wells showed an average percentage difference of 15.5% ranging from 3 to 29% for the oil production in the late time period. Slightly higher differences were observed when the overall period was considered, due to the large difference at the early time period of the simulation. The results indicated that IC-FERST, when incorporating the necessary rock characterization information – which highlight the heterogeneity of the reservoir – can produce results that can compete with the industry standard ECLIPSE. Additional aspects need to be considered within the current real field IC-FERST simulation, the inclusion of possible fractures and faults, as these were incorporated in the computational domain of ECLIPSE. Additional capabilities also still need to be embedded into IC-FERST, such as the incorporation of the fluid density and viscosity variations with pressure and the consideration of the volume factors, in order to enhance its competitiveness with existing commercial reservoirs simulators such as ECLIPSE

Parallel numerical modeling of hybrid-dimensional compositional non-isothermal Darcy flows in fractured porous media

This paper introduces a new discrete fracture model accounting for non-isothermal compositional multiphase Darcy flows and complex networks of fractures with intersecting, immersed and non immersed fractures. The so called hybrid-dimensional model using a 2D model in the fractures coupled with a 3D model in the matrix is first derived rigorously starting from the equi-dimensional matrix fracture model. Then, it is dis-cretized using a fully implicit time integration combined with the Vertex Approximate Gradient (VAG) finite volume scheme which is adapted to polyhedral meshes and anisotropic heterogeneous media. The fully coupled systems are assembled and solved in parallel using the Single Program Multiple Data (SPMD) paradigm with one layer of ghost cells. This strategy allows for a local assembly of the discrete systems. An efficient preconditioner is implemented to solve the linear systems at each time step and each Newton type iteration of the simulation. The numerical efficiency of our approach is assessed on different meshes, fracture networks, and physical settings in terms of parallel scalability, nonlinear convergence and linear convergence

Two-phase flow in rocks : new insights from multi-scale pore network modeling and fast pore scale visualization

Many geological applications involve the flow of multiple fluids through porous geological materials, e.g. environmental remediation of polluted ground water resources, carbon dioxide storage in geological reservoirs and petroleum recovery. Commonly, to model these applications, the geological materials in question are treated as continuous porous media with effective material properties. Since these properties are a manifestation of what goes on in the pores of the material, we have to study the transport processes at the pore scale to understand why and how they vary over space and time in different rocks and under different conditions. As the high cost of acquiring and testing samples in many of these applications is often a limiting factor, numerical modelling at the pore scale is becoming a key technology to gain new insights in this field. This could be crucial in reducing uncertainties in field scale projects. The work presented in this thesis focuses on the investigation of two-phase flow in sedimentary rocks, and is an integrated numerical and experimental study. It deals primarily with two outstanding issues. First, image-based pore scale simulation methods have difficulties with representing the multiple pore scales in rocks with wide pore size distributions, due to a trade-off in the size and resolution of both modeling and imaging methods. Therefore, performing two-phase flow simulations in a number of important rock types, such as many carbonates and tight, clay-baring sandstones has remained an outstanding challenge. To tackle this problem, a new numerical model was developed to calculate capillary pressure, relative permeability and resistivity index curves during drainage and imbibition processes in such materials. The multi-scale model was based on information obtained from 3D micro-computed tomography images of the internal pore structure, complemented with information on the pores that are unresolved with this technique. In this method, pore network models were first extracted from resolved pores in the images, by using a maximal ball network extraction algorithm. Then, pores which touched regions with unresolved porosity were connected with a special type of network element called micro-links. In the quasi-static simulations that were performed on these network models, the micro-links carried average properties of the unresolved porosity. In contrast to most previous models, the new approach to taking into account unresolved porosity therefore allowed efficient simulations on images of complex rocks, with sizes comparable to single-scale pore network models. It was able to reproduce most of the behaviour of a fully resolved pore network model, for both drainage and imbibition processes, and for different pore scale wettability distributions (water-wet, oil-wet and different mixed-wet distributions). Furthermore, simulations on images of carbonate rocks showed good agreement to experiments. A sensitivity study on carbonate rocks and tight, clay-bearing sandstones produced results that were in qualitative agreement with experiments, and allowed to analyse how the two-phase flow behaviour of these rocks is influenced by their pore scale properties. The second issue which is treated in this thesis is related to the validation of pore scale models. Comparing predicted effective properties to experimentally measured values is useful and necessary, but is complicated by the typical difference in size between the model and the experiment. Furthermore, it does not always give a clear indication of the reasons for an observed mismatch between models and experiments. Comparing two-phase flow models to pore scale experiments in which the evolution of the fluid distributions is visualized is thus extremely useful. However, this requires to image the two-phase flow process while it is taking place in a rock, and it is necessary to do this with time resolutions on the order of tens of seconds and spatial resolutions on the order of micrometers. Previous experimental approaches used synchrotron beam lines to achieve this. In this thesis, we show that such experiments are also possible using laboratory-based micro-computed tomography scanners, which are orders of magnitude cheaper and therefore more accessible than synchrotrons. An experiment in which kerosene was pumped into a water-saturated sandstone is presented, showing that individual Haines jumps (pore filling events) could be visualized during this drainage process. Because the image quality is lower than at synchrotrons, care had to be taken to adapt the image analysis work flow to deal with high image noise levels. The work flow was designed to allow to track the fluid filling state of individual pores. The results indicate that the dynamic effects due to viscous and inertial forces during Haines jumps do not significantly impact the evolution of the fluid distributions during drainage, which may thus be adequately described by quasi-static models