Field-scale Example Research Articles

Downhole flow control: A key for developing enhanced geothermal systems in horizontal wells

Field evidence indicates that only a few large fractures in enhanced geothermal systems (EGS) may dominate fluid flow and lead to the development of thermal short-circuiting. This problem would worsen in heat harvesting through horizontal wells with abundant fractures (induced or natural ones). To limit flow shortcuts that may cause early thermal breakthroughs, we propose a temperature-sensitive flow management system and explore its potential benefits during the development of EGS in horizontal wells. The proposed downhole flow management system consists of sensors for real-time temperature monitoring, and flow control devices for adjusting injection distribution in the wellbore. We evaluate the performance of such systems over 50 years of operation by numerical analysis. The results indicate that, when the proposed system is utilized, the produced fluid temperature will be increased by up to 60 K for a field-scale example. Besides, the application of the proposed flow management system can increase the cumulative heat extraction by up to 48.25 % (0.69 × 1016 J) after 50 years. The heat extraction efficiency can be improved by up to 94.16 %. During the EGS operation, it is suggested to implement multi-stage fluid control, but it is not recommended to reopen the fluid injection that has been previously shut down. Finally, the flow management system can mitigate the negative impacts of geological heterogeneities or the heterogeneity in fracture hydraulic conductivities. This paper proposes a new concept of flow management to integrate horizontal wells into efficient EGSs for power generation and heat extraction in the future.

Cross-gradient joint inversion and clustering of ERT and SRT data on structured meshes incorporating topography

Summary The combination of electrical resistivity and seismic refraction tomography is a common practice for the characterization of subsurface features. Presently, the cross-gradient inversion scheme stands out as one of the most robust joint approaches, and some authors modified it to manage complex topographies on unstructured meshes even if at the expense of introducing additional parameters in the inversion process. We propose in this work a cross-gradient algorithm for jointly inverting electrical and seismic tomographic data on structured meshes in cases with non-flat topography. The proposed approach preserves the benefit of the classical cross-gradient approach without the need to impose physical length scales, as for irregular meshes. The quality of the results is evaluated in comparison with independent inversion through a new standardized cross-gradient index and a fuzzy c-means analysis that provides an assessment of the reconstruction accuracy through the membership function. The proposed method was applied to both synthetic models and field-scale examples located in Central Italy, where an accurate geophysical reconstruction is needed for the rehabilitation of existing dams. For all cases, joint inversion yielded superior results compared to independent inversion, demonstrating better agreement with available borehole data. The effectiveness of the joint approach was also demonstrated by the post-inversion tools, where the new cross-gradient index highlighted changes in structural similarity whilst fuzzy c-means clustering allowed for a quantitative reconstruction (position and shape) of the main units at the sites, facilitating the detection of site layering modifications.

A new SDDA-based numerical approach for simulating rock cracking induced by temperature stresses

Temperature-induced rock failure occurs in geothermal exploitation, nuclear disposal, and other underground engineering scenarios. In this paper, the conventional spherical discontinuous deformation analysis (SDDA) method is extended to simulate the temperature-induced rock failure problems. Firstly, an improved bonded sphere algorithm is proposed to precisely modeling rock failure behavior in the SDDA framework. Secondly, a heat conduction model based on the thermal conductivity pipe between spheres is proposed and further implemented in the SDDA program through an explicit thermal–mechanical coupling procedure. Thirdly, three typical examples are selected to verify the accuracy of the heat conduction model by comparing the temperature evolution between numerical and analytical results. Finally, the improved SDDA model was applied to analyze several experimental cases involving thermal cracking, including lab-scale experiments and field-scale examples. The simulation results show that the improved SDDA approach is effective for the simulation of the temperature-induced crack propagation process.

Numerical Benchmark Studies on Flow and Solute Transport in Geological Reservoirs

Predicting and characterising groundwater flow and solute transport in engineering and hydrogeological applications, such as dimensioning tracer experiments, rely primarily on numerical modelling techniques. During software selection for numerical modelling, the accuracy of the results, financial costs of the simulation software, and computational resources should be considered. This study evaluates numerical modelling approaches and outlines the advantages and disadvantages of several simulators in terms of predictability, temporal control, and computational efficiency conducted in a single user and single computational resource set-up. A set of well-established flow and transport modelling simulators, such as MODFLOW/MT3DMS, FEFLOW, COMSOL Multiphysics, and DuMuX were tested and compared. These numerical simulators are based on three numerical discretisation schemes, i.e., finite difference (FD), finite element (FE), and finite volume (FV). The influence of dispersivity, potentially an artefact of numerical modelling (numerical dispersion), was investigated in parametric studies, and results are compared with analytical solutions. At the same time, relative errors were assessed for a complex field scale example. This comparative study reveals that the FE-based simulators COMSOL and FEFLOW show higher accuracy for a specific range of dispersivities under forced gradient conditions than DuMuX and MODFLOW/MT3DMS. FEFLOW performs better than COMSOL in regard to computational time both in single-core and multi-core computing. Overall computational time is lowest for the FD-based simulator MODFLOW/MT3DMS while the number of mesh elements is low (here < 12,800 elements). However, for finer discretisation, FE software FEFLOW performs faster.

An ultra-fast single phase reservoir model for multi-well developments

This paper addresses the problem of reservoir modeling in the context of large scale developments, in which multiple wells with hundreds of fractures are placed in a formation. In particular, the goal is to develop an ability to compute the production rate for each well for the given bottomhole pressure variation and also to evaluate the associated change of stress in the reservoir, e.g. for the purpose of subsequent modeling of hydraulic fracturing in neighboring wells. In addition, it is desired to compute the solution rapidly, in which case this makes it possible to consider sensitivities of the solution to various parameters. In order to achieve the goal, i.e. having an ability to solve large scale problems quickly, it is necessary to consider a series of simplifications in the model. The primary assumptions are zero vertical permeability and single phase flow, which makes the flow equations linear and decoupled for each layer. In addition, the use of an analytical solution that captures linear flow for imposing the boundary condition at the fracture surface allows to avoid having fine discretization near the fracture surface. Finally, the use of a uniform grid together with employing Fast Fourier Transform algorithm and Graphics Processing Unit for calculations leads to the desired performance. The model has been benchmarked by comparing its predictions to reference numerical and analytical solutions. Computational performance of the algorithm is analyzed and it is shown that it is possible to simulate large scale problems within minutes. Finally, a field scale example with eight wells is presented, which illustrates a potential application of the algorithm and quantifies the characteristic variations of pressure and stress caused by injection of the fracturing fluid and production.

Applicability of heat-exchanger theory to estimate heat losses to surrounding formations in a thermal flood

Heat losses to cap and base rocks undermine the performance of a thermal flood. As a contribution to this subject, this paper investigates the applicability of the principles of heat exchanger to characterise heat losses between a petroleum reservoir and the adjacent geologic systems. The reservoir-boundary interface is conceptualised as a conductive wall through which the reservoir and adjacent formations exchange heat, but not mass. For a conduction-dominated process, the heat-transport equations are formulated and solved for both adiabatic and non-adiabatic conditions. Simulations performed on a field-scale example show that the rate of heating a petroleum reservoir is sensitive to the type of fluids saturating the adjoining geologic systems, as well as the characteristics of the cap and base rocks of the subject reservoir. Adiabatic and semi-infinite reservoir assumptions are found to be poor approximations for the examples presented. Validation of the proposed model against an existing model was satisfactory; however, remaining differences in performances are rationalised. Besides demonstrating the applicability of heat-exchanger theory to describe thermal losses in petroleum reservoirs, a novelty of this work is that it explicitly accounts for the effects of the reservoir-overburden and reservoir-underburden interfaces, as well as the characteristics of the fluid in the adjacent strata on reservoir heating. These and other findings should aid the design and management of thermal floods.

Optimizing CO2- and Field-Gas-Injection EOR in Unconventional Reservoirs Using the Fast-Marching Method

SummaryRecently, there has been an increasing interest in enhanced oil recovery (EOR) from shale-oil reservoirs, including injection of carbon dioxide (CO2) and field gas. For the performance assessment and optimization of CO2- and field-gas-injection processes, compositional simulation is a powerful and versatile tool because of the capability to incorporate reservoir heterogeneity, complex fracture geometry, and multiphase and multicomponent effects in nanoporous rocks. However, flow simulation accounting for such complex physics can be computationally expensive. In particular, field-scale optimization studies requiring a large number of high-resolution compositional simulations can be challenging and sometimes computationally prohibitive. In this paper, we present a rapid and efficient approach for the optimization of CO2- and field-gas-injection EOR in unconventional reservoirs using a fast-marching-method (FMM) -based flow simulation.The FMM-based simulation uses the concept of diffusive time of flight (DTOF). The DTOF is a representation of the travel time of pressure-front propagation and accounts for geological heterogeneity, well architecture, and complex fracture geometry. The DTOF can be efficiently obtained by solving the Eikonal equation using the FMM. The 3D flow equation is then transformed into an equivalent 1D equation using the DTOF as a spatial coordinate, leading to orders of magnitude faster computation for high-resolution and compositional models as compared to full 3D simulations. The speed of computation enables using robust population-based optimization techniques such as genetic- or evolutionary-based algorithms that typically require a large number of simulation runs to optimize the operational and process parameters.We demonstrate the efficiency and robustness of our proposed approach using synthetic and field-scale examples. We first validate the FMM-based simulation approach using an example of CO2 huff ‘n’ puff for a synthetic heterogeneous dual-porosity model with a multistage hydraulically fractured well. Next, we present a field-scale optimization of operating strategies for gas-injection EOR in the Eagle Ford Formation. The rapid computation of the FMM-based approach enabled a comprehensive evaluation of the EOR project, including sensitivity studies, parameter-importance analysis, and optimal operating strategies using high-resolution geologic models.

Robust Life-Cycle Production Optimization With a Support-Vector-Regression Proxy

Summary We design a new and general work flow for efficient estimation of the optimal well controls for the robust production-optimization problem using support-vector regression (SVR), where the cost function is the net present value (NPV). Given a set of simulation results, an SVR model is built as a proxy to approximate a reservoir-simulation model, and then the estimated optimal controls are found by maximizing NPV using the SVR proxy as the forward model. The gradient of the SVR model can be computed analytically so the steepest-ascent algorithm can easily and efficiently be applied to maximize NPV. Then, the well-control optimization is performed using an SVR model as the forward model with a steepest-ascent algorithm. To the best of our knowledge, this is the first SVR application to the optimal well-control problem. We provide insight and information on proper training of the SVR proxy for life-cycle production optimization. In particular, we develop and implement a new iterative-sampling-refinement algorithm that is designed specifically to promote the accuracy of the SVR model for robust production optimization. One key observation that is important for reservoir optimization is that SVR produces a high-fidelity model near an optimal point, but at points far away, we only need SVR to produce reasonable approximations of the predicting output from the reservoir-simulation model. Because running an SVR model is computationally more efficient than running a full-scale reservoir-simulation model, the large computational cost spent on multiple forward-reservoir-simulation runs for robust optimization is significantly reduced by applying the proposed method. We compare the performance of the proposed method using the SVR runs with the popular stochastic simplex approximate gradient (StoSAG) and reservoir-simulations runs for three synthetic examples, including one field-scale example. We also compare the optimization performance of our proposed method with that obtained from a linear-response-surface model and multiple SVR proxies that are built for each of the geological models.

Optimal rate control under geologic uncertainty: water flood and EOR processes

Much of the current world oil production comes from mature and partially depleted fields. Increasing the ultimate oil recovery from these fields is critical for meeting growing energy demands in the coming years. Many secondary oil recovery methods have been developed to improve oil recovery after primary depletion. The most widely used is water flooding because it is effective and relatively inexpensive to implement. However, the presence of reservoir heterogeneities, for example high permeability channels, can lead to premature breakthrough and poor sweep efficiency, resulting in reduced oil recovery. One way to improve the sweep efficiency is flood front management via the optimal allocation of production and injection rates. In this paper, we propose an optimal rate control strategy to maximize sweep efficiency and accelerate production during water flooding and EOR processes, in particular, polymer flooding and CO2 injection. We describe our approach and the underlying mathematical formulation, and then we illustrate its power using field-scale examples. We demonstrate the practical feasibility of our method in realistic production scenarios using a 3D synthetic benchmark field example, the Brugge field. We also use stochastic optimization to take geological uncertainty into consideration. The value of using multiple realizations in improving the robustness of the optimization in terms of oil recovery and enhancing NPV is clearly illustrated by the 3D example.

Three-Dimensional Numerical Model for Double-Porosity Media with Two Miscible Fluids Including Geomechanical Response

The finite-element formulation of a coupled fluid flow and geomechanics for two-phase fluid flow through fractured porous media are presented. Two porosities, pores and fractures, and five phases are introduced. The two fluids are taken as wetting and nonwetting. The governing equations are derived based on the theory of poroelasticity, the effective stress principle, and the balance equations of mass and momentum, taking into account the solubility of nonwetting fluid into wetting fluid. Spatial and temporal discretization of the governing equations has been realized through the Galerkin method and the finite-difference technique, respectively. A three-dimensional numerical code has been developed and validated based on previously published data. Various applications of the model have been demonstrated through three field-scale examples.

Pore-Scale Controls on Reaction-Driven Fracturing

In this article we attempt to shed some light on the factors that determine whether volume-increasing reactions and growth in pores will reduce or increase permeability. We will start by describing fi eld-scale examples of reaction-driven fracturing, and use a Discrete Element Model (DEM) to analyze how the resulting pattern and the rate and progress of reaction depend on the initial porosity of the rock. Ultimately, however, stress generation is related to growth processes taking place at the pore scale. We will therefore zoom in and describe pore-scale growth processes and how these are associated with fracturing and the production of new reactive surface area and new transport channelways for migrating fl uids. Stress generation by growth in pores requires that crystals continue to grow even after having ‘hit’ the pore wall. This implies that the fl uid from which the crystals precipitate is not squeezed out from the reactive interface by the normal stress generated by the growth, but can be kept in place as a thin fi lm by opposing forces that operate at very small scales. To understand the dynamics of crystal growth against confi ning pore walls, we need to zoom in even further and examine interface processes taking place at the nanometer scale. Hence, the last part of this chapter focuses on the nanometer-scale morphology of the reacting interface and the mechanical and transport properties of the fl uids confi ned along reactive grain boundaries.

Field Applications of Waterflood Optimization via Optimal Rate Control With Smart Wells

SummaryWaterflood optimization by means of rate control is receiving considerable attention because of increasing deployments of smart well completions and i-field technology. The use of inflow control valves (ICVs) allows us to optimize the production/injection rates of various segments along the wellbore, thereby maximizing sweep efficiency and delaying water breakthrough. Field-scale rate-optimization problems, however, involve highly complex reservoir models, production and facility constraints, and a large number of unknowns. In this paper, we propose an approach that is computationally efficient and suitable for large field cases. It is based on our previous work (Alhuthali et al. 2007, 2008), which relies on equalizing arrival time of the waterfront at all producers to maximize the sweep efficiency. We use streamlines to efficiently and analytically compute the sensitivity of the arrival times with respect to well rates. We also account for geologic uncertainty by means of a stochastic optimization framework using multiple realizations. Analytical forms for gradients and Hessian of the objective functions are derived, making our optimization computationally efficient for large-scale applications. Finally, optimization is performed under operational and facility constraints using a sequential quadratic programming approach.We demonstrate our approach using two field-scale examples. The first is a synthetic example called "Brugge" field, a benchmark case based on a North Sea Brent-type field. The production optimization of this field is carried out as part of a closed-loop process where the production history is matched prior to the production optimization. The production optimization is performed over multiple realizations for 20 years and involves 30 wells equipped with three ICVs per well. The second example is a super-giant Middle Eastern field that has more than 50 years of historical oil production. The optimization is performed for 20 years on a portion of this field that contains nearly 300 wells consisting of conventional vertical and horizontal wells and smart horizontal wells. In both examples, multiple field-related constraints are imposed, such as the maximum well injection and production rates, the maximum allowable drawdown, restriction on high-water-cut wells, and voidage replacement for pressure maintenance. The results clearly demonstrate the viability of our approach and the benefits of optimal rate control, with a considerable increase in cumulative oil production and a substantial decrease in the associated water production.

Compressible Streamlines and Three-Phase History Matching

Summary Reconciling high-resolution geologic models to field production history is still by far the most time-consuming aspect of the workflow for both geoscientists and engineers. Recently, streamline-based assisted and automatic history-matching techniques have shown great potential in this regard, and several field applications have demonstrated the feasibility of the approach. However, most of these applications have been limited to two-phase water/oil flow under incompressible or slightly compressible conditions. We propose an approach to history matching three-phase flow using a novel compressible streamline formulation and streamline-derived analytic sensitivities. First, we use a generalized streamline model to account for compressible flow by introducing an "effective density" of total fluids along streamlines. This density term rigorously captures changes in fluid volumes with pressure and is easily traced along streamlines. A density-dependent source term in the saturation equation further accounts for the pressure effects during saturation calculations along streamlines. Our approach preserves the 1D nature of the saturation equation and all the associated advantages of the streamline approach with only minor modifications to existing streamline models. Second, we analytically compute parameter sensitivities that define the relationship between the reservoir properties and the production response, viz. water-cut and gas/oil ratio (GOR). These sensitivities are an integral part of history matching, and streamline models permit efficient computation of these sensitivities through a single flow simulation. Finally, for history matching, we use a generalized travel-time inversion that has been shown to be robust because of its quasilinear properties and converges in only a few iterations. The approach is very fast and avoids much of the subjective judgment and time-consuming trial-and-error inherent in manual history matching. We demonstrate the power and utility of our approach using both synthetic and field-scale examples. The synthetic case is used to validate our method. It entails the joint integration of water cut and gas/oil ratios (GORs) from a nine-spot pattern in reconstructing a reference permeability field. The field-scale example is a modified version of the ninth SPE comparative study and consists of 25 producers, 1 injector, and aquifer influx. Starting with a prior geologic model, we integrate water-cut and GOR history by the generalized travel-time inversion. Our approach is very fast and preserves the geologic continuity.

A VSA-based strategy for placing conservation buffers in agricultural watersheds.

Conservation buffers have the potential to reduce agricultural nonpoint source pollution and improve terrestrial wildlife habitat, landscape biodiversity, flood control, recreation, and aesthetics. Conservation buffers, streamside areas and riparian wetlands are being used or have been proposed to control agricultural nonpoint source pollution. This paper proposes an innovative strategy for placing conservation buffers based on the able source area (VSA) hydrology. VSAs are small, variable but predictable portion of a watershed that regularly contributes to runoff generation. The VSA-based strategy involves the following three steps: first, identifying VSAs in landscapes based on natural characteristics such as hydrology, land use/cover, topography and soils; second, targeting areas within VSAs for conservation buffers; third, refining the size and location of conservation buffers based on other factors such as weather, environmental objectives, available funding and other best management practices. Building conservation buffers in VSAs allows agricultural runoff to more uniformly enter buffers and stay there longer, which increases the buffer's capacity to remove sediments and nutrients. A field-scale example is presented to demonstrate the effectiveness and cost-effectiveness of the within-VSA conservation buffer scenario relative to a typical edge-of-field buffer scenario. The results enhance the understanding of hydrological processes and interactions between agricultural lands and conservation buffers in agricultural landscapes, and provide practical guidance for land resource managers and conservationists who use conservation buffers to improve water quality and amenity values of agricultural landscape.

Numerical Simulation of Three-Phase Flow in Deforming Fractured Reservoirs

The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is presented in this paper. The present formulation accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly nonlinear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behavior for the case of a reservoir where the impact of coupling is also considered.

Three-dimensional finite element simulation of three-phase flow in a deforming fissured reservoir

The development of a capacity to predict the exploitation of structurally complicated and fractured oil reservoirs is essential for the rational use of investment capital. A poor understanding of how the reservoir behaves during production may lead to inept, costly and inefficient development schemes. The mathematical formulation of a three-phase, three-dimensional fluid flow and rock deformation in fractured reservoirs is hence presented. The present formulation, consisting of both the equilibrium and multiphase mass conservation equations, accounts for the significant influence of coupling between the fluid flow and solid deformation, an aspect usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretise the governing equations in space and a finite difference scheme is used to march the solution in time. The final set of equations, which contain the additional cross coupling terms as compared to similar existing models, are highly non-linear and the elements of the coefficient matrices are updated implicitly during each iteration in terms of the independent variables. A field scale example is employed as an alpha case to test the validity and robustness of the currently formulation and numerical scheme. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered.

Alluvial Fans Formed by Channelized Fluvial and Sheet Flow. II: Application

The formulation of the companion paper describing the evolution of mean elevation in a radially symmetric alluvial fan is applied to the specific case of the tailings basin of an iron mine. The tailings basin provides a simple field-scale example of a fluvial fan-delta system. Calculation procedures are developed to determine the effect of changing water and sediment discharge on fan evolution. The analysis is used to evaluate options for the extension of the lifetime of the tailings basin.

A novel finite element double porosity model for multiphase flow through deformable fractured porous media

Based on the theory of double-porosity, a novel mathematical model for multiphase fluid flow in a deforming fractured reservoir is developed. The present formulation, consisting of both the equilibrium and continuity equations, accounts for the significant influence of coupling between fluid flow and solid deformation, usually ignored in the reservoir simulation literature. A Galerkin-based finite element method is applied to discretize the governing equations both in the space and time domain. Throughout the derived set of equations the solid displacements as well as the fluid pressure values are considered as the primary unknowns and may be used to determine other reservoir parameters such as stresses, saturations, etc. The final set of equations represents a highly non-linear system as the elements of the coefficient matrices are updated during each iteration in terms of the independent variables. The model is employed to solve a field scale example where the results are compared to those of ten other uncoupled models. The results illustrate a significantly different behaviour for the case of a reservoir where the impact of coupling is also considered. © 1997 by John Wiley & Sons, Ltd.