Simulating fractured wells is challenging and impractical with local grid refinement (LGR) in full-field models with a large number of wells each with multiple fractures. This paper describes a modeling technique by which hydraulic fractures are represented as part of the well model rather than as any form of refinement in the simulation grid. In this approach, a planar fracture is modeled by the mesh formed from the interconnected branches of a multilateral, multisegment well (MSW).
Introduction
Hydraulic fracturing can dramatically change the flow dynamics of a reservoir, so its correct modeling in reservoir simulation can be critical. However, the presence of hydraulic fractures presents a challenge in flow simulation. This is because these fractures introduce effects that operate on different length and time scales than do usual reservoir dynamics.
To overcome this problem, a multitude of modeling techniques and workarounds has been developed. These include the use of dual-porosity models, enhancement of the productivity index of the fractured wells, virtual well perforations to simulate the fractures, and explicit fine-scale gridding.
In full-field simulations, where an entire reservoir with complex geometry, multiple wells, and possible faults is modeled, LGR is a popular method representing hydraulic fractures. However, this approach introduces its own set of problems. For example, in structured grids, the overall orientation of the grid may not easily accommodate fractures, particularly if they are at arbitrary angles.
This paper investigates the modeling of hydraulic fractures as part of the well model. MSWs are a discretized model of a well where fluid flow inside the wellbore is computed by solving physical flow model equations in one dimension. This domain is made up of the segments of the well that consist of nodes, which are connected by pipes. MSWs allow for lateral branches off the main stem and for looped flow paths; both features are employed here for the modeling of hydraulic fractures.
Hydraulic Fractures as Part of an MSW
Motivation. The idea behind this modeling approach is that hydraulic fractures become independent of the simulation grid. This means that multiple fractures per well and multiple fractured wells per reservoir can be modeled easily without constraints on orientation. Furthermore, there is no need to introduce small cells into the reservoir model and thus the reservoir model is concerned only with fluid flows on a large scale. Rapid fluid movement and rapid solution changes are localized to the well model, where these are commonplace and can be controlled more easily. MSW uses a nested iteration scheme in which the well-model equations are fully solved at each reservoir iteration. This allows the effects of discrete events such as changes in a controlling target rate or the opening of new connections to be resolved locally without forcing additional, computationally expensive iterations across the entire reservoir system. Using MSW to model hydraulic fractures in a full-field model means that local changes in fracture flows can also be modeled in a similarly efficient manner.
Fracture Discretization. The hydraulic fractures here are assumed to be planar and square (although this assumption is not a limitation of this approach; the method readily generalizes to any shape of fracture). To compute the fluid flow within the fracture and into the well, the fracture domain is discretized into facets that are arranged in a 2D regular structure. This structure may be modeled by an MSW if each facet is represented by a node, and flows between facets are represented by pipes that connect the well nodes; this is shown in Fig. 1. The fracture is thus effectively modeled by lateral looped branches, with the nodes in these branches connected to the nonfractured reservoir.
Fracture Inflow. The flow between the reservoir grid and the well nodes that represent the fracture uses a linear-inflow model in which the connection factor depends on the reservoir grid cell’s permeability as well as on the inflow area. This inflow area is computed from the intersection of a fracture facet and a grid cell. The fracture-to-grid connection is generic in that many grid cells can be connected to a single fracture facet and vice versa.
Numerical Experiments
The hydraulic-fracture-modeling approach has been evaluated with regard to suitability and utility. Suitability relates to the stability and reliability of simulation runs as well as to the accuracy and trustworthiness of simulation results. Utility relates to the performance, scalability, and ease of use of the new approach and shows its applicability to practical real-world modeling scenarios. This approach is evaluated by running a variety of numerical experiments that prove the desired accuracy and usability. These experiments consist of reference-case comparisons and scenario evaluations.
Reference-Case Comparisons
- Test Case 1: Artificial box-shaped models with a single-phase black-oil fluid model. The purpose of these models is to investigate changes in fracture properties and dimension and the different shapes of wells to which hydraulic fractures are applied.
- Test Case 2: Artificial tilted models with water/oil contact. These models have been constructed to show water coning and to investigate the effects of saturation changes (during water breakthrough) on the simulation run.
- Test Case 3: Models with long horizontal well and multistage fractures. Water injection is used to provide pressure support. Some models have heterogeneous (layered) rock properties to make the model more realistic.
- Test Case 4: Models with two fractured wells, one producer and one injector. The purpose of these models is to show that fractured injection wells can be modeled with this approach.
- Test Case 5: Real field sector model. This model showcases the new technology in a realistic model of a deepwater tight reservoir. Multiple production scenarios have been investigated.
In all cases, the model pairs were identical except in how the fracture was modeled, with the reference case using LGRs or tartan grids. This can introduce subtle differences that required the adjustment of model parameters such as well diameter and connection factors. The aim was to keep the differences always to a minimum, for example by using the same number of MSW nodes in the fracture as there are cells in the LGR.
One aspect of the model that caused many problems was the fracture width. Having a realistic fracture width of ½ in. caused numerical instability and problems with the well completions in most LGR cases, so the decision was made to use a pseudowidth of 1 ft for the fractures. This is clearly larger than fractures are in reality, but, by adjusting the fracture permeability accordingly, the correct dynamic behavior was preserved.
Test Case 1: Single-Phase Model. The simple model presented here was used to investigate the effect of changing the fracture permeability on the oil-production rate. The model is a simple 13×13 grid with a vertical well and fracture. To create the reference case, a 1-ft-wide row of cells has been inserted (in the form of a tartan grid), giving overall dimensions of 15×13.
Close agreement was seen between the production data for the reference cases and the MSW cases. However, after close inspection, it is apparent that the discrepancies are larger for the poor-quality fracture. Examining the discrepancies in more detail has revealed that the difference in grids between the reference case and the MSW case is the root cause. For high-throughput fractures, the results are virtually identical, and similar findings have been made for many test cases.
Test Case 5: Real Field Sector Model. The more-complex model setup is shown in Fig. 2 Here, the fracture has been modeled using two logarithmic LGRs.
As expected, the fracturing dramatically increased the plateau time of the production well compared with the nonfractured case. Furthermore, the comparison of oil-production rates and bottomhole pressures with the reference results shows good agreement.
These two cases and the other experiments show generally good agreement between the reference-case results and the MSW fracture results. Furthermore, the MSW fracture simulations were more numerically stable in general than the equivalent reference cases.
Scenario Evaluations
The aim of the scenario evaluations was to provide a broader spectrum of modeling scenarios than have been tested with the MSW fracture model. The purpose of these experiments was to determine if the approach is applicable to common modeling scenarios and is useful in real-world engineering studies.
Long Realistic Well. This experiment used a real field sector model with a 3-km-long well. The well was subjected to a multistage hydraulic-fracturing treatment with nine stages. Each stage is represented by a single fracture that extends at odd angles to both grid and well. It would be very hard (if not impossible) to create a reference case for this scenario using traditional modeling techniques.
With the MSW prototype, it is possible to create such a fractured well in minutes; this shows that the new approach opens the possibility of model scenarios that were prohibitively complex in the past, and it has a clear advantage over existing techniques on the grounds of usability. The simulation ran to completion without numerical issues, although, of course, it was not possible to verify these results.
Multiwell Parallel Scalability. This experiment was concerned with performance. A model with 4 million grid cells and 400 vertical wells, each with a single hydraulic fracture, has been created and run on a cluster. Different degrees of parallelism were used to show the scalability of the new technique with large models. The model has been decomposed into domains by the simulator for parallel execution, with the fluid flows in the grid cells, wells, and fractures in each domain computed on separate processors.
Significant parallel speedups (over serial results) were noted for runs with and without hydraulic fractures, demonstrating the effectiveness of splitting the well solves among processors. This experiment shows that the new technique has been integrated successfully into the existing high-performance infrastructure of a commercial simulator, allowing large-scale scenarios to be investigated in an efficient and scalable manner.
This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 163644, “Representing Hydraulic Fractures by Use of a Multilateral, Multisegment Well in Simulation Models,” by D.A. Edwards, SPE, Schlumberger; N. Cheng, SPE, Statoil; T.P. Dombrowsky (now with Longhorn Technologies) and G. Bowen, SPE, Schlumberger; and H. Nasvik, SPE, Statoil, prepared for the 2013 SPE Reservoir Simulation Symposium, The Woodlands, Texas, USA, 18–20 February. The paper has not been peer reviewed.