Multi-stage fractured horizontal wells are widely applied to develop tight reservoirs and shale gas reservoirs. Testing and evaluating well productivity are necessary in horizontal well multi-stage fracturing. Through analyzing the post-fracturing transient pressure data, key parameters affecting the productivity, such as effective fracture lengths, fracture conductivities, fracture skin factors and average formation permeability, can be estimated.
This paper presents a semi-analytical model based on Green's function and source/sink method to facilitate the transient pressure analysis for a multi-stage fractured horizontal well in a closed box-shaped reservoir. The fluid flow for a multi-stage fractured horizontal well includes the fluid flowing from the reservoir to fractures, the fluid directly from the reservoir to the horizontal wellbore, fluid flow inside the fractures and fluid flow inside the horizontal wellbore. Compared with previous models, fluid flow directly from the reservoir to the horizontal wellbore and pressure drop caused by pipe flow inside the wellbore are considered. In this model, fractures and horizontal wellbore are discretized into vertical plane segments and horizontal line segments, respectively. The fluid flow from the reservoir to fracture and that directly from the reservoir to the horizontal wellbore at each segment are modeled based on analytical solutions of vertical plane source and horizontal line source, respectively. The fluid flow inside the fracture is modeled based on 1-D linear flow. The fluid flow inside the horizontal wellbore is described with Penmatcha and Aziz's model (1999). Then, the flow equations are coupled together by using the flux- and pressure-continuity conditions on the interfaces.
The effects of the fracture lengths, fracture conductivities and fracture skin factors on the transient pressure behavior are studied and type curves are generated. The results suggested that in a tight or shale-gas reservoir, the transient pressure behavior during a testing period is mainly dominated by fracture stages, fracture lengths, conductivities and skin factors. The fluid flow directly from the reservoir into the horizontal wellbore reduces the pressure drop slightly. A field case is analyzed and reliable results are obtained. This model can be applied to optimize the fracture spacing and fracture length for a multi-stage fractured horizontal well.
From the microseismic data collected during multi-stage hydraulic fracturing, we may pick out the first arrival times for both P- and S-waves for each event and at each geophone. With triaxial geophones, the azimuths of the events may be derived from the hodograms. The P- and S-wave arrival times contain the distance information from the event location to the geophones as well as the event initiating time. The azimuth from hodograms gives the orientation information of the event locations. Inverting these interpreted microseismic data yields the event location parameters, which can be used to characterize the hydraulic fractures for reservoir modeling. This paper presents an efficient gradient-based microseismic event location inversion method. The forward model that is used to calculate the first arrival times is the finite-difference solution of the Eikonal equation. A novel method is devised to obtain the gradient of the first arrival times to the event location parameters in addition to the first arrival times in one forward model run. The method is applied to a realistic multilayer shale gas reservoir with a horizontal well and several stages of hydraulic fractures. The results show that the first arrival times obtained from the surface geophones yield better event location parameter estimation assuming we can pick up the events from the surface geophone signal. When the geophones are placed downhole in nearby wells, the inverted event locations are less accurate than the ones with surface geophones but can have a relative good characterization fo the fracture propagation.
Pei, Peng (Department of Geology and Geological Engineering, University of North Dakota) | Zeng, Zhengwen (Department of Geology and Geological Engineering, University of North Dakota) | Liu, Hong (Department of Geology and Geological Engineering, University of North Dakota) | Ahmed, Salowah (Department of Geology and Geological Engineering, University of North Dakota)
Dual-porosity and dual-permeability models for naturally fractured reservoirs assume that the fractures in the reservoir are connected with each other and uniformly distributed. However, in some cases, the reservoir characteristics exhibit a discrete-fracture system, which means that the fractures might be unconnected and their distribution is not uniform. In this paper, a new computational model is developed to compute the transient-pressure behaviour for reservoirs with a discrete-fracture system. This computational model is based on Laplace transforms. The fluid flow in the fracture system and reservoir are computed separately, and flux and pressure equivalent conditions in Laplace space are applied in the fracture wall to couple the fluid flow in both systems.
The results suggest that the pressure response in a reservoir with a discrete-fracture system has three flow regions: fluid flow near the wellbore, fracture-dominated fluid flow, and fluid flow in the matrix away from the fracture. The distance between the fracture and the well, fracture parameters (fracture conductivity and non-Darcy effects), and fracture distribution are the main factors affecting the pressure response. In some particular situations, the fracture-dominated fluid-flow region in the pressure-derivative curve may present two valleys, which has been observed in some field cases (Clarkson 2009). The transient-pressure behaviour of a discrete-fracture system is also compared with that for a composite model. It is suggested that in these two scenarios, the early- and middle-time transient-pressure behaviour may be similar and latetime behaviours are quite different. The model provides a tool for identifying the fracture pattern in a specific reservoir.