Jianchun Xu

Rate Transient Analysis for Multistage Fractured Horizontal Well in Tight Oil Reservoirs considering Stimulated Reservoir Volume

A mathematical model of multistage fractured horizontal well (MsFHW) considering stimulated reservoir volume (SRV) was presented for tight oil reservoirs. Both inner and outer regions were assumed as single porosity media but had different formation parameters. Laplace transformation method, point source function integration method, superposition principle, Stehfest numerical algorithm, and Duhamel’s theorem were used comprehensively to obtain the semianalytical solution. Different flow regimes were divided based on pressure transient analysis (PTA) curves. According to rate transient analysis (RTA), the effects of related parameters such as SRV radius, storativity ratio, mobility ratio, fracture number, fracture half-length, and fracture spacing were analyzed. The presented model and obtained results in this paper enrich the performance analysis models of MsFHW considering SRV.

Pressure transient and rate decline analysis for hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs

Producing gas from shale strata has become an increasingly important factor to secure energy over recent years for the considerable volume of natural gas stored. Unlike conventional gas reservoirs, gas transport in shale reservoirs is a complex process. In the organic nano pores, slippage effect, gas diffusion along the wall, viscous flow due to pressure gradient, and desorption from Kerogen coexist; while in the micro fractures, there exist viscous flow and slippage. Hydraulic fracturing is commonly used to enhance the recovery from these ultra-tight gas reservoirs. It is important to clearly understand the effect of known mechanisms on shale gas reservoir performance. This article presents the pressure transient analysis (PTA) and rate decline analysis (RDA) on the hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs considering multiple flow mechanisms including desorption, diffusive flow, Darcy flow and stress sensitivity. The PTA and RDA models were established firstly. Then, the source function, Laplace transform, and the numerical discrete methods were employed to solve the mathematical model. At last the type curves were plotted and different flow regimes were identified. The sensitivity of adsorption coefficient, storage capacity ratio, inter-porosity flow coefficient, fracture conductivity, fracture skin factor, and stress sensitivity were analyzed. This work is important to understand the transient pressure and rate decline behaviors of hydraulic fractured vertical wells with finite conductivity in shale gas reservoirs.

Nonlinear Flow Characteristics and Horizontal Well Pressure Transient Analysis for Low-Permeability Offshore Reservoirs

Threshold pressure gradient (TPG) and stress sensitivity which cause the nonlinear flow in low permeability reservoirs were carried out by experiments. Firstly, the investigation of existing conditions of TPG for oil flow in irreducible water saturation low-permeability reservoirs was conducted and discussed, using the cores from a real offshore oilfield in China. The existence of TPG was proven. The relationship between TPG and absolute permeability was obtained by laboratory tests. TPG increases with decreasing absolute permeability. Then, stress sensitivity experiment was carried out through depressurizing experiment and step-up pressure experiment. Permeability modulus which characterizes stress sensitivity increases with decreasing absolute permeability. Consequently, a horizontal well pressure transient analysis mathematical model considering threshold pressure gradient and stress sensitivity was established on the basis of mass and momentum conservation equations. The finite element method (FEM) was presented to solve the model. Influencing factors, such as TPG, permeability modulus, skin factor, wellbore storage, horizontal length, horizontal position, and boundary effect on pressure and pressure derivative curves, were also discussed. Results analysis demonstrates that the pressure transient curves are different from Darcy’s model when considering the nonlinear flow characteristics. Both TPG and permeability modulus lead to more energy consumption and the reservoir pressure decreases more than Darcy’s model.

Production forecast of fractured shale gas reservoir considering multi-scale gas flow

The shale gas experiences many different spatial scales during its flow in the reservoir, which will engender different flow mechanisms. In order to accurately simulate the production performance of shale gas well, it is essential to establish a multi-continuum model for shale gas reservoir. Based on the geometrical scenario of multistage horizontal well fracturing, this paper builds up a triple-continuum model incorporating three systems: matrix with extremely low permeability, less permeable natural fractures and highly permeable hydraulic fractures. This numerical model employs Langmuir adsorption equation to present the influence of desorption gas in matrix and considers the Klinkenberg effect in matrix and natural fractures by adjusting the apparent permeability. The solution of this model is achieved using implicit scheme. Eventually, this model is applied on the single well production situation in a synthetic reservoir, production decline curves and cumulative production curves are obtained, then the sensitivity analysis is made on various kinds of parameters; thus, the influences of these parameters on production rate are obtained: The gas rate will rise with the increase in hydraulic fracture half-length, meshing size, Langmuir volume and Langmuir pressure, but with the decrease in hydraulic fracture spacing.

A Perturbation Boundary Element Model to Simulate Nonplanar Fracture Networks in Shale Gas Reservoirs

In reality, hydraulic fracturing creates unstructured fracture networks in which nonplanar fractures with varying fracture width exist. Pressure and rate transient analysis for such a complex fracture network is quite challenging. We proposed a perturbation boundary element model to handle the nonplanar varying-width fractures within non-orthogonal fracture network considering stress-sensitivity effect. Line source function is obtained by solving the reservoir flow equation. Hydraulic fractures are represented explicitly and divided into small elements. We established governing equations for each fracture segment in local coordinate system, with sufficient flexibility to set up each segment with different fracture width, permeability and orientation. The stress-dependent fracture permeability is adopted to account for the effect of stress sensitivity. Pedrosa’s transformation and a perturbation technique are employed to solve the nonlinear diffusivity equations. Superposition principle is employed to obtain the pressure responses in shale formations. We performed case studies which compared two fractured horizontal wells, one with three constant-width fractures and another with three varying-width elliptical fractures. We found that the difference of well performance decreases with fracture conductivity increasing. It shows that pressure behavior is strongly dependent on the fracture geometry. The nonplanar fracture geometry and stress sensitivity have negative effects on well performance.