A Semianalytical Method for Two-Phase Flowback Rate-Transient Analysis in Shale Gas Reservoirs

Summary We propose a new semianalytical method for analyzing flowback water and gas production data to estimate hydraulic fracture (HF) properties and to quantify HF dynamics. The method includes a semianalytical flowback model, a set of two-phase diagnostic plots, and a workflow to evaluate initial fracture volume and permeability, as well as fracture compressibility and permeability modulus. The flowback model incorporates two-phase water and gas flow in both HF and matrix domains and considers variations of fluid and rock properties with pressure. The HF domain is modeled by boundary-dominated flow, whereas an infinite-acting linear flow is assumed for the matrix domain. The flowback model is developed by assigning the variable average pressure in the fracture as the inner boundary condition for matrix according to Duhamel's principle. The average pressure in the fracture and distance of investigation (DOI) in the matrix are calculated from a modified material-balance equation by updating the matrix DOI as well as phase saturation and relative permeability in both the fracture and matrix domains. A modified DOI equation is used for two-phase flow in the matrix, which considers the pressure-dependent fluid and rock properties in pseudotime. The diagnostic plots shed light on the identification of flow regimes during the coupled two-phase flow in both fracture and matrix. The proposed workflow quantifies the HF dynamics through the loss of both fracture volume and fracture permeability by reconciling flowback and long-term production data. The accuracy of the new method is tested against numerical simulations conducted by a commercial numerical simulator. The validation results confirm that the proposed method accurately predicts initial fracture volume, permeability, and permeability modulus. Further, we use production data from a multifractured horizontal well (MFHW) drilled in Marcellus Shale to test the practicality of the proposed method. The results show a significant reduction in fracture volume and permeability during production attributable to the HF closure.

Transient Pressure and Rate Decline Analysis for Horizontal Well in Stress-Sensitive Composite Reservoir

The existence of stress sensitivity effect made the percolation mechanism of low-permeability reservoirs significantly complex. Further, numerous reservoirs have composite stratum properties in actual development procedure. This paper based on the concept of permeability stress sensitivity presents an unsteady flow model for horizontal well taking both stress sensitivity and composite reservoir into account. Analytic solutions for the transient pressure and the rate decline behaviors are obtained by comprehensive utilization of regular perturbation method, Laplace transformation, orthogonal transformation, and Stehfest numerical inversion. The example analysis verifies that the proposed model is reliable and practical. Likewise, there is a discussion of the influence of permeability modulus and other relevant parameters on the transient pressure and the rate decline for horizontal well in stress-sensitive composite reservoir. The work of this paper improved the previous researches and provided a more accurate basis for transient flow analysis and formation evaluation of this typical reservoir.

Approximate Analytical-Pressure Studies on Dual-Porosity Reservoirs With Stress-Sensitive Permeability

Summary Pressure-transient analysis in dual-porosity media is commonly studied by assuming a constant reservoir permeability. Such an assumption can result in significant errors when estimating pressure behavior and production rate of naturally fractured reservoirs as fracture permeability decreases during the production. At present, there is still a lack of analytical pressure-transient studies in naturally fractured reservoirs while taking stress-sensitive fracture permeability into account. In this study, an approximate analytical model is proposed to investigate the pressure behavior and production rate in the naturally fractured reservoirs. This model assumes that fracture permeability is a function of both permeability modulus and pressure difference. The pressure-dependent fracture system is coupled with matrix system with an unsteady-state exchange flow rate. A nonlinear diffusivity equation in fracture system is developed and solved by Pedrosa's transformation and a perturbation technique with zero-order approximation. A total of six solutions in the Laplace space are presented for two inner-boundary conditions and three outer-boundary conditions. Finally, pressure behavior and production rate are studied for both infinite and finite reservoirs. Pressure behavior and production rate from the models with and without stress-sensitive permeability are compared. It is found that, for an infinite reservoir with a constant-flow-rate boundary condition, if permeability modulus is 0.1, dimensionless pressure difference at the well bottom from the model with fracture-permeability sensitivity is 80% higher than that of the constant fracture-permeability model at a dimensionless time of 106. Such difference can be as high as 216% if permeability modulus increases to 0.15. On the contrary, for the infinite reservoirs with a constant-pressure boundary, the constant fracture-permeability model tends to overestimate the flow rate at wellbore and cumulative production. The proposed model not only provides an analytical and quantitative method to investigate the effects of fracture-permeability sensitivity on reservoir-pressure distribution and production, but it also can be applied to build up analysis of well test data from stress-sensitive formations.

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.