No abstract

Summary Vertically fractured wells are used widely to achieve efficient development of low-permeability reservoirs and unconventional tight reservoirs. Currently, there are some commonly adopted productivity models for a fractured vertical well, including the Giger (1985) model, the Economides model (Economides et al. 1989), the Joshi (1991) model, the Guo model (Guo and Evans 1993), the Zhang (1999) model, and others. However, these models are only suitable for either short fractures or long fractures, and thus cannot satisfy the need for arbitrary-length fracture selection. In addition, these models have certain requirements for boundary conditions, and few models consider the nonuniform flow in actual hydraulic factures. Therefore, it is desirable to establish a productivity model for vertically fractured wells with arbitrary fracture length under complex boundary conditions. In this paper, first, we evaluate the existing fractured-vertical-well productivity models in detail. After that, on the basis of the potential superposition principle and mirror-image method, we develop the productivity model for a fractured vertical well with arbitrary fracture length under different boundary conditions. Grounded in this model, further considering the frictional pressure drop caused by fracture-flow nonuniformity, we establish the productivity equation of a finite-conductivity-fracture vertical well with nonuniform flow in the fracture. Finally, after comparing with the existing model under certain conditions, the reliability of the proposed model is verified successfully. Results show that the Giger model assumes that the boundary in the fracture-extension direction is impermeable, and the pressure wave reaches the boundary earlier than the constant-pressure boundary, which is perpendicular to the extension direction of the fracture, whereas both the Economides model and the Joshi model assume that the boundary in the fracture-extension direction is far, and is always farther than the boundary perpendicular to the direction of the fracture extension. The results forecast by the previous models will deviate greatly from actual well-production performance, if the real field case cannot meet the requirements of these models. The proposed model is not only in good agreement with the previous models at given conditions, but is also suitable for fractured vertical wells under arbitrary-length fractures and complex boundary conditions. Compared with the existing models, the correctness and reasonableness of the model are shown, and the application of the proposed model is broadened. For the development of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells, the establishment and application of this model have great theoretical significance and application value for production prediction. This model can be a foundation or reference for productivity prediction of low-permeability and unconventional tight oil and gas reservoirs with fractured vertical wells or fractured horizontal wells.

No abstract

No abstract

This paper analyzes the low production rate caused by the hydration of shale formations embedded into a naturally fractured reservoir. Results show that the induced stresses of shale hydration are the major reason to cause the permeability impairment for the stress sensitive reservoir. Experimental and numerical simulation methods for fracture closure and effect on permeability impairment discussed in the paper. Field application of the methods introduced in the paper also presented. Introduction In petroleum industry, people emphasize shale formation because it is a cover layer of a reservoir or it causes a lot of trouble during drilling. However, the hydration of shale formation under reservoir condition generates enormous hydration stresses which cause permeability impairment for stress sensitive reservoirs. There are three kinds of typical situations should be noted. First, the shale formation which has a very strong swelling tendency generates enormous hydration stress under reservoir condition. This hydration stress sometimes exceeds the overburden pressure. The permeability impairment for normal reservoirs can be as high as 10% to 40% under this condition. Second, the shale formation which does not have large swelling volume, but the reservoir is highly stress sensitive. A small swelling volume of the shale formation will introduce a large permeability impairment, such as a reservoir with horizontal fractures, coal bed with high density of cracks and loose sand reservoirs. Third, the shale formation has large swelling tendency and the formation is highly stress sensitive, such as coal bed. The shale swelling will cause dramatic reduction of permeability of a coal bed, which is the major problem in coal bed methane production in China. This paper focuses on the effect of shale hydration and swelling on permeability impairments for naturally fractured reservoir. The effect on porous reservoir will be discussed in other papers. Analysis of Fracture Closure Caused by Shale Swelling for Stress Sensitive Naturally Fractured Reservoir Physical models of fracture surface morphology There are four kinds of fractures; parallel, arc, multi-supports and conjugate network fracture. The parallel fracture can be characterized by that the both surfaces is parallel and smooth. Most tension fractures can be classified as this kind. Arc fracture has arcs on both fracture surfaces. Except that the end points of an arc contact, there are no contact points in the arc, such as fractures in volcanic fractured reservoir which is formed by the volcanic rock shrinkage due to cool process. Multi-supports fracture is the most seeing fracture, as indicated in Fig. 1. This fracture is formed by coaxial shear or compressive shear. Most horizontal and low angle fractures are this kind. Conjugate network fractures are formed either non-coaxial shear, horizontal compress or rock shrinkage (such as coal bed). For a single conjugate fracture, it can be classified as the multi-supporting fracture. In above fractures, the multi-supports fracture and conjugate fracture network are the most stress sensitive. The following paper will discuss the closure of the multi-supports fracture under shale hydration stress. The model of fracture closure The closure of the multi-supports fracture can be simulated by finite element method for a given stress and mechanical properties. For simplicity, the model shown in Fig. 2a was used. Fig. 2b shows the settlement of single support. This can be calculated by using the solution of H. Hertz problem.(1) P. 287