Influenced by the complex sedimentary environment, a well always penetrates multiple layers with different properties, which leads to the difficulty of analyzing the production behavior for each layer. Therefore, in this paper, a semi-analytical model to evaluate the production performance of each layer in a stress-sensitive multilayer carbonated gas reservoir is proposed. The flow of fluids in layers composed of matrix, fractures, and vugs can be described by triple-porosity/single permeability model, and the other layers could be characterized by single porosity media. The stress-sensitive exponents for different layers are determined by laboratory experiments and curve fitting, which are considered in pseudo-pressure and pseudo-time factor. Laplace transformation, Duhamel convolution, Stehfest inversion algorithm are used to solve the proposed model. Through the comparison with the classical solution, and the matching with real bottom-hole pressure data, the accuracy of the presented model is verified. A synthetic case which has two layers, where the first one is tight and the second one is full of fractures and vugs, is utilized to study the effects of stress-sensitive exponents, skin factors, formation radius and permeability for these two layers on production performance. The results demonstrate that the initial well production is mainly derived from high permeable layer, which causes that with the rise of formation permeability and radius, and the decrease of stress-sensitive exponents and skin factors, in the early stage, the bottom-hole pressure and the second layer production rate will increase. While the first layer contributes a lot to the total production in the later period, the well bottom-hole pressure is more influenced by the variation of formation and well condition parameters at the later stage. Compared with the second layer, the scales of formation permeability and skin factor for first layer have significant impacts on production behaviors.
A Unified Formula for Determination of Wellhead Pressure and Bottom-hole Pressure
