The conventional analysis of rate decline curve has been used to determine the deliverability and to forecast the performance of gas well, but it can't estimate reservoir properties. Modern rate decline analysis can be used to interpret the transient rate-time data and estimate reservoir properties and evaluate the information of formation damages. This method doesn't require shutting well down, and induces valuable information from production data. In this paper, a mathematical model for transient rate analysis at variable flowing pressure is proposed, based on the principle of superposition. The hybrid approach combined genetic algorithm (GA) with convention nonlinear optimization is presented to estimate these parameters of the fractured well. The hybrid mechanism has unified the behavior of more effective searching and quicker convergence than the conventional method. This modern analysis of rate decline method provides a new approach to monitor reservoir behavior.
Conventional analysis of rate decline curve is used to determine deliverability and to forecast performance of gas well, but it is limited to estimate reservoir properties. From transient flow rate at the condition with a constant pressure or variable pressure, the reservoir properties and formation damages information can be estimated by matching the production data. The benefit of this method is that reservoir information can be obtained without shutting down well and affecting production. The bottom-hole pressure Pwf can be varied in term of the different operation strategies, as well as the flowing response q(t) at the specified pressure. As a result, problems of estimating reservoir parameters will be occurred by using conventional decline analysis. Without an initial value, the non- linear regression also can't match the production data well and the optimizing procedure maybe creates unreasonable results.
In this paper, a mathematical model for the transient rate at variable flowing pressure is proposed, based on the principle of superposition. Aimed at the difficulty of interpreting data, the hybrid way of combined genetic algorithm (GA) with conventional nonlinear optimization is presented to estimate reservoir properties and formation damages. This approach is much efficiency to solve GA, reach global optimizing and quicker converge than the conventional optimizing algorithm.
The mathematical model for an infinite homogeneous reservoir is following:(Equations (1) Available in full paper) Where, (Equations (2) Available in full paper) (Equations (3) Available in full paper) (Equations (4) Available in full paper) (Equations (5) Available in full paper) To solve Eq.1, Laplace space solution of dimension rate can be obtain as following:(Equations (6)) (Available in full paper) By changing (Figure)(Available in full paper), the solution for dual media reservoir is obtained. Where, 0 and K1 are the Bassel function.
There is a relationship between the solution of (Figure) (Available in full paper) (dimensionlee of rate) of at the constant pressure and the (Figure) (Available in full paper) (dimensionless pressure solution) at the const flowing rate. Van Everdingen and Hurst demonstration reported this relationship as a relation in the Laplace space: (Equations (7)) (Available in full paper)
