Determination of the Production Rate and Cumulative Production in the “No Flow” Boundary Condition Utilizing the Finite Element Method

The No Flow outer boundary condition also known as the PSEUDO-STEADY STATE occurs When reservoirs outside boundary lines are all closed boundaries in the late time region. This condition is relevant to bounded reservoirs. In this research, we employed the well the rate of production and cumulative production in a circular reservoir adopting the Finite Element Method (FEM). The FEM was used to analyze the diffusivity equation (governing equation). The reservoir was divided into fragments, which is referred to finite element. These components were examined and then put together to create the reservoir's domain. The research was conducted under the presumption that the pressure in the reservoir was uniformly distributed prior to the well starting production. Due to the nature of the diffusivity equation, dimensional analysis was carried out to make the equation dimensionless. The dimensionless results indicate a linear increase in cumulative production over time. Thereafter, the dimensionless cumulative production becomes asymptotically constant with a very slight increase as the dimensionless time increases. This continues throughout this flow regime. The results indicate a decline in the production rate of the reservoir over time. The rate of decrease at the initial stage is high and later in the regime, becomes steady. The finding of this study was juxtaposed with the obtained results of Christine. The comparison reveals that the two approaches have a high positive correlation, with an overall percentage error of 1.5512 & 0.0891 and a minimal percentage error of 0.0001 & 0.0111 produces the dimensionless cumulative production & the dimensionless production rate, respectively. Again, Christine solutions only stated the reservoir's production rate and cumulative production at certain times, but this work estimates the reservoir's overall production rate and cumulative output simultaneously.