Horizontal drilling technology is advancing rapidly day after day. That is due to the much higher productivity of horizontal wells relative to vertical wells. However, the paycheck of drilling a horizontal well is also higher. Therefore, the productivity of a horizontal well not just needs to be estimated whatsoever, but the estimation has to be reliable enough. As a faulty-estimated productivity shall result in a faulty economic feasibility of drilling this well, and may cause huge economic losses.
Several types of models discussed the productivity of horizontal wells. Analytical models (ex. Furui) are the most common to use because they are easy to use. Nevertheless, this easiness comes at the expense of the infinite borehole conductivity assumption, which does not account for any pressure drop along the lateral length of the well. This assumption causes severe errors in some situations. On the other hand, semi-analytical models (ex. M. Tabatabaei and A. Ghalambor) couple reservoir inflow with wellbore outflow to estimate the productivity of horizontal wells.
This paper concentrates on showing the value of production rate error resulting from using Furui's model applied on published data of three wells, the error in rate is calculated based on the M. Tabatabaei and A. Ghalambor's model which is assumed to yield the right rate. First, a MATLAB code was developed to implement the M. Tabatabaei and A. Ghalambor's model. Then, after matching the code results with the rates of the 3 wells mentioned in the original work of M. Tabatabaei and A. Ghalambor, sensitivity studies were made on all the reservoir and production parameters in both productivity models. They were to show the effect of changing each parameter on the production rate error. The analysis of results showed that the error comes from a combination of parameters with different weight factors.
A productivity error correlation is the output of the second part of this paper. The correlation is developed by non-linear regression on the results of the sensitivity runs as inputs, and the errors as the output. A neural network model was also developed, using the same inputs, to confirm the reliability of the developed correlation. The correlation could be used to get a rough estimate of the actual production rate of a horizontal well, as well as judge the validity of the infinite borehole conductivity models.