**Amjed Hassan, Salaheldin Elkatatny \* and Abdulazeez Abdulraheem**

College of Petroleum Engineering and Geosciences, King Fahd University of Petroleum & Minerals,

31261 Dhahran, Saudi Arabia; g201205100@kfupm.edu.sa (A.H.); aazeez@kfupm.edu.sa (A.A.)

**\*** Correspondence: elkatatny@kfupm.edu.sa; Tel.: +96-659-466-3692

Received: 25 August 2019; Accepted: 29 October 2019; Published: 1 November 2019

**Abstract:** Fishbone multilateral wells are applied to enhance well productivity by increasing the contact area between the bottomhole and reservoir region. Fishbone wells are characterized by reduced operational time and a competitive cost in comparison to hydraulic fracturing operations. However, limited models are reported to determine the productivity of fishbone wells. In this paper, several artificial intelligence methods were applied to estimate the performance of fishbone wells producing from a heterogeneous and anisotropic gas reservoir. The well productivity was determined using an artificial neural network, a fuzzy logic system and a radial basis network. The models were developed and validated utilizing 250 data sets, with the inputs being the permeability ratio (Kh/Kv), flowing bottomhole pressure and lateral length. The results showed that the artificial intelligence models were able to predict the fishbone well productivity with an acceptable absolute error of 7.23%. Moreover, a mathematical equation was extracted from the artificial neural network, which is able to provide a simple and direct estimation of fishbone well productivity. Actual flow tests were used to evaluate the reliability of the developed model, and a very acceptable match was obtained between the predicted and actual flow rates, wherein an absolute error of 6.92% was achieved. This paper presents effective models for determining the well performance of complex multilateral wells producing from heterogeneous reservoirs. The developed models will help to reduce the uncertainty associated with numerical methods, and the extracted equation can be inserted into commercial software, thereby significantly reducing deviation between the actual data and simulated results.

**Keywords:** fishbone multilateral wells; artificial intelligence; predictive models; well productivity
