Decline Curves For Predicting Production Performance From Horizontal Wells
Authors: Poon D.C. 
Published: March 2010

Abstract
Most of the equations for predicting the production rates of a horizontal well are based on the assumption of steady-state flow conditions. These equations require an estimation of the horizontal well drainage radius which is not known until the well has been on production and a pressure buildup or drawdown test conducted. Also the steady-state production rate cannot be used to estimate the ultimate recovery of the well. Production decline curves for horizontal wells under various reservoir boundary conditions have been developed using the Green's and source functions. These decline curves can be used to determine the production forecast and the ultimate recovery of a horizontal well. Results of a parameter study using the decline curves also show that wellbore stimulation, well spacing and length are probably the most important factors determining the effectiveness of a horizontal well.

Introduction
Production forecasts are required to evaluate the economics of a horizontal well project. Reliable production forecasts are most needed during the early stage of the project when the horizontal well has not yet been drilled and only a minimum amount of geological data is available. In a recent literature survey, we found more than twenty papers on the prediction of horizontal well productivity. The most widely used methods are the steady-state equations published by Giger(1), Borisov(2), Joshi(3) and others. These equations require an estimation of the horizontal well drainage radius which is not known until the well has been on production and a pressure buildup or drawdown test conducted. The assumption of steady-state flow condition is valid only for a reservoir with a constant pressure applied at the outer boundary such as the water flood recovery process. Also, it is not possible to estimate the ultimate recovery from a bounded reservoir using the steady-state production rates.
Recently, several horizontal well analytical models have been developed which do not require the assumption of the drainage radius and are not based on the steady-state Darcy's equation. Babu(4) presented an equation for calculating the productivity of a horizontal well in a bounded reservoir during pseudo steady-state flow. Its application requires the determination of two parameters. The first is the geometric factor which accounts for the effect of anisotropic permeability, the well location and the drainage area. The second is the skin factor which accounts for the effect of well length. Similarly, Kuchuk et al. (5) developed an equation for predicting the inflow performance of a horizontal well in a bounded rectangular reservoir which is influenced by the presence of a gas cap of bottomwater sand. The inflow performance is calculated using the long time approximation to the analytical solutions of a three-dimensional reservoir problem.
Duda(6) and Chang(7) developed type curves for predicting the cumulative production of a horizontal well using the numerical simulation results. In the formulation of the numerical models, the wellbore is represented by grid blocks much larger than its diameter and the wellbore transmissibility must be approximated using simplified analytical equations. For example, Chang used an analytical equation developed by Abou-Kassem and Aziz(8) to estimate the wellbore transmissibility.