# A Semi-Analytical Analysis of the Gas and Water Forecasts from Unconventional Reservoirs

Restricted (Penn State Only)
Author:
Alzaabi, Abdulla Saleh
Petroleum and Mineral Engineering
Degree:
Master of Science
Document Type:
Master Thesis
Date of Defense:
March 21, 2019
Committee Members:
• Gregory R King, Thesis Advisor
Keywords:
• Material Balance
• Unconventional Reservoirs
• Coalbed Methane
• Runge-Kutta
• Muskat
Abstract:
Material balance is an essential reservoir engineering tool that is used to determine original hydrocarbon in place and the production performance of a reservoir. There are several types of material-balance approaches developed, each with its own application. Such approaches include integral material balance, differential material balance and flowing material balance. In this thesis, a form of differential material balance, similar to the one developed by Muskat for Solution Gas Drive Reservoirs, has been derived for unconventional gas-water reservoirs impacted by adsorption. Originally, the developed Muskat-type equation is in the pressure domain, but it can also be derived in other domains such as the time domain and the cumulative produced fluids domains. The resulting system of ordinary differential equations (ODEs) are then solved using fourth order Runge-Kutta method which is a traditional ODE solver. The system of two differential equations for the Muskat-type equation in the time domain (time as an independent variable), are formulated with pressure and water saturation as the dependent variables. These resulting ODEs are then used to forecast and analyze the production profiles of a gas-water reservoir considering adsorption. The semi-analytical model is then validated internally using finite difference and analytical rate derivative equations, and externally by benchmarking it with a numerical simulator. The significant factor that caused the disparity between the semi-analytical model proposed in this study and the numerical simulator is the time it takes to reach pseudo-steady state flow (t_pss) with lower times producing better results. At t_pss less than 0.111 days , numerical simulation is almost replaceable in forecasting rates. However, at t_pss less than 0.717 days, cumulative gas produced can be accurately forecasted. This is to be expected and a reservoir simulator is fully transient, while material balance is based on the pseudo steady-state flow regime. This study provided a unique opportunity to investigate the characteristics of the production profile such as the peak rate and the observed inflection points while also identifying the reservoir parameters that affect them. Moreover, an equation has been developed that can be used to identify and describe the peak rate. This equation makes use of the byproduct of the Muskat-type equation ((dS_w)/dP) which can be modified in terms of rock and fluid properties to aid in history matching. Furthermore, three well specifications were investigated (constant well pressure, constant drawdown, and constant water production rate) with only two of the three producing a peak rate – no peak gas production rate was observed for water rate specified wells. This study also showed that material balance can be used to replace decline curve analysis under certain conditions. This is mainly due to the reduced time to pseudo-steady state (t_pss) caused by the low total compressibility (rock and water), high permeability, low water viscosity, and low drainage area. At a threshold of t_pss less than 0.178 days, an accurate late-time forecast can be attained. Since the proposed semi-analytical model provided water saturation values for different pressures, a non-iterative methodology has been developed to improve upon King’s (G. R. King, 1993) iterative integral material balance equation for unconventional reservoirs. Through this study, a number of significant observations were made. It was found that at a low rock compressibility, the change in saturation over time can be estimated using the water production profile and initial porosity and water formation volume factor. Also, the saturation of gas can be estimated using the percentage of water produced from the original water in place (OWIP), adjusted for desorption time, at an increasing accuracy as the rock compressibility is decreased. Additionally, the cause of a phenomenon known as “dual peaking” which occurs in field and simulation data of CBM reservoirs has been identified to be due to the transient-state production.