A Simple Physics-Based Model Predicts Oil Production from Thousands of Horizontal Wells in Shales
Authors: Patzek Tadeusz W. , Saputra Wardana , Kirati Wissem 
Published: October 2017

Summary
Over the last six years, crude oil production from shales and ultra-deep GOM in the United States has accounted for most of the net increase of global oil production. Therefore, it is important to have a good predictive model of oil production and ultimate recovery in shale wells. Here we introduce a simple model of producing oil and solution gas from the horizontal hydrofractured wells. This model is consistent with the basic physics and geometry of the extraction process. We then apply our model thousands of wells in the Eagle Ford shale.
Given well geometry, we obtain a one-dimensional nonlinear pressure diffusion equation that governs flow of mostly oil and solution gas. In principle, solutions of this equation depend on many parameters, but in practice and within a given oil shale, all but three can be fixed at typical values, leading to a nonlinear diffusion problem we linearize and solve exactly with a scaling "type" curve. After the initial 1−3 months of the generally unstable production, the scaled production rate declines as one over the square root of time early on and later it declines exponentially. The three governing parameters are the mean cumulative gas-oil ratio, GOR, the mass of saturated oil in place, M, and the characteristic time of pressure interference between each pair of consecutive hydrofractures, τ. This time depends on the effective formation permeability to oil, porosity, oil saturation, and the overall reservoir compressibility. GOR influences ultimate recovery, while the other two parameters determine where on the master curve production from a given well falls, depending on the M, and how it stretches or shrinks, depending on the τ. The distribution of τ also provides constraints on infill well locations. We implemented our automatic fitting procedure on a PC.
In February 2017, there were 13,057 physical oil wells in the Eagle Ford shale. However, there were only 4,734 unallocated well records because of the peculiar reporting requirements in Texas, explained in the paper. This means that up to 71 physical wells can be reported as one unallocated lease production record in the Eagle Ford. Since we are only interested in black oil horizontal wells, we have selected 2,611 wells with at least 6 months of oil production, GOR less than 2500 scf/stb and liquid gravity less than 40° API. In practice, we match the production data for each well to a dimensionless
master curve with the recovery factor, RF = Np/M, as the y-axis and the dimensionless time, t/τ, as the x-axis. The match relies on adjusting the unknown parameters M and τ. Here Np is cumulative mass production of oil and t is elapsed time on production in months. 429 selected wells were still in the early time flow regime with t/τ &lt; 1. In the remaining 2,182 wells, hydrofractures started pressure interfering in less than 46 months on production. Our scaling of production of the 2,611 black oil wells and back allocating production to the corresponding physical wells gives the total EUR close to 440 million bbl of oil.
Compared with reservoir simulation, the scaling curve method is more robust for thousands of wells and several orders of magnitude faster. Our method is especially useful for shale plays with limited access to reservoir data and it allows one to predict EURs of individual wells on a small laptop. Because we base our approach on the essential physics of oil recovery and on hydrofractured well geometry, the proposed method is highly predictive, while the popular hyperbolic decline curve analysis is not. To our knowledge, the proposed method is new.