Tadeusz W. Patzek

Production Forecasting with Logistic Growth Models

With the commercial development of extremely low permeability oil and gas reservoirs, new challenges have arisen both from operational and reservoir standpoints. Reservoir models, which previously yielded reasonable results for reserves estimates and production forecasts, no longer do so. Various new models and techniques have been proposed to improve the accuracy and reliability of reserves estimates; however, none have gained widespread industry acceptance. This paper will propose a new empirical model for production forecasting in extremely low permeability oil and gas reservoirs based on logistic growth models. The new model incorporates known physical volumetric quantities of oil and gas into the forecast to constrain the reserve estimate to a reasonable quantity. The new model is easy to use, and it is very capable of trending existing production data and providing reasonable forecasts of future production. The logistic growth model does not extrapolate to non-physical values. Introduction One source of production to meet the demand for oil and gas has come from extremely low permeability oil and gas reservoirs, often referred to as unconventional resources. These unconventional resources typically exhibit permeabilities in the nanodarcy to microdarcy range. The production from these wells is characterized by very long and extended periods of transient flow before reaching the reservoir boundary, and entering into boundary-dominated flow. Thanks to drastic improvements in both horizontal drilling and hydraulic fracturing, these resources have been able to be successfully exploited in North America. Along with providing many new challenges in successfully drilling and completing unconventional wells, they have also provided new challenges in accurately forecasting the reserves. The traditional empirical Arps’ equation used to forecast reserves in conventional reservoirs, often gives over estimates of reserves when used in these extremely low permeability formations. Commonly the b values obtained are greater than 1, which results in an unrealistic production rate that never approaches 0. The purpose of this paper, however, is not to discuss the errors encountered when using the Arps’ equation, as the problem has already been thoroughly discussed in the past. Lee (2010) and Ilk et al. (2008) have both provided good explanations of the problems encountered with the traditional models as have numerous other authors over the years. Various new models for use in production forecasting in tight reservoirs have been proposed including Maley (1985), Ilk et al. (2010), Kupchenko et al. (2008), and Valko (2009). The industry has been slow to adopt the new methods for forecasting reserves despite the apparent over estimation of reserves encountered when using the traditional decline curve models. This paper presents a new method for empirically forecasting production based on the logistic growth model. Logistic Growth Models Logistic growth curves are a family of mathematical models used to forecast growth in numerous applications. Originally developed by the Belgian mathematician Pierre Verhulst in the 1830s, logistic growth curves were used to model population growth. Verhulst based his ideas on the works of Malthus who believed that the population of a particular country or region would only be able to grow to a certain size before competition for resources would cause the growth to stabilize. Verhulst took this idea and by adding a multiplicative factor to the equation for exponential growth, created the logistic growth model.

Modeling Gas Adsorption in Marcellus Shale With Langmuir and BET Isotherms

Abstract It is believed that gas in shale reservoirs is mainly composed of free gas within fractures and pores and adsorbed gas in organic matter (kerogen). It is generally assumed in the literature that the monolayer Langmuir isotherm describes gas adsorption behavior in shale gas reservoirs. However, in this chapter, we analyze four experimental measurements of methane adsorption from the Marcellus Shale core samples that deviate from the Langmuir isotherm, but obey the BET (Brunauer, Emmett, and Teller) isotherm. To the best of our knowledge, it is the first time to find that methane adsorption in a shale gas reservoir behaves like multilayer adsorption. Consequently, investigation of this specific gas desorption effect is important for accurate evaluation of well performance and completion effectiveness in shale gas reservoirs based on the BET isotherm. The difference in calculating original gas in place based on both isotherms is discussed. We also perform history matching with one production well from the Marcellus Shale and evaluate the contribution of gas desorption to the wells performance. This chapter provides better understanding of gas desorption in shale gas reservoirs and updates our current analytical and numerical models for simulation of shale gas production.

History Matching and Rate Forecasting in Unconventional Oil Reservoirs With an Approximate Analytical Solution to the Double-Porosity Model

Production data from most fractured horizontal wells in gas and liquid-rich unconventional reservoirs plot as straight lines with a one-half slope on a log-log plot of rate vs. time. This production signature (half-slope) is identical to that expected from a 1D linear flow from reservoir matrix to the fracture face, when production occurs at constant bottomhole pressure. In addition, microseismic data obtained around these fractured wells suggest that an area of enhanced permeability is developed around the horizontal well, and outside this region is an undisturbed part of the reservoir with low permeability. On the basis of these observations, geoscientists have, in general, adopted the conceptual double-porosity model in modeling production from fractured horizontal wells in unconventional reservoirs. The analytical solution to this mathematical model exists in Laplace space, but it cannot be inverted back to real-time space without use of a numerical inversion algorithm. We present a new approximate analytical solution to the double-porosity model in real-time space and its use in modeling and forecasting production from unconventional oil reservoirs. The first step in developing the approximate solution was to convert the systems of partial-differential equations (PDEs) for the double-porosity model into a system of ordinary-differential equations (ODEs). After which, we developed a function that gives the relationship between the average pressures in the highand the low-permeability regions. With this relationship, the system of ODEs was solved and used to obtain a rate/time function that one can use to predict oil production from unconventional reservoirs. The approximate solution was validated with numerical reservoir simulation. We then performed a sensitivity analysis on the model parameters to understand how the model behaves. After the model was validated and tested, we applied it to field-production data by partially history matching and forecasting the expected ultimate recovery (EUR). The rate/time function fits production data and also yields realistic estimates of ultimate oil recovery. We also investigated the existence of any correlation between the model-derived parameters and available reservoir and well-completion parameters.

Offshore Drilling and Production: A Short History

Drilling in Louisiana’s marshes and shallow waters is as old as anyone there can remember, and – for better or worse – the expanding presence of the oil and gas industry has changed everyone’s lives. An oral history1 captures the richness and complexity of interactions between people and the technology that invaded the small fishing and shrimping communities. Here is but one short excerpt.

Our Energy and Complexity Dilemma: Prospects for the Future

If fish were scientists, suggests our colleague T. F. H. Allen, the last thing they would discover would be water. We are not sure where this saying originates. Something like it appeared in The New York Times in 1920 in a report on a talk by British scientist Sir Oliver Lodge. “Imagine a deep-sea fish at the bottom of the ocean,” lectured Sir Oliver. “It is surrounded by water; it lives in water; it breathes water. Now, what is the last thing that fish would discover? I am inclined to believe that the last thing the fish would be aware of would be water.”1 We like a variant of this conundrum: imagine that you could talk to a fish, and ask the question: Is your nose wet?

The Energy–Complexity Spiral

Engineers build many wonderful things that few of us would choose to live without. Yet, as we have seen, some structures are of such complexity and magnitude that an unforeseen failure can kill nearly a dozen men, ruin thousands of livelihoods, and pollute a valuable ecosystem. Failure on this scale is obviously undesirable, yet it happens to bridges, space shuttles, and giant drilling rigs. In response, our instinct is to seek proximate causes, which include such factors as mistakes, oversights, and technical failures, the very things on which most attention has been concentrated in the news media. By applying some fixes – better training, better oversight, a different corporate culture – we assume that the accident could have been prevented and that we can avoid future ones. Engineers must examine and learn from these proximate causes of failure, but as a society we are bound to seek the ultimate cause of tragedies such as the Deepwater Horizon’s blowout. The alternative is to lurch from failure to failure of increasing magnitude. We will find that the ultimate cause lies deep within humanity’s history, and in the very essence of what it means to be a civilization. A civilization is a complex society, and complexity is a phenomenon that we must understand in order to comprehend our potential futures and shaping events such as the Gulf tragedy.

History Matching and Rate Forecasting in Unconventional Oil Reservoirs Using an Approximate Analytical Solution to the Double Porosity Model

Production data from most fractured-horizontal wells in gas and liquid-rich unconventional reservoirs plot as straight lines with a one half slope on a log-log plot of rate versus time. This production signature (half slope) is identical to that expected from a one-dimensional linear flow from reservoir matrix to the fracture face, when production occurs at constant-bottomhole pressure. In addition, microseismic data obtained around these fractured wells suggest that an area of enhanced permeability is developed around the horizontal well, and outside this region is an undisturbed part of the reservoir with low permeability. Based on these observations geoscientists have, in general, adopted the conceptual double-porosity model in modeling production from fractured horizontal wells in unconventional reservoirs. The analytical solution to this mathematical model exists in Laplace space but it cannot be inverted back to real-time space without using a numerical inversion algorithm. We present a new approximate analytical solution to the double-porosity model in real-time space and its use in modeling and forecasting production from unconventional-oil reservoirs. The first step in developing the approximate solution was to convert the systems of partial differential equations for the dual-porosity model into a system of ordinary-differential equations. After which we developed a function that gives the relationship between the average pressures in the high-and the low-permeability regions. Using this relationship, the system of ordinary differential equations was solved and used to obtain a rate/time function that can be used to predict oil production from unconventional reservoirs. The approximate solution was validated with numerical reservoir simulation. We then performed a sensitivity analysis on the model parameters to understand how the model behaves. Once the model was validated and tested, we applied it to field production data by partially history matching and forecasting the expected ultimate recovery. The rate/time function fits production data and also yields realistic estimates of ultimate oil recovery. We also investigated the existence of any correlation between the model-derived parameters and available reservoir and well completion parameters. Introduction Many studies have been published that focus on the solution of the double porosity model for flow in hydraulically fractured horizontal wells. Barenblatt and Zheltov (1960) presented the first formulation of the double-porosity model. Warren and Root (1962) presented the first application of the double-porosity model to flow problems in the petroleum industry. Since then many authors (de Swaan, 1976; Mayerhofer, 2006; Carlson and Mercer, 1989; El-Banbi, 1998; Ozkan et al., 1987) have presented applications of the model. All the analytical solutions presented have all been in Laplace space and have had to be numerically transformed to real time space using some form of inversion algorithm of which the Stehfest algorithm (Stehfest 1970) is the most popular. More recently, Bello and Wattenbarger (2008) presented the solution to the double porosity model for linear flow in which they were able to obtain closed form analytical solutions for certain ranges of time. To do this they broke their Laplace space solution in to smaller bits using special properties of the solution which they could invert to real-time space. This piece-wise solution would have to be applied sequentially. Samandarli et al. (2011) presented the application of this solution to history matching and forecasting the performance of shale gas wells. Song (2014) presented a finite-difference solution to this problem and its application to oil production from hydraulically fractured wells. In this study, we present an approximate analytical solution to the double-porosity model in real-time space that is valid across all time domains, that is, it is a continuous function that is valid during the transient and late time flow from the fracture and matrix. We validate our solution against numerical simulation and also show that our solution reproduces the production behavior obtained from the inverted Laplace space solution. We also present example applications of our solution to field data.

Why the Gulf Disaster Happened

Transocean and Halliburton’s crews finished cementing the Macondo well at 12:40 a.m. on April 20, 2010. At 5 p.m. on the same day, or some 16 hours later, the fateful negative pressure test began.

The Significance of Oil in the Gulf of Mexico

It was 9:15 p.m. on April 20, 2010, and the captain of the Deepwater Horizon was entertaining heavyweights from British Petroleum (BP) and Transocean, by showing off the computers and software at his disposal. After the Captain welcomed his visitors on the bridge, Yancy Keplinger, one of two dynamic-positioning officers, began a tour while the second officer, Andrea Fleytas, was at the desk station. The officers explained how the rig’s thrusters kept the Deepwater Horizon in place above the well, showed off the radars and current meters, and offered to let the visitors try their hands at the rig’s dynamic-positioning video simulator. One of the visitors, a man named Winslow, watched as the crew programmed-in 70-knot winds and 30-foot seas, and hypothetically put two of the rig’s six thrusters out of commission. Then they set the simulator to manual mode and let another visitor work the hand controls to maintain the rig’s location. While Keplinger was advising about how much thrust to use, Winslow decided to grab a quick cup of coffee and a smoke. He walked down to the rig’s smoking area, poured some coffee, and lit his cigarette.

The Benefits and Costs of Complexity

Here is how to boil a frog. Place the frog in a pan of tepid water. Raise the temperature so gradually that the frog does not realize it is being cooked. It may even fall into a stupor, as a person might in a hot bath. Eventually it will die. According to experiments done in the nineteenth century, you can indeed boil a frog this way. Biologists today claim that you can’t. Either way, please don’t try it.