Abstract The preferred method of reserves evaluation for producing wells is deterministic. However, when deterministic methods are used, evaluators cannot reliably assign reserves that satisfy the prescribed certainty for each reserves category. In addition, they have no method to quantify the impact that aggregation will have on reserves certainty. Deterministic reserves estimates are single-valued and may result from analogy, reservoir simulation, decline analysis, or other analytical methods. Because the certainty associated with deterministic reserves assignments are unknown, the norm is that the 2P (proved plus probable) reserves are the evaluator’s best estimate, and the other categories are the evaluator’s best judgment for a high and low estimate. This standard defeats the objective of consistency between evaluators. When an evaluation is for a group of wells, the reserves certainty for the group will increase and the assigned reserves will be closer to the mean. Therefore, the 1P (proved) and 2P reserves for the group will exceed the sum of the 1P and 2P reserves for individual wells within the group. This aggregation benefit of increasing 1P and 2P reserves is not available for wells with deterministically calculated reserves because evaluators require probability distributions to make the calculations. The objective of this paper is to demonstrate how evaluators may overcome these deficiencies and improve the accuracy of their reserves reporting through a new method of statistically enhanced decline analysis (SEDA). Our method was to identify a statistical distribution from which we could assign reserves. We chose to work with a statistically significant number of older analogous wells with reliable best estimate reserves. Using subsets of the available production history (usually annual increments), we forecasted using truncated data and compared that to the remaining reserves using all data. The result of the comparison was the remaining reserves ratio (RRR) that is the ratio of the remaining reserves, calculated using truncated data, to the best estimate of remaining reserves using all data. With Monte Carlo simulation, we created a probability distribution of RRR for a group of specified size and production life. 2P reserves occur when RRR = 1.0. We transformed the best estimate to 2P, and achieved certainty by shifting the probability distribution so that RRR would equal 1.0 at 50 percent probability. For a specified certainty, we obtained the RRR from the adjusted distribution and multiplied it by the 2P reserves to obtain the reserves for that certainty. Evaluators now have a method for accurate, consistent reporting of deterministic reserves. Productivity improves because 1P and 3P (proved plus probable plus possible) are automatically determined through the SEDA process. To our knowledge, SEDA is the only method available to resolve deficiencies of deterministic reserves estimates. The method adapts well to existing reserves evaluation software and improves accuracy and consistency at reduced cost.

Summary This paper presents original research on how to improve the predictive ability of type wells used in evaluating unconventional-resource-drilling programs by extending traditional Monte Carlo calculations. The paper addresses three critical questions engineers must answer before constructing a type well: which well to use in the construction, the relative importance (weighting) appropriate for each well, and how to adapt the results to reflect certainty (e.g., P10, P50, or P90). The proposed method involves determining the aggregated distribution of estimated ultimate recovery (EUR) for the specified number of wells by running a statistically significant number of Monte Carlo trials. From this distribution, one can determine mean EURs for the desired type-well certainties, such as P50 or P90. Additional Monte Carlo trials yielding the desired mean EUR will help determine which wells to average. Monte Carlo sampling results in several hundred trials that match the desired EURs. The relative frequency of well selection from these trials defines the weighting factor and thus the relative importance of each well. Type wells result from a weighted averaging of history and production from the selected wells. Engineers can use this new methodology to prepare production-profile forecasts for the evaluation of multiwell unconventional-resource-drilling programs. They can also gain an understanding of the effect that aggregation will have on their evaluation work. Our research concludes that current type-well-construction practices may not be appropriate for evaluating future drilling because the production profiles for the wells used to build the type well may differ from the production profiles of the planned wells. This paper presents a new method to obtain more-representative type wells. The method permits defining any uncertain parameters, such as EUR, net present value (NPV), or payout time, and then building a type well for various measures of probability of attaining that parameter. This paper presents new concepts that contribute to the technical knowledge base. We present a method to calculate probabilistic type wells dependent on the likelihood of drilling wells that make up the distribution of EUR (or other parameters). The method combines the concepts of aggregation and Monte Carlo simulation to calculate weighting factors for use when averaging rate/time profiles. We introduce the paradigm that one can build probabilistic type wells from distributions of parameters other than EUR. EUR is only suitable for determining reserves. When conducting an evaluation, one may want a more-relevant type well; for instance, one that examines the ability to self-finance by representing the probability of recovering a percentage of capital expenditure (Capex) in the first year. We present a method to scale rate/time profiles from representative wells to the fracture geometry and reservoir quality of future drilling prospects. These scaled wells are for use in building type wells. The scaling algorithms also prove useful in estimating fracture geometry and reservoir quality where it is unknown.

非常规资源的开发使北美油气的供应发生了根本性的改变.在很大程度上,关于页岩气资源开发的投资决策取决于精确预测未来产量的能力.常规的预测方法存在一些严重的缺点.为了避免这些缺陷,开发了一系列经验递减方程以及广延指数(stretched exponentials)函数.这些方程目标是非常规气,并很有希望用于预测以前用联立超级双曲线/指数方程预测的井储量.不幸的是,广延指数方程由于求解难度大而未得到充分利用.本文提出了三大方程(Ilk-SPE116731、Valko-SPE134231、Duong-SPE137748)的求解算法.由于措施或储层的改变导致多重生产趋势的产生,介绍了数据处理的方法,包括生产数据的过滤以及生产趋势的求解.介绍了防止产生单一解或错误解的条件.广延指数方程比较复杂,没有像Arps方程般易于求解.比如,利用Ilk方程确定某井产量达指定值的时间是不可能的.本文将介绍一个公式,该公式可使广延指数方程的计算更方便.管理者需要不能低于某一极小值的递减指数,该公式可满足该要求.通过实例计算验证解法的正确性,对三大方程所得的结果进行比较,论证有时失败的原因.

Executive Summary The increasing attention and development of unconventional resources has many in the industry searching for suitable analogs to supplement their evaluation. A common approach is the use of type wells. Type wells are created by averaging the rate of several analogous wells. This type well rate and corresponding volume is used as a benchmark for evaluating and guiding forecasts for similar wells. The concept of type wells is not new but there are aspects that can be refined to improve results. The current industry practice has a flaw that when combined with development practices will provide inaccurate results. When creating a type well from historical data only, forecasts are implicitly calculated for wells that do not have enough production to reach the end of the type well time interval. Adding to this is the fact that operators will optimize profit by drilling their best wells first. In this instance the type wells will have a greater rate profile and expected ultimate recovery (EUR) than the underlying data will support. This is because the implicit forecasts for the newer, less productive wells are created from the older, better wells. Conversely, type wells will under-predict rate and EUR in technical plays where performance improves with experience. This paper proposes an approach to address the flaw. When historical production data is merged with reliable production forecasts to build a type well, the resulting type well is the best available representation of the underlying data. Measures to ensure accurate forecasts on individual wells are recommended. As an extension to predicting a single rate for similar wells, type wells are also employed to predict different percentile outcomes for similar wells. A common method considers all of the data and calculates a percentile at each time step (Time Slice approach). This approach does not produce consistently reliable results. This paper will propose an alternative approach to creating Type Wells at varying percentiles by analyzing actual wells whose outcome is close in value to the desired percentile.

Abstract The advent of unconventional petroleum resources has radically altered the landscape when it comes to project development. Most of the traditional methods to predict reserves are no longer useful. This paper will review the traditional evaluation practices and recommend improvements. Forecasting conventional oil and gas reserves has traditionally been done using Arps equations that were designed for Boundary Dominated Flow (BDF), but unconventional wells may experience transient flow for up to a decade or more before the onset of BDF. Arps requires the combination of a super-hyperbolic period that smoothly transitions to an exponential tail to model this unconventional behavior. Unfortunately, the Arps equations offer no information as to when this transition occurs. A new class of empirical decline equations, termed stretched exponentials, is gaining favor in forecasting shale oil or gas. These equations are beneficial because an exponential period is not required. This paper will review the three most popular methods and compare them to Arps. Other decline issues covered include: how much data is necessary to provide a reliable forecast, and how to efficiently forecast hundreds or thousands of wells. When building type wells, it can be challenging to obtain statistically valid and significantly similar wells. For instance, fracture size, fracture fluid type, completion technique, well location and many other factors may need to be considered in order to obtain meaningful groups. This paper will suggest possible groupings and propose methods to confirm their validity. This paper will also demonstrate that type wells created with only historical data, as is standard practice, are logically flawed. When historical production data is merged with reliable production forecasts to build a type well, the resulting type well is the best available representation of the underlying data. A detailed review and analysis of the type well equations plus real-world examples will demonstrate this point.

Abstract The advent of unconventional resources has radically changed the gas and oil supply landscape in North America. To a great extent, investment decisions with respect to development of unconventional resources depend on the ability to accurately forecast future recovery. Conventional forecasting methods have serious shortcomings. A class of empirical decline equations, termed stretched exponentials, was meant to address these forecasting weaknesses. These equations targeted unconventional gas and held great promise for predicting reserves from wells that were previously forecast using linked super-hyperbolic/exponential equations. Unfortunately, stretched exponentials have been underutilized, possibly because the equations are difficult to solve. This paper will present solution algorithms for the three most popular equations proposed by Ilk (SPE116731), Valko (SPE 134231) and Duong (SPE 137748). Methods will be presented to identify which data should be rejected and which production trend should be solved when operational or reservoir changes result in multiple trends. Conditions will be described that prevent finding a solution or that will result in an inaccurate solution. Stretched exponential equations are complex and, unlike the Arps’ equations, they cannot be readily manipulated. For example, it is not possible to use Ilk's equation to determine when a well's recovery will reach a specified amount. A formulation will be presented to make stretched exponentials calculator friendly. Regulators require that the decline factor not exceed a specified minimum and the new formulation honors this requirement. Case studies will be shown to verify the solutions, compare the expected recovery from the three equations and demonstrate why they sometimes fail.