Zalavadia, Hardikkumar (Texas A&M University) | Sankaran, Sathish (Anadarko Petroleum Corporation) | Kara, Mustafa (Anadarko Petroleum Corporation) | Sun, Wenyue (Anadarko Petroleum Corporation) | Gildin, Eduardo (Texas A&M University)
Model-based field development planning and optimization often require computationally intensive reservoir simulations, where the models need to be run several times in the context of input uncertainty or seeking optimal results. Reduced Order Modeling (ROM) methods are a class of techniques that are applied to reservoir simulation to reduce model complexity and speed up computations, especially for large scale or complex models that may be quite useful for such optimization problems. While intrusive ROM methods (such as proper orthogonal decomposition (POD) and its extensions, trajectory piece-wise linearization (TPWL), Discrete Empirical Interpolation Method (DEIM) etc.) have been proposed for application to reservoir simulation problems, these remain inaccessible or unusable for a large number of practical applications that use commercial simulators.
In this paper, we describe a novel application of a non-intrusive ROM method, namely dynamic mode decomposition (DMD). We specifically look at reducing the time complexity involved in well control optimization problem, using a variant of DMD called DMDc (DMD with control). We propose a workflow using a training dataset of the wells and predict the state solution (pressure and saturation) for a new set of bottomhole pressure profiles encountered during the optimization runs. We use a novel strategy to select the basis dimensions to prevent unstable solutions. Since the objective function of the optimization problem is usually based on fluid production profiles, we propose a strategy to predict the fluid production rates from the predicted states from DMDc using machine learning techniques. The features for this machine learning problem are designed based on the physics of fluid flow through well perforations, which result in very accurate rate predictions. We compare the proposed methodology using another variant of DMD called ioDMD (input-ouput DMD) for system identification to predict output production flow rates.
The methodology is demonstrated on a benchmark case and a Gulf of Mexico deepwater field that shows significant time reduction in production control optimization problem with about 30 – 40 times speedup using the proposed DMDc workflow as compared to fine scale simulations, while preserving the accuracy of the solutions. The proposed "non-intrusive" method in this paper to reduce model complexity can substantially increase the range of application of ROM methods for practical field development and reservoir management.
Calibrating production and economic forecasts (objective functions) to observed data is a key component in oil and gas reservoir management. Traditional model-based data assimilation (history matching) entails first calibrating models to the data and then using the calibrated models for probabilistic forecast, which is often ill-posed and time-consuming. In this study, we present an efficient regression-based approach that directly predicts the objectives conditioned to observed data without model calibration.
In the proposed workflow, a set of samples is drawn from the prior distribution of the uncertainty parameter space, and simulations are performed on these samples. The simulated data and values of the objective functions are then assembled into a database, and a functional relationship between the perturbed simulated data (simulated data plus error) and the objective function is established through nonlinear regression methods such as nonlinear partial least square (NPLS) with automatic parameter selection. The prediction from this regression model provides estimates for the mean of the posterior distribution. The posterior variance is estimated by a localization technique.
The proposed methodology is applied to a data assimilation problem on a field-scale reservoir model. The posterior distributions from our approach are validated with reference solution from rejection sampling and then compared with a recently proposed method called ensemble variance analysis (EVA). It is shown that EVA, which is based on a linear-Gaussian assumption, is equivalent to simulation regression with linear regression function. It is also shown that the use of NPLS regression and localization in our proposed workflow eliminates the numerical artifact from the linear-Gaussian assumption and provides substantially better prediction results when strong nonlinearity exists. Systematic sensitivity studies have shown that the improvement is most dramatic when the number of training samples is large and the data errors are small.
The proposed nonlinear simulation-regression procedure naturally incorporates data error and enables the estimation of the posterior variance of objective quantities through an intuitive localization approach. The method provides an efficient alternative to traditional two-step approach (probabilistic history matching and then forecast) and offers improved performance over other existing methods. In addition, the sensitivity studies related to the number of training runs and measurement errors provide insights into the necessity of introducing nonlinear treatments in estimating the posterior distribution of various objective quantities.
History matching within the Bayesian framework in practice assumes perfect simulation models. However, for real field cases this assumption may lead to a spurious reduction in forecast uncertainty when a large number of data is used to constrain imperfect reservoir models. To mitigate this spurious uncertainty reduction, we propose a new approach to automatically and consistently inflate the standard deviation of measurement errors for the constraining field data. In previous work we applied the simple mitigation strategy of using a single inflation factor for all data. In this work we propose to use information from the Hessian matrix evaluated at the maximum a posteriori (MAP) points in parameter space: data are regrouped into different categories according to their sensitivities with respect to principal directions of the posterior Hessian matrix. For each group a suitable inflation factor can then be estimated from the number of data and observed mismatches in that group. The proposed procedure is applied to a synthetic as well as a field scale model. The truth of the synthetic model is selected from one unconditional realizations of a real field model with three facies. Synthetic measured production data are generated by adding Gaussian noise to those predicted from the true simulation model. During the process of history matching, a few uncertain model parameters are artificially fixed to values that are inconsistent with the truth to mimic the unknown real field case and make the model imperfect. Numerical results indicate that the proposed approach is able to give a balanced and reasonable range of forecast uncertainty for the cases considered.
Luo, Kai (Research Institute of Petroleum Exploration and Development) | Li, Shi (Research Institute of Petroleum Exploration and Development) | Zheng, Xitan (Research Institute of Petroleum Exploration and Development) | Chen, Gang (Research Institute of Petroleum Exploration and Development) | Liu, Ning (Research Institute of Petroleum Exploration and Development) | Sun, Wenyue (Research Institute of Petroleum Exploration and Development)
A high condesate saturation ring usually forms in a gas condensate reservoir where pressure decreases below the dew point, especially around the wellbore. Gas injection/cycling is a main recovery process of choice for preventing loss of valuable condensate liquids. In this process the reservoir is often maintained above the dew point. Although full pressure maintenance development seems ideal in terms of preventing liquid loss, for economic reasons, this process may not be profitable. In recent years, many gas condensate reservoirs discovered have very high dew point pressures, say above 50MPa, in this case the full pressure maintenance will result in much expensive cost of the injection equipment and a large risk of safety problem. Thus one thought usually arises that whether the reservoir may be cycled at lower pressure after undergoing previous depletion below the dew point.
To address this issue, a series of experiments in this paper are performed and compared to quantitatively investigate the revaporization efficiency of retrograde condensate by lean gas injection. The studies include three main parts: (1) gas injection below the dew point in the PVT cell; (2) gas injection above and (3) below the dew point in long core equipment. Instead of the simple synthetic fluid and the packed core systems used in the previous literature, the actual gas condensate fluid and about 1m long-core are employed here. The gas condensate used is rich and has high wax content. As a comparative basis, the phase behavior is first detailed at length, including constant mass expansion and constant volume depletion. The measurements in the PVT cell show that lean gas injection leads to increase in the dewpoint of the rich gas condensate. An interesting finding from the first part is that lean gas can effectively revaporize not only the intermediate but also heavy hydrocarbon (i.e., C20+), which is contrary to the common belief that the heavy hydrocarbon cannot be revaporized by lean gas. Comparison of the second and the third parts illustrates that more condensate recovery of the former is obtained than the latter. This value is consistent with the conventional idea that full pressure maintenance is superior to the partial pressure maintenance according to the condensate recovery. However, when the expensive investments of the high pressure equipment are taken into account, the full pressure maintenance may not be the best choice. Therefore, it is recommended that an economic analysis be done to evaluate its feasibility. This is beyond the scope of the present study. To our knowledge, this paper is the first report of experimental studies on the revaporization of condensate using actual reservoir fluid/core system in long core equipment.
Historically, there are mainly three schemes of withdrawal of gas condensate from a reservoir1: natural pressure depletion to abandonment pressure, full pressure maintenance by gas cycling and partial pressure maintenance by means of gas cycling after previous depletion. The natural depletion is the simplest development scheme due to the requirements of low initial capital investments, high initial revenue and the least engineering design. Field experiences usually show that, however, gas condensate well productivity decreases rapidly when the reservoir is producing below the dew point, resulting in a high condesate saturation ring near the wellbore. In order to alleviate the impairment of condensate accumulation about the wellbore, gas cycling is frequently applied to prevent the condensate liquid loss and revaporize the retrograde liquid.