Clarkson, Christopher R. (University of Calgary) | Yuan, Bin (University of Calgary) | Zhang, Zhenzihao (University of Calgary) | Tabasinejad, Farshad (University of Calgary) | Behmanesh, Hamid (NCS Multistage) | Hamdi, Hamidreza (University of Calgary) | Anderson, Dave (NCS Multistage) | Thompson, John (NCS Multistage) | Lougheed, Dylan (NCS Multistage)
The dominant transient flow regime for multi-fractured horizontal wells producing from low-permeability and shale (unconventional) reservoirs has historically been interpreted to be transient linear flow (TLF) in the framework of classical diffusion (CD). Recently, observed deviations away from this classical behavior for Permian Basin Wolfcamp shale (oil) wells have been attributed to anomalous diffusion (AD). The objective of the current study is to systematically investigate other potential causes of deviations from TLF.
The conventional log-log diagnostics used to identify flow regimes do not account for reservoir complexities such as multi-phase flow and reservoir heterogeneity. Failure to correct for these effects when they are occurring may result in misdiagnosis of flow regimes. A new workflow is therefore introduced herein to improve flow regime identification when reservoir complexities are exhibited, and to provide a more confident diagnosis of AD behavior. The workflow involves the correction of log-log diagnostics for complex reservoir behavior through the use of modified pseudo-variables (pseudo-pressure and pseudo-time) after the complex reservoir behavior is identified. Although reservoir heterogeneity is an accepted cause of deviations from TLF, the impact of multi-phase flow has not been investigated in detail. Therefore, in this study, corrections to pseudo-variables for multi-phase flow, a known reservoir complexity exhibited by Wolfcamp shale wells, are presented. Pressure-dependent permeability is also accounted for in the pseudo-variable calculations, although its impact is demonstrated to be relatively minor in this study.
Application of the new workflow to a simulated case and a Wolfcamp shale field case demonstrates the following: 1) multi-phase flow, and in particular the appearance of a mobile gas phase after two-phase oil and water production, results in deviations from classical TLF behavior when data is analyzed using conventional (uncorrected) diagnostics; 2) this deviation has characteristics similar to that expected for sub-diffusion; 3) application of the modified diagnostics to a simulated case that includes multi-phase flow results in the “true” flow regime signature of TLF being observed; 4) application of the modified diagnostics to a field case exhibiting evidence of multi-phase flow reduces the deviation from TLF.
Recent studies have indicated that Huff-n-Puff (HNP) gas injection has the potential to recover an additional 30-70% oil from multi-fractured horizontal wells in shale reservoirs. Nonetheless, this technique is very sensitive to production constraints and is impacted by uncertainty related to measurement quality (particularly frequency and resolution), and lack of constraining data. In this paper, a Bayesian workflow is provided to optimize the HNP process under uncertainty using a Duvernay shale well as an example.
Compositional simulations are conducted which incorporate a tuned PVT model and a set of measured cyclic injection/compaction pressure-sensitive permeability data. Markov chain Monte Carlo (McMC) is used to estimate the posterior distributions of the model uncertain variables by matching the primary production data. The McMC process is accelerated by employing an accurate proxy model (kriging) which is updated using a highly adaptive sampling algorithm. Gaussian Processes are then used to optimize the HNP control variables by maximizing the lower confidence interval (μ-σ) of cumulative oil production (after 10 years) across a fixed ensemble of uncertain variables sampled from posterior distributions.
The uncertain variable space includes several parameters representing reservoir and fracture properties. The posterior distributions for some parameters, such as primary fracture permeability and effective half-length, are narrower, while wider distributions are obtained for other parameters. The results indicate that the impact of uncertain variables on HNP performance is nonlinear. Some uncertain variables (such as molecular diffusion) that do not show strong sensitivity during the primary production strongly impact gas injection HNP performance. The results of optimization under uncertainty confirm that the lower confidence interval of cumulative oil production can be maximized by an injection time of around 1.5 months, a production time of around 2.5 months, and very short soaking times. In addition, a maximum injection rate and a flowing bottomhole pressure around the bubble point are required to ensure maximum incremental recovery. Analysis of the objective function surface highlights some other sets of production constraints with competitive results. Finally, the optimal set of production constraints, in combination with an ensemble of uncertain variables, results in a median HNP cumulative oil production that is 30% greater than that for primary production.
The application of a Bayesian framework for optimizing the HNP performance in a real shale reservoir is introduced for the first time. This work provides practical guidelines for the efficient application of advanced machine learning techniques for optimization under uncertainty, resulting in better decision making.
Vahedian, Atena (University of Calgary) | Clarkson, Chris R. (University of Calgary) | Ghanizadeh, Amin (University of Calgary) | Zanganeh, Behnam (University of Calgary) | Song, Chengyao (University of Calgary) | Hamdi, Hamidreza (University of Calgary)
This paper was prepared for presentation at the Unconventional Resources Technology Conference held in Houston, Texas, USA, 23-25 July 2018. The URTeC Technical Program Committee accepted this presentation on the basis of information contained in an abstract submitted by the author(s). The contents of this paper have not been reviewed by URTeC and URTeC does not warrant the accuracy, reliability, or timeliness of any information herein. All information is the responsibility of, and, is subject to corrections by the author(s). Any person or entity that relies on any information obtained from this paper does so at their own risk. The information herein does not necessarily reflect any position of URTeC.
Hamdi, Hamidreza (University of Calgary) | Clarkson, Chris R. (University of Calgary) | Ghanizadeh, Amin (University of Calgary) | Ghaderi, Seyed A. (University of Calgary) | Vahedian, Atena (University of Calgary) | Riazi, Naimeh (University of Calgary) | Esmail, Ali N. (Encana)
He observed that an additional recovery of around 20% could be achieved by implementing EOR techniques compared to primary production scenarios. He also noted that reservoir permeability is the dominant factor controlling the recovery increase. Wan (2013) used black-oil models for simulating cyclic miscible rich gas injection and concluded that HNP could be an effective EOR technique when it is accurately designed to control the number of cycles, and the injection and production periods. Yu et al. (2014) history-matched a well completed in the Bakken Formation for the purposes of evaluating EOR.
Behmanesh, Hamid (Anderson Thompson Reservoir Strategies and University of Calgary) | Hamdi, Hamidreza (University of Calgary) | Clarkson, Chris R. (University of Calgary) | Thompson, J. M. (Anderson Thompson Reservoir Strategies) | Anderson, D. M. (Anderson Thompson Reservoir Strategies) | Chin, A. (Anderson Thompson Reservoir Strategies)
T he mathematical models used for RTA are reasonably mature for these cases. However, the complexities associated with multi - phase flow impede direct adaptation of these methods for wells experiencing multi - phase flow production . The characteristics of two - p hase flow in gas condensate volatile oil reservoirs are significantly different from single - phase oil and gas reservoir - fluid systems.
Khani, Hojjat (University of Calgary) | Hamdi, Hamidreza (University of Calgary) | Nghiem, Long (Computer Modelling Group Ltd.) | Chen, Zhangxing (University of Calgary) | Sousa, Mario Costa (University of Calgary)
The overall objective of reservoir modeling is to reduce the uncertainty in production forecasts by utilizing all available data to construct a calibrated reservoir model. Geological heterogeneities have a fundamental impact on the growth of a steam chamber and the performance of a SAGD (steam assisted gravity drainage) process. The objective of this work is to incorporate geological heterogeneities into the history matching process using a probability perturbation method (PPM) to preserve the geological consistency of a reservoir model.
A PPM is a geological data integration framework which employs a multiple-point geostatistics (MPS) algorithm. The heart of this method is to systematically perturb the underlying probabilities used to generate the reservoir facies. A PPM generally consists of two loops: an outer loop which is responsible for randomly generating a global configuration of the facies and an inner loop which systematically perturbs the generated facies to match the dynamic data. The combination of these two iterations creates a set of realizations that preserve the geological information.
In this paper, a training image is built based on a 3D outcrop description of a meandering channelized reservoir that is analogous to some of the Canadian heavy oil reservoirs. All other available data including reservoir properties at well locations, trends and production data are also incorporated into the PPM framework for this history matching process. The reservoir model is characterized by three facies: clean sands, medium-grained sandstones and silts, which have different porosity, horizontal permeability and vertical permeability. The SAGD performance is a function of steam chamber development, which depends on the level of heterogeneity in the reservoir. The results show that the heterogeneity distribution has a large impact on the fluid flow at different stages of production. The results show that such complexities can be well preserved during the history matching process using the PPM by generating the geological patterns depicted in a training image. The PPM is shown to be an efficient approach for history matching in presence of complex reservoir geology.
The fracturing of horizontal wells is a recently developed tool to help enable tight and shale formations to produce economically. Production data analysis of the wells in such formations is frequently performed using analytical and semi-analytical methods. However, in the presence of nonlinearities such as multi-phase flow and geomechanical effects, the numerical simulations are necessary for interpretations and history-matching techniques as they are required for model calibration.
Reservoir history-matching techniques are usually based on the frequentist approach and can provide a single solution that can maximize the Likelihood function. Production forecasts using a single calibrated model cannot honor the uncertainty in the model parameters. Therefore, a Bayesian approach is suggested where we can combine our prior knowledge about the model parameters together with the Likelihood to update our knowledge in light of the data. The Bayesian approach is enriched by applying a Markov chain Monte Carlo process to updated the prior knowledge and approximate the posterior distributions.
In this paper, a one-year production data of a real gas condensate well in a Canadian tight formation (lower Montney Formation) is considered. This is a horizontal well with eight fracture stages. A representative 2D model is constructed which is characterized by 17 parameters which include relative permeability curves, capillary pressure, geomechanical effects, fracture half-length, fracture conductivity, and permeability and water saturation in the stimulated region and the matrix. Careful analysis of available data provide acceptable prior ranges for the model parameters using non-informative uniform distributions. Markov chain Monte Carlo algorithm is implemented using a Gibbs sampler and the posterior distributions are found. The results provide an acceptable set of models that can represent the production history data. Using these distributions, a probabilistic forecast is performed and P10, P50 and P90 are estimated.
This paper highlights the limitations of the current history-matching approaches and provides a novel workflow on how to quantify the uncertainty for the shale and tight formations using numerical simulations to provide reliable probabilistic forecasts.
Transient well test data conveys significant information about the subsurface heterogeneities in terms of some variations in the well test pressure response curves. It is therefore important to enhance the use of the well test data for building a validated geological model to include the effective reservoir heterogeneities that are reflected on the well test plots. In this work, we present a novel geoengineering workflow for geologically consistent updating of the geostatistical facies models using pressure transient data.
We use Multi-Point Statistical (or Geostatistical) simulations (MPS) with conditioning hard and soft data to generate the geostatistical realizations that can preserve the spatial connectivity of the facies. Static model transient tests are then generated using high resolution numerical simulations. The results are compared with the measured well test data for an inversion. The inversion step involves a geologically consistent Probability Perturbation Method (PPM) for perturbing the geostatistical models which are combined with a Gaussian Process (GP) modeling approach for finding the optimum spatial distribution of the facies and the other unknown model parameters. Conditional two-dimensional models of a low-energy anastomosing channelized model are considered in this study. The results show that using such an approach the spatial variation of the facies is maintained and the transitions across the facies boundaries are consistently preserved. In this paper, the geostatistical models are updated simultaneously with other unknown model parameters, including the PPM's parameter (
Reservoir history matching is a computationally expensive process, which requires multiple simulation runs. Therefore, there is a constant quest for more efficient sampling algorithms that can provide an ensemble of equally-good history matched models with a diverse range of predictions using fewer simulations. We introduce a novel stochastic Gaussian Process (GP) for assisted history matching where realizations are considered to be Gaussian random variables. The GP benefits from a small initial population and selects the next best possible samples by maximizing the expected improvement (EI). The maximization of EI function is computationally cheap and is performed by the Differential Evolution (DE) algorithm. The algorithm is successfully applied to a structurally complex faulted reservoir with 12 unknown parameters, 8 production and 4 injection wells. We show that the GP algorithm with EI maximization can significantly reduce the number of required simulations for history matching. The ensemble is then used to estimate the posterior distributions by performing the Markov chain Monte Carlo (McMC) using a cross-validated GP model. The hybrid workflow presents an efficient and computationally-cheap mechanism for history matching and uncertainty quantification of complex reservoir models.
Hydraulically-fractured vertical and horizontal wells completed in the tight formations typically exhibit long periods of transient linear flow that may last many years or decades. From this transient linear flow period, the linear flow parameter (xfk) may be extracted. However, changes in effective permeability to the oil phase during production, caused by wellbore pressure falling below the saturation pressure, affect the flow dynamics in tight oil reservoirs and complicate the analysis. The use of methods that assume single-phase flow properties, such as the square-root of time plot, can lead to significant errors in linear flow parameter estimates.
In this study, an analytical method is introduced to mathematically correct the slope of the squareroot- of-time plot for the effects of multi-phase flow through the use of modified pseudovariables. Although the correction was derived for wells producing at constant flowing pressure during transient linear flow, the method is extended for wells producing at variable rate/flowing pressures. In order to evaluate pseudovariables used in the correction, the saturation-pressure relationship must be known. In this work, an analytical method for evaluating the saturation-pressure relationship is also developed.
The results of our new analytical method for linear flow analysis are validated against numerical simulation. The new method yields linear flow parameter estimates that are within 10% of those input into the numerical simulator.