An ensemble-based history-matching framework is proposed to enhance the characterization of petroleum reservoirs through the assimilation of crosswell electromagnetic (EM) data. As one of advanced technologies in reservoir surveillance, crosswell EM tomography can provide a cross-sectional conductivity map and hence saturation profile at an interwell scale by exploiting the sharp contrast in conductivity between hydrocarbons and saline water. Incorporating this new information into reservoir simulation in combination with other available observations is therefore expected to enhance the forecasting capability of reservoir models and to lead to better quantification of uncertainty.
The proposed approach applies ensemble-based data-assimilation methods to build a robust and flexible framework under which various sources of available measurements can be readily integrated. Because the assimilation of crosswell EM data can be implemented in different ways (e.g., components of EM fields or inverted conductivity), a comparative study is conducted. The first approach integrates crosswell EM data in its original form which entails establishing a forward model simulating observed EM responses. In this work, the forward model is based on Archie's law that provides a link between fluid properties and formation conductivity, and Maxwell’s equations that describe how EM fields behave given the spatial distribution of conductivity. Alternatively, formation conductivity can be used for history matching, which is obtained from the original EM data through inversion using an adjoint gradient-based optimization method. Because the inverted conductivity is usually of high dimension and very noisy, an image-oriented distance parameterization utilizing fluid front information is applied aiming to assimilate the conductivity field efficiently and robustly. Numerical experiments for different test cases with increasing complexity are carried out to examine the performance of the proposed integration schemes and potential of crosswell EM data for improving the estimation of relevant model parameters. The results demonstrate the efficiency of the developed history-matching workflow and added value of crosswell EM data in enhancing the characterization of reservoir models and reliability of model forecasts.
It is well-known that oil- and gasfield development is a high-risk venture. Uncertainties originating from geological models (e.g., structure, stratigraphy, channels, and geobodies) are coupled with uncertainties of reservoir models (e.g., distribution of permeability and porosity in the reservoir) and uncertainties of economic parameters (e.g., oil and gas prices and costs associated with drilling and other operations). It is critically important to properly quantify the uncertainty of such parameters and their effect on production forecasts and economic evaluations. Recently, multiobjective-optimization techniques have been developed to maximize expectations of some economic indicators (e.g., net present value) and, at the same time, to minimize associated uncertainty or risk. Because of limited access to the subsurface reservoir (e.g., it is impossible to measure the permeability and porosity at the location of each gridblock of a simulation model), reservoir properties have quite large uncertainties.
This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 181611, “Uncertainty Quantification for History-Matching Problems With Multiple Best Matches Using a Distributed Gauss-Newton Method,” by Guohua Gao, SPE, Jeroen C. Vink, SPE, Chaohui Chen, SPE, Mohammadali Tarrahi, SPE, and Yaakoub El Khamra, Shell, prepared for the 2016 SPE Annual Technical Conference and Exhibition, Dubai, 26–28 September. The paper has not been peer reviewed.
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.
Chen, Chaohui (Shell International Exploration & Production Inc.) | Li, Ruijian (Shell Exploration & Production Co.) | Gao, Guohua (Shell Global Solutions (US) Inc.) | Vink, Jeroen C. (Shell Global Solutions International B.V.) | Cao, Richard (Shell Exploration & Production Co.)
For unconventional reservoirs, it is very difficult to determine the values of key parameters or properties that govern fluid flow in the subsurface due to unknown fracture growth and rock properties. These parameters generally have quite large uncertainty ranges and need to be calibrated by available production data. Using an ensemble of history matched reservoir models to predict the Estimated Ultimate Recovery (EUR) is one of popular approaches when parallelized computing facilities become cheaper and cheaper to customers. The Randomized Maximum Likelihood (RML) method has been proved quite robust for generating multiple realizations by conditioning to production data. However, it is still expensive to apply traditional optimization algorithms to find a conditional realization by minimizing the objective function defined within a Bayesian framework, especially when adjoint-derivatives are unavailable. How to generate multiple conditional realizations efficiently is critically important but still a very challenging task for proper uncertainty quantification.
In this paper, a novel approach that hybrids the direct-pattern-search and the Gauss-Newton algorithm is developed to generate multiple conditional realizations simultaneously. The proposed method is applied to history match a real unconventional Liquid Rich Shale reservoir. The reservoir is stimulated by multiple stage hydraulic fractures. In this example, uncertainty parameters include those characterizing uncertainties of reservoir properties (including matrix permeability, permeability reduction coefficient, porosity, initial water saturation and pressure) and those for hydraulic fractures (height, width, length, and effective permeability of SRV zone). Uncertainty of production forecasts are quantified with both unconditional and conditional realizations.
The case study indicates that the new method is very efficient and robust. Uncertainty ranges of parameters and production forecasts before and after conditioning to production data are quantified and compared. The new approach enhances the EUR assessment confidence level and therefore significantly reduces risks for unconventional assets development.
For unconventional reservoirs, the key reservoir properties, such as effective flowing fracture length (Xf), effective fracture height (Hf), permeability and permeability reduction coefficient, fracture conductivity (FCD), drainage area (A) etc., that govern fluid flow in subsurface are very difficult to obtain due to unknown fracture growth in tight rock. Uncertainties associated with these parameters are usually quite large. Understanding the uncertainty of the subsurface model is helpful to define how to drill wells and determine fracture stages spacing or the number of wells. There are mainly three categories of Estimated Ultimate Recovery (EUR) prediction methodologies for unconventionals:
Traditional history matching involves calibration of reservoir models by use of well response such as production or tracer data aggregated during multiple producing intervals. With the advent of novel tracer technologies, we now can obtain distributed water or tracer arrival-time information along the length of horizontal or vertical wellbores. This provides significantly improved flow resolution for detailed reservoir characterization through inversion of distributed water or tracer arrival times in a manner analogous to travel tomography in geophysics. In this paper, we present an efficient approach to incorporate novel tracer-surveillance data and distributed water arrival-time information during history matching of high-resolution reservoir models. Our approach relies on a streamline-based work flow that analytically computes the sensitivity of water-arrival times with respect to reservoir heterogeneity, specifically porosity and permeability variations. The sensitivities relate the changes in arrival time to small perturbations in reservoir properties and can be obtained efficiently with the streamline-based approach with a single flow simulation. This makes the approach particularly wellsuited for high-resolution reservoir characterization. Finally, the sensitivities are used in conjunction with an iterative inversion algorithm to update the reservoir models with existing and proven techniques from seismic tomography. The power and utility of our proposed approach are demonstrated with both synthetic and field examples. These include the SPE benchmark Brugge field case and an offshore field in North America. Compared with traditional history-matching techniques, the proposed tomographic approach is shown to result in improved resolution of heterogeneity through matching of water arrival time at individual completions in addition to the aggregated well-production response. This results in improved performance predictions and better identification of bypassed oil for infill targeting and enhanced-oil-recovery (EOR) applications.
The oil & gas industry has been the backbone of the world's economy in the last century and will continue to be in the decades to come. With increasing demand and conventional reservoirs depleting, new oil industry projects have become more complex and expensive, operating in areas that were previously considered impossible and uneconomical. Therefore, good reservoir management is key for the economical success of complex projects requiring the incorporation of reliable uncertainty estimates for reliable production forecasts and optimizing reservoir exploitation. Reservoir history matching has played here a key role incorporating production, seismic, electromagnetic and logging data for forecasting the development of reservoirs and its depletion. With the advances in the last decade, electromagnetic techniques, such as crosswell electromagnetic tomography, have enabled engineers to more precisely map the reservoirs and understand their evolution. Incorporating the large amount of data efficiently and reducing uncertainty in the forecasts has been one of the key challenges for reservoir management. Computing the conductivity distribution for the field for adjusting parameters in the forecasting process via solving the inverse problem has been a challenge, due to the strong ill-posedness of the inversion problem and the extensive manual calibration required, making it impossible to be included into an efficient reservoir history matching forecasting algorithm. In the presented research, we have developed a novel Finite Difference Time Domain (FDTD) based method for incorporating electromagnetic data directly into the reservoir simulator. Based on an extended Archie relationship, EM simulations are performed for both forecasted and Porosity-Saturation retrieved conductivity parameters being incorporated directly into an update step for the reservoir parameters. This novel direct update method has significant advantages such as that it overcomes the expensive and ill-conditioned inversion process, applicable to arbitrary reservoir geometries and enables efficient integration with real field crosswell EM data.
The oil and gas industry has a long history of model construction relying on the integration on multiple disciplines including seismic, sedimentology, geology and petrophysics. It is undeniable that all steps are required to lead to a good characterization of the studied reservoir and to provide reliable and realistic predictions. However the necessary time to finalize each step often leads to a modeling process of several years. This paper therefore discusses an alternative workflow, or Fast-Track modeling approach, which allows generating a representative and matched reservoir model in a considerably reduced time. This approach consists in:
This workflow ensures achieving a better petrophysical properties consistency between logs, cores and models, a more representative asset volume estimates and also prevents utilization of non-measured parameters such as irreducible water saturation (Swc's) or unproven and extensive permeability multipliers. This altogether contributes in reducing convergences problems as well as providing more consistent dynamic model setup.
This workflow was applied on a complex offshore reservoir consisting of a large gas cap and significant oil rim. The results and achievements are presented within this paper and demonstrate the suitability of this workflow as a short term alternative and shortcut to complex simulation modeling, in waiting of all adequate studies to be completed and integrated in a detailed reservoir model.
Castellini, Alexandre (Chevron ETC) | Vahedi, Arman (Chevron Australia Pty. Ltd.) | Singh, Updesh (Chevron Australia Pty. Ltd.) | Sawiris, Ramzy Shenouda (Chevron Australia Pty. Ltd.) | Roach, Thomas (Chevron Australia Pty. Ltd.)
This reference is for an abstract only. A full paper was not submitted for this conference.
The paper presents a method to tackle complex inverse problems where highly non-linear responses are involved. Geological models are built within an experimental design framework and are characterized by an objective function that estimates the quality of the history-match. The goal is to efficiently find combinations of parameters that minimize the objective function. Genetic algorithms are the main optimization tool in the workflow. In order to reduce the number of actual simulations and to accelerate the overall procedure, non-linear response surfaces, built with kriging interpolants at each iteration of the optimization routine, filter out unnecessary combinations of parameters. The models that reasonably honor the historical data are selected via cluster analysis techniques and provide an estimate of future production. The final distribution of the prediction variables defines the range of uncertainty conditioned to production history.
The practicality of the workflow is demonstrated on the Malampaya field, a Gas Condensate reservoir in the Philippines. The field is a Tertiary Carbonate build-up situated offshore, below 800-1200m of water. It has been supplying gas from five subsea production wells since 2001 to three Gas-to-Power plants. Available subsurface data include a high resolution 3D seismic survey, five production wells with downhole pressure gauges and six appraisal wells with wireline and borehole image data, pressure and well test data.
The strategy ensures multiple and significantly different history-matched models that provide estimation of the future performance of the reservoir. The coupling of space-filling sampling strategies, optimization algorithms, non-linear response surfaces and high performance computer clusters proved efficient in addressing the issue. In addition to a robust assessment of ranges in production forecast, representative P10, P50 and P90 individuals were selected from the portfolio of models for further analysis including optimization of development plan.
Understanding the impact of subsurface uncertainties on production responses is an integral part of the decision making process. A more accurate quantification of the uncertainty band around production forecasts contributes to better business decisions. Traditional experimental design workflows might be well suited for new field developments. However, when a field has been produced for several years, all models have to be conditioned to available production data in order to obtain meaningful predictions. This paper addresses the limitations of conventional techniques and provides a practical, structured workflow to reconcile the processes of data integration and uncertainty assessment.