Tengiz Reservoir Uncertainty Characterization and Modeling

SummaryIn this paper we demonstrate how key geological uncertainties in a giant onshore carbonate reservoir in the Middle East, most notably fracture permeability and saturation distributions, impact the quality of the history match and change the performance forecasts of a planned miscible water alternating gas (MWAG) injection process.Different geological models for the reservoir were designed by integrating static and dynamic data. These data indicated the need to consider fault-related fractures using effective medium theory (EMT) and to update the saturation distribution by integrating special core analysis and log-derived J-functions in the reservoir model during the history matching. Afterward, multiobjective optimization (MOO) was applied for each history-matched model to identify well controls that optimally balanced the need to maximize the time on the plateau rate while adhering to the field's gas production constraints.Our results clearly show that including low-intensity fault-controlled fractures in the reservoir model improved the quality of the history match for the gas/oil ratio (GOR), BHP and water cut (WC). This is especially true for wells located near faults, which were difficult to match in the past. Moreover, our results further show that the updated saturation model improved the quality of the history match for the WC, and honored water saturation from the log with high accuracy, particularly for wells located in the transition zone.Applying MOO for each history-matched model then allowed us to identify well controls for the MWAG injection that could extend the time at which the reservoir would be produced at the plateau rate for up to 11 years and the risk of losing production plateau down to 2 years, while always adhering to the current field operational constraints.We demonstrate how the integration of MOO with an innovative workflow for fracture and saturation modeling impacts the prediction of a planned MWAG injection in a giant onshore carbonate reservoir. Our work clearly illustrates the potential of integrating MOO with new reservoir characterization methods to improve the quantification of uncertainties in reservoir performance predictions in carbonate reservoirs.

Using commercial numerical reservoir simulators to build a full field reservoir model and simultaneously history match multiple dynamic variables for a highly complex, offshore mature field in Malaysia, had proven to be challenging, manpower intensive, highly expensive, and not very successful. This field includes almost two hundred wells that have been completed in more than 60 different, non-continuous reservoir layers. The field has been producing oil, gas and water for decades. The objective of this article is to demonstrate how Artificial Intelligence (AI) and Machine Learning is used to build a purely data-driven reservoir simulation model that successfully history match all the dynamic variables for all the wells in this field and subsequently used for production forecast. The model has been validated in space and time. The AI and Machine Learning technology that was used to build the dynamic reservoir simulation and modeling is called spatio-temporal learning. Spatio-temporal learning is a machine-learning algorithm specifically developed for data-driven modeling of the physics of fluid flow through porous media. Spatio-temporal learning is used in the context of Deconvolutional Neural Networks. In this article Spatio-temporal Learning and Deconvolutional Neural Networks will be explained. This new technology is the result of more than 20 years of research and development in the application of AI and Machine Learning in reservoir modeling. This technology develops a coupled reservoir and wellbore model that for this particular oil & gas field in Malaysia uses choke setting, well-head pressure and well-head temperature as input and simultaneously history matches Oil production, GOR, WC, reservoir pressure, and water saturation for more than a hundred wells through a completely automated process. Once the data-driven reservoir model is developed and history matched, it is blind validated in space and time in order to establish a reliable and robust reservoir model to be used for decision making purposes and opportunity generation to maximise the field value. The concepts and the methodology of history match of multiple wells, individual offshore platforms, and the entire field will be presented in this article along with the results of blind validation and production forecasting. Results of using this model to perform uncertainty quantification will also be presented. A case study of a highly complex mature field with large number of wells and years of production has been used to be studied and simulated by this data-driven approach. Time, efforts, and resources required for the development of the dynamic reservoir simulation models using AI and Machine Learning is considerably less than time and resources required using the commercial numerical simulators. It is validated that the TDM developed model can make very reasonable prediction of field behavior and production from the existing wells based on modification of operational constraints and can be a prudent complementary tool to conventional numerical simulators for such complex assets.

Structural, stratigraphic, and petrophysical uncertainties result in a wide range of geologic interpretations. For fields with long production and pressure history, 3D-dynamic simulations have been very useful in providing feedback to geologic modelers, which results in improved static models. The Chuchupa Field has produced 1.9 Tscf of dry gas, or approximately 40% of the Original Gas in Place (OGIP). At the time of this study, 3 new horizontal wells were being planned, and new gas sales agreements were being considered. We developed a dynamic workflow to create a range of probabilistic simulation models to forecast dry-gas production under several production scenarios in the Chuchupa field. Recent seismic re-interpretation, a new stratigraphic study and a revision of the petrophysical model resulted in new probabilistic static models for the field. While these static models were being built, a parallel numerical simulation study was conducted to determine the range of OGIP values that could be successfully history-matched. Nine numerical reservoir models were generated by applying pore volume multipliers to the prior-generation reservoir model, yielding a range of OGIP from 3.8 to 6.6 Tscf. We attempted to history match each of these nine models by using an optimization routine to adjust aquifer support, vertical transmissibility across a potential seal, and rock compressibility. The optimization routine proved to be a very useful and efficient tool to attain good quality history matches in short periods of time. Good matches were obtained for models with OGIP ranging from 4.3 to 5.8 Tscf. Based on this information, the geologic modelers revised petrophysical parameters and generated 27 static models. These models encompassed 3 structural interpretations, 3 porosity distributions, and 3 possible positions of gas/water contact (GWC). From experimental design we obtained the P10, P50, and P90 OGIP values of 4.1, 4.7, and 5.3 Tscf respectively. We scaled up and built reservoir simulation models for 8 geologic interpretations to represent the range of OGIP and reservoir geometries. Again, these models were history matched using the optimization routine. The match parameters were static well pressures and the absence of water production. Six out of the eight the models could be satisfactorily history-matched with reasonable adjustments to aquifer strength, vertical transmissibility, and rock compressibility. The OGIP range for these models was 4.1 to 5.6 Tscf. We selected 3 models to forecast future gas production. These models match the P10, P50, and P90 OGIP values determined in the probabilistic static model, and combine the low, mid, and high structures, porosity and Swi distributions, and the range of GWC positions. We also calibrated the various models with historical bottomhole and tubinghead flowing pressures, and coupled the reservoir model with a network consisting of surface lines and equipment; pipelines from two platforms to the onshore sale-point station; and multi-stage compression to 1,215 psia. The model is currently used to evaluate various production and market scenarios.

Hydrocarbon saturation below present-day free water levels (FWL) is observed in many fields and can be attributed to either past geologic events or more recent production-related pressure changes and fluid movement. However, modeling residual oil saturation (Sorw) below a present-day FWL is a topic of limited understanding within reservoir characterization, particularly in evaluating the impact on water injection efficiency and reserves uncertainty in dynamic reservoir modeling. The presence of significant volumes of residual oil below the FWL can have profound implications for reserves estimations and development scenarios in field development plans. This study, inspired by a recent oil discovery in clastic sediments on the Norwegian Continental Shelf, explores this phenomenon through an integrated approach that spans from core and log scale analyses to field-scale assessment. This paper will present a case-study showing the recognition of a significant paleo-oil column based on petrophysical logs and core data, and both the definition of a present-day FWL and prediction of a paleo FWL. This paper will further describe a versatile technique for modeling residual oil saturation below the current FWL by integrating geological and engineering data from routine (RCA) and special core analyses (SCAL), well logs, and 3D reservoir models. The methodology begins with a rigorous quality check of core analysis data and other relevant information to ensure accuracy and suitability of the data used. We then applied a novel rock typing technique based on similarities in pore geometry and structure (PGS), incorporating RCA and SCAL data. These were integrated into a newly developed Corey SCAL modeling method to establish static and dynamic saturation functions for each rock type, which were then used in 3D reservoir modeling and simulation. Subsequently, we estimated the SCAL uncertainty range for each rock type and integrated it into the reference 3D static and dynamic models. After assimilating all input data into the 3D reservoir models, production forecasts were generated, including sensitivity and uncertainty workflows. Additionally, we developed new water saturation model workflows for static modeling by implementing saturation depth functions (SDF) with established Pc-imbibition curves. Furthermore, a fishbone completion model for water injection wells was constructed, and production was forecasted under the selected scenario. A key result of this work is effectively modelling residual oil saturation below a current FWL by implementing PGS rock typing and a saturation depth function based on Pc- imbibition in both static and dynamic models. The presence of oil saturation below the current FWL matched the observation from core and logs and increased Initial Oil in Place (IOIP) by approximately 25% compared to the original case without residual oil modeling. Meanwhile, this also reduced the recoverable oil volume by approximately 11% compared to the reference case primarily due to decreased injectivity in water injection following relative permeability corrections based on SCAL modeling techniques. To mitigate this negative impact, we evaluated methods for improving injectivity using a fishbone completion model in water injector wells during reservoir simulation, which resulted in an incremental oil recovery of up to 9% compared to the base case scenario of this study. As a novelty, this study proposes a new solution for estimating oil saturation below the current FWL based on saturation depth functions that are consistent with rock typing and wettability physics derived from imbibition capillary pressure curves. Additionally, the value of SCAL modeling, particularly in capturing the uncertainty in reserves evaluation through relative permeability and PGS rock types, proves suitable for full-field reservoir simulations, uncertainty analyses, and field performance assessments. This workflow also facilitates permeability prediction as a function of porosity and irreducible water saturation while generating systematic saturation functions based on capillary pressure data.

Summary The reservoir sands in Block 1, Offshore Turkmenistan, have high heterogeneity and uncertainty on the vertical and lateral continuity, distribution and fluid contact. In this study, both simultaneous and geostatistical seismic inversions have been carried out. Simultaneous inversion was carried out first to obtain a single model solution that best fits the seismic data, using all available set of well data, seismic wavelets and structural framework. While geostatistical inversion was performed after simultaneous inversion to derive multiple reservoir model scenarios that express such reservoir heterogeneity and uncertainty. This paper highlights the main steps taken to improve the predictability of major reservoirs in the main field via seismic conditioning as well as the use of geological constraints through geostatistical inversion. All the results were analysed to identify the high, mid and low cases representing the different level of uncertainties of the reservoir, which could then be used as input for future reservoir simulation, modelling and development.

History matching is a challenging reverse problem due to the inherited uncertainty from Earth modeling. History matching process mandates building one or more sets of representative reservoir models with minimum misfit between the reservoir models and observed field data. There are several commercial assisted history matching tools and workflows to facilitate and orchestrate this process. This paper provides performance assessment and process evaluation between two of the commonly used optimization algorithms: the Evolutionary Algorithm (EA) and the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) in an automated and closed loop workflows. The workflow starts with a parametrization step to identify and quantify the static and dynamic uncertainties in the reservoir model. The objective function is then constructed to guide and measure the convergence of the optimization process. The workflow is then executed to start the model calibration and history matching process. The algorithms, EA and ES-MDA, take different routes during the optimization process. EA works by selecting the best cases (i.e. most fitting genes that resulted in a minimum misfit) in each cycle, and generates a number of simulation cases (new generation) based on the predefined gene selection criteria. The iterative ES-MDA algorithm maintains the same number of simulation cases in each iteration (as many as in the initial Ensemble) throughout the assimilation process. The EA and ES-MDA optimization algorithms have their advantages and disadvantages to the history matching process. For instance, both workflows preserve the geological consistency with the dynamic reservoir models. The automation that both workflows provide incorporates G&G (Geological and Geophysical) workflows to capture, and carryover the static uncertainty to ensure consistency throughout the history matching process. In addition, in both cases, multiple simulation models are generated to cover reservoir static and dynamic uncertainties, which are crucial to the predictive capabilities of the history matched models. Both algorithms, as known, are stochastics in nature (i.e. cannot guarantee one deterministic solution) and, therefore. the results are highly dependent on the initial ensemble. EA is highly effective in searching the solution space, it requires a large number of simulation runs to converge a solution. On the other hand, ES-MDA does not exceed the number of initial ensembles in each iteration regardless of the number of iterations. This paper presents an automated workflow that leads to multiple reliable history matched simulation models. All of the generated models are geologically consistent and capture all model uncertainties that are needed to be preserved and carried forward in prediction. Moreover, this helps in updating the models seamlessly whenever new data is available by simply re-running the workflow with the model updates.

Oil-water relative permeability curves are the basis of oil field development. In recent years, the calculation of oil-water relative permeability in sandstone reservoirs by resistivity logging data has received much attention from researchers. This article first analyzed the existing mathematical models of the relationship between relative permeability and resistivity and found that most of them are based on Archie formula, which assumes the reservoir is clean sandstone. However, in view of the fact that sandstone reservoir is commonly mixed with shale contents, this research, based on the dual water conductivity model, Poiseuille’s equation, Darcy’s law, and capillary bundle model, derived a mathematical model (DW relative permeability model) for shaly sandstone reservoir, which calculates the oil-water relative permeability with resistivity. To test and verify the DW relative permeability model, we designed and assembled a multifunctional core displacement apparatus. The experiment of core oil-water relative permeability and resistivity was designed to prove the effectiveness of the DW relative permeability model in shaly sandstone reservoirs. The results show that the modified Li model can well express the transformational relation between resistivity and relative permeability in sandstone reservoir with low clay content. Compared with the modified Li model and the Pairoys model, the DW relative permeability model is more helpful to collect better results of relative permeability in shaly sand. These findings will play a significant role in the calculation of oil-water relative permeability in reservoirs based on resistivity logging data and will provide important data and theory support to the shaly sandstone reservoir characterized oil field development.

History matching integrated with uncertainty reduction is a key process in the closed loop reservoir development and management methodology which is used for decision analysis related to the development & management of petroleum fields. Despite developments over the last decades in history matching & uncertainty analysis, the challenge of capturing complex interaction among several attributes and several reservoir responses acting simultaneously for complex models still remains. This paper describes the use of a probabilistic and multi-objective history matching integrated with uncertainty reduction as a systematic and iterative process for obtaining a set of reservoir models that honors dynamic data in a complex field case. The methodology is an iterative process that simultaneously matches different objective functions, one for each well production profile. The procedure uses a re-characterization step, where the uncertainties of the attributes (represented by their probability density functions) are updated using indicators that show global and local problems and a correlation matrix to capture the interaction between several reservoir uncertainties and the different objective functions. The methodology was applied to the Norne Field benchmark case considering production data up to 2001 and the remaining part of the provided history is used to estimate the quality of production forecast. The major benefit derived from the application of the methodology was the identification of global and local problems. The initial reservoir models presented high discrepancies between simulated and observed data. The use of independent objective functions in conjunction with the concise plot that is based on the normalized quadratic error of each production data highlighted when new parametrization of the reservoir was necessary. New reservoir attributes were added, such as separated permeability curves for each reservoir formation and new gas permeability curves that better describe the fluid behavior. The initial number of uncertain attributes was twenty seven; the correlation matrix clearly showed which one of those had major influence on the results. Some attributes with significant impact in the study were water-oil and gas-oil contact and faults transmissibility. We updated the probability of the most influencing attributes in order to identify the uncertain levels that improved the history match results. The methodology integrated the process of history matching with uncertainty analysis, addressing both processes simultaneously for a complex case. The methodology was effective and simple to use, even in the complex case study where the reservoir characterization is important.

This paper presents a procedure to estimate relative permeability curves together with gridblock porosities and permeabilities by automatic history matching three-phase flow production data using the LBFGS algorithm for optimization and the adjoint method for generating sensitivity coefficients. Both power law and B-splines are considered for the representation of relative permeability curves. Power law is a simple representation; however, B-splines have the advantage of being able to accurately represent any set of relative permeability curves. In the B-spline representation, we provide a simple procedure based on a transformation of parameters (control points) defining the B-splines to ensure that monotonic curves are obtained. Without this transformation, the automatic history-matching process fails. If endpoint saturations are included as parameters, we show how to modify the adjoint procedure to account for the fact that initial conditions are sensitive to endpoint saturations. While the history-matching process is inherently non-unique, we show that reasonable estimates of relative permeability curves and porosity/ permeability fields can be obtained for a synthetic reservoir example. We also show the uncertainty quantification of the model parameters and reservoir performance prediction using the Randomized Maximum Likelihood (RML) method. Introduction Relative permeabilities are important parameters in reservoir performance calculations. Usually the relative permeability curves are obtained from labs through core flood tests. They can also be incorporated into the history matching procedure as model parameters. ARCHER and WONG (1973), and YANG and WATSON (1991) were among the early researchers to consider the estimation of relative permeability curves by history matching laboratory core flood data. A detailed literature review is given in REYNOLDS et al. (2004). REYNOLDS et al. (2004) also discussed the estimation of three-phase relative permeabilities by history matching roduction data. The current work is a natural extension of REYNOLDS et al. (2004). In this paper, we provide an alternative method for relative permeability estimation based on B-spline approximation. Compared to power law representation, Bsplines ave the advantage of being able to accurately represent any set of relative permeability curves. In the B-spline representation, we provide a simple procedure based on logtransformation of parameters (control points) defining the Bsplines to ensure the B-spline curves are monotonic or convex as used in CHEN et al. (2005). Since a reservoir simulator requires monotonic relative permeability curves, without this transformation, the automatic history-matching process may generate non-monotonic relative permeability curves and result in failed reservoir simulation run. A prior model for porosity and absolute permeability and relative permeability parameters is assumed to provide regularization, i.e., Bayesian estimation is applied to generate estimates. Model parameters, which are estimated by automatic history matching of production data, consist of gridblock porosties, gridblock absolute logpermeabilities and the parameters defining the relative permeability curves. We do not assume the endpoint saturations (i.e. irreducible water saturation, critical gas saturation and residual oil saturation) to be known and consider them as independent model parameters in history matching procedure.

A novel prediction model of oil-water relative permeability based on fractal theory in porous media

New Perspectives for 3D Visualization of Dynamic Reservoir Uncertainty

Recently, the Ensemble Kalman Filter (EnKF) has emerged as an effective tool for performing continuous updating of petroleum reservoir simulation models. The method is firmly grounded on the theory of Kalman filters and sequential Monte Carlo techniques. The ability of the method to sequentially update the spatial properties in petroleum reservoir models, such as permeability and porosity, by integrating the dynamic production data makes it a very attractive approach. Moreover, the method takes into account the production uncertainty in the reservoir models by using error covariance matrices for the measurement vector (Production and injection rates, Gas-Oil ratio, Steam-Oil ratio, etc.) and the state vector (pressure, saturation, permeability, porosity). Similar to the traditional Kalman filter, the covariance matrices have to be tuned to reflect the uncertainty in the model and the measurements. We consider two unconventional oil reservoir models: 1) highly heterogeneous black-oil reservoir model, and 2) heterogeneous SAGD reservoir model. The results will demonstrate the advantage of using the localized EnKF for effective history matching using ensemble sizes relatively lower than what otherwise would be required with the ordinary EnKF. The results will also show the advantages of using prior knowledge available from the wells (permeability and porosity measurements) to generate initial realizations. One of the main practical advantages of history matching using the EnKF over traditional optimization based approaches is its low computational effort. The computational cost is dominated by Monte Carlo simulation of the ensemble of models only. Thus, significant computational time saving is possible by running each of the ensemble simulations on independent processors in a parallel mode. Moreover, the method can be easily integrated with any commercial reservoir simulation software.

Proposal The BP Trinidad and Tobago (bpTT) portfolio of assets consists of six producing gas assets, three mature oil fields and several undeveloped gas fields. In addition to significant efforts to meet a growing gas demand for Trinidad and Tobago's LNG and domestic markets, the focus is currently on optimization of oil production. Understanding the uncertainties and optimizing depletion plans is key to successful reservoir management in gas and oil fields. BpTT uses reservoir simulation to history match and then predict future reservoir performance from highly faulted, stacked sands in Trinidad. Traditionally, a reservoir engineer spends a significant portion of the project time in the construction and history match of the reservoir model to gain confidence for performance prediction. Due to time and resource constraints this generally means that only one model is history-matched. A handful of single parametric uncertainties might be investigated, but decisions are frequently based on the one model thought to be most likely. BpTT began applying BP's Top-Down Reservoir Modeling (TDRM) philosophy [Williams, et al] in October 2003. TDRM uses a genetic algorithm to assist the engineer in building multiple history matches of the dynamic data based on a user-defined precision, ranges and probability distributions for key input uncertainties. This workflow incorporates a variety of reservoir uncertainties in multiple, probable reservoir models, all of which match the production history within specified precision. Future field and well performance is then optimized by evaluating a range of potential outcomes, rather than by prediction from one single description, as often seen in a traditional manual modeling approach. This paper relates the successful use of TDRM in bpTT for optimization of infill well locations in a mature oil field. It includes the history match of 30-years of production from 13 wells in the Teak field (Figure 1). The TDRM cycle including history match and prediction was completed in three weeks. The study used multiple scenarios with 16 history-matched models to broaden the scope of analysis of the reservoirs in a time efficient manner.

This paper was prepared for the 48th Annual Fall Meeting of the Society of Petroleum Engineers of AIME, to be held in Las Vegas, Nev., Sept. 30-Oct. 3, 1973. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgement of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers Office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract An apparatus has been constructed for laboratory measurement of water-oil relative permeabilities by the steady-state technique at elevated temperatures. Experiments were conducted on consolidated porous teflon and Berea sandstone cores with three oils: Kaydol, Protol and tetradecane having viscosities at room temperature of 130, 68 and 2 cp, respectively. For the oil-water systems, teflon was strongly oil wet and sandstone cores were water wet. Measurements were made under isothermal conditions at room temperature and were repeated at 200 degrees F for the teflon and 300 degrees F for the sandstone cores. Results of these measurements indicated that the effects of temperature on relative permeability curves were similar in both oil-wet and water-wet systems. At higher temperature, relative permeability to oil was found to be higher and residual oil saturation was lower. The rate of increase in relative permeability to water with increasing water saturation appeared to be higher at higher temperature. These effects seemed to be larger in systems with Kaydol and Protol than with tetradecane. Interpretations of results were made in light of fluids, fluid-fluid and fluids-solid properties. The changes in viscosity ratio with temperature appear to be a factor that influences relative permeability curves. Introduction The oil recovery mechanism involved in hot water flooding is generally believed to be the results of viscosity reduction and thermal expansion. The effect of lowering of the viscosity leads to a more efficient displacement. Test results have indicated that relative permeabilities to oil and to water, and the equilibrium saturations of residual oil and irreducible water also change due to an increase in temperature. Presently, the mechanism leading to these changes is not known. In the work on the effect of temperature on relative permeability of consolidated rocks, Weinbrandt and Ramey found that an increase in temperature from room temperature to 175 degrees F in Boise sandstone has caused the increase in irreducible water saturation, decrease in residual oil saturation and increase in the relative permeability to oil. Decrease in the relative permeability to water at saturations of below room-temperature residual oil but increase at flood-out were observed. By comparing their results to those of Owens and Archie, the latter dealing with the effect of wettability on relative permeability, Weinbrandt and Ramey suggested that the changes in relative permeability resulting from an increase in temperature may have been due to wettability changes.

Chapter 13 - Geologic and Engineering Modeling