Reservoir simulations constitute a cornerstone to predict the flow of fluids through porous media. Various numerical models called simulators are developed to simulate the performance of hydrocarbon reservoirs. These models are used in field development since production forecasts are necessary to make investment decisions. Nowadays, numerical simulators are widely used by reservoir engineers.
In recent times, machine learning applications have garnered the interest of the oil and gas industry due their unorthodox approach to creating complex models. The more historical data that can be provided in the training phase of the computation, the more accurate the predictions utilizing less time and computational power required by the alternative. The alternative, reservoir simulation applications, require more robust hardware for processing large amounts of data in sophisticated ways. This will require several iterations and may require long computation to validate the model. Running time for a simulation is dependent on software, which can be dependent on hardware. This creates a matrix of time and resources needed to complete simple to complicated simulations.
A few studies have proposed the use of the Lanczos decomposition method in reservoir simulation studies. The attractiveness of this method appears to be the avoidance of time stepping in simulation and allows the computation of reservoir pressures at any given time directly.
In this study, two new simulators were developed using Lanczos Decomposition Method (LDM) and Conventional Implicit Time-Stepping Method (ITSM). The study focuses on 2-D flow for slightly compressible fluid of constant viscosity with multiple wells. Derivation of the model equations was performed using the continuity equation for both methods through the use of MATLAB. The simulators were written using the MATLAB programming language. The simulators developed in this study are capable of assigning uniform and non-uniform gridblock distribution; porosity and permeability distributions, as well as developing various production and injection scenarios for single or multiple wells depending on different areas of application. Validity and accuracy of the 2D flow simulator were examined by comparing simulation results with that obtained from the commercial software called ECRIN. The results of the simulator were almost identical with the results obtained from the commercial software. During the model runs, the CPU time of the two simulators were compared. A special case was also studied for a single well with variable rate history using both ITSM and LDM written with FORTRAN.
To date, in petroleum engineering literature, there is no work published that compares the performances (in terms of computational aspects as well as CPU times) of the Lanczos method and the conventional implicit-time stepping method.
Multi-rock type cores can be characterized by complex higher order connectivity relationships within an agglomerated petrophysical system. A solution that relates multiphase flow simulation in cores to time-lapse seismic properties in order to examine closed-loop 4D integration is performed at a high level on a plug. While a 4D workflow is not explicitly examined in this work, the requisite petro-elastic modeling (PEM) method based on a simulation-driven interpretation of the Gassmann equation is described and a comparison is made with its empirically derived counterpart. This work illustrates that a simulation-driven petro-elastic modeling approach can be used to generate time-dependent saturated rock properties consistent with seismic attribute description at the plug and core scales. The results demonstrate the simulation-driven approach, of a petro-elastic model embedded in a reservoir simulator, as an alternative to relating pressure and saturation from reservoir simulator-to-seismic-derived properties using a priori empirically based correlations. The method discussed in this paper maintains appreciable continuity with the results of empirically based petro-elastic methods but demonstrates differences commensurate with principal fluid differentiation capability inherent to reservoir simulator-derived data and observed time-lapse seismic response. The significance of applied multi-porosity relationships is further realized upon examination of the time-dependent petro-elastic model results.
Chhatre, Shreerang (ExxonMobil Upstream Research Company) | Chen, Amy (ExxonMobil Upstream Research Company) | Al-Rukabi, Muhammed (ExxonMobil Upstream Research Company) | Berry, Daniel (ExxonMobil Upstream Research Company) | Longoria, Robert (ExxonMobil Upstream Research Company) | Guice, Kyle (ExxonMobil Upstream Research Company) | Maloney, Daniel (ExxonMobil Upstream Research Company)
Relative permeability is a significant source of uncertainty in current modeling practices for performance prediction of unconventional reservoirs. Due to the lack of reliable measurements or representative analogs, relative permeability is often used as an unconstrained history matching parameter for tight/shale rock formations. To date, reliable laboratory measurements of gas-oil relative permeability have been limited to rocks with permeability on the order of hundreds of microDarcies or greater. This work describes laboratory measurements on rock with permeability of hundreds of nanoDarcies, and the use of that data to reduce uncertainty in modeling and performance prediction.
Laboratory measurements of full gas-oil relative permeability curves were made on an unconventional core sample from a tight oil producing interval from the Permian Basin with permeability of hundreds of nanoDarcies. These difficult measurements were achieved through novel experiment design, equipment, and technique. In addition, these measurements were made using a combination of steady-state and unsteady-state techniques that resulted in direct measurement of the relative permeability curves over a broad range of saturations.
The measured steady-state gas-oil relative permeability curves were used to constrain Corey exponents and endpoint saturation values for gas-oil relative permeability curves in history matching simulation models and reducing uncertainty in performance predictions for tight/shale formations. Examples will be discussed.
This work describes the first known successful laboratory measurement of full gas-oil relative permeability curves on rocks with permeability on the order of hundreds of nanoDarcies (~1,000 times tighter than previous measurements). Measured laboratory data assists in constraining parameters used for history matching simulation models and significantly reduces the uncertainty in performance predictions.
Oil and gas production from tight/shale formations has increased from a small value a decade ago to 59% of total U.S. crude oil production in 2018.  Hydrocarbon production from such tight rocks has been commercially viable due to large improvements in horizontal drilling and hydraulic fracturing technologies. Characterization of the tight/shale rock matrix, however, remains an open challenge given the extremely low permeability of the rock matrix and relatively small production history. Intervals like the Spraberry, Bone Spring, and Wolfcamp in the Permian Basin region in West Texas and Southeast New Mexico account for a dominant share (~ 4.1 million barrels/day oil and ~14 Bcf/day associated gas), based on a recent EIA estimate of production from tight/shale rocks. 
Objectives - Image-Based Rock Physics (IBRP) simulation of petrophysical properties based on sub-micron to micron-scale images of very fine-grain rocks is constrained by the resolution and range of various imaging techniques used. Unlike some conventional sandstone and carbonate reservoir rock where a single Micro-Computed X-ray Tomography (μCT) volume images nearly all of the significant pores and pore throats, many low-permeability rock types contain phase regions with micro-pores and pore throats, including intergranular microcrack pores, that are not accurately resolved at the required μCT scale needed for a representative elementary volume (REV) for the whole rock. Properties for these regions are obtained at a finer-scale or using a different measurement method and these properties then assigned to the phase regions at the larger REV scale. This study explores the methodology involved in obtaining and assigning microcrack properties in μCT rock images and demonstrates a workflow to handle uncertainty in the location and properties of microcracks using two representative low-permeability sandstones.
Methods/Procedures/Process - The workflow combines μCT images of a mini-plug sample (~50mm3), which represents the rock REV, with Focused Ion Beam - Scanning Electron Microscopy (FIB-SEM) images (~200μm3) of regions of various types of observed microporosity (including intergranular microcrack pores) which occur within the REV sample. Different representative types of microporosity regions were imaged and properties calculated from the higher-resolution FIB-SEM image volumes. For some fraction of μCT microporosity regions, such as micro-fractures, their locations in the REV μCT sample was known but the micro-fracture properties were not known. A sub-resolution micro-fracture model was numerically constructed, honoring the mineral facies morphology and microporosity types assigned based on their respective distributions as observed in high resolution SEM images. Resultant porosity, capillary pressure and flow properties on the larger REV volume were cross-validated with independent core analysis measurements.
Results/Observations/Conclusions - This study illustrates a workflow for assigning properties, obtained at finer scales or using other measurement methods, to regions in the REV at larger scale but lower resolution. The resulting rock model produces the same porosity, permeability, and capillary pressure as core analysis measurements, and has the potential to predict relative permeability.
Applications/Significance/Novelty - It is expected that the majority of low-permeability rocks require an upscaling methodology similar to that developed in this study for IBRP computations and integration with core analysis. Using this methodology IBRP offers deeper understanding of building blocks of the upscaled-properties measured by core analysis. IBRP also offers the ability to measure/compute relative permeabilities that are nearly physically impossible to measure on core and the ability to construct digital rocks that allow evaluation of complete suites of rocks and their properties.
Al-Rudaini, Ali (Heriot-Watt University) | Geiger, Sebastian (Heriot-Watt University) | Mackay, Eric (Heriot-Watt University) | Maier, Christine (Heriot-Watt University) | Pola, Jackson (Heriot-Watt University)
We propose a workflow to optimise the configuration of multiple interacting continua (MINC) models and overcome the limitations of the classical dual-porosity model when simulating chemically enhanced oil recovery processes. Our new approach captures the evolution of the concentration front inside the matrix, which is key to design a more effective chemically enhanced oil recovery projects in naturally fractured reservoirs. Our workflow is intuitive and based on the simple concept that fine-scale single-porosity models capture fracture-matrix interaction accurately and can hence be easily applied in a commercial reservoir simulator. Results from the fine-scale single-porosity system are translated into an equivalent MINC method that yields more accurate results than the classical dual-porosity model or a MINC method where the shells are arbitrarily selected.
Our approach does not require the tuning of capillary pressure curves ("pseudoisation"), diffusion coefficients, MINC shells, or the generation of recovery type curves, all of which have been suggested in the past to model more complex recovery processes. A careful examination of the fine-scale single-porosity model ("reference case") shows that a number of nested shells emerge, describing the advance of the concentration and saturation fronts inside the matrix. The number of shells is related to the required degree of refinement, i.e. the number of shells, in the improved MINC model. Using the results from a fine-scale single-porosity simulation to set up the shells in the MINC model is easy and requires only simple volume calculations. It is hence independent of the chosen simulator.
Our improved MINC method yields significantly more accurate results compared to a classical dual-porosity model, a MINC method with equally sized shells, or a MINC model with arbitrarily refined shells for a number of recovery scenarios that cover a range of matrix wettabilities and permeabilities. In general, improved results can be obtained when selecting five or fewer shells in the MINC. However, the actual number of shells is case-specific. The largest improvement is observed for cases when the matrix permeability is low.
The novelty of our approach is the easy-to-use method to define shells for a MINC model to predict chemically enhanced oil recovery from naturally fractured reservoirs more accurately, especially in cases where the matrix has low permeability. Hence the improved MINC method is particularly suitable to model chemical EOR processes in (tight) fractured carbonates.
Many gas reservoirs at the appraisal stage exhibit evidence of persistent gas saturations below free water levels (FWL's). The amounts of gas contained here may, under some situations, be a sizable fraction of the gas cap volumes. Many engineers appear poorly equipped to include, and model, paleo gas in simulation models. This often results in paleo gas being simply ignored when development plans are being considered. This is unfortunate because paleo gas upon pressure depletion can expand, displacing brine towards well completions. This means that while some additional gas production may occur from the paleo zone, the risk of water production may be significantly underestimated if paleo gas is simply omitted. This work discusses the evidence for paleo gas and shows that it may be described and incorporated in simple simulation models provided the user avoids some common misconceptions. It is demonstrated that under depletion conditions, paleo gas can be entirely visible to material balance pressure responses, while at the same time increasing the risk of produced water volumes. For higher pressure paleo gas reservoirs the common P on Z diagnostic plots can also provide early trends that are frequently misinterpreted. This work quantifies the curvature that can result in such systems, and shows that simulation models inherently predict the expected curvature in P on Z. The approach taken here is by design simplistic and is applicable to scoping evaluations where the paleo gas volumes could be a significant volumetric uncertainty. Where possible, we indicate where additional, or more rigorous, descriptions can be applied.
The Alvheim field, offshore Norway, has subsea wells with long horizontal branches completed with sand screens. After 10 years of production, water production starts to constrain the oil production. Mechanical water shut-off is impossible in these wells, hence other methods are of interest. In a well workover in 2013, two high-viscous polymer pills were bull-headed and squeezed into the reservoir. The well productivity was reduced with around 50% while the water-cut dropped and pointed to potentially 3 mmstb of extra oil recovery. A research study was initiated with the objectives to understand the changed well performance and if polymer bull-heading can be a future method to reduce water production and enhance oil production.
An experimental laboratory program started with filtration tests of polymer solutions based on the polymer used in the well operation. Core flood experiments were performed by injecting polymer into two parallel mounted cores, then back producing these individually with either water or oil. Several combinations of parallel cores were tested with polymer injection: high vs. low permeability, high oil saturation vs. low oil saturation, outcrop sandstone vs. Alvheim core, as well as two different polymer versions.
The polymer recipe as used in the well operation showed to plug standard filters with filter size larger than the reservoir pore sizes but did not plug the cores. The polymer recipe as used in the well gave a better disproportionate permeability reduction (DPR) than the alternative polymer variant with similar viscosity. A theoretical model for the shear rate in the porous media matched the experimental measured data excellent. The core results show a stable permeability reduction factor of 100-450 for water, while only a factor 2-10 and decreasing with time for oil. The achieved DPR ratio of 45-80 is better than the trend from earlier published results.
The DPR as measured in the laboratory was next integrated in the reservoir model as part of the history match of the treated well. The Alvheim field has several reservoir zones separated with thin shales, and this reservoir zonation seems key for this EOR method to work.
The laboratory work, the reservoir studies and the field experience all point to a possible robust and simple EOR method for Alvheim and similar oil fields. The polymer seems to act as a "magic filter", allowing oil to pass while not water. Future work includes more research and maturing a new polymer pilot on Alvheim.
Sun, Zheng (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)) | Shi, Juntai (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)) | Wu, Keliu (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)) | Zhang, Tao (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)) | Feng, Dong (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing)) | Li, Xiangfang (MOE Key Laboratory of Petroleum Engineering and State Key Laboratory of Petroleum Resources and Engineering, China University of Petroleum (Beijing))
Low-permeability coalbed-methane (CBM) reservoirs possess unique pressure-propagation behavior, which can be classified further as the expansion characteristics of the drainage area and the desorption area [i.e., a formation in which the pressure is lower than the initial formation pressure and critical-desorption pressure (CDP), respectively]. Inevitably, several fluid-flow mechanisms will coexist in realistic coal seams at a certain production time, which is closely related to dynamic pressure and saturation distribution. To the best of our knowledge, a production-prediction model for CBM wells considering pressure-propagation behavior is still lacking. The objective of this work is to perform extensive investigations into the effect of pressure-propagation behavior on the gas-production performance of CBM wells. First, the pressure-squared approach is used to describe the pressure profile in the desorption area, which has been clarified as an effective-approximation method. Also, the pressure/saturation relationship that was developed in our previous research is used; therefore, saturation distribution can be obtained. Second, an efficient iteration algorithm is established to predict gas-production performance by combining a new gas-phase-productivity equation and a material-balance equation. Finally, using the proposed prediction model, we shed light on the optimization method for production strategy regarding the entire production life of CBM wells. Results show that the decrease rate of bottomhole pressure (BHP) should be slow at the water single-phase-flow stage, fast at the early gas/water two-phase-flow stage, and slow at the late gas/water two-phase-flow stage, which is referred to as the slow/fast/slow (SFS) control method. Remarkably, in the SFS control method, the decrease rate of the BHP at each period can be quantified on the basis of the proposed prediction model. To examine the applicability of the proposed SFS method, it is applied to an actual CBM well in Hancheng Field, China, and it enhances the cumulative gas production by a factor of approximately 1.65.
Hydrocarbon-reservoir-performance forecasting is an integral component of the resource-development chain and is typically accomplished using reservoir modeling, by means of either numerical or analytical methods. Although complex numerical models provide rigorous means of capturing and predicting reservoir behavior, reservoir engineers also rely on simpler analytical models to analyze well performance and estimate reserves when uncertainties exist. Arps (1945) empirically demonstrated that certain reservoirs might decline according to simple, exponential, hyperbolic, or harmonic relationships; such behavior, however, does not extend to more-complex scenarios, such as multiphase-reservoir depletion. Because of this limitation, an important research area for many years has been to transform the equations governing flow through porous media in such a way as to express complex reservoir performance in terms of closed analytical forms. In this work, we demonstrate that rigorous compositional analysis can be coupled with analytical well-performance estimations for reservoirs with complex fluid systems, and that the molar decline of individual hydrocarbon-fluid fractions can be expressed in terms of rescaled exponential equations for well-performance analysis. This work demonstrates that, by the introduction of a new partial-pseudopressure variable, it is possible to predict the decline behavior of individual fluid constituents of a variety of gas/condensate-reservoir systems characterized by widely varying richness and complex multiphase-flow scenarios. A new four-region-flow model is proposed and validated to implement gas/condensate-deliverability calculations at late times during variable-bottomhole-pressure (BHP) production. Five case studies are presented to support each of the model capabilities stated previously and to validate the use of liquid-analog rescaled exponentials for the prediction of production-decline behavior for each of the hydrocarbon species.
Special Core Analysis, SCAL data has a direct impact on the way fluids are allocated and distributed in the reservoir simulation models, which would directly impact reservoirs’ STOIIP estimation and their distribution. Moreover, it directly affects the performance of secondary and EOR flooding processes, and in turn impacts the accuracy of the oil and gas reserve estimates, and the management of these reserves. Therefore, SCAL data could be considered as one of the most critical reservoir input data for reservoir simulation models. This course will shed light on the theoretical and experimental background of SCAL data. It will explain the concept of reservoir wettability and different factors that could induce changes in reservoir wettability.