Curtis Hays Whitson

Peng-Robinson predictions for hydrocarbons, CO2, N2, and H2 S with pure water and NaCI brine

Abstract Soreide, I. and Whitson, C.H., 1992. Peng-Robinson predictions for hydrocarbons, CO2, N2 and H2S with pure water and NaCI brine. id Phase Equilibria 77: 217-240. Attempts at predicting mutual solubilities with a conventional cubic equation of state (EOS) including the effect of salts in the aqueous phase have so far been limited. The main purpose of this work is to provide a simple and novel approach for predicting mutual solubilities of brine/hydrocarbon mixtures with an EOS at high pressures and temperatures, including the effect of salinity in the aqueous phase. The Peng-Robinson EOS 2 has been applied in this study with two modifications: (1) an α-term in the EOS constant a has been developed specifically for the water/brine component as a function of sodium chloride (NaCl) brine salinity and pure water reduced temperature, TI, and (2) two sets of binary interaction parameters (BIP) in the classical mixing rule for mixture EOS constant a have been determined as a function of acentric factor, temperature, and salinity. Experimental data of vapor pressures and mutual solubilities provide the basis for the proposed methods. Applications of the methods described include phase behavior prediction of reservoir gas-oil/brine systems at high pressures, including (1) gas solubility in water/brine and (2) water solubility in hydrocarbon reservoir fluids.

APPLICATION OF THE GAMMA DISTRIBUTION MODEL TO MOLECULAR WEIGHT AND BOILING POINT DATA FOR PETROLEUM FRACTIONS

This paper applies the gamma distribution model for describing both the molar and boiling point distributions of heptanes-plus (C7+) fractions. The three-parameter distribution model has been fit to TBP (true boiling point) data from forty-four samples of stabilized petroleum liquid (stock tank oil and condensate), obtained from separation of reservoir fluids. An excellent fit was achieved for both molar and boiling point distributions, though molar distribution seems to be more accurately described by the distribution model. Two of the parameters, α and η, were correlated and fit to empirical equations for both molar and boiling point distributions. Since the third parameter, β, is defined in terms of α,η, and either average molecular weight or boiling point, it appears that a generalized correlation for molar and boiling point distributions may exist. We have not developed such correlations in this work, but our results provide the necessary groundwork for further research.

Optimized Well Modeling of Liquid-Rich Shale Reservoirs

This paper presents an integrated modeling approach for history matching and economic optimization of wells producing from liquid-rich shale reservoirs (LRSR). History matching uses daily pressures and gas-oil-water production data to estimate average parameters in a 2D/3D finite-difference (FD) horizontal multi-fractured well model: rock permeability, fracture halflength, relative permeabilities, and in-situ fluid (solution gas-oil ratio). Economic-based well design uses the same FD model to maximize net present value (NPV) by finding optimal well completion parameters: number of fractures, and fracture size. Revenue optimization (short-term and long-term) is performed with the same FD well model by finding the drawdown that maximizes revenue. For undersaturated gas condensate LRSR wells, optimal drawdown is often equal to or somewhat below the reservoir dewpoint pressure. We study optimal drawdown control for new wells that are optimized from start of production, and for wells that are optimized only after some initial period of sub-optimal drawdown control. We also compare short-term versus long-term economic optimization strategies. We provide examples that clearly show the potential for improved economic development of LRSR using optimized well design and drawdown control, for new and existing wells. Our study shows a significant economic upside to proper selection of completion design, and for undersaturated gas condensate wells, optimal drawdown has significant potential to increase daily revenues.

Modelling of diffusional mass transfer in naturally fractured reservoirs

Abstract Based on a set of laboratory experimental data, a simple mathematical model has been developed for estimating the amount of mass transfer in a matrix-fracture system when a non-equilibrium gas (N 2 , CO 2 , or natural gas) is injected into a naturally fractured reservoir. Two cases are considered; first when gas in the fracture is stagnant, and second when there is a high flow of gas in the fracture. The proposed model can be applied to any matrix-fracture system geometry with natural gas and oil present in the matrix. The equilibrium conditions between gas and oil both inside the matrix block and at the matrix-fracture interface are imposed at all times. Using the proposed one-dimensional model, compositions and concentrations of all compounds in the system as well as the gas saturation in the matrix can be calculated at any time. Comparison of results calculated from the model with measured laboratory data confirms reliability of proposed model.

Cyclic Shut-in Eliminates Liquid-Loading in Gas Wells

This paper presents a method to eliminate production loss due to liquid-loading in tight gas wells. Cyclic shut-in control is a simple production strategy that particularly benefits lower-permeability stimulated wells, including but not limited to shale gas wells. Comparison is made between a gas well producing (1) in a “ideal” situation where 100% of liquids entering from the reservoir or condensing in the tubing are continuously removed (without shut-ins), (2) in a meta-stable liquid-loading condition with low gas rate, typical of most wells today, and (3) by the proposed strategy of cyclic shut-in control. We show that cyclic shutin control of stimulated low-permeability vertical wells to ultra-low-permeability horizontal multi-fraced wells can produce without ever experiencing liquid loading, and with little-to-no delay of ultimate recovery. Cyclic shut-in control can be applied to all stimulated, lower-permeability gas wells, from the onset of gas rates that result in liquid-loading. The strategy can also be used for wells which already have experienced a period of liquid-loading , but the expected performance improvement may be less because of near-well formation damage caused by historic liquid-loading – e.g. fresh-water backflow and liquid-bank accumulation. In historically liquid-loading wells, an initial period of liquid removal and/or light stimulation may be needed prior to initiating cyclic shut-in control. We show that the shut-in period should optimally be as short as operationally possible. Cyclic shut-in control is shown to work equally well for layered no-crossflow systems with significant differential depletion at the onset of liquid loading. Minimizing rate and recovery loss of liquid-loading gas wells is of international interest. We believe that cyclic shut-in control will become an industry standard practice for shale gas wells, and should lead to a significant ultimate increase in worldwide gas reserves. The method is extremely simple and requires only a rate-controlled wellhead shut-in device.

Target-rate Tracking for Shale-gas Multi-well Pads by Scheduled Shut-ins ?

Abstract The recent success of shale-gas production relies on drilling of long horizontal wells and stimulation with multistage hydraulic fracturing. This practice normally leads to an initial peak production with a subsequent rate decline, followed by low and erratic production rates caused by water accumulation in the wells. Shale-gas recovery requires a large number of wells in order to maintain a sustainable total gas supply. To reduce the surface area disturbances caused by this extensive drilling and to share available surface infrastructure, the use of multi-well pads is a key driver in shale-gas developments. Furthermore, the inherent rate decline of shale-gas wells, the water accumulation in them and the large number of wells, leads to severe operational challenges for well operators. The fact that shut-ins may be used as a means to prevent liquid loading and boost late-life production rates from shale-gas wells, suggests scheduling of shut-ins to perform maintenance and clean-up of the wells, and to track a target rate for the multi-well pad. In this paper we propose an optimization scheme for shale-gas multi-well pads to schedule shut-ins and to track a target rate. The optimization problem is formulated as a discrete time mixed integer linear program (MILP) with binary variables defining at which times the well is either shut-in or producing. A reservoir proxy model and a well model for each well is designed and tuned against a realistic multi-fractured reservoir model. We demonstrate the benefits and the potential of the proposed methodology through a one-month production planning problem for an eight-well shale-gas pad.

Multi-Field Asset Integrated Optimization Benchmark

Integrated modeling of multi-field assets, from subsurface to market, is challenging due to the complexity of the problem. This paper is an extension of the SPE 121252, model based integration and optimization gas cycling benchmark [Juell, et al., 2009], extending two gas-condensate fields to two full-field multi-well models. Additionally, a full-field model is added to the Juell benchmark, introducing an oil field undergoing miscible WAG injection, where most data are taken from the SPE 5 Reservoir Simulation Comparative Project. All reservoir models are compositional, but using different EOS representations. A base case scenario is defined with fixed numbers and locations of producers and injectors. A common field-wide surface processing facility is modeled with emphasis on water handling, NGL extraction, sales-gas spec, and gas reinjection. The surface process model interacts with the three reservoir models through two main mechanisms – (1) waterand gas-handling constraints, and (2) distribution of available produced gas for reinjection into the three reservoirs. The field asset model provides long-term production forecasts of gas, oil, and NGL revenue. Cost functions are introduced for all major control variables (number of wells, surface facility selection and operating conditions, injection gas composition). Net present value is used as the target objective function. This paper will evaluate optimal production strategies for the base case benchmark problem, using several key control variables and field operational constraints. Optimization performance will be tested with a few solver algorithms. The benchmark will be provided to the industry through application data files, network infrastructure, and results from our integrated optimization model. Introduction Operation of complex assets may require a holistic view of the value chain. This is particularly important if the different parts of the value chain are tightly connected. Present industrial practice typically takes a silo approach in the sense that one part of the supply chain is treated quite separate from other parts. This is pronounced in the upstream area where for instance a decision support application for optimally allocating well production may include well and pipeline models. The downstream boundary condition is typically a constant pressure at the inlet separator. Similarly an optimizer for the surface process does not include models of the upstream system. This implies that the inlet separator acts as a “dividing wall” between two optimizers even though the two subsystems might be tightly connected. An example of this is when the gas output from the surface facility is fed back into the upstream system through gas-lift wells or gas injectors. There are many reasons for the silo-like situation. Different parts of the supply chain recruit people with different backgrounds and they use quite different decision support tools. This limits integration even in situations where integration has an obvious potential. Several researchers have conducted research on various integration topics. [Bailey et al., 2005] and [Cullick et al., 2003] discussed complex petroleum field projects applying uncertainty analysis, but the surface process facility was not considered. [Nazarian, 2002] integrated ECLIPSE and HYSYS simulators to calculate integrated field operation in a deepwater oil field. 2 [SPE 130768] Those simulators were coupled by using Automation and Parallel Virtual Machine and applying a genetic algorithm for the optimization. [Hepguler & Barua, 1997] and [Hepguler et al., 1997] discussed an integrated application for reservoir-production strategies and field development management. In this case, the ECLIPSE reservoir simulator was coupled with the surface and production network simulator and the optimizer (Netopt). Run time can be a challenge in integrated application, especially when closely linked high-fidelity models are tightly connected. [Barroux et al., 2000] proposed a practical solution to reduce run time of the coupled simulators. [Trick, 1998] applied a somewhat different procedure from [Hepguler et al., 1997], using the same interface. In this case an ECLIPSE black oil reservoir simulator was coupled to a surface gas deliverability forecasting model, FORGAS. The use of integrated optimization in a day-to-day operations setting of the LNG value chain was studied by [Foss and Halvorsen, 2009)]. To reduce computation time they chose simple models for all system components. A sizable gain could be identified by integrating all models into one decision support application as opposed to dividing them into two applications; one for the upstream part and the other for the LNG plant. [Tomasgard et al., 2007] presents a natural gas value chain model and integration applying an upstream perspective and a stochastic portfolio optimization. The literature citings above identifies a potential for integrating models in decision support tools. Moreover, integrated simulation and optimization is clearly regarded as an interesting but challenging topic. Hence, in this paper we present a benchmark problem which is designed to assess the potential of an integrated approach in decision support tools. A realistic benchmark as well as a base case will be defined in the following sections. Further, a sensitivity analysis of key decision variables will be presented in addition to some early optimization results. The paper ends with some conclusions and directions for further work. Integrated Model The model presented in this paper is rich and complex enough to represent the value chain from reservoir to export and thus suitable as a benchmark for integrated operations and optimization (I-OPT). The upstream part of the I-OPT model includes two gas-condensate reservoirs and an oil reservoir while the surface process system includes gas and liquid separation as well as an NGL plant. The model also includes an economic component as indicated in Fig. 1. All model components have been designed using realistic assumptions and parameter values. Further, the project is designed with close links between the upstream and downstream parts of the model, partly due to gas re-injection. This is important since the I-OPT model is designed to study and assess the business value of integrated optimization as a decision support method. Integrated optimization in this context is defined as applications which utilize several different models along the value chain, for instance a reservoir model and a surface process model, in one optimization-based application as opposed to two separate applications for the reservoir and surface part, respectively. Hence, the I-OPT model is designed to challenge the conventional silo approach. The I-OPT model is further designed to study decisions both on a life-cycle horizon as well as shorter time frames. The surface facility model is a steady-state model while the reservoirs are modeled using dynamic models to account for depletion effects. The model is an extension of the full-field model from a previous paper [Juell, et al., 2009]. The I-OPT model will be presented in the following sections. Complete documentation of the I-OPT model including the base case discussed later will also be made available. Reservoir Description The reservoir models include two gas-condensate reservoirs and an oil reservoir. The gas-condensate reservoirs are scaled up from [Juell, et al., 2009] and the oil reservoir is a scaled up version of a miscible WAG project [Killough and Kossack, 1987]. In the base case each reservoir is producing through 5 production wells and injection operations are conducted through 8 injection wells which perform gas injection wells in the gas-condensate reservoirs and WAG injection in the oil reservoir. The production and injection wells are perforated through all layers. The well locations for each reservoir are shown in Fig. 2(b) and are given in Table 10. The gas-condensate reservoir models consist of 36 36 4 grid blocks and the oil reservoir 35 35 3 grid blocks. The horizontal permeability distributions for the three reservoirs vary from a low value in the south west region towards higher permeability values in the north east. This is shown for one layer in Fig. 2(a). The permeability distribution range is presented on Table 1. There are two faults in the horizontal direction, one is non-communicating and the other is partially communicating. The non-communicating fault separates low permeability and medium permeability areas. The partially communicating fault separates the medium and high permeability areas. The non-communicating shale in the vertical direction occurs between layers 3 and 4 in [SPE 130768] 3 the lean gas-condensate reservoir, between layers 1 and 2 in the rich gas-condensate reservoir and between layers 2 and 3 in the oil reservoir. The reservoir models are compositional. The composition for the gas-condensate reservoirs consist of 9 components and the composition for the oil reservoir consists of 6 components. The initial fluid composition for the gas–condensate reservoirs are referred to [Juell, et al., 2009] and for the oil reservoir is presented in Table 7 to Table 9. The compositional reservoir models are run using the SENSOR reservoir simulator. Fig. 1 – Integrated optimization schematic. (a) Transmissibility distribution for lean gas-condensate reservoir in first layer. (b) Production and injection well placement for the lean gascondensate reservoir. Fig. 2 – Reservoir description of heterogeneity and well placement. PVT Description Compositional reservoir modeling usually offers better accuracy than black oil reservoir modeling, but in many cases a black oil model is still preferred due to shorter computation time. Therefore, Black Oil Tables (BOT) are supplied as an alternative to the EOS PVT models. BOT is generated by Constant Compositional Expansion (CCE) experiment for the same surface process us

CO2 EOR Potential in Naturally-Fractured Haft Kel Field, Iran

In this thesis, CO2 injection in matrix/fracture systems has been studied using a finely-gridded compositional simulator representing a single matrix block. Three laboratory experiments were modeled to investigate whether CO2 injection in a fracture-matrix system could be simulated using commercial simulators that include basic fluid flow physics, phase behavior, and molecular diffusion.The first experiment was performed by Karimaie (2007) using an equilibrium, saturated gas-oil fluid system (C1-n-C7) at 220 bar and 85 oC. Because no recovery was expected from non-equilibrium thermodynamic mass transfer, reported recovery stemmed only from Darcy displacement driven by gravity and capillary forces. When the oil production stopped from the equilibrium gas displacement, a second injection period with pure CO2 followed.The numerical modeling was conducted using a compositional reservoir simulator (SENSOR) without diffusion. The 2-dimensional r-z model used fine grids for the core matrix and surrounding fracture. Automated history matching was used to determine parameters which were not accurately known (fracture permeability, fracture and matrix porosity, and separator conditions), using surface volumetric oil production rates reported experimentally. The final model match was relatively unique with a high degree of confidence in final model parameters. The oil recovery improved significantly with CO2 injection.Our model indicated that the recovery mechanism in the Karimaie experiment was dominated, for both equilibrium gas and CO2 injection, by top-to-bottom Darcy displacement caused by low conductivity in the artificial fracture; little impact of capillary-gravity displacement was found. Changes in CO2 injection rate had a significant impact on recovery performance. This experiment was also modeled using ECL300, with the same production performance as SENSOR for the set of history-match parameters determined without diffusion. When molecular diffusion was used in ECL300, results were nearly identical with those found without diffusion.Two other experiments were performed by Darvish (2007) at a higher temperature and pressure (130 oC and 300 bara) using a similar chalk and live reservoir oil. A similar modeling approach to that described above was also used for these experiments. In both experiments, the matching process based on reported oil production data gave a high degree of confidence in the model. The reported experimental mass fractions of produced-stream components were also matched well.Our modeling study indicates that gravity drainage affects the displacement process, but that mass transfer – including vaporization, condensation and molecular diffusion – also impact the recovery performance of CO2 injection in the Darvish experiments. The CO2 injection rate and initial water saturation were investigated by comparing the two Darvish experiments.Our studies from all of the Karimaie and Darvish experiments show a strong influence of the surface separator temperature on surface oil production, and this is an important consideration in designing and interpreting laboratory production data consistently.Once the laboratory recovery mechanisms had been successfully modeled, predictive numerical simulation studies were conducted on field-scale matrix/fractured systems, albeit mostly for single matrix blocks surrounded by a fracture. The effects of several key parameters on recovery production performance were studied in detail for field-scale systems: matrix permeability, matrix block size, matrix-matrix capillary continuity (stacked blocks), and the use of mixtures containing CO2 and hydrocarbon gas.The field-scale results were affected by gridding, so grid was refined to the degree necessary to achieve a more-or-less converged solution – i.e. recovery production performance didn’t change with further refinement.We studied the effect of molecular diffusion on oil recovery by CO2 injection in laboratory experiments and field-scale systems. Because the fluid systems considered had complex phase behavior and a wide range of conditions from strongly immiscible to near-miscible, the diffusion driving potential used was total component potential including chemical and gravity effects; concentrationdriven diffusion did not represent the more-complex non-equilibrium CO2 injection processes observed in the laboratory tests.A key result of this study was that diffusion can have an important effect on oil recovery, and that this effect varies with matrix block size and CO2 injection rate. We have shown that diffusion has a dominant effect on the recovery mechanism in experimental tests, except at very low rates of CO2 injection (and equilibrium hydrocarbon gas injection). For the field-scale matrix/fracture systems, diffusion can have a significant effect on the rate of recovery, with the effect becoming noticeable for low reservoir pressures and/or matrix block sizes less than ~40 ft.

Scale Dependence of Diffusion in Naturally Fractured Reservoirs for CO2 Injection

In this thesis, CO2 injection in matrix/fracture systems has been studied using a finely-gridded compositional simulator representing a single matrix block. Three laboratory experiments were modeled to investigate whether CO2 injection in a fracture-matrix system could be simulated using commercial simulators that include basic fluid flow physics, phase behavior, and molecular diffusion.The first experiment was performed by Karimaie (2007) using an equilibrium, saturated gas-oil fluid system (C1-n-C7) at 220 bar and 85 oC. Because no recovery was expected from non-equilibrium thermodynamic mass transfer, reported recovery stemmed only from Darcy displacement driven by gravity and capillary forces. When the oil production stopped from the equilibrium gas displacement, a second injection period with pure CO2 followed.The numerical modeling was conducted using a compositional reservoir simulator (SENSOR) without diffusion. The 2-dimensional r-z model used fine grids for the core matrix and surrounding fracture. Automated history matching was used to determine parameters which were not accurately known (fracture permeability, fracture and matrix porosity, and separator conditions), using surface volumetric oil production rates reported experimentally. The final model match was relatively unique with a high degree of confidence in final model parameters. The oil recovery improved significantly with CO2 injection.Our model indicated that the recovery mechanism in the Karimaie experiment was dominated, for both equilibrium gas and CO2 injection, by top-to-bottom Darcy displacement caused by low conductivity in the artificial fracture; little impact of capillary-gravity displacement was found. Changes in CO2 injection rate had a significant impact on recovery performance. This experiment was also modeled using ECL300, with the same production performance as SENSOR for the set of history-match parameters determined without diffusion. When molecular diffusion was used in ECL300, results were nearly identical with those found without diffusion.Two other experiments were performed by Darvish (2007) at a higher temperature and pressure (130 oC and 300 bara) using a similar chalk and live reservoir oil. A similar modeling approach to that described above was also used for these experiments. In both experiments, the matching process based on reported oil production data gave a high degree of confidence in the model. The reported experimental mass fractions of produced-stream components were also matched well.Our modeling study indicates that gravity drainage affects the displacement process, but that mass transfer – including vaporization, condensation and molecular diffusion – also impact the recovery performance of CO2 injection in the Darvish experiments. The CO2 injection rate and initial water saturation were investigated by comparing the two Darvish experiments.Our studies from all of the Karimaie and Darvish experiments show a strong influence of the surface separator temperature on surface oil production, and this is an important consideration in designing and interpreting laboratory production data consistently.Once the laboratory recovery mechanisms had been successfully modeled, predictive numerical simulation studies were conducted on field-scale matrix/fractured systems, albeit mostly for single matrix blocks surrounded by a fracture. The effects of several key parameters on recovery production performance were studied in detail for field-scale systems: matrix permeability, matrix block size, matrix-matrix capillary continuity (stacked blocks), and the use of mixtures containing CO2 and hydrocarbon gas.The field-scale results were affected by gridding, so grid was refined to the degree necessary to achieve a more-or-less converged solution – i.e. recovery production performance didn’t change with further refinement.We studied the effect of molecular diffusion on oil recovery by CO2 injection in laboratory experiments and field-scale systems. Because the fluid systems considered had complex phase behavior and a wide range of conditions from strongly immiscible to near-miscible, the diffusion driving potential used was total component potential including chemical and gravity effects; concentrationdriven diffusion did not represent the more-complex non-equilibrium CO2 injection processes observed in the laboratory tests.A key result of this study was that diffusion can have an important effect on oil recovery, and that this effect varies with matrix block size and CO2 injection rate. We have shown that diffusion has a dominant effect on the recovery mechanism in experimental tests, except at very low rates of CO2 injection (and equilibrium hydrocarbon gas injection). For the field-scale matrix/fracture systems, diffusion can have a significant effect on the rate of recovery, with the effect becoming noticeable for low reservoir pressures and/or matrix block sizes less than ~40 ft.

A Study of Recovery Mechanisms in a Nitrogen Diffusion Experiment

To understand the peculiar recovery phenomenon in a core nitrogen diffusion experiment, anumerical study has been carried out to investigate various governing forces and their interactions. The mathematical model used to simulate the experiment combines the analytical solution in the fracture (open space) and numerical solutions in the core. The analytical solution of the composition distribution in the fracture includes both molecular diffusion and bulk velocity of the gas stream. The numerical solution in the core includes molecular diffusion, capillary pressure, gravity, and Darcy flow. The fully implicit compositional formulation used in the numerical model is necessary because of the large capillarity and composition effects, and the small pressure gradients in the system.