Generalized Material Balance Equation Research Articles

The generalized method for estimating reserves of shale gas and coalbed methane reservoirs based on material balance equation

As the main unconventional natural gas reservoirs, shale gas reservoirs and coalbed methane (CBM) reservoirs belong to adsorptive gas reservoirs, i.e., gas reservoirs containing adsorbed gas. Shale gas and CBM reservoirs usually have the characteristics of rich adsorbed gas and obvious dynamic changes of porosity and permeability. A generalized material balance equation and the corresponding reserve evaluation method considering all the mechanisms for both shale gas reservoirs and CBM reservoirs are necessary. In this work, a generalized material balance equation (GMBE) considering the effects of critical desorption pressure, stress sensitivity, matrix shrinkage, water production, water influx, and solubility of natural gas in water is established. Then, by converting the GMBE to a linear relationship between two parameter groups related with known formation/fluid properties and dynamic performance data, the straight-line reserve evaluation method is proposed. By using the slope and the y -intercept of this straight line, the original adsorbed gas in place (OAGIP), original free gas in place (OFGIP), original dissolved gas in place (ODGIP), and the original gas in place (OGIP) can be quickly calculated. Third, two validation cases for shale gas reservoir and CBM reservoir are conducted using commercial reservoir simulator and the coalbed methane dynamic performance analysis software, respectively. Finally, two field studies in the Fuling shale gas field and the Baode CBM field are presented. Results show that the GMBE and the corresponding straight-line reserve evaluation method are rational, accurate, and effective for both shale gas reservoirs and CBM reservoirs. More detailed information about reserves of shale gas and CBM reservoirs can be clarified, and only the straight-line fitting approach is used to determine all kinds of reserves without iteration, proving that the proposed method has great advantages compared with other current methods.

Two deterministic methodologies for estimation of OGIP by production dynamics diagnostic of gas-condensate reservoir

This study presents two independent methodologies for estimation of original gas in place (OGIP) by production dynamics diagnostic of gas-condensate reservoir with no-flow outer boundary based on black-oil concept. Classic Blasingame decline-type curves are also extended to apply in gas-condensate reservoir to calculate kh . Both numerically simulated case and field data are used to demonstrate the applicability and validity of proposed methodologies. One method develops a novel analytical model to obtain average reservoir pressure, OGIP and Diatz shape factor at the same time by coupling flow equation of gas-condensate reservoir for boundary dominated flow (BDF) and general material balance equation (GMBE). The two-phase variable-rate flow equation at late time for BDF is clearly and concisely derived in this study in terms of defined two-phase pseodopressure and two-phase material balance pseudotime. In addition, another innovative, simple and effective method for estimation of OGIP is proposed in this study requiring input data of only cumulative production of well and reservoir fluid PVT characteristics of Constant Volume Depletion (CVD) experiment. The fundamental concept of this method suggests that transient cumulative production GOR is determined by only current gas recovery degree and fluid PVT characteristics of the reservoir. Due to the accurate, simple and relaxed data-requiring nature of this method, widespread use in field to estimate OGIP of gas-condensate reservoir is potentially encouraging. On the contrary, if OGIP is already known, an intermediate equation of the method can also be applied to check accuracy of CVD experiment results from laboratory. The first methodology extends OGIP estimation to gas-condensate reservoir from Blasingame and Lee (1988)’s method for dry-gas reservoir. Often used two-phase z factor, which is inconvenient to evaluate and easy to yield error, for gas-condensate reservoir in material balance equation is avoided in this methodology by applying more analytical and accurate Walsh et al. (1994)’s GMBE instead. The second methodology, to the authors’ knowledge, is the first proposed allowing OGIP estimation of gas condensate reservoir without requiring bottom hole flowing pressure (BHFP), pressure tests and complex calculation.

Prediction Modeling for Combination Drive Reservoir Performance

Depletion performance of combination drive oil reservoirs is highly influenced by changes in reservoir rock and fluid data, relative permeability data, and PVT data of reservoir. Therefore, future prediction of combination drive oil reservoirs is difficult due to the long terms, huge equations and the sensitivity of data especially the PVT data and relative permeability data. In this paper, an integrated analytical model was developed to simulate the combination drive oil reservoir’s performance. It couples the general material balance equation with equations for water influx, water-invaded pore volume, gas-invaded pore volume, oil and gas saturation, and fluid contacts for combination oil reservoirs. All these equations are merged and solved simultaneously with reservoir depletion stages. A comparison with the various equations’ results for the integrated model has been developed so that it can be utilized in history match mode. This is used to estimate fluid saturation distribution after water influx and gas-cap invasion, original fluids in place, aquifer parameters and type, fluid contact levels, and effective recovery factor during gas and water aquifer movement towards the productive hydrocarbon zone in all reservoir depletion stages. The developed model has been validated using published cases for various oil reservoirs’ conditions, resulting in a good match between published case results and developed model results for these reservoirs. After validating the model, it has been used for two Egyptian combination drive fields. The field production history has been matched and future production performance for these reservoirs was simulated. Finally, the developed model also has the capability to predict reservoir performance for another Egyptian combination drive oil reservoir field under water and or gas injection, integrated with decline curve analysis.

Multiwell, Multiphase Flowing Material Balance

Summary Flowing-material-balance (FMB) analysis is a practical method for determining original hydrocarbon volumes in place. It is attractive because it enables performing material-balance calculations without shutting in wells to obtain estimates of reservoir pressure. However, with some exceptions, its application is limited to single-phase oil and/or gas reservoirs over limited pressure ranges during depletion. In unconventional reservoirs, reservoir and/or production complexities may further restrict FMB use. Among these complexities are significant production/injection of water, production resulting in higher gas/oil ratios (GORs) and pressure drawdowns, geomechanical effects, and multiwell-production effects. As a result, application of the conventional FMB to unconventional reservoirs may lead to significant errors in hydrocarbons-in-place estimation. This paper first discusses the application of conventional FMB to the analysis of single-phase or multiphase flow in single or multiwell scenarios, and then provides a new, comprehensive version of the FMB to address the previously mentioned complications. For the new FMB, pseudopressure is used to account for two-phase oil/gas flow. In addition, by use of a general material-balance equation, water production/injection and multiwell effects are included in the analysis. The new FMB-analysis approach is validated by comparing results with numerical simulation of multifractured horizontal wells (MFHWs). These comparisons demonstrate that, not only gas production, but also water production/injection can have a significant effect on the calculated original-in-place hydrocarbon volumes. The new FMB-analysis approach provided herein successfully accounts for all flowing phases in the reservoir, and is demonstrated to be applicable for multiwell scenarios. The methodology presented in this paper maintains the simplicity of FMB, yet accounts for multiphase flow and multiwell complications. The developed FMB and the presented approach can be used by reservoir engineers to reasonably determine the original volumes of hydrocarbons in place in both conventional and unconventional reservoirs.

A comprehensive model to history match and predict gas/water production from coal seams

Coalbed methane (CBM) currently accounts for approximately 5% of U.S. annual gas production. The performance prediction of CBM is very complex. It is highly affected by the complexity of porosity–permeability variation, reduction due to formation compaction, enhancement due to matrix shrinkage, and the two-phase flow effects. An additional complexity is added if the initial gas content, permeability, and porosity are not available. In this paper an integrated model was developed to simulate the behavior of CBM. A developed generalized material balance equation is used to account for the solubility of the methane in water, and the changes of porosity and permeability with pressure depletion. The equation is formatted similarly to the conventional material balance of oil reservoirs.An optimization algorithm was also used with the integrated model. The model could be used as a history matching tool to estimate the original gas-in-place (the adsorbed gas-in-place and the free gas-in-place), the initial formation permeability, the gas and water relative permeability exponents, and the matrix shrinkage coefficient that reflected the permeability changes.The developed model was validated by use of different simulation cases generated with a commercial simulator. The results show a good match between the simulation cases and the integrated model. The model was then used to analyze the production data of different CBM formations (the Fruitland and the Upper Pottsville Formations, USA). The model was used to match the production history data (gas and water rates) in order to estimate the gas-in-place and the formation properties. These parameters were then used to predict the production performance. The model can be run with different production control conditions such as the constant water rate or the constant bottom-hole flowing pressure.This model could be used as a helpful tool in CBM investment and development. It can also be used to obtain the key reservoir parameters for newly discovered reservoirs such as gas-in-place, initial water-in-place, water production rate, gas production rate, and the peak gas rate. With this information, an investor will better determine the feasibility of a project. Also, this model can be used to optimize the dewatering rate (initial water production rate) in order to optimize the time taken to reach the peak gas rate.

English

This work presents a general, straight-line method to estimate the original oil and gas in-place in a reservoir without restrictions on fluid composition. All past efforts are applicable to only restricted ranges of reservoir fluids. The work supersedes these and it is applicable to the full range of reservoir fluids-including volatile-oils and gas-condensates. The work is based on the new generalized material-balance equation recently introduced by Walsh. The superiority of the new method is illustrated by showing the error incurred by preexisting calculation methods; guidelines are offered to help identify when preexisting calculation methods must be abandoned and when the new methods featured herein must be employed. Empirical correlations for the volatile oil-gas ratio Rv for volatile-oils and gas-condensates have been introduced to accurately define how much fluid volatility a reservoir oil can exhibit before one can no longer justifiably use the CMBE and one must apply the generalized material balance equation (GMBE). Thus, if there is interest in applying the conventional material-balance equation (CMBE) and its applicability is in question, we recommend measuring the fluid's volatile oil-gas ratio Rv at its saturation pressure and comparing it to the critical value offered herein. Key words: Volatile oil, undersaturated, volumetric, material balance, reserve estimation, oil-gas ratio, black oil, gas condensate.

New technique for calculation of well deliverability in gas condensate reservoirs

Well deliverability is an important issue in forecasting the performance of many gas condensate reservoirs. Condensate accumulations near the wellbore may cause a significant reduction in the well productivity, even in the case of very lean fluids. Generally, the well deliverability is affected by two pressure-drop sources due to depletion and condensate buildup. Recently rapid spreadsheet tools have been developed to evaluate the well performance using material balance equation for depletion and two-phase pseudo pressure integral for well inflow performance. Most of them account for the effects of negative inertia and positive coupling in the calculation of gas relative permeabilities. This paper introduces a new method for calculation of well productivity in gas condensate reservoirs. This method uses the concept of two-phase pseudo pressure integral without any need to estimate the radius of two-phase region. In this approach the average reservoir pressure is calculated by using a general material balance equation. The only data required for implementing this method is PVT data, relative permeability curves and a table of well flowing pressure versus time. The new technique can be encoded on a spreadsheet in order to forecast the gas condensate well performance very rapidly. To validate the proposed approach we have used several single-well fine grid compositional simulations of a hypothetical reservoir model over a typical range of gas condensate reservoir parameters. We have shown that there is a reasonable agreement between the result of fine grid simulation and the prediction from the proposed approach.

Analysis of a non-volumetric gas-condensate reservoir using a generalized material balance equation with fluid properties from an equation of state

Predicting the expansion of an underlying aquifer can be of paramount importance in certain aspects of petroleum engineering, such as the control of water coning, calculating reserves, designing well completions, designing surface facilities such as separators, pumps, etc. Predicting water encroachment can be of critical importance in describing and managing a hydrocarbon reservoir. This study focuses on the use of a generalized material balance equation (GMBE) along with the analytical solution to the diffusivity equation for a constant inner boundary pressure to determine the size of a water-bearing formation in contact with a gas-condensate reservoir. When the hydrocarbon reservoir fluid is a gas-condensate, it is essential to use the GMBE. Should the conventional material balance equation (CMBE) be used in lieu of the GMBE, considerable errors could be introduced as will be demonstrated in this paper. The main goal of this paper is to illustrate the ability of the GMBE to determine the size of an aquifer encroaching into a gas-condensate reservoir. Once this size is obtained, it could be used as an input parameter to a reservoir simulator to forecast the future expansion of the aquifer as depletion proceeds. When the CMBE is used to describe black oil reservoirs, certain simplifying assumptions are normally made. Those include neglecting the effect of the compressibilities of the connate water and the reservoir rock, in addition to the volatilized liquid in the gas phase. The effect of these assumptions in gas-condensate reservoirs will be examined.

A Generalized Approach to Reservoir Material Balance Calculations

Abstract This work completes the search for a generalized material balance equation. No restrictions are placed on reservoir fluid compositions. Unlike the conventional material balance equation, the new equation specifically accounts for volatilized-oil and, therefore, is uniquely applicable to the full range of fluids, including volatile-oils and gas-condensates. Equally important, the new material balance equation retains the same simplicity with which the conventional material balance equation has become known. The new, generalized material balance equation is featured here by showing how it is used to predict reservoir performance and estimate reserves in example volatile-oil and gas-condensate reservoirs. In comparison, the conventional material balance equation is shown to lead to erroneous results. The new, generalized material balance equation leads to an improved method of reservoir performance analysis. Introduction Material balance calculations are a useful method of reservoir performance analysis. They are routinely used to estimate oil and gas reserves and predict future reservoir performance. Schilthuis(l), in 1936, was among the first to formulate and apply material balances. Inherent in his and others' use of material balances were the following assumptions:at most, there are two hydrocarbon phases: oil and gas,at most, there are two hydrocarbon components: stock-tank oil and separator (surface) gas,the reservoir oil-phase consists of stock-tank oil and separator-gas,the reservoir gas-phase consists of only separator-gas and no stock-tank oil, andthere are no compositional gradients within the system. Assumptions 1 and 2 define the popular two-hydrocarbon- component formulation. Assumption 3 effectively accounts for the effects of dissolved- or solution-gas.Assumption 4 ignores the possibility of volatilized-oil and. therefore, restricts application to black-oils and dry-gases and precludes application to volatile-oils, gas-condensates, or wet-gases. Volatilized-oil is the stock-tank oil content of the free reservoir gas-phase, Assumption 5 means that the system is effectively treated as a tank with no gradients; accordingly, Coats(2) and others have sometimes referred to this type of model as a tank or zero-dimensional model. Despite their apparent oversimplicity, early tank models found widespread use in reservoir engineering applications(3–16). As time progressed, more sophisticated material balance models evolved, each striving for greater generality. Eventually, following the advent of digital computers, the material balance equations were discretized and the first generation of multi-dimensional, black-oil, finite-difference reservoir simulators were developed in the 1960's (17–19). These models, like their zero-dimensional counterparts, could effectively simulate black-oil and dry-gas reservoirs but could 1I0t model volatile-oil and gas-condensate reservoirs. To address this limitation, Cook et al 20 in 1974 introduced a volatile-oil, finite-difference simulator. Their formulation retained the simplicity of two hydrocarbon components, but allowed for volatilized-oil. Consequently, their formulation was applicable to the full range of reservoir fluids. The resulting formulation was applicable to the full range of reservoir fluids. Coats(21) later, in 1986, verified the applicability of the black- and volatile-oil approaches in reservoir simulation by showing agreement with a fully-compositional, equation-of-state (EOS) reservoir simulator.

Depletion Performance of Volumetric High-Pressured Gas Reservoirs

Summary A method to predict the percent recovery of volumetric, high-pressured gas reservoirs from the initial pressure to the abandonment pressure with only initial reservoir data is presented. This method can also be used with early-life production data to predict the initial gas in place. The method is based on an incremental solution to the general material-balance equation. All parameters in the material balance are pressure-dependent and are recalculated for every 100-psi [690-kPa] drop in reservoir pressure. Procedures were developed to calculate these parameters with correlations and data available in the literature. PV compressibilities, formation-water compressibilities, and gas compressibility factors were determined for temperatures and pressures ranging up to 400°F and 20,000 psia [204°C and 137.9 MPa], respectively. The pressure dependency of the PV compressibility and the formation-water compressibility is a unique feature of this model. The reservoir depletion model presented here was applied to a field example, as were three published techniques for determining reserves in abnormally pressured reservoirs. When predictions of initial gas in place were compared, the reservoir depletion model yielded a more accurate value than the other techniques.

Analysis of the effectiveness of the fractionation of chemically inhomogeneous mixtures of macromolecules on the basis of the generalized material balance equation

To analyse the effectiveness of the fractionation of chemically inhomogeneous mixtures of macromolecules, the authors have employed the generalized material balance equation. Using model systems they evaluate the thermodynamic parameters ensuring optimal separation of the mixtures according to the chemical structure of the macromolecules.

The theory of phase equilibria in multicomponent systems. Problems of analytical fractionation

In order to solve the thermodynamic problem involved in establishing the interrelation between the experimentally determined solubility parameters of a polymer and its molecular mass distribution, the theory of phase equilibria developed from the classical Flory-Huggins model has been applied. An efficient procedure for numerically calculating the parameters of the equilibrium phases for mixtures of a polydisperse polymer with liquid components has been developed. A generalized material-balance equation has been derived and its accuracy assessed; it has been put forward to solve theoretical problems in the analytical fractionation of polymers and copolymers in real dilute systems whose special features are taken into account by including in the equation the experimentally recorded parameters.

Solution of problems of analytical fractionation of polymers and copolymers by using a generalized material balance equation

Solution of problems of analytical fractionation of polymers and copolymers by using a generalized material balance equation