An Optimization-Based Method for the Explicit Production Data Analysis of Gas Wells

This work aims at the exploration of production data analysis (PDA) methods without iterations. It can overcome limitations of the advanced type curve analysis relying on the iterative calculation of material-balance pseudotime and current explicit methods reckoning on specific production schedule assumptions. The dynamic material balance equation (DMBE) is strictly proved by the integral variable substitution based on the gas flow equation under the boundary dominated flow (BDF) condition and the static material balance equation (SMBE) of a gas reservoir. We introduce the pseudopressure level function γ(p) and the recovery factor function R(p) to rewrite the DMBE in terms of observed variable Y and estimated variable Ye; then the PDA can be transformed into an optimization problem of minimizing the error between Y and Ye. An optimization-based method for the explicit production data analysis of gas wells (OBM-EPDA), therefore, is developed in the paper, capable of determining the BDF constant and gas reserves explicitly and accurately for variable rate and/or variable flowing pressure systems. Three stimulated cases demonstrate the applicability and validity of OBM-EPDA with small errors less than 1% for estimated values of both reserves and Y. Not second to previous studies, the field case analysis further proves its practicability. It is shown that the nonlinear relation of γ to R can be represented by a polynomial function merely dependent on the inherent properties of the gas production system even before sorting out the production data. The errors of observed variable Y provided by OBM-EPDA facilitate the data quality control, and the elimination of outliers not subject to the BDF condition improves the reliability of the analysis. For various gas systems producing whether at a constant rate, a constant bottomhole pressure (BHP), or under variable rate and variable BHP conditions, the proposed method gives insights into the well-controlled volume and production capacity of the gas well whether in a low-pressure or high-pressure gas reservoir, where the compressibilities of rock and bound water are considered.

Performance Analysis of Gas Wells Based on the Conventional Decline Parameters and the Flow Integral Equation

The estimation of reserves and performance prediction are two vital tasks for the development of gas reservoirs where the evaluation of gas in place or well-controlled reserves, as the foundation of the performance analysis of gas wells, turns to be exceedingly significant. Advanced production data analysis or modern rate transient analysis (RTA) methods mainly depend on the iterative calculations of material balance quasitime ( t ca ) and type curve fitting, the essence of which is to update the average reservoir pressure data time and again. The traditional Arps’ decline models are of empirical nature despite the convenience and applicability to the constant bottomhole pressure (BHP) condition. In order to avoid the implicit iteration, this paper develops an explicit method for estimating the average reservoir pressure on the basis of dynamic material balance equation (DMBE), termed “flow integral method,” which can be applied to various gas production systems under boundary-dominated flow (BDF). Based on the flow integral method and the decline parameter evaluation, we employ the hyperbolic decline model to model the gas well performance at a constant BHP. The analytical formulations of decline rate and decline exponent are deduced from the DMBE and the static material balance equation (SMBE) considering the elastic compressibilities of rock pore and bound water. The resulting decline parameter method for explicit estimation of gas reserves boasts a solid and rigorous theory foundation that production rate, decline rate, and average reservoir pressure profiles have reference to each other, and its implementation steps are explained in the paper. The SMBE can, combined with the estimated pressure profile by the flow integral method, also be used to determine gas reserves which is not limited to the constant-BHP condition and can calibrate the estimates of the decline parameter method. The proposed methods are proven effective and reliable with several numerical cases at different BHPs and a field example.

Quantitative Evaluation of Water Flooding in a Low Resistivity Heavy Oil Reservoir with NMR and Conventional Logs

The classification of water flooding severity is crucial for planning reservoir production and improving the recovery ratio. In this paper, we study a siliciclastic heavy oil reservoir in Bohai Bay, with resistivity reading close to, or even lower than the wet zone (3~5Ω.m). In this environment, computing original reservoir Sw using Traditional hydrocarbon saturation equation is challenging. As a result, the displacement efficiency of a water drive cannot be accurately determined. In order to properly evaluate displacement efficiency, we must estimate initial reservoir Sw (Swirr) and the modern day Sw. Sw can typically be estimated from NMR data with a proper T2 time cutoff. However, in heavy oil reservoirs, the relaxation times of oil and capillary bound water overlap, leading to an over-estimation of Sw. We propose to compensate for the heavy oil effect by adjusting the cutoff until NMR Sw matches the Sw from core Mercury Injection for Capillary Pressure (MICP). As oilfield development proceeds, water displaces some oil in the pore space. Since the injected water has higher salinity than reservoir water, formation resistivity (Rw) becomes lower. Based on the material balance theory, the variable multiple water injection material balance equation is established, and the equation set is established by combining the material balance equation with the Simandoux equation and the calculation formula of mixed water resistivity (Rwz). According to the rock electricity experiment under different salinity, the dynamic rock electricity parameters are used in the Simandoux equation, and the mixed water resistivity and modern day Sw after water flooding are solved iteratively under the original SW constraint. The displacement efficiency is calculated as the difference between Sw and modern day Sw. The proposed method was applied to 10 wells and improved the Sw accuracy by 5%-15%. The continuous solution Rw from our method matches Rw measured in the lab. The calculated displacement efficiency is compared with actual production history and the accuracy improved from 68% to 80%.

Dynamic Material Balance Method for Estimating Gas in Place of Abnormally High-Pressure Gas Reservoirs

Determination of gas in place (GIP) is among the hotspot issues in the field of oil/gas reservoir engineering. The conventional material balance method and other relevant approaches have found widespread application in estimating GIP of a gas reservoir or well-controlled gas reserves, but they are normally not cost-effective. To calculate GIP of abnormally pressured gas reservoirs economically and accurately, this paper deduces an iteration method for GIP estimation from production data, taking into consideration the pore shrinkage of reservoir rock and the volume expansion of irreducible water, and presents a strategy for selecting an initial iteration value of GIP. The approach, termed DMBM-APGR (dynamic material balance method for abnormally pressured gas reservoirs) here, is based on two equations: dynamic material balance equation and static material balance equation for overpressured gas reservoirs. The former delineates the relationship between the quasipressure at bottomhole pressure and the one at average reservoir pressure, and the latter reflects the relationship between average reservoir pressure and cumulative gas production, both of which are rigidly demonstrated in the paper using the basic theory of gas flow through porous media and material balance principle. The method proves effective with several numerical cases under various production schedules and a field case under a variable rate/variable pressure schedule, and the calculation error of GIP does not go beyond 5% provided that the production data are credible. DMBM-APGR goes for gas reservoirs with abnormally high pressure as well as those with normal pressure in virtue of its strict theoretical foundation, which not only considers the compressibilities of rock and bound water, but also reckons with the changes in production rate and variations of gas properties as functions of pressure. The method may serve as a valuable and reliable tool in determining gas reserves.

A Critical Review on Material Balance Equation

Engineers have been using the material balance equation (MBE) for almost the last five decades to estimate cumulative production. However, it still is an effective tool to estimate the original hydrocarbon (oil and gas) available in the reservoir. The conventional material balance method has been successfully applying for the regular structure of a typical reservoir. In this method, all formation properties are assumed constant. However, it is very important to take care of the alteration of rock and fluid properties concerning space and time during the production history of the reservoir. Therefore, there is an immense need to understand how rocks and fluid properties change with space and time. In this paper, a thorough review and critical analysis of MBE are presented so that researchers can find a solution to why and how the incorporation of continuous alteration phenomena is needed to be considered during the development of new and dynamic MBE. Besides, the need for incorporation of all unconventional properties is detailed in this review research This review will help the new researcher to get a guideline for starting further research on the material balance equation. This study makes a crucial scope for carrying research to make a way out for the nonlinear behavior of the reservoir. This article also shows how different unconventional properties of the reservoir have been overlooked in many researches works. Finally, a guideline is provided to overcome the previous challenges in estimating hydrocarbon reserve, and workflow is presented to develop a new dynamic MBE.

Operation Control of In Situ Combustion Based on the Material Balance Equation

The stability of combustion in the process of fire flooding requires not only a reasonable gas injection rate but also a matching exhaust rate. A reasonable injection-production balance system is very important. Based on the material balance of injection-production, the expression of injection-production ratio suitable for normal fire flooding production is established. The air injection rate of fire flooding combustion and oxygen consumption of formation pressurization is analyzed by this formula to calculate the gas production and liquid production in combustion. The reasonable injection and production parameters for the oilfield are calculated by using the oilfield parameters. It can be seen that the calculated value of injection-production ratio is consistent with the actual value, which shows that the injection-production ratio is reasonable and can guide the adjustment of production parameters in the oilfield.

Methods for simultaneously evaluating reserve and permeability of undersaturated coalbed methane reservoirs using production data during the dewatering stage

In this work, a flowing material balance equation (FMBE) is established for undersaturated coalbed methane (CBM) reservoirs, which considers immobile free gas expansion effect at the dewatering stage. Based on the established FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, original gas in place, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against a reservoir simulation software with and without considering free gas expansion. Finally, the proposed methods are applied in a field case when considering free gas expansion effect. Validation cases show that the straight-line relationships for the proposed five FMBE methods are excellent, and good agreements are obtained among the actual reserves and permeabilities and those evaluated by the proposed five FMBE methods, indicating the proposed five FMBE methods are effective and rational for CBM reservoirs. Results show that a small amount of free gas will result in a great deviation in reserve evaluation; hence, the immobile free gas expansion effect should be considered when establishing the material balance equation of undersaturated CBM reservoirs at the dewatering stage.