Four major factors affecting horizontal well gravel pack were studied using a 3D simulator developed for horizontal well gravel packing. The factors included settling effect, gravel concentration, injection rate and carrier fluid viscosity. Three actual field horizontal well gravel pack jobs obtained from the literature were performed using the simulator to study these factors. The effect of carrier fluid viscosity on gravel pack efficiency was studied by varying the viscosity between 1 and 51 cP, injection rate between 0.159 and 0.636 m3/min and gravel concentration between 0.50 and 4.0 pound mass per gallon. Simulation results demonstrate the validity of the solution routine and the capability of the simulator, because the results were in agreement with the field results. The predicted pack efficiency for cases that considered settling effect are consistently higher than the cases without settling effect. The study also showed that the settling factor decreases with increasing gravel concentration and injection rate. Introduction Several authors have investigated the factors affecting gravel transportation and placement towards achieving an effective gravel pack. Gruesbeck et al.(1) performed experiments to measure pack efficiency as a function of screen parameter, fluid and gravel properties, completion configuration and angle of inclination of the wellbore. They concluded that packing efficiency increases with lower gravel concentration, lower gravel density, higher flow rate and increasing resistance to fluid flow in the tailpipe/screen annulus. Hodge(2) substantiated Gruesbeck et al.'s work by determining the accuracy of the predicted equilibrium bank height. Elson et al.(3) reported a study conducted to define optimum gravel pack procedures and completion design factors for high angle wells. Results of the study showed that high viscosity carrier fluids with high gravel concentration provide good gravel transport, but are unsuitable in wells with angles of 80 º from vertical. Skaggs(4) presented the results of a large-scale vertical wellbore model he used to study gravel transport through perforations during a high-density squeeze gravel packing operation. He concluded that the transport efficiency through perforations increases with increased fluid viscosity, gravel concentration and annular velocity. Winterfeld and Schroeder(5) developed a finite element numerical simulator and used it with a full-scale wellbore model to study gravel placement in perforations and annulus. Their model was based on mass and momentum conservation equations, as well as those for vertical wells. Peden et al.(6) developed some mathematical design models for predicting the optimum combination ofrequired design parameters, such as tailpipe diameter, slurry flow rate and gravel concentration, for an optimum packing efficiency. These models were based on extensive experimental study of factors affecting packing efficiency and dimensional analysis of obtained data. In 1988, Wahlmeier and Andrews(7) improved on the earlier works of Gruesbeck et al. and Peden et al. by developing a pseudo-three-dimensional mathematical model suitable for designing and evaluating gravel pack treatments. Shryock(8) worked on a full-scale deviated model and had similar conclusions with earlier works.

The material balance is a very important part of the reservoir engineer's toolbox that is being relegated to the background in today's reservoir evaluation workflow. This paper examines some issues that normally preclude its regular use especially as a pre-step before moving into full reservoir simulation and the use of a new method of analyzing the material balance equation called the dynamic material balance method for solving some of these issues. The dynamic material balance method allows the simultaneous determination of the initial oil-in-place (N) or initial gas-in-place (G), ratio of initial gas to oil (m), reservoir permeability (K) or skin factor (S) and average pressure history of a reservoir from the combination of solution to the material balance equation and pressure transient analysis theory. Cumulative production history and PVT data of the reservoir are used with limited or no pressure data. By introducing a time variable into the classical material balance equation (MBE) and combining the solutions of the resulting equations with the theory of pressure transient analysis, the cumulative production history of the reservoir and readily available PVT data of the reservoir fluids, we can estimate not only the original reserves in place, but also determine the average reservoir pressure decline history as indicated by the net fluid withdrawal from the reservoir. The reservoir permeability and skin factor as seen within the drainage area of each producing well can then be estimated from the already determined average pressure decline history. This method is expected to improve the use of material balance by expanding the list of problems that can be tackled using material balance especially to reservoirs in marginal fields and reservoirs in which limited pressure data is available. Introduction The material balance equation (MBE) is a very import tool used by reservoir engineers in the oil and gas industry. MBE can provide an estimate of initial hydrocarbon in place independent of geological interpretation and can also serve the purpose of verifying volumetric estimates. It can also help determines the degree of aquifer influence, understanding the applicable "drive mechanism" and in some cases estimate recovery factor and recoverable reserves. Conventionally, MBE is applied by considering different time intervals in the production history of the reservoir and maintaining that there exists a volumetric balance in the reservoir at these different time intervals. Several methods have been developed and published on applying the MBE to various types of reservoirs and solving the equation to obtain the initial oil-in-place (N) or initial gas-in-place (G) and the ratio of the initial free gas to oil (m) in the reservoir. One of such methods is the straight-line method popularized by Havlena and Odeh2,3 which instead of considering each time interval and corresponding production data as being separate from other time interval, combines all time intervals and obtain a solution that satisfies all the intervals together. In applying the straight-line method however, it is usually required that an independent source of determining the value of m exist. Most application uses an m that is derived from geological data on relative ratio of gas cap to oil column volumes. Another important requirement is the need to accurately estimate the average reservoir pressure at the various time intervals. The standard practice is to estimate the average reservoir pressure from well test conducted on individual wells producing from the reservoir. In thick formations with high permeability and low viscosity hydrocarbons, average pressures obtained from the individual well tests are good estimates of the average reservoir pressures in the drainage area of the well. But for thinner formations of lower permeability and higher viscosity hydrocarbons, there are often large variations in reservoir pressure throughout the reservoir and obtaining an average drainage area reservoir pressure usually require longer testing times and obtained values are often inaccurate. Accurately determining this average reservoir pressure is critical to the accuracy of the reserves estimate obtained from the MBE.

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This paper presents a method that allows the simultaneous determination of the initial oil-in-place (N), ratio of initial gas to oil (m), reservoir permeability (K) or skin factor (S), and average pressure decline history of a reservoir from the combination of a solution to the material balance equation and pressure transient analysis theory. Cumulative production history and pressurevolume- temperature (PVT) data of the reservoir are used without any pressure data. The measured cumulative production from a reservoir, because it captures the processes that occur throughout the life cycle of the reservoir, is expected, especially for a fully developed reservoir, to give global reservoir-wide heterogeneity effects and also the extent and size of the reservoir. By accurately measuring and analyzing the production performance and how it changes with time, we are able to determine how the average pressure in the reservoir is declining and how large the reservoir is. By introducing a time variable into the classical material balance equation (MBE) and combining the solutions of the resulting equations with the theory of pressure transient analysis, the cumulative production history of the reservoir and readily available PVT data of the reservoir fluids provide an estimate not only of the original reserves in place, but also determine the average reservoir pressure decline history as indicated by the net fluid withdrawal from the reservoir. The reservoir permeability and skin factor as seen within the drainage area of each producing well can then be estimated from the already determined average pressure decline history. This is obtained from equations derived from solutions to analytical pressure-transient analysis equations. The solution method considers the material balance equation and its derivative with time to obtain the reservoir average pressure history as predicted by the measured net fluid withdrawals from the reservoir. This method assumes a fully-developed bounded reservoir in which no flow exist across its boundary. The obtained average reservoir pressure, N and m values, can then be used to estimate for each producing well, the reservoir permeability (as seen at the well) and/or the skin factor for the well from its production rate history. This method is very useful because the analysis procedure can easily be programmed and solved with a computer without much input from the user. Introduction The material balance equation (MBE) is one of the several methods used for estimating reserves for oil and gas reservoirs and thus allows for the making of critical decisions concerning depletion plans and development strategies regarding the reservoir. The MBE makes these estimates by considering different time intervals in the production history of the reservoir and maintaining that there exist a volumetric balance in the reservoir at these different time intervals. Several methods have been developed and published applying the MBE to various types of reservoirs and solving the equation to obtain the initial oil-in-place (N) and the ratio of the initial free gas to oil (m) in the reservoir.