Drawdown Tests Research Articles

Overflow Tests Analysed by Theoretical and Numerical Methods

ABSTRACTThe assumptions inherent in the theoretical analysis of constant drawdown overflow tests are difficult to achieve in practice. This paper shows that, even if there is a restriction in the flow which causes some delay in the achievement of the constant drawdown condition, the theoretical discharge curve is followed once the constant drawdown condition is reached. Recovery tests following overflow are also examined and it is shown that the discharge used in the calculation should be the discharge at the instant that the test is stopped. Further, it is demonstrated that if well and formation losses occur, the aquifer response is distinctly different from that of the theoretical analysis.A brief description is given of an alternative method of analysis using a numerical model. A preliminary study of a field test yields promising results.

Use of Type Curve Analysis In Predicting the Behaviour of a Water-drive Reservoir

Abstract Results of a coning simulation study on five wells in the Fenn-Big Valley D-2A pool were extended to predict the performance of other wells in the field by the use of type curves. Reservoir characterization was based on permeability anisotropy in this strong bottom-water-drive carbonate reef system. The study shows that the ultimate oil recovery is insensitive to rate variations. An evaluation of plugbacks in open hole completions and cement squeezes in cased holes, based on performance, is also presented. Introduction The performance of bottom-water-drive reservoirs can be simulated by cross-sectional or three-dimensional models. However, this can be expensive in a reservoir with a large number of wells. Quite often, single well performance is simulated and extrapolated to other wells in the reservoir by correlating a characteristic parameter. A method is outlined in this paper whereby five wells have been simulated in a large reservoir and type curves have been generated with anisotropy as the parameter of characterization. These type curves are then used to match the performance of over a hundred wells and to predict their future behaviour. Water coning behaviour has been studied extensively in the last five years(1–7), with rate sensitivity to oil recovery being the main subject of study. Approaches to solving coning behaviour range from correlations such as those of Bournazel and Jeanson(l) to the sophisticated numerical models of Aziz et al (2). Correlations are usually based on several assumptions, includinghomogeneity with respect to permeability, and incompressible and steady-state flow. Numerical models eliminate these assumptions in that compressible fluid flow and variations in permeability in all three directions can be handled. One correlation that should be mentioned here is that of Chappelear and Hirasaki(4), in which a coning-model equation has been developed and inserted in a two-dimensional areal simulator. This procedure treats the horizontal movement of fluids and also accounts for vertical coning behaviour by using the developed equation near a well. However for a reservoir with a large number of wells areal simulation with the additional calculations of coning equations can be expensive. Type curves have been used in predicting the performance of wells by matching rate decline curves. However the most extensive use of type curves is made in well test analyses, where they can be used for drawdown, build-up interference and constant pressure testing. The curves themselves are generated by the solution of equations describing a specific situation, such as pressure in a closed square system without wellbore storage and skin, and should always be dimensionless. A type curve that approximates the actual problem to be solved in chosen and a match is obtained graphically. By their very nature, the actual data will be incomplete with respect to time, and extrapolation to desired time is obtained by the type curve match. Alternatively if the data are reasonably complete and match a particular type curve, inference can be made on a certain characteristic; for example, shape of the reservoir.

Practicalities of Detecting Faults From Buildup Testing

The influence of a sealing fault (and other linear discontinuities) on transient well tests is a widely discussed subject. The topic first was presented by Horner for pressure buildup testing. Fig, 1 illustrates ideal pressure behavior in a tested well near a fault. This figure is a schematic semilog plot that applies to any kind of single-well transient test; doubling of the straight-line slope is the key to the existence of a fault. The material presented in this paper applies to falloff and buildup tests. It does not paper applies to falloff and buildup tests. It does not apply to flowing-only tests, such as drawdown, injectivity, and multiple-rate flow tests. The information in this paper assumes horizontal radial flow in a homogeneous, unfractured reservoir and assumes that wellbore storage effects are unimporant.There an pitfalls in detecting faults (used here to mean any linear discontinuity) from pressure buildup and falloff tests that generally are not recognized. The reason is that flow time determines how much reservoir a test investigates. So, for a pressure buildup test, the flow time before shut-in determines if it will be possible to recognize a fault from buildup data. If flow time is long enough, then the shut-in time need only be long enough to obtain data that show the dope doubling. A shortflow time cannot be compensated for by a long shut-in time. Interestingly enough, the pressure behavior caused by a fault is such that if shut-in time is not long enough to show the double slope, it is possible to interpret the data incorrectly as indicating a small closed system rather than a large system with a nearby fault.Flow times too short to detect faults during buildup testing are particularly apt to occur in two common types of well testing. One is drillstem testing, which generally has a short flow period. The second is the testing of a gas well where no pipeline facilities are available, so a short flow period is used while the shut-in period may last weeks or months.The theory describing pressure behavior in a well near a fault is relatively simple. Fig. 1 shows pressure buildup curve shape and indicates that the pressure buildup curve shape and indicates that the second slope, m2, is twice the first slope, m1. From the first slope, one calculates skin factor and permeability. permeability. The doubling of the slope is a strict theoretical requirement and not an approximation. P. 18

Pressure transient testing at Cerro Prieto geothermal field

The Cerro Prieto geothermal reservoir may be classified as a liquid-dominated system whose initial temperature and pressure conditions place it in the liquid-saturated region. In this field commercial power production began in 1973 and has continued since that date. Because of the inherent problems in applying pressure build-up tests to wells producing two-phase fluids, it was decided to use variable flow tests of short duration known as two-rate tests. In these tests a variation in the well flow rates can be used to interpret the transient pressure response in order to determine reservoir parameters such as permeability, well-bore damage and mean reservoir pressure in the well drainage area. Some examples will illustrate the application of this technique. Pressure drawdown tests have been planned in some of the wells in the field. On the other hand, a well interference test has been made in the southern part of the field using M-90, M-91, M-50 and M-51 as production wells and M-101 as an observation well. The interpretation of this test using curve-matching procedures is illustrated. In the future, several of these tests are planned which will take advantage of the wells being drilled in new areas of the field.

A Method for Estimating the Interporosity Flow Parameter in Naturally Fractured Reservoirs

Abstract For naturally fractured reservoirs of the double-porosity type, Warren and Root defined two parameters characterizing such systems, F ft, and epsilon. While F ft may be obtained easily from the straight lines of the buildup or drawdown plot, no explicit method for estimating epsilon was plot, no explicit method for estimating epsilon was suggested in the original paper.This paper presents a method whereby the coordinates of the inflection point on a buildup or drawdown plot may be used to estimate epsilon. We show that for pressure drawdown tests, epsilon can be estimated under certain conditions, while for pressure buildup tests, only the ratio of the interporosity flow parameter to the total system porosity/compressibility parameter to the total system porosity/compressibility product, epsilon/[(phi ct)f + (phi Ct)ma], is obtained. product, epsilon/[(phi ct)f + (phi Ct)ma], is obtained. By using the concept of inflection points, an equation is derived where F ft may be obtained from a pressure buildup or drawdown test when no early- or late-time data are available. Introduction Warren and Root presented a solution to the problem of radial flow of a slightly compressible problem of radial flow of a slightly compressible fluid in a naturally fractured reservoir. They assumed that flow occurs only in the fractures and that the matrix blocks, assembled as a uniformly distributed source, deliver the fluid to the fracture system. They characterized such a system by two parameters related to the properties of the reservoir. One of these parameters, the fluid capacitance coefficient, F ft, parameters, the fluid capacitance coefficient, F ft, is used to represent the ratio of the porosity/ compressibility product for the fractures to that for the entire system: (phi ct)f/[(phi ct)f + (phi ct)ma]. The second parameter, epsilon, is defined as the interporosity flow parameter, which indicates the degree of interporosity flow between the matrix blocks and the fracture system. As shown by Kazemi, the fluid capacitance coefficient may be obtained from the following equation: F ft = antilog (-delta p/m)...................(1) where, delta p = vertical separation of the two straight lines on a buildup or drawdown test plot, psi (kPa); and m = slope of the straight lines on a buildup or drawdown test plot, psi/cycle (kPa/cycle). While the computation of F ft from this equation is straight-forward, no clear method of finding epsilon has yet been proposed. In the original paper, Warren and Root did not elaborate on a suitable method for the determination of epsilon. Kazemi discussed the use of interference test data to find the total system porosity/compressibility product, (phi ct) f + (phi ct)ma. Using this information, a trial-and-error procedure may be applied to the pressure buildup equation procedure may be applied to the pressure buildup equation to obtain a satisfactory answer for epsilon. The optimum epsilon was defined as the value resulting in the best curve fit of the theoretical equations to the field data. SPEJ p. 324

The analysis and planning of step drawdown tests: a clarification

I have received letters from Mr D. M. Milne and Dr P. F. Worthington pointing out an error in the application of the analytical methods in this paper, (published in 1977 in Q. Jl Engng Geol . 12 , 125–143). I would therefore like to take this opportunity to clarify the matter. The source of the error lies in the use of mixed time-units in the evaluation of the storage coefficient S. Time is given in minutes while the discharge rates are given in m3/day throughout the paper. These units, if applied consistently throughout an analysis, will give correct values for the various well-loss equations and the aquifer transmissivity. The value of the storage coefficient, however, will be 1440 times too great. The storage coefficient is obtained (p. 139) by the evaluation of the equation: The discharge rates used in obtaining a and T in this equation are expressed in m 3 /day. However, a is derived through Figs. 4 and 5 using the specific drawdown at unit time, t = 1 minute, in order to remove the expression ( b log t ) from ( a + b log t ) (p. 132). The units in this equation above have to be made consis- tent with this derivation and the equation therefore becomes: where 1440 = number of minutes in one day. This procedure was carried out in the original paper in order to get the storage coefficient in Table 2 but was not adequately explained in the text. It is possible to remove the source of

Analysis and planning of step drawdown tests : Clark, C Q J Engng Geol, V10, N2, 1977, P125–143

Analysis and planning of step drawdown tests : Clark, C Q J Engng Geol, V10, N2, 1977, P125–143

Reply by Dr L. Clark

I would like to thank Mr Milne-Home for his discussion. I agree that a weighted average of the discharge rates in a step drawdown test will give a more accurate value of T than a mere arithmetic mean of the discharge rates (p. 139). Mr Milne-Home's adaption of Sternbergs' work is of great value because it allows an accurate measurement of this weighted mean discharge rate.

Discussion on ‘The analysis and planning of step drawndown test’ by

Dr Clark has presented an excellent review of the theory of the step drawdown test and its applications. The purpose of this communication is to comment on the use of the recovery portion of a step drawdown test to calculate aquifer transmissivity. The Theis method may be applied if the variable discharge rate is replaced by the average of the pumping rates. This average may be expressed as: where Q̄ = mean pumping rate, V = total volume pumped, t = total pumping time. Equation (1) is equivalent to Clark's formulation. Although it is a useful working approximation, more accurate results would be obtained if Q̄ were calculated by weighting each discharge rate by the time elapsed since that rate began. Sternberg (1967) has described such a method which can be modified slightly to determine transmissivity from the recovery portion of a step drawdown test. The transmissivity T, of an infinite, confined aquifer is shown to be: where t e = 2{t-(ʃ10Q(γ)γ dγ /V)}, γ = time from start of pumping to time t, ť = time since pumping stopped, Q e = V/t, e , Q(γ) = variable pumping rate, sW' = residual drawdown in the pumped well (replacing the residual drawdown at any point radially distant r from the well in Sternberg's derivation). For short step drawdown tests with steps of equal length, t c may be approximated by: where n = number of steps, Δt = length of each step, t e = time intervals since pumping started, Q ti + ti+1 =

Discussion on ‘The analysis and planning of step drawdown tests’ by L. Clark

May I congratulate Lewis Clark on his paper covering the analysis and planning of step drawdown tests. I think the subject of well performance is due for a ‘shake-up’ and this paper will hopefully initiate some useful scientific discussion in the right direction. I have two main criticisms to make. The first one is that the author considers only continuous step drawdown tests; he makes no mention of conducting discontinuous or intermittent step drawdown tests in which each drawdown step is followed by a recovery period of at least equal duration. I have used both types of test and have found the latter provides the more reliable results for the following reasons: (i) the problem of errors caused by fluctuations in pumping rate within a given step affecting the reliability of data from subsequent steps does not arise; (ii) the problem of errors caused by extrapolating the time-drawdown trend in order to calculate incremental drawdown does not arise; (iii) the analysis of transmissivity from the time-drawdown data is straightforward; each drawdown step is treated simply as a short constant rate test, and since errors caused by (i) and (ii) will not exist, the values thus obtained will be more reliable; (iv) there will be as many recovery steps to analyse as there are drawdown steps, and hence more ‘stabs’ at transmissivity. The recovery ‘ Q ’ values are the same as the preceding drawdown step value; the problem of estimating an averaged or weighted effective ‘ Q ’ for the recovery test does not

Discussion on ‘The analysis and planning of step drawdown tests’ by L. Clark

I agree with much of Mr Connorton's first point. I recognise the intermittent step drawdown test as a valid variant of the more normal continuous step drawdown test, and would agree that the results from such tests are possibly more precise than from continuous step drawdown tests. The intermittent step drawdown test can be analysed by the methods mentioned in the paper. The intermittent test has a major drawback for use in most groundwater investigations where manpower, time and money are in short supply. The intermittent test takes considerably longer than the continuous test. It is not possible to make more than one or, at the most, two steps per day and a standard one day step drawdown test is extended for several days. The extra cost involved in the extended test must be balanced against the extra accuracy derived from such a test. I have no data to make such an assessment but intuitively I believe that the extra accuracy in transmissibility or well-loss determination will be only a few percent and is unlikely to justify the extra cost. Mr Connorton's second point is really taking the analysis of step drawdown tests into areas where it is not theoretically applicable. All the analyses mentioned in the paper except that of Rorabaugh (1953), assume that the well drawdown is shown by the equation s w = BQ + CQ 2 (1) The analyses are applicable only while this relationship holds. Mr Connorton's question implies that at low discharges the above relationship is

Results of Interference Tests From Two Geothermal Reservoirs

Results are presented from interference tests on two liquid-dominated geothermal reservoirs in the U.S. The collected pressure data show that interference effects can be masked by earth tides and other effects. Well known techniques of petroleum engineering and hydrogeology are used to estimate hydraulic characteristics and to infer the presence of barrier and leaky boundaries. Introduction An important facet in the problem of geothermal energy development is assessing the productivity and size of a geothermal reservoir. Modern techniques of well-test analysis (pressure drawdown, buildup, and interference tests) developed in petroleum engineering and hydrogeology have been applied successfully to two liquiddominated geothermal reservoirs in the U.S.: one in the Raft River Valley of Idaho and the other at East Mesa in the Imperial Valley of California. These tests gave reasonable estimates of the permeability and storage parameters for the two reservoirs. In addition, the tests also parameters for the two reservoirs. In addition, the tests also illustrate the type of instrumentation that can be used in testing geothermal wells as well as the nature of the data that can be collected. A large body of literature is available on well testing in both petroleum engineering and hydrogeology. Ramey recently has summarized the practical aspects of modern well-test analysis. This paper reviews the results of interference tests performed with a very sensitive pressure-measuring performed with a very sensitive pressure-measuring device on two geothermal reservoirs. As used in this paper, the term "interference test" denotes the fluid production from one well and measurement of pressure transients in a nearby observation well. The geologic setting for each reservoir is given and the instrumentation is presented. Some unusual features of the data are discussed, followed by the methods of interpretation that were used. Description of the Geothermal Reservoirs Raft River Valley Field, Idaho The Raft River Valley geothermal field (Fig. 1) is located on a graben filled with Tertiary and Pleistocene sediments and volcanics, with an aggregate thickness of about 5,000 ft. The sediments rest on a basement of quartzites, schists, and quartz monzonites of Precambian age. Precambian age. Wells RRGE 1 and RRGE 2 were drilled in 1975 and successfully produced hot water at approximately 295 deg. F from a geothermal reservoir occurring at the base of the sediments at 3,500 to 5,000 ft below the land surface. Well RRGE 2 is northeast and 4,000 ft from Well RRGE 1. Both wells are artesian with wellhead pressures of about 150 psi when shut in. During construction, both wells indicated free flows of about 400 gal/min. The completion details for the two wells are summarized in Table 1. Subsurface correlations of borehole data suggest that the sediments dip toward Well RRGE 2 with apparent northeasterly dips increasing from about 3 deg. in the upper portion to about 7 deg. toward the bottom. Also, it is known portion to about 7 deg. toward the bottom. Also, it is known that Well RRGE 1 pierced a fault zone between 3,800 and 4,500 ft. Apparently, Well RRGE 2 did not intercept any faults. East Mesa Field, California The East Mesa geothermal field (Fig. 2) is located on the eastern part of the Salton Trough in the Imperial Valley of California. JPT P. 10

Determination of characteristics of steam reservoirs by Radon-222 measurements in geothermal fluids

The authors conducted a Rn222 survey in wells of the Larderello geothermal field (Italy) and observed considerable variations in concentrations. Simple models show that flow-rate plays an important part in the Rn222 content of each well, as it directly affects the fluid transit time in the reservoirs. Rn222 has been sampled from two wells of the Serrazzano area during flow-rate drawdown tests. The apparent volume of the steam reservoir of each of these two wells has been estimated from the Rn222 concentration versus flow-rate curves.

The Automatic Liquid Level Monitor for Pumping Wells

The Automatic Liquid Level Monitor digitally measures and records the depth to the liquid, the time of the measurement, and the casing pressure of a well at preselected time intervals. These data are used to calculate the bottom-hole pressure to obtain the buildup and drawdown characteristics of a pumping well. Introduction Pressure measurements in producing wells have been Pressure measurements in producing wells have been performed since the early 1920's. Since that time, much performed since the early 1920's. Since that time, much has been published on the importance of pressure tests and methods of analysis in oil and gas wells. Detailed analyses of pressure buildup and drawdown tests are used primarily to determine pump efficiency, formation primarily to determine pump efficiency, formation permeability, reservoir pressure, productivity index, and permeability, reservoir pressure, productivity index, and skin factor. The bottom-hole pressure in flowing wells is relatively easy to obtain with the use of a wireline bottom-hole pressure gauge. However, it is much more difficult to obtain accurate bottom-hole pressure data on pumping wells because of the production tubing and pumping wells because of the production tubing and pump in the well. In an attempt to overcome this pump in the well. In an attempt to overcome this problem, pressure gauges have been developed that mount on problem, pressure gauges have been developed that mount on the bottom of the production tubing. The pressure then is recorded on the surface by means of a cable that is clamped to the tubing. These gauges yield accurate data, but their expense for obtaining information on only one well at a time has limited their use. Some effort also has been made to lower a wireline bottom-hole pressure gauge through the casing annulus, but this, too, generally has proved to be impractical Acoustic well sounding of the liquid level in producing wells has received wide acceptance in the field and can be used to calculate the actual bottom-hole pressure. Several different types of manually operated well sounders presently are available. Each of these devices requires the presently are available. Each of these devices requires the operator to initiate the acoustic pulse into the well casing and to interpret a resultant strip chart, which records the reflections from the tubing collars and the liquid interface. The distances between the collar reflections are measured and are used to determine the depth to the liquid level. To define the shape of a buildup curve, it is necessary to obtain a large number of soundings over a long period of time. Because of the excessive operator time period of time. Because of the excessive operator time required to obtain these readings, the manually operated sounder seldom is used in this way. The Automatic Liquid Level Monitor, developed by Mobil Research and Development Corp., overcomes this difficulty so that the liquid level during buildup and drawdown tests can be measured automatically often enough and long enough to provide an accurate measure of the shape of the bottom-hole pressure curves. This is a digital system that prints out not only the actual depth to the liquid level in feet, but also the time of the sounding and the casing pressure, These measurements are made automatically on a preselected schedule without having an operator in attendance. Description of the Automatic Liquid Level Monitor The Automatic Liquid Level Monitor uses the same method of acoustic well sounding as do the manually operated devices. However, instead of determining the liquid depth by counting tubing collars, the travel time of the acoustic pulse is measured accurately by counting the number of pulses from a very precise 1-MHz crystal-controlled oscillator. This system yields a high degree of sensitivity to the liquid movement in a well with a precision limited only by the initial calibration of the monitor and the stability of the oscillator. JPT P. 1019

The analysis and planning of step drawdown tests

Summary A step drawdown test is a pumping test in which the drawdown in a well is observed while the discharge rate from the well is increased in steps. The methods of analysis and the criteria for planning step drawdown tests are discussed and evaluated in order to produce an optimum test programme and a comprehensive test analysis. Step drawdown tests can be used to determine the aquifer transmissivity and the well loss component of the drawdown in the pumped well. The aquifer storage coefficient can also be estimated.

An Investigation of Transient Flow of Reservoir Fluids Considering Pressure-Dependent Rock and Fluid Properties

Abstract In this study we investigate the influences of pressure-dependent fluid properties and pressure-dependent fluid properties and stress-sensitive rock properties on pressure transient analysis. Single-phase flow through the porous medium is considered. These pressure-dependent terms are accounted for by use of a dimensionless pseudopressure mD(1, tD); a large variety of rates, pseudopressure mD(1, tD); a large variety of rates, geometries, and inner and outer boundary conditions are studied. For all practical production rates and most boundary conditions the pseudopressure solutions, in terms of mD(1, tD) are essentially the same as the conventional solutions using pD(1, tD) that have been documented for constant-property liquid flow. The only exceptions occur when the system studied has a closed outer boundary, and the pressure transient bas occurred for a long enough time to be affected by this boundary. in these cases, a simple adjustment can be made to the mD(1, tD) solutions to bring them in line with the pD(1, tD) solutions. Introduction As early as 1928, it was recognized that porous media are not always rigid and nondeformable. porous media are not always rigid and nondeformable. This problem is usually handled by means of properly chosen "average" properties. This method properly chosen "average" properties. This method only reduces the errors involved and generally does not eliminate these errors. Classical treatments solve the diffusivity equation, which assumes that the diffusivity is a constant independent of pressure. When both pressure and property changes are small, the constant-property property changes are small, the constant-property assumption is justified. If, instead, rock and fluid property changes are important over the pressure property changes are important over the pressure range of interest, these changes cannot be neglected and a variable-property solution should be obtained. Raghavan et al. derived a flow equation considering that rock and fluid properties vary with pressure. This equation, when expressed as a pressure. This equation, when expressed as a function of a pseudopressure, m(p), resembles the diffusivity equation. They studied pressure drawdown tests in radial bounded reservoirs produced at a constant mass rate. These test results were obtained for only a specific set of rock and fluid properties. Because this work included only a few cases, there was a need to study the use of the m(p) method for a greater variety of flow conditions. This paper presents the results of an investigation of the application of the m(p) method to drawdown, buildup, injection, and falloff testing. Results were obtained for five different sets of rock and fluid properties. The investigation also includes the effects of wellbore damage and wellbore storage. MATHEMATICAL FORMULATION To formulate the mathematical model, the assumptions usually used in well-testing theory are applied. We assume horizontal flow with no gravity effects, a fully penetrating well, isothermal single-phase fluid obeying Darcy's law, an isotropic and homogeneous formation, and purely elastic rock properties. That is, physical property changes with properties. That is, physical property changes with stress changes are reversible. In the radial systems, allowance is made for a region of reduced or improved permeability near the wellbore. The assumption of horizontal flow is not quite valid because of changes in porosity and height with pressure. However, it is easily shown that the vertical component of flow is negligible for practical rock properties and can properly be practical rock properties and can properly be neglected. Gavalas and Seinfeld also made this assumption. The rock properties needed in the flow equation porosity, permeability, and pore compressibility as porosity, permeability, and pore compressibility as functions of pressure - are found in the literature only for sandstones. It has been concluded that, in consolidated sandstones, the deformations are usually purely elastic. Therefore, only these are considered in this study. Other rocks may not behave as elastic materials. SPEJ P. 140

Reservoir Limit Tests in a Naturally Fractured Reservoir - A Field Case Study Using Type Curves

Pressure buildup, interference, and pulse tests in a naturally fractured Pressure buildup, interference, and pulse tests in a naturally fractured dry gas reservoir are influenced by reservoir limits. Type curves are matched to test data to estimate drainage area and to compute porosity and permeability. Calculated porosity and permeability values compare well permeability. Calculated porosity and permeability values compare well with published data for natural fracture systems. Introduction The case studied is a dry gas reservoir in which three wells are completed. The wells are spaced 2 and 8 miles apart in a 10-mile line along the crest of an anticline with about 100 sq miles of closure (Fig. 1). The dashed contour in Fig. 1 is the drainage boundary that was initially estimated from geologic and production test data assuming a uniform gas-water contact. This drainage area is about 18 miles long and 3 miles wide. Only one productive stratigraphic unit is common to all three productive stratigraphic unit is common to all three wells. This is a naturally fractured zone of thinly bedded, clean orthoquartzites that accounts for 90 percent of deliverability at Well 1, 95 percent at Well 2, and 100 percent at Well 3. Type of completion, fractured zone thickness, and other reservoir data are presented in Table 1. No cores were taken directly from the naturally fractured orthoquartzite zone, but cores from other orthoquartzites had 2.5-percent average porosity and less. than 0.1-md permeability to air. Test data studied in this field case history have two chronological groupings:data recorded when Well 2 was completed, consisting of one pressure drawdown and four pressure buildup tests at Well 2; anddata obtained 4 years later, consisting of pressure interference at Wells 3 and 1 caused by flowing Well 2 for 450 hours, pressure buildup at Well 2 immediately following the interference test, and pulse response at Well 3 caused by pulsing Well 2. The field was never on production except to conduct pressure transient and production except to conduct pressure transient and deliverability tests. Analysis of the field tests data is organized into four sections:(1)general discussion of the pressure drawdown and buildup behavior in light of recently published well-test theory;(2)computation of porosity and published well-test theory;(2)computation of porosity and estimation of drainage area by matching the buildup data to type curves;(3)computation of porosity, permeability, and drainage area by matching the permeability, and drainage area by matching the interference data to type curves; and(4)analysis of pulse behavior in the presence of reservoir limits. General Pressure-Buildup Behavior Buildup Tests 1 through 4, recorded at completion of Well 2, are presented in Tables 2 through 5. The pressure drawdown corresponding to Buildup Test 4 is also pressure drawdown corresponding to Buildup Test 4 is also shown in Table 5. Fig. 2 is a graph of pressure as a function of the logarithm of time for the drawdown test. All four buildup tests are plotted in Fig. 3, using the technique of Horner. Pressure buildup during Test 1 becomes a linear function of the logarithm of the Horner time ratio, and extrapolates to initial pressure at infinite shut-in time. Each of the other tests plotted in Fig. 3 has an early period in which pressure is a linear function of the period in which pressure is a linear function of the logarithm of the Horner time ratio and a late period in which pressure bends upward. JPT P. 1097

Well Test Analysis: Wells Producing by Solution Gas Drive

Abstract Drawdown and buildup data in a homogeneous, uniform, closed, cylindrical reservoir containing oil and gas and producing by solution gas drive at a constant surface oil rate were investigated. The well was assumed to be located at the center of the reservoir. Gravity effects were not included. Though the reservoir systems studied were assumed to be homogeneous, the effect of a damaged region in the vicinity of the wellbore was examined. Recently, alternate expressions for describing multiphase flow through porous media have been presented. These expressions incorporate changes presented. These expressions incorporate changes in effective permeability and fluid properties (formation volume factor, viscosity, gas solubility) with pressure by means of a pseudopressure function. The validity of applying the pseudopressure-function concept to drawdown and pseudopressure-function concept to drawdown and buildup testing for multiphase-flow situations was investigated. The pseudopressure function for analyzing drawdown behavior is calculated difrerently from that required to analyze buildup data. Consequently, two pseudopressure functions are required for analysis of well behavior in multiphase-flow systems. Dimensionless groups are used to extend the results to other situations having different permeabilities, spacing, reservoir thickness, well permeabilities, spacing, reservoir thickness, well radii, porosity, etc., provided the PVT relations and relative-permeability characteristics are identical to those used in this study. The pseudopressure-function concept used to analyze pseudopressure-function concept used to analyze drawdown and buildup behavior extends the applicability of the results to a wide range of PVT relations and relative-permeability characteristics. Introduction During the past 30 years, more than 300 publications have considered various problems publications have considered various problems pertaining to well behavior. Except for a few (about pertaining to well behavior. Except for a few (about 10), most papers examining transient pressure behavior assume that the fluids in the reservoir obey the diffusivity equation. This implies the use of a single-phase, slightly compressible fluid. The reason for the popularity of this approach is twofold:(1)the ease with which the diffusivity equation can be solved for a wide variety of problems, and(2)the demonstration by some problems, and(2)the demonstration by some workers that, for some multiphase-flow situations, single-phase flow results may be used provided appropriate modifications are made. The necessary modifications are summarized in Ref. 1. The main objective of this study is to present a method for rigorously incorporating changes in fluid properties and relative-permeability effects in the properties and relative-permeability effects in the analysis of pressure data when two phases of oil and gas are flowing. This should enable the engineer to calculate the absolute formation permeability rather than the effective permeability to each of the flowing phases. This method is based on an idea suggested by Fetkovich, who proposed that if an expression similar to the real gas pseudopressure is defined, then equations describing pseudopressure is defined, then equations describing simultaneous flow of oil and gas through porous media may be simplified considerably. The validity of the equations and methods for calculating the pseudopressure function, however, was not presented pseudopressure function, however, was not presented by Fetkovich. LITERATURE REVIEW AND THEORETICAL CONSIDERATIONS General equations of motion describing multiphase flow in porous media have been known since 1936. These equations, and the assumptions involved in deriving them, are discussed thoroughly in the literature and will not be considered here. Equations for two-phase flow were first solved by Muskat and Meres for a few special cases. Evinger and Muskat studied the effect of multiphase flow on the productivity index of a well and examined the steady radial flow of oil and gas in a porous medium. Under conditions of steady radial porous medium. Under conditions of steady radial flow the oil flow rate is given by (1) SPEJ P. 196

Determining Well Drainage Pore Volume and Porosity From Pressure Buildup Tests

Abstract Well drainage pore volume and effective porosity can be determined using the results of a pressure buildup test. The procedure uses theoretical, dimensionless Horner type curves to analyze the buildup test data. Limitations and applications of the procedure are discussed, and an example is given. Introduction Knowledge of the well drainage pore volume and effective porosity of a reservoir is of vital importance to the petroleum engineer. These values, when combined with the associated hydrocarbon saturation, are necessary for estimating the reserves of a particular reservoir. Furthermore, these reserves are particular reservoir. Furthermore, these reserves are used to plan additional wells, to establish operating procedures, and to study the feasibility of various procedures, and to study the feasibility of various enhanced recovery processes. The need for an accurate value of the hydrocarbon pore volume is obvious. The use of geologic and well logging data to estimate both effective porosity and well drainage pore volume is well established. Unfortunately, pore volume is well established. Unfortunately, these methods are limited to a determination of rock properties at or near the wellbore. Accordingly, many important decisions affecting reservoir performance are based on information that performance are based on information that represents, at best, a minute fraction of the total reservoir system. A method of analysis that encompasses a larger portion of the reservoir is clearly needed. It has long been recognized that the pressure response of a well following a disturbance in flow rate is indicative of the reservoir properties within the drainage volume of the test well. This idea has led to the development of several types of transient pressure tests that can be used to determine, among pressure tests that can be used to determine, among other things, the average permeability and volumetric average pressure associated with the well. Unfortunately, the effect of porosity on pressure response is not as explicit as the effect of permeability. Consequently, only moderate success has been achieved in calculating porosity from the results of a pressure test. The pressure drawdown test is currently the only transient pressure test commonly used for obtaining well drainage pore volume. Although the pressure drawdown test offers the advantage of surveying a large fraction of the well drainage volume, its application is severely restricted by a number of factors. First, this test must be conducted for a longer time than that necessary to achieve pseudosteady state within the drainage volume of the well. The producing time required to meet this condition, particularly in low-permeability reservoirs, often makes the test impractical. Second, the test requires that a constant flow rate be maintained. From an operational standpoint, this can be very difficult for the long test times required. Third, for large drainage volumes the rate of pressure change may be too small to measure during the pseudosteady-state flow period. This is a major limitation since the pore volume is inversely proportional to the rate of pressure decline. Finally, if the reservoir is in communication with an aquifer, the test will give optimistic and misleading results. Therefore, this method has very limited application in the determination of reservoir pore volume. The design and analysis, as well as the limitations of the pressure drawdown test have been detailed in the pressure drawdown test have been detailed in the literature. A more versatile and commonly used transient pressure test for evaluating reservoir properties is pressure test for evaluating reservoir properties is the pressure buildup test. The two methods most commonly used to evaluate pressure buildup tests were published by Horner and Miller et al. Horner showed that plotting buildup pressure vs the logarithm of the time ratio, (t + delta t)/delta t, yields a straight line with slope inversely proportional to the average formation permeability. Horner assumed an infinite reservoir to develop his method of analysis. SPEJ P. 209

Theoretical and experimental drawdown pore pressures in porous embankments : GREEN, DC MILLS, KG MOORE, PJ 5F, 10R. 2ND AUS-N.Z. CONF. GEOMECH, BRISBANE, 1975, INST. ENGRS, AUS, NAT. CONF. PUBL. NO. 75/4, P154–158

The development and verification are described of a finite element computer program for solution of problems of two-dimensional Darcian seepage flow with particular application to evaluation of pore pressures in embankments during and after reservoir drawdown. The program was used to compare theoretical pore pressures with pore pressures measured during an extensive series of drawdown tests on model dam embankments constructed of two different sands. An attempt was also made to compare pore pressures predicted, using the finite element program, with measured values reported in the literature for two actual dams. Conclusions are then drawn regarding the usefulness of the program.