Chapter 2 RESERVES ESTIMATION

PNGE 343 Dr. Parlaktuna Chapter 2 RESERVES ESTIMATION VOLUMETRIC CALCULATIONS The following equation is used in the volumetric calculation of reserves: STOIIP  Vb  1 N    (1  S w )  Bo G (1) where: Vb = bulk volume of the reservoir rock, bbl N/G = net/gross ratio of formation thickness, fraction  = porosity, fraction Sw = water saturation, fraction Bo = oil formation volume factor, rbbl/STB STOIIP = stock-tank oil initially in place, STB Equation 2 is used to calculate bulk volume of the reservoir (Vb) Vb  A  h where: A h = area of the reservoir, ft2 = thickness of the reservoir, ft We will now examine the details how to determine the parameters of Equations 1 and 2. Thickness: An important parameter in volumetric estimating is the thickness of producing zone. Various types of thickness definitions used in oil industry are illustrated in Figure 1. Each of these definitions can play a part in the estimating procedure. Within the reservoir interval, there are almost always intercalations of shale or other rock, which, owing to their low porosity and permeability or high water saturation, do not contain recoverable reserves. The thickness of these non-productive strata should be subtracted from the gross thickness of the reservoir to obtain the net pay thickness. Gross thickness: It is the thickness of the stratigraphically defined interval in which the reservoir beds occur, including such non-productive intervals as may be interbedded between the productive intervals. Net pay (net productive) thickness: It is the thickness of those intervals in which porosity and permeability are known or supposed to be high enough for the interval to be able to produce oil or gas. Net oil-bearing thickness: It includes those intervals in which oil is present in such saturation that the interval may be expected to produce oil, if penetrated by a properly completed well. 1 PNGE 343 Dr. Parlaktuna The diagram in Figure 1 represents a simple case in which the difference between oil-bearing and nonoil-bearing rock is clearly visible on the logs. This is not always the case, especially in carbonate reservoirs it is often very difficult to establish whether a certain interval will produce clean oil, or oil and water, or water only. Figure 1. Definitions of various thicknesses The ratio of the sum of thicknesses P1, P2 and P3 (net pay thickness) to thickness G (gross thickness) is the parameter that should be used in Equation 1 as N/G. In order to estimate the gross thickness of the producing zone GOC and WOC depths must be located. Knowledge of fluid pressure regimes is the tool to determine the depths of fluid contacts. The total pressure at any depth, resulting from the combined weight of the formation rock and fluids (oil, water or gas) is known as the overburden pressure (OP). In the majority of sedimentary basins the overburden pressure increases linearly with depth and typically has a pressure gradient of 1 psi/ft (Figure 2). At a given depth, the overburden pressure can be equated to the sum of the fluid pressure (FP) and the grain or matrix pressure (GP) acting between the individual rock particles (Equation 3). OP FP  GP (3) A reduction in fluid pressure will lead to a corresponding increase in the grain pressure, and vice versa, since the overburden pressure remains constant at any particular depth. 2 PNGE 343 Dr. Parlaktuna d(FP)  d(GP) Figure 2. Overburden and hydrostatic pressure regimes In the concept of the petroliferous sedimentary basin as a region of water into which sediment has accumulated and hydrocarbons have been generated and trapped, we may have an expectation of a regional hydrostatic gradient. That is, in a water column representing vertical pore fluid continuity, the pressure at any point is approximated by the relationship: PX  XG w where: X Gw = the depth below a reference datum, ft = hydrostatic pressure gradient, psi/ft The value of Gw depends on the salinity of the waters and on the temperature in the system. Fresh water exhibits a gradient of 0.433 psi/ft and reservoir water systems are commonly encountered with gradients in the range of 0.44 psi/ft to 0.53 psi/ft. In reservoirs found at depths between 2000 m subsea and 4000 m subsea we might use a gradient of 0.49 psi/ft to predict pore fluid pressures around 5500 to 9000 psi as shown in Figure 3. 3 PNGE 343 Dr. Parlaktuna Figure 3. Fluid pressure regimes in North Sea reservoirs(1) Under certain depositional conditions, or because of movement of closed reservoir structures, fluid pressures may depart substantially from the normal range. Abnormal pressure regimes are evident in Figure 3, which is based on data from a number of Brent Sand reservoirs in the North Sea. All show similar salinity gradients but different degrees of overpressure, possibly related to development in localized basins. One particular mechanism responsible for overpressure in some North Sea reservoirs is the inability to expel water from a system containing rapidly compacted shales. Fluid pressures in hydrocarbon zones are calculated by defining a fluid contact between oil and water as the depth in the reservoir at which the pressure in the oil zone (Po) is equal to the pressure in the water phase (Pw). Figure 4 shows such a condition as an equilibrium condition. Strictly speaking, the position Po=Pw defines the free water level (FWL), as in some reservoirs a zone of 100 % water saturation can occur above the FWL by capillarity. At the WOC, Pw is given by the average temperature-salinity gradient of water from the surface datum of sea level. As an equation of straight line this is: Pw  X WOC G w  C1 where: C1 = a constant representing any degree of underpressure or overpressure, psi At the same depth, XWOC, we can therefore write: Pw(WOC)  Po(WOC) 4 PNGE 343 Dr. Parlaktuna Figure 4. Pressure equilibrium in a static system(1) Above the WOC, the pressure in the oil phase is the pressure that the oil had at the WOC less the density head of the oil. At any depth XD above the WOC, the pressure in the oil phase will be as follows:  PoX(D)  Po(WOC)  ρ o g ' (X WOC  X D )  (8) where: o g’ At the GOC: = The local oil density, lb/cuft = The ratio of gravitational acceleration to the universal constant gc. Po(GOC)  Pg(GOC) The pressure in the gas phase at the top of reservoir XT will therefore be:    PgX(T)  Po(WOC)  ρ o g ' (X WOC  X GOC )  ρ g g ' (X GOC  X T )  (10) There can be a significant difference at depth XT between PgX(T) and the calculated Pw at the same depth using the equation: Pw  X T G w  C1 This difference accounts for gas-kicks encountered sometimes during drilling operations as gas sands are penetrated. The estimation and recognition of fluid contacts are essential in evaluating hydrocarbons in place. Having determined the fluid contacts in the reservoir, the engineer is then in a position to calculate the net bulk volume Vb required to calculate the hydrocarbon in place. An application of fluid contact determination using fluid pressure regimes can be found in the book by Dake(2). 5 PNGE 343 Dr. Parlaktuna Water saturation (Sw) and porosity (): These two parameters are normally determined by petrophysical analysis (core measurements) and interpretation of wireline logs. These techniques are the subject of other courses therefore will not be described in this text. Oil formation volume factor (Bo): As all the other PVT properties, oil formation volume factor is measured by laboratory experiments performed on samples of the reservoir oil, plus its originally dissolved gas. Area: The areal extent of reservoirs are defined with some degree of uncertainty by evidence from drilled wells combined with geophysical interpretation of seismic data. For the purpose of reservoir volume calculations, two types of maps are particularly desirable, isopach (isopay) map or subsurface contour (isobath) map. Isopach (isopay) map is the map showing lines connecting points of equal net formation thickness (Figure 5). Subsurface contour (isobath) map is the map showing lines connecting points of equal elevations from a datum plane, therefore a map showing equal structure (Figure 6). This map is used in preparing the isopach (isopay) map where there is an water-oil, gas-water, or gas-oil contact. The contact line is the zero isopach line. The volume is obtained by planimetering the areas between the isopach lines of the entire reservoir. One of the convenient methods for the determination of bulk volume is area versus depth graph. It is suitable for all cases where the geometry of the reservoir is represented by contour maps, either structural or some form of thickness map. The case illustrated in Figure 7 is a fault block reservoir of simple structure and fairly uniform thickness. Structural contour maps on top and base reservoir are available. The area enclosed by each contour is measured. These measured areas are plotted against the corresponding depth; this results in separate curves for top and base reservoir. The area enclosed by these two curves represents the reservoir volume. It will be clear that the area measured for any contour includes also the areas enclosed by all lowernumbered contours. For instance, the area of the 2100 m contour includes also the area of the 200 m contour, etc. The method is, of course, not confined to use in simple reservoirs as shown in the sketch. In case the entire oil-bearing volume is underlain by bottom water, a horizontal line at the WOC depth replaces the curve for base reservoir. Also the method can be used on thickness maps. If a reservoir is flat, but the net sand thickness varies appreciably over the reservoir area, it is convenient to construct an isochore map. An isochore map shows the vertical distance between top and bottom marker of an interval, while the isopach map depicts the true thickness of an interval along the true dip direction. The “Area vs. Depth Graph” is then replaced by and “Area vs. Thickness Graph”, constructed on the same principle (Figure 8). 6 PNGE 343 Dr. Parlaktuna Figure 5. Isopach (isopay) map for a hydrocarbon-bearing formation Figure 6. Subsurface contour (isobath) map for a hydrocarbon-bearing formation 7 PNGE 343 Dr. Parlaktuna Figure 7. Area vs Depth Graph Figure 8. Area vs Thickness Graph 8 PNGE 343 Dr. Parlaktuna The use of some equations is another method to approximate the volume of a productive zone from planimeter readings. Volume of a pyramid and volume of a trapezoid are the two commonly used equations. Volume of a pyramid is given with the following equation: ΔVb  h (A n  A n 1  A n A n 1 ) 3 (1 where: Vb An An+1 h = bulk volume between two isopach lines, acre-ft = area enclosed by the lower isopach line, acre = area enclosed by the upper isopach line, acre = the interval between two isopach lines, ft The equation for the calculation of the volume of a trapezoid is: ΔVb  h (A n  A n 1 ) 2 or for successive trapezoids: ΔVb  h (A 0  2A1  2A 2  .......... ...  2A n 1  A n )  t avg A n 2 (14) where tavg = average thickness above the top isopach line, ft Use the equation for pyramid if the area ratio of two successive isopach lines is less than 0.5. Study the example given in Craft and Hawkins(3). From the bulk volume (gross oil-bearing rock volume), determined by one of the methods discussed in the preceding sections, the volume of hydrocarbon reserves now has to be calculated. The commonly used fundamental equation was given in Equation 1 and is also shown in Figure 9. In the tabulation the various parameters involved are listed, together with the symbols conveniently used. Assumed values for each parameter are also listed. These values are the common values often found in practice, which will give some idea of the magnitudes that can occur. The final column shows how an original gross volume of 100 arbitrary units is reduced at each subsequent step in the calculations. 9 PNGE 343 Dr. Parlaktuna Figure 9. Calculation of STOIIP STOIIP is the quantity of oil originally present in the reservoir, not all of which can be produced. How much can be produced, depends on the production techniques applied and on the reaction of the reservoir to these techniques. The fraction, or percentage, of STOIIP that can eventually be produced is called the recovery factor and the following equation applies: Ultimate recovery = STOIIP  Recovery factor (15) The recovery factor can vary over a very large range. A factor of 10% is probably the minimum that is economically acceptable in most cases. In very favorable conditions, for instance a strong natural water drive in a homogeneous reservoir, values up to 75 % may be reached. REFERENCES 1. Archer, J.S., Wall, C.G., Petroleum Engineering-Principles and Practice, Graham and Trotman, London, 1986. 2. Dake, L.P., Fundamentals of Reservoir Engineering, Elsevier, Amsterdam, 1978, 1-12. 3. Craft, B.C., Hawkins, M.F., Applied Petroleum Reservoir Engineering, Prentice Hall, New Jersey, 1959. 10 PNGE 343 Dr. Parlaktuna RESERVE CLASSIFICATION AND NOMENCLATURE The need for one universal classification and nomenclature system for petroleum reservoirs has long been recognized by the various technical societies, professional organizations, governmental agencies, and the petroleum industry. In this chapter three approaches will be introduced: McKelvey box(1), SPE deterministic definitions(2) and the 1983 World Petroleum Congress (WPC) probabilistic definitions(3). McKelvey Box(1): This concept was developed by McKelvey in 1972(1). The box represents the total volume of unproduced mineral resources and classifies such volumes with reference to a horizontal axis representing degree of geologic and engineering certainty and a vertical axis representing the range of economic feasibility of mineral recovery (Figure1). Figure 1. The McKelvey box(1) The economic and geologic axes each have two principal divisions. On the geologic axis, the logical division is between discovered mineral deposits and those that are postulated with varying certainty but remain undiscovered. This line moves right as more resources are discovered and converted to reserves. On the economic axis, the division is between volumes that have technical characteristics and a combination of costs and prices that make them profitable to recover and volumes that do not. This line moves down as technological advances increase the fraction of the resource base that is economically extractable and moves down in response to changing prices and costs. The upper left sector of the McKelvey box contains reserves. The horizontal, or geologic, axis includes the oil and gas volumes for which there is the greatest confidence in their existence and characteristics. They have been discovered and characterized by information obtained through drilling. The vertical, or economic, axis includes only those volumes of discovered minerals for which there is the highest certainty about the economic feasibility of recovery. 11 PNGE 343 Dr. Parlaktuna Resources fill the rest of the McKelvey box. These resources are minerals that are undiscovered or have been discovered but for which economic recovery is uncertain. SPE definitions(2): SPE definitions are deterministic: that is, a single figure is calculated for each reservoir category. The reserves categories represent different confidence levels, with proved reserves representing those that can be recovered with reasonable certainty under prevailing economic conditions. The reasonable certainty test is not quantified, but is left to the evaluator’s professional judgment. Probable and possible reserves are defined by SPE, but such definitions are so vague, they are of little consistent quantitative value. Probable reserves are defined as being less certain than proved but likely to be recovered, and possible reserves are less certain than probable reserves. A fundamentalist approach to these statements would imply that 50 % certainty separates probable from possible reserves and that proved reserves (reasonable certainty) are bounded by 100 % certainty at the top end, but with the boundary between proved and probable not formally quantified by a certainty level of probability. WPC definitions(3): WPC definitions are probabilistic: the range of potential reserves in a reservoir is determined as a distribution and that distribution is sampled at defined levels of cumulative probability (certainty) to become the defined reserves values. Monte Carlo techniques are used to construct the initial distribution of potential reserves in a reservoir. Although definitions and use vary, general use is that proven reserves (1P) represents a 90 % certainty level; proven + probable (2P), a 50 % certainty level; and proven + probable + possible (3P), a 10 % certainty level (Figure 2). Figure2. WPC reserves definitions(3,4). The area of a reservoir considered proved includes(5): 12 PNGE 343 Dr. Parlaktuna 1. that portion delineated by drilling and defined by fluid contacts, if any, and 2. the adjoining portions not yet drilled that reasonably can be judged economically productive on the basis of available geological and engineering data (frequently limited to direct offset locations). Probable reserves include(5): 1. reserves that appear to exist a reasonable distance beyond the proved limits of productive reservoirs, where water contacts have not been determined, and proved limits are established only by the lowest known structural occurrence of hydrocarbons, 2. reserves in formations that appear to be productive from log characteristics only but lack definitive tests or core analyses data, 3. reserves in a portion of a formation that has been proved productive in other areas in a field but is separated from the proved area by sealing faults, provided that the geologic interpretation indicates the probable area is related favorably to the proved portion of the formation, 4. reserves obtainable by improved recovery where an improved recovery program, which has yet to be established through repeated economically successful operations, is planned but is not yet in operation and a successful pilot test has not been performed, but reservoir and formation characteristics appear favorable for its success, 5. reserves in the same reservoir as proved reserves that would be recoverable if a more efficient recovery mechanism develops than was assumed in estimating the proved reserves, and 6. reserves that depend on a successful workover, treatment, retreatment, change of equipment, or other mechanical procedures for recovery, unless such procedures have been proven successful in wells exhibiting similar behavior in the same reservoir. Possible reserves include(5): 1. reserves that might be found if certain geologic conditions exist that are indicated by structural extrapolation from developed areas, 2. reserves that might be found if reasonably definitive geophysical interpretations indicate a productive area larger than could be included within the proved and probable limits, 3. reserves that might be found in formations that have somewhat favorable log characteristics but leave a reasonable doubt as to their certainty, 4. reserves that might exist in untested fault segments adjacent to proved reservoirs where a reasonable doubt exists as to whether such fault segment contains recoverable hydrocarbons, 5. reserves that might result from a planned improved recovery program that is not in operation and that is in a field in which formation fluid or reservoir characteristics are such that a reasonable doubt exist as to its success. In the example sketched in Figure 3, the central block has been proved oil productive by three wells and the structure and the position of the WOC have been established with fair reliability. The amount that would be estimated for this block would be estimated for this block would come in the proved category. 13 PNGE 343 Dr. Parlaktuna The west and north blocks have been brought into the probable category. In both blocks one well has been drilled and has proved the presence of producible oil. However, in the west block the depth of the WOC has not yet been established; for a reserve estimate the same depth as in the central block would be assumed but this is by no means certain. If the WOC is higher than assumed, the reserve estimate would be too high. In the north block the structure on both sides, away from the central well, is still known only poorly and this leaves a considerable margin of uncertainty. The east block, which no wells has yet penetrated, represents the possible category. This case demonstrates the fundamental difficulty in attempting to define the uncertainties involves in the reserves estimating; in fact, two types of uncertainty have to be considered. First, there is the question whether or not any producible oil is present in the block at all. In this case the chance that the answer to the question is positive seems fairly good: oil has already been proved on the three other blocks on the structure. Secondly, there is the possibility of inaccuracies in the volumetric estimates, because on insufficiency of the database. This uncertainty, of course, also exists in the probable category and, to a lesser extent in the proven category. Figure 3. Proved-Probable-Possible definitions REFERENCES 1. McKelvey, V.E., “Concepts of Reserves and Resources”, Methods of Estimating the Volume of Undiscovered Oil and Gas Resources, Ed. John D. Haun, AAPG, Tulsa, (1975), 11. 2. “Proved Reserves Definitions”, JPT, (Nov. 1981), 2113-2114. 3. “Classification and Nomenclature Systems for Petroleum and Petroleum Reserves”, 1933 and 1983 Study Group report, 11th World Petroleum Congress, London (1984). 4. Grace, J.D., Caldwell, R.H., Heather, D.I., “Comparative Reserves Definitions: U.S.A., Europe, and the Former Soviet Union”, JPT, (September, 1993), 866-872. 5. Garb, F.A., “Oil and Gas Reserves Classification, Estimation and Evaluation”, JPT, (March, 1985), 373-390. 14 PNGE 343 Dr. Parlaktuna PROBABILISTIC ESTIMATION AND CLASSIFICATION OF RESERVES Experienced reservoir engineers know that uncertainty exists in geologic and engineering data and, consequently, in results of calculations made with these data. The degree of uncertainty in most reservoir engineering calculations, however, usually is not quantified. Reserve estimates historically have been deterministic - i.e., “single valued”- with the degree of uncertainty indicated by terms like proved, probable, or possible. Strictly speaking deterministic implies a unique answer to a given set of facts and natural laws. Reserve estimation involves both uncertain “facts” and ill-defined natural laws. Reserve estimates are not unique and can hardly be considered deterministic in the classical sense. In geologic settings and operating areas where the industry has substantial experience and in fully developed, mature fields – situations considered having a relatively low degree of uncertainty – deterministic estimates of reserves usually are considered acceptable. However, for new geologic settings and in new operating areas the industry developed probabilistic procedures to estimate and classify reserves. Discussion and comparison of deterministic and probabilistic procedures must involve basic statistical terms. Statistics deals with sets of samples from populations and provides methods to characterize these sets as measures of the nature of the populations. For example, core and/or log data for a reservoir may be considered sample sets from which some of the characteristics of the reservoir – the population – may be estimated. To facilitate computation and comparison, it is convenient to approximate data sets with theoretical frequency distributions. Frequency distributions are called probability density functions or PDF’s. Number of samples (occurrences) From a statistical point of view, a specific data set (measurement of porosity in a well-zone) may be described by several attributes. Some of these attributes may be illustrated with a histogram, Figure 1. A histogram may be fitted with a smooth curve, a PDF, shown by the solid line on Figure 1. The area under the curve defines the domain of 100% of occurrence of all the samples, the sampled population. Core porosity (fraction) Figure 1 Histogram illustrating statistical distribution of a set of data Different types of theoretical PDF’s may be used to approximate specific observations of nature – for example, porosity, permeability, water saturation, bulk volume. Such distributions may be symmetric or skewed. PDF’s have several attributes that are relevant to probabilistic calculations: - the arithmetic average, mean or expected value, 15 PNGE 343 Dr. Parlaktuna - the most likely value, or mode, - the median, or 50th percentile, - the degree of variation, or standard deviation, and - the nature of the distribution of values about the mode, or type and degree of skew. Curves “A” and “B” in Figure 2 illustrate distributions where values are symmetric about the mean. Curve “B” exhibits the same type of symmetry as Curve “A”, but the variation about the mean – the standard deviation – is larger than that of Curve “A”. Curves “A” and “B” are each Normal or Gaussian distributions. The mean, the mode and the median of a symmetric distribution are the same. Curves “C” and “D” in Figure 2 illustrate Skewed distributions. The mean, the mode, and the median are identified on both curves. Skewness, or skew, is a measure of the nature of the variation. Curves with the mode less that the mean are said to exhibit positive skew, those with the mode greater than the mean, negative skew. The skew of Curve “C” is positive; that of curve “D”, negative. Triangular PDF’s are often used to approximate skewed distributions. Figure 3 illustrates two different observations (net pay and area) expressed as triangular distributions. The input data for these PDF’s are given in Table 1. Figure 2. Normal (Gaussian) and Skewed distributions. 16 PNGE 343 Dr. Parlaktuna 0.6 Probability (fraction) 0.5 0.4 0.3 0.2 0.1 0 0 50 100 150 200 250 300 Net pay (ft) 0.6 Probability (fraction) 0.5 0.4 0.3 0.2 0.1 0 0 200 400 600 800 1000 1200 1400 1600 1800 Area (acres) Figure 3. Triangular PDF’s 17 PNGE 343 Dr. Parlaktuna Table 1. Data for Figure 3 Netpay (ft) Area (acres) Minimum 20 500 Most Likely 100 1000 Maximum 250 1700 If the PDF of the logarithms of the values can be approximated by a Gaussian PDF, the PDF of is said to be log normal. An example for a log normal PDF is given in Figure 4, which gives the distribution of initial reserves, Npa, for a set of wells in a given geologic trend. Curve “A” in Figure 4 illustrates a log normal distribution and can be approximated by a Gaussian PDF, like Curve “B” by using the logarithm of values. Such distributions exhibit positive skew, as illustrated by Curve “A” in Figure 4. Figure 4. Log normal distribution 18 PNGE 343 Dr. Parlaktuna Some data set may have a constant PDF between its two parameters a (the minimum) and b (the maximum). This type of distribution is known as the uniform distribution (also called rectangular distribution). Figure 5 shows an example of a uniform distribution in which the probability of having a porosity value between 10 and 20 % is 0.1. 0.12 Probability (fraction) 0.1 0.08 0.06 0.04 0.02 0 9 11 13 15 17 19 21 Porosity (%) Figure 5. Uniform distribution Cumulative PDF also called cumulative density function; CDF is determined by plotting the cumulative sum of probabilities versus the parameter (porosity, permeability, OOIP etc.) Figure 6 shows a triangular PDF and the corresponding CDF, the dashed curve labeled “∑Pr(X)”. CDF, usually expressed in decimal form, is numerically equal to percentile. The complement of a CDF, the solid curve in Figure 6 labeled “Pr(XaPX)” is called the expectation curve. An expectation curve indicates the probability that the actual value, Xa, will equal or exceed the estimated value X. With reference to Figure 6, for example, there is 10% probability that the actual value of X will equal or exceed 73. An example of an expectation curve for the reserve estimation of an oil reservoir is given in Figure 7 with the classification of proved, probable and possible reserves. 19 PNGE 343 Dr. Parlaktuna Figure 6. Cumulative distribution function, CDF and Expectation curve Figure 7. An expectation curve for oil reserve estimation (arbitrary units) 20