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Concepts Infinite Acting and Boundary Dominated Flow Flow in a reservoir is often characterized as being one of two types, namely transient or boundary-dominated. Transient flow takes place during the early life of a well, when the reservoir boundaries have not been felt, and the reservoir is said to be infinite-acting. During this period, the size of the reservoir has no effect on the well performance, and from analysis of pressure or production, nothing can be deduced about the reservoir size. (in theory, the size of the reservoir does have an effect even at very early times, but in reality, this effect is so small as to be negligible --and not quantifiable with any kind of confidence). Transient flow forms the basis of a domain of reservoir engineering called Pressure Transient Analysis (P.T.A.), also known as well test interpretation. The field of well testing relies heavily on equations of flow for a well flowing at constant rate. Initially, the flow regime is transient, but eventually when all the reservoir boundaries have been felt, the well will flow at steady state (if a constant pressure boundary exists) or at pseudo-steady state (if all the boundaries are no-flow boundaries). During pseudo-steady state, the pressure throughout the reservoir declines at the same rate, and the reservoir acts like a tank (hence the alternative name, tank-type behaviour). The concept of pseudo-steady state is applicable to a situation where the well is flowing at a constant flow rate.

When a well is flowing at a constant flowing wellbore pressure, as is often the case in production operations, there is a period of time during which boundaries have no influence, and the flow behavior is "transient". However, after a period of time, when the radius of investigation has reached the outer boundary, the boundary starts to influence the well’s performance, and the pressure drops throughout the reservoir. But unlike pseudo-steady state, where the pressure drop is uniform throughout the reservoir, the pressure at the well is kept constant and the pressure at the boundary is dropping due to depletion. This is a case where the

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boundary is affecting the reservoir pressure, and hence the production rate, but it cannot be called pseudo-steady state, because the pressure drop in the reservoir is not uniform, so it is called boundary-dominated flow.

Thus boundary-dominated flow is a generic name for the well performance when the boundaries have a measurable effect. Pseudo-steady state is only one type of boundary-dominated flow, which takes place when the well is flowing at a constant rate.

Equivalence of Constant Rate and Constant Pressure Solutions A well produced at a constant rate exhibits a varying (declining) bottomhole flowing pressure, whereas a well produced at a constant bottomhole pressure exhibits a varying decline rate. There is a strong symmetry between the two solutions, as both are obtained from the same equation, namely the equation that governs fluid flow in porous media. The symmetry is not exact, however, because the boundary conditions under which the two solutions are obtained are different. The constant rate solution can be converted to a constant bottomhole pressure solution (and vice versa) using the principle of superposition. The constant bottomhole pressure solution would be obtained by superposing a large number of very short constant rate solutions in time. When plotted against superposition time, the superposed constant rate solution is very similar to the constant pressure solution, provided the discretization intervals are sufficiently small. It turns out that the two solutions are quite similar during transient flow anyway, and therefore superposition is not required to make one look like the other. However, they quickly diverge once boundary dominated flow begins. The constant rate solution behaves like the harmonic stem of the Arps type curves, while the constant pressure solution declines exponentially. The figure below compares the two solutions by plotting the dimensionless typecurves of each.


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A method for forcing one solution to look like the other during boundary dominated flow would be useful because the necessity of using superposition in time would be avoided completely. Because of pressure transient analysis, diagnostic tools for analyzing the constant rate solution are widely known and understood. Therefore, there is value in being able to analyze other types of solutions using the same diagnostic tools. The concept of material-balance time provides the normalization necessary to make constant pressure and constant rate solutions equivalent. Material-balance time converts the boundary dominated flow portion of the constant pressure solution into the pseudo-steady state portion of the equivalent constant rate solution. Plotting using materialbalance time also allows solutions with both declining rates and pressures to look like the equivalent constant rate solution.

Single Well Versus Multiple Well Analysis All of the methods used in RTA apply to single well analysis only. When considering the production of multiple wells in a field and/or reservoir, the available methods are as follows 1. Empirical- Group production decline plots 2. Material Balance Analysis- Shut-in data only 3. Reservoir Simulation 4. Semi-analytic production data analysis methods (Blasingame et al) The first step in analyzing multiple wells is to identify the objective of the analysis. The following is a list of situations where multiple well analysis is required. 1. Situations where high efficiency is required - Scoping studies / A & D - Reserves auditing 2. Single well methods sometimes don’t apply - Interference effects evident in production / pressure data- Wells producing and shutting in at different times - Predictive tool for entire reservoir is required - Complex reservoir behavior in the presence of multiple wells (multi-phase flow, reservoir heterogeneities) The vast majority of production data can be analyzed effectively without using multi-well methods. The following is a list of situations where single well analysis would suffice.


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1. Single well reservoirs 2. Low permeability reservoirs - Pressure transients from different wells in reservoir do not interfere over the production life of the well 3. Cases where "outer boundary conditions" do not change too much over the production life of the well - Wide range of reservoir types

Identifying Interference

Blasingame et al Interference Analysis Blasingame et. al. Interference Analysis extends the concept of single well decline analysis using typecurves to a multi-well pool. The process involves analysis of the single well normalized rate response (q/Dp), but plotted against a material balance time that includes the effect of the offset wells in the reservoir.


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Blasingame Type Curve Matching: Multiple Well Pools For Blasingame typecurve analysis in multi-well pools, the material balance time function is adjusted to account for total pool production as follows:

Oil Wells Where Qtot = pool cumulative production at time t

Gas Wells

Where qtot = pool total production rate at time t tce and tcae are refered to as ”total material balance time” (for oil) and ”total material balance pseudo-time” for gas. The three rate functions are as follows (defined exactly the same as for single well analysis, except that material balance time is replaced by total material balance time):

1. Normalized Rate Oil Wells

Gas Wells


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2. Rate Integral The rate integral is defined at any point in the producing life of a well, as the average rate at which the well has produced until that moment in time. The normalized rate integral is defined as follows:

Oil Wells

Gas Wells<

3. Rate Integral Derivative The rate integral derivative is defined as the semi logarithmic derivative of the rate integral function, with respect to material balance time. It is defined as follows:

Oil Wells

Gas Wells

Calculation of Parameters The calculation of parameters for the multi-well pool case is very similar to that of the single well typecurve analysis. However, total material balance time (and total material balance pseudo-time) is used in place of material balance time. In addition, a new variable

D is introduced. The dimensionless group reD/

D replaces reD as the typecurve matching parameter for the multi-

well case. D is defined as the ratio of total pool production to individual well production. Strictly speaking, this will vary with time. However, it can be approximated as:


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The parameters k, s, xf, Area and GIP(OIP) are calculated in the same manner as in the single well typecurve analysis. The parameters GIP(OIP) and Area, however, apply to the entire pool, not just the individual well.

Type Curve Matching Equations: Multi-Well Radial Oil Wells We define qDde as follows (this is the dimensionless decline rate that accounts for total pool production):

k is obtained from rearranging the definition of qDde

Now, tDde is defined as follows:

Solve for rwa as follows:

Solve for re from the product of qDde and tDde


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(Acres) (Mbbl)

Blasingame Type Curve Matching: Radial Gas Wells k is obtained from rearranging the definition of:

Solve for rwa from the definition of:


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Solve for re from the product of qDd and tDd

(Acres)

Type Curve Matching Equations: Multi-Well Fractured Oil Wells k is obtained from rearranging the definition of:

Solve for Xf from the definition of:


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Solve for re from the product of qDde and tDde.

(Acres) (Mbbl)

Gas Wells k is obtained from rearranging the definition of:

Solve for Xf from the definition of:


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Solve for re from the product of qDde and tDde:

(Acres)

(bcf)

Multi-Well Pools It is common practice to apply decline-curve analysis to aggregated production from a lease or pool. The extension of decline analysis from a single well to aggregated production from a number of wells is sometimes difficult to justify theoretically. For example, the sum of the flow rates from two wells with exponential decline is not exponential in general, unless both wells have the same decline. However, this concern is lessened, when there are sufficient wells to result in a statistical distribution. Purvis has written two papers in which the decline performance of a pool is studied in a statistical manner. Most of the difficulty in extending the single well analysis to an aggregate of wells is often due to the inevitable variation in the number of producing wells over time. If the wells have reasonably similar declines, it is suggested that the decline analysis be performed on an "average well per operating day", and that the pool forecast be obtained from the performance of the averagewell combined with a forecast of the number of producing wells, and adjusted by a factor to account for downtime. The economic abandonment rate for an aggregate of wells can be misleading. Consider, for example, the case of three producing wells, two of which are at a rate below the economic limit and one is producing at a high rate. It is very possible that the total rate of the three wells would be higher than three times the economic limit of any one well. Analysis of the aggregate production would result in continuation of the operation of all three wells (because their total flow rate is larger than the aggregate economic abandonment rate). Yet analysis of the individual well rates would clearly show that two of the wells should be abandoned. Another consideration in multi-well pools is to initialise the production rate of each well to a common start time. This makes it easier to arrive at the "average well" performance.


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Practical Diagnostics Using Production Data and Typecurves Type curve analysis is useful for estimating reservoir parameters such as permeability, skin and OGIP. Furthermore, there is important diagnostic value in type curve analysis. Some practical diagnostics include: Identifying skin damage Qualifying fracture effectiveness Identifying transition between transient and boundary dominated flow Identifying liquid loading Identifying pressure support Characterizing overpressured reservoirs Identifying interference See Anderson et. al. for field cases.

Base Model


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Material Balance Diagnostics

Productivity Diagnostics


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"Bad Data" Diagonostics

Material Balance Time The Fetkovich type curves are applicable to wells that produce at constant bottom hole pressure. Many wells, particularly gas wells experience a decline in their bottomhole pressure during their life. Blasingame and his students/co-workers (McCray, Palacio) developed a time-function that enables the matching of production rate data on Fetkovich type curves, even when the flowing pressure is varying. After developing different time-functions, they came up with a simple function they called "material-balancetime" which works very well when the change in bottomhole pressure is smooth, as is often the case in production operations. They, and Agarwal-Gardner et al, also demonstrated that using material-balance-time converts the constant pressure solution into the constant rate solution, which is the solution widely used in the field of well testing. Conceptually, the material-balance-time is defined as the ratio of cumulative production, Q , to instantaneous rate, q: tc = Q / q The symbol tc has been adopted as it represents a corrected time based on cumulative production. It is also similar to the


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corrected "Horner" time that is used in build-up analysis in well testing, for correcting the effect of a varying flow rate. It is the value of time that a well would have to flow at the current rate in order to produce the same amount of fluid (and hence honour the material balance principle). In the illustration below, the cumulative production is represented by the area under the graph. The definition of material-balance-time is such as to make these areas the same.

When analyzing oil wells,

Where Np is the cumulative oil production, and qo is the instantaneous oil rate. For gas wells, the ratio of (cumulative production,G p / instantaneous flow rate,q g ) is still valid and honours the material balance, but it does not honour the pressure balance, because of the varying gas PVT properties. (Gas rate/pressure analysis is not valid in terms of pressure, but is only valid in terms of pseudo-pressure, also known as real gas potential). Accordingly, the simple concept of material-balance-time given by


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tc = G p / q g has limited application and is considered to be only an approximation of the more rigorous material-balance-time for gas, which must be defined in terms of pseudo-time. Derivation of material-balance-time for slightly compressible systems, focuses on the flow of liquids, and does not address the pseudo-time issues for gas reservoirs. It is fundamental to two basic ideas, namely the equivalence of constant pressure and constant rate solutions, and the harmonic stem of decline curves. Derivation of material-balance pseudo-time for gas accounts for changing PVT properties with reservoir pressure.

Constant Compressibility Fluids Consider an oil reservoir. A comparison of the constant-rate (declining pressure) and constant-pressure (declining rate) type curves obtained when plotting against dimensionless time (based on area) illustrates the equivalence of the two solutions during the transient period, and their divergence during boundary dominated flow. This is shown in the next figure.

Palacio and Blasingame have developed a time function, which normalizes the boundary-dominated portion of the constantpressure solution, so that it appears identical to the constant-rate solution. Their time function is called material balance time and it

is defined as follows (for slightly compressible fluids): As it turns out, material balance time also normalizes production histories in which both the rate and the pressure decline, provided that both sets of data decline monotonically. Another way to state the functionality of material balance time is to say that it is effective in normalizing any rate / pressure history (so that it looks like the constant rate solution), provided that the rate / pressure history does not contain any disturbances large enough to disrupt boundary-dominated flow. A disturbance that is large enough to disrupt boundary-dominated flow, such as a sudden (and significant) decrease in back pressure, would introduce a new transient flow period. Since material balance time is designed to normalize boundary-dominated flow only, it would lose its effectiveness if a new transient were introduced. When the same type curves (in Figure 1) are plotted against dimensionless material balance time, the late-time portion of the constant pressure overlays the constant rate solution, precisely. This is an important result because it illustrates that the same diagnostic plots used in pressure transient analysis can be inverted and used for rate transient analysis, provided that the material balance time function is used.


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From the above figure it can be seen that the inverse logarithmic derivative behaves very similarly to the logarithmic derivative on a welltest type-curve. During transient (radial) flow, it has a constant value of 2 (1 divided by ½). Upon reaching boundary dominated flow, the inverse logarithmic derivative falls off with a constant slope of 1 on the log-log plot. The primary pressure derivative has the opposite behavior to the inverse log derivative, in that it exhibits a slope of negative 1 during transient flow, and becomes constant during boundary dominated flow. This follows from the fact that the pressure decline for a well produced at a constant rate has a constant slope on log-log paper, during pseudo-steady state. The 1/pD (qD) data, for different combinations of re/rw, exhibit a fan of transient stems which converge into one harmonic depletion stem, when plotted against dimensionless time based on area. If the data are plotted against a dimensionless time based on effective wellbore radius, rather than reservoir area, the transient stems merge together, while the depletion stems fan out. The main difference in appearance between AG type-curves and Fetkovich type-curves is that the depletion stems for AG typecurves all collapse to the harmonic case. This follows from the fact that the AG type curve normalizes all rate and pressure solutions, so that they behave like the constant-rate solution for slightly compressible fluids. Figure 3 shows the AG type curves for a vertical, unfractured well.


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The presence of the inverse log derivative and pressure derivative plots on the AG type-curve aids in the identification of transient and boundary dominated flow regimes, in the same way that the logarithmic pressure derivative aids in flow regime identification on welltest type-curves.

Material Balance Time for Oil The following development, see Palacio and Blasingame, applies rigorously to a system with constant compressibility, for example an undersaturated oil reservoir. It does not apply to gas because the compressibility of gas is a very strong function of pressure. The material-balance-time for gas is developed in terms of pseudo-time. Using the definition of compressibility, the oil production from a reservoir is related to the drop in average reservoir pressure, as follows:

(1) Separating the variables and integrating,


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(2) and recognizing that the left-hand side is the cumulative oil production, N p , the reservoir pressure, p av, can be calculated from:

(3-a) where, N is the original oil-in-place (OOIP). The important characteristic of Equation (3-a) is that it is always valid, regardless of time, flow regime or production scenario whether it is constant or variable flow rate. This is due to the fact that Equation (3-a) is a material-balance equation. Note that if p is plotted vs. N p , then a straight line of slope 1/ Nct , and intercept p i , is obtained. Of course, p is typically not available in practice, so we must use an alternate approach to applying this concept. Before doing so, we recast Equation (3) in the following form:

(3-b) The time function, is called material-balance-time. The second equation to be used is the pseudo-steady state solution to single-phase liquid flow under constant rate,

(4) Although Equation (4) was derived for constant rate (variable p wf), Blansingame and Lee (SPE 15028) showed that it is also valid when the bottomhole pressure is constant (variable rate). Combining the material-balance Equation (3-b) and the pseudo-steady state flow Equation (4) gives:

(5) where,

, and

.

Equation (5) suggests that a plot of D p/q as a function of material balance-time is a straight line, very similar to the PSS plot of D p vs. time for the constant flow rate problem. Blasingame and Lee state that the importance of Equation (5) is that it is also valid for moderately changing flow rate and bottomhole pressure conditions, so long as the transients caused by the changing inner boundary condition do not obscure the boundary-dominated flow behaviour. In particular, Equation (5) is directly related to two concepts, namely, the equivalence of the constant pressure and constant rate solutions, and the harmonic stem of decline curves.

Material Balance Pseudo-Time for Gas The concept of material-balance-time and the derivation have been previously discussed. Material-balance-time is defined as the ratio of cumulative production, Q , to instantaneous rate, q:


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Application of this concept to oil was very straight-forward. However, its application to gas is more complex, because of the varying PVT properties of gas. Accordingly, the simple concept of material-balance-time given by:

has limited application and is considered to be only an approximation of the more rigorous material-balance-time for gas, which must be defined in terms of pseudo-pressure, p p and pseudo-time, tca, and can be written as:

(1) and:

.

Derivation of Equation (1) can be found at the end of this section, Derivation of Material Balance Pseudo-Time for Gas. Equation (1) can be coupled with the pseudo-steady state flow equation for the flow of single-phase gas, (which is the gas equivalent of Equation (4), in the section derivation of material-balance-time) to give:

(2) Addition of Equation of (1) and (2) results in an equation very similar to that for oil (Equation (5) in the section derivation of material-balance-time),

(3) where:

and:

. As discussed in harmonic stem of decline curves, taking the reciprocal of Equation (3) results in the harmonic decline equation. Gas flow rate data when normalized with respect to change in bottomhole pseudo-pressure should overlay the harmonic


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stem of Fetkovich type-curve when plotted vs. material-balance pseudo-time. Calculation of the time-function however requires knowledge of the original gas in place (OGIP). This becomes an iterative process

Pseudo-Time for Gas Reservoirs with Variable Formation Compressibility The following is a rigorous development for pseudo-time, assuming a variable formation compressibility and non-zero initial water saturation, for gas reservoirs. We start by defining the material-balance equation for gas with non-zero formation and water compressibility terms.

Material Balance Equation

(1) where: DVp = Reduction in Hydrocarbon Pore Volume (HCPV) due to pore compressibility

If cf is a function of pressure then,

DVw = Expansion of initial water volume (reduces HCPV)


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Assuming that water compressibility is constant with pressure Vwi and Vpi are the initial pore volume and water volume, respectively. They are defined as follows:

Thus, equation 1 becomes:

Which reduces to:

where:


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Derivation of Pseudo-Time The derivation of pseudo-time requires the development of the PSS equation for gas. This development involves using pseudopressure and the time based derivative of the gas material-balance equation. The definition of pseudo-pressure is:

(6) To derive pseudo-time, we use the definition of pseudo-pressure and the chain rule, as follows:

(7) The first term in the numerator of (7) is calculated as follows:

Where:

Recognizing that:


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(9) Where:

(10) from the definition of pseudo-pressure. Combining equations (9) and (10), we get

(11) The denominator of (7) is calculated as follows:

(12) Also, recognizing that:

(13) Substituting equation (11) into (8) and equations (12), (10), (13) and (8) into (7), collecting like terms, and simplifying, we get

Integrating both sides of (14) with respect to dt, we get:

(16)

(17)

Where: (18) Expanding 18, we get:


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Finally, pseudo-time is defined as:

(19) Now, equation (17) is rewritten as:

(20)

Effective Use of Advanced Properties in RTA The advanced fluid properties section in FAST RTA allows the user to specify PVT properties for gas, oil and water, and compare against published correlations. To obtain realistic results, it is critical to understand how RTA uses these properties when the various methods are applied. The analytical methods (advanced typecurves, FMB and analytical models) only use pressure dependent fluid properties under certain conditions, regardless of whether or not they are input in the Advanced Properties page. The numerical model continually evaluates the pressure or rate solution under conditions of changing PVT properties.

Gas Properties Gas properties (Z, Bg, and cg) vary significantly with pressure. The analytical models use pseudo-time and pseudo-pressure to accommodate these changing properties, both at sandface (pseudo-pressure) and average reservoir conditions (pseudo-time). It is important to note that the analytical methods focus on the Z, will have no impact on any of the analytical methods.

and cg tables. For instance, inputting a user defined Bg table

The numerical model also uses variable gas properties. However, the underlying numerical solution uses the Bg and Thus, the Z and cg tables have no impact on the numerical solutions.

tables.

It is clear that gas properties Z, Bg and cg are not independent. Rather they are related through the real gas law.

Thus, the user should strive to ensure that consistent gas properties are entered, if user definable PVT is desired. In the vast majority of cases, it is not necessary to use input tables to define gas PVT properties, even if a laboratory study exists. Gas properties can be predicted very accurately under a wide range of pressures and temperatures. Only in extreme cases, such as very high pressure / high temperature environments or high H2S and/or CO2 content, would user defined gas properties be required. In the majority of cases, the analytical and numerical methods for single phase gas analysis will yield nearly identical results.


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Oil Properties Oil properties (Bo,

, co, Rs) are much more complex, and require more sophisticated procedures of application, than gas

, co and Rs. The properties. The analytical models follow the conventional welltest theory and assume constant values of Bo, oil properties are usually evaluated at initial conditions and assumed constant throughout the entire analysis. Traditionally, this has been considered a reasonable approximation, necessary for the efficient solution of the welltest equations. The approximation is considered valid for short flow and buildup tests, because oil has very low compressibility, and thus its volume does not change appreciably with pressure and temperature. Extended production scenarios may limit the validity of the approximation for reasons: 1. The reservoir and flowing pressures may change significantly in a production test: Minor changes in pressures can be ignored in welltest situations. However, large drawdowns and appreciable reservoir depletion cause inevitable variations in the oil properties (especially compressibility and viscosity). 2. Pressures in the well / reservoir system may fall below the bubble-point. Analytical methods are only applicable if there is a single mobile phase in the reservoir. Extended oil production scenarios are frequently associated with free gas (saturated) conditions. In general, the advanced analysis of oil production and pressure data has limited reliability if only the analytical methods are used. The best course of action is to compliment the analytical methods with numerical reservoir modeling. The numerical model in RTA is designed to overcome the limitations of oil production analysis and modeling associated with the standard analytical techniques. Again, it is critical to understand how the PVT tables are used in the numerical model solution.

Saturated vs Undersaturated PVT Properties Oil properties Bo, co and have values that can be established assuming either saturated or undersaturated condtions. In RTA, the fluid properties listed in the default table are always for gas-saturated conditions (oil compressibility is the only exception). The graphs that accompany the tables show the undersaturated properties in a different color (usually red). The undersaturated properties are displayed on the graph for pressures ranging from initial conditions, down to the user-specified bubble point pressure. Below the bubble-point pressure, only saturated properties are displayed. Gas saturated oil properties are also continued above the initial bubble-point pressure, to initial pressure conditions.

Viscosity, Formation Volume Factor and Solution Gas Ratio When entering laboratory (or simulator) PVT data into the user tables for Bo, and Rs, it is important to use the saturated values only. The RTA properties tables are structured such that the undersaturated properties will be calculated automatically from the saturated data profile. This allows the numerical model to function with variable bubble-point conditions. In other words, different grid cells may have different bubble-points (oil composition changes as solution gas is produced) at different times during the simulation. This is the most accurate and robust way to model variable rate / pressure oil production. To illustrate the above, a simple example is shown, whereby PVT data is input into RTA. 1. Laboratory formation volume factor data is tabulated and graphed as follows:


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2.To enter this into RTA, we must remove the undersaturated data component:

RTA then extrapolates the user defined data above the bubble-point pressure up to initial conditions. The undersaturated portion is automatically calculated using the Vasquez and Beggs correlation. The above process is performed similarly for solution GOR and oil viscosity tables. However, RTA provides an additional


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calibration parameter for viscosity, the viscosity modulus . The viscosity modulus changes the slope and shape of the undersaturated portion of the viscosity correlation. This parameter can be varied to calibrate the oil viscosity correlation to laboratory data.

Oil Compressibility Oil compressibility has limited application in the numerical model and is handled differently than the other properties. Contrary to the other properties, co’s critical component in the numerical model is the undersaturated portion of the data. The single phase oil compressibility is used to control the mass transfer in the numerical model for all grid cells containing no free gas. Thus, for accurate history matching in this regime, it is critical that the oil compressibility be predicted accurately. Entering user data in the co table is advisable here, if a laboratory PVT study is available. If a co table is not included in the laboratory study, co can be calculated using the following formula:

Analytical Methods and PVT Properties As stated previously, the analytical oil methods assume constant PVT properties. Any user defined PVT data will be honored by the analytical methods in so far as the extrapolated initial values will be used in the analytical solutions. It is not possible to explicitly enter user defined properties at initial conditions in RTA, unless the oil is saturated at initial conditions. In all other cases, the properties are extrapolated to initial conditions using a PVT correlation. In the default graphed data, this is the red line (Bo, and Rs). The values of the properties being used in the analytical methods (always at initial conditions), are also displayed in the "Quick Properties" page if the "Enable Advanced…" option is deactivated.

Water Properties Water properties may be viewed and manipulated in RTA. This may be a required step under any of the following conditions: A. To properly and accurately define the total material balance of an oil or gas reservoir: There may be significant initial water saturation in an oil or gas reservoir. The compressibility of the water may have an impact on the overall solution, especially if the reservoir is over pressured. B. If water is a mobile fluid in the reservoir. In RTA, water may be a mobile reservoir fluid under two conditions. Produced water volumes are recorded and "Water" is selected from the "Current Analysis" pull down menu. Under these conditions, the analytical and numerical methods are nearly identical to those for oil analyses. The most notable exception is that the gas solubility in water is assumed to be zero. Critical water saturation (Relative Permeability tables) is set to below the initial water saturation value, and the numerical model is used. Under these conditions, the numerical model will allow water to be produced and the specified water properties will have an impact on the total solution. C. If there are significant produced water volumes in a gas or oil analysis and accurate wellbore modeling of the fluids is required.

Simultaneous Oil-Gas-Water Flow Decline curves are used for analyzing the production of gas or oil. However they can also be used to analyze the performance of wells producing mixtures of gas, oil and water. By simultaneous use of all the data, i.e. both the individual rates and their ratios (oil rate, water rate, gas rate, gas-oil ratio (GOR), water-oil ratio (WOR), gas-liquid ratio (GLR), water-gas ratio (WGR)), a more consistent analysis can be performed. The trend of ratio curves can be opposite to that of the primary fluid curve. For example, it is very common for the water-gas ratio to show an increasing trend while the gas rate is showing a decreasing trend. The extrapolation of ratio curves must be done with due regard to the appropriate reservoir mechanism responsible for the observed trend. An example of a consistent analysis is that of a well producing oil and water. If the water rate and the oil rate are analyzed and forecast individually, then these forecasts must also be consistent with an independent analysis and forecast of the water-oil ratio. There are clear inter-relationships that must be honoured between individual flow rates and their ratios. The question often arises as to whether the individual flow rates should be analyzed or the total fluid rates (e.g. oil or oil+water); Similarly, which of the ratios (e.g. gas-oil or gas-liquid) should be used. Also, should one extrapolate the rates or the ratios? Because decline curve analysis is an empirical process and is not fully supported in theory, there are no simple answers to these


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issues. The most appropriate answer is simply to plot whatever variable in whatever scales that will give a recognizable trend, and to extrapolate that trend. For example, in some cases, plotting the oil rate will give an exponential decline; whereas in other instances, it is the total liquids (oil+water) that will give an exponential decline. However in all cases the inter-relationship between the rates and ratios must be honoured. Some of these inter-relationships are discussed below, and are displayed in the form of performance charts. If the total fluid (qo + qw) and oil (qo) production rates are linear trends on semi-log co-ordinates (exponential declines), then their quotient (qo + qw)/ qo (i.e. WOR + 1) will be linear on a semi-log plot. (qw will NOT behave exponentially). If both qo and qw rates are linear trends on semi-log paper, then the quotient of the water and oil rates (WOR) is linear on a semi-log plot. (Total fluid volume will not behave exponentially). If both the gas rate and the oil rate are exponential, then the gas-oil ratio (GOR) must also be exponential. Often, total liquids (oil+water) can have an increasing trend while the oil rate has a decreasing trend. Their interdependence could be controlled by the water-oil ratio trend. Regardless of the declines being exponential or not, the consistency between different plots needs to be appreciated. Once two variables are fitted to a trend (e.g. qo and qw) the third one (e.g. WOR or qo+qw) is automatically predetermined. The product or quotient of two exponentials is another exponential. The sum of two exponentials declines is not an exponential unless the individual declines are equal.

Performance Charts A performance chart is a graph, often in semi-log coordinates (log qo, qw ,qo+qw, WOR, GOR, WOR+1, WGR versus time), which displays simultaneously the individual and total flow rates and ratios. Because any analysis must honour all the components and their interdependence, the resulting decline analysis should be more reliable because more of the data has been used to arrive at the analysis. An example of a performance chart is shown below.


Concepts

Ratio Curves The ratio curves are plots of the ratios of oil, gas and water rates in various combinations. These various combinations are utilized to reflect different production mechanisms. They are usually displayed in performance charts along with the individual rates. In this way, the interdependence of rates and ratios becomes more evident, resulting in a more consistent analysis. Some of the more commonly used ratios are: GOR (gas-oil-ratio) = qg / qo ; WOR (water-oil-ratio) = qw / qo : These reflect the efficiency of the reservoir production mechanism. An increasing GOR or WOR is usually associated with a decreasing oil rate. A production forecast should be terminated when either the GOR or the WOR become excessive. WOR+1 is a commonly used ratio. It is equal to the ratio of the total liquids to the oil rate (qo+qw) / qo. It is equivalent to 1/(oilcut). It is used because it often displays an exponential behaviour. CGR (condensate-gas-ratio) : is a measure of the richness of a condensate gas. Usually, the higher the CGR, the more valuable the production; however too high a CGR can result in wellbore liquid lifting problems.


Concepts

WGR (water-gas-ratio) = qw / qg ; LGR (liquid-gas-ratio) : is a measure of potential production problems associated with lifting of liquids in the wellbore. A production forecast should be terminated when the LGR becomes too high for the production system to handle. Water-Cut = qw / (qo+qw) , is sometimes used instead of WOR for convenience of traditional terminology. Copyright © 2010 Fekete Associates Inc.


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