Treatment of Variations of Composition With Depth in Gas-Condensate Reservoirs (includes associated papers 23549 and 24109 )

Abstract

Summary. Considerable variations of hydrocarbon composition withdepth have been reported in several North Sea gas-condensate fields. Within the gas phase, the mole fraction of methane present, for example, may change by several percent between the top and bottom of the field. These compositional gradients can cause dewpointvariations of as much as 4 psi/ft [90 kPa/m]. Neglect of theseeffects in simulation will lead to significant errors in theestimates of hydrocarbons initially in place. These errors can, inturn, cause errors of up to 20% in predicted cumulative oilproduction in some condensate fields. In this paper, we develop atheoretical treatment of variations of composition with depth inhydrocarbon reservoirs. Results of sample calculations show thetype of results predicted by the theory and the extent of theerrors that may occur if compositional gradients are neglected. Introduction Because of gravity, hydrocarbons in a reservoir will lie aboveany aquifer present, while the hydrocarbon region may be split into alighter gas cap above an oil region. The pressure gradient of each of the phases present will depend on the phase density. We wouldtherefore expect a plot of pressure vs. depth to have the formshown in Fig. 1. This form is equivalent to that for gas, oil, andwater lying one above the other in a tank. Two factors complicate this picture. First, in a reservoir, fluids are found within the pore space of a rock where the smallsize of the pores can cause capillary forces to be significant. Surface forces are then acting in opposition to gravity, with thenet result that we do not have the abrupt phase changes with depthshown in Fig. 1, but find "transition regions"in which two orthree phases exist at one level. Fig. 2 shows a typical plot of pressure vs. depth with all three phases present. We have a gas cap containing gas plus connate water only. Below the gas cap ties agas/oil transition zone, where gas saturation decreases from itsmaximum value to zero as we move downward. Within this zone, theoil saturation reaches a value where oil becomes mobile; the levelat which this occurs is called the gas/oil contact (GOC). Beneaththe gas/oil transition zone, we have the mobile oil regionconsisting of oil plus connate water, and below this, an oil/watertransition zone, where water saturation increases from connate tosome maximum saturation (at which the oil is discontinuous andimmobile). The depth at which this maximum water saturation isreached is called the oil/water contact (OWC). If the oil zone isnarrow, the two transition zones may overlap, and clearly if no oilis present in the reservoir, the OWC becomes the gas/water contact. Second, because the columns of gas and oil may be severalhundred feet deep and contain multicomponent fluids, a change incomposition with depth will occur. A number of factors appearto cause these compositional gradients to be larger than normal:the presence of small amounts of very heavy hydrocarbons andparticularly aromatic components in the gas or oil andthepresence of a large "middle fraction" (C2 through C4), which normallyputs a mixture near its critical composition. Both of thesefactors appear common in North Sea condensate fields. When significant compositional gradients occur, the criticaltemperature of the hydrocarbon mixture may be below reservoir tem-perature at the top of the reservoir but above it at the bottom. If this is the case and if the reservoir pressure is abovedewpoint/bubblepoint pressure throughout, then, although we have gasat the top and oil at the bottom of the reservoir, there is no true GOC and no gas/oil transition zone. It is clearly not possible to model reservoirs of this type without recognizing changes in com-position with depth. Because at least three fields of this type (North Brae, Statfjord, and a field in the Viking Graben) have beenfound in the North Sea, it is important that a means to account forcomposition change with depth should be available. For a full and accurate simulation of gas-condensate fields, there- fore, the initial composition, saturation, and pressure of eachphase(gas, oil, or water) should be known for all depths withinthe reservoir. A "block-by-block" entering of these values frommeasured field data is not normally practical because suchmeasurements are difficult and costly to obtain. In the nextsection, a theoretical treatment is developed that enables us toderive a set of equations describing a field in a state of equilibrium. These equations can then be solved with the simulatorto determine the necessary parameters from measurements at a singledatum depth. Derivation of Equation for a Reservoir In Equilibrium We consider a reservoir containing a total of n components in amaximum of phases, which we assume to have reached a state of static equilibrium. For the entire reservoir, because phase pres-sures, chemical potentials, etc. are dependent only on depth, D, the Helmholtz free energy of the reservoir is given by (1) where DT and DB are the depths of the top and bottom of the reservoir, respectively, and (2) In Eq. 2, the final term, summing the surface free energies, includes the solid/fluid interfaces by taking the solid as phase. Discretizing in the D-direction by dividing the reservoir intoblocks, each having a width of and numbered from the top (k = 1)through k=kow at the hydrocarbon/water contact to the bottom(k=nb), we obtain an expression for the free energy of the entirereservoir: (3) where superscript k refers to vertical Block k. We must now minimize F subject to the following constraints. 1. The total number of moles of each component present in the reservoir must be constant. SPERE P. 239^